{"model_name":"glm-5.1","codes":{"1":{"ahc001":"#include \nusing namespace std;\n\nint n;\nvector x, y, r;\nvector a, b, c, d;\n\nvoid solve(vector indices, int left, int bottom, int right, int top) {\n if (indices.empty()) return;\n if (indices.size() == 1) {\n int i = indices[0];\n a[i] = left; b[i] = bottom; c[i] = right; d[i] = top;\n return;\n }\n \n long long total_r = 0;\n for (int i : indices) total_r += r[i];\n \n int width = right - left;\n int height = top - bottom;\n \n double best_score = 1e18;\n bool use_vertical = true;\n int best_k = -1;\n int best_split = -1;\n \n // Try vertical splits\n {\n sort(indices.begin(), indices.end(), [](int i, int j) { return x[i] < x[j]; });\n long long sum = 0;\n for (int k = 1; k < (int)indices.size(); k++) {\n sum += r[indices[k-1]];\n if (x[indices[k-1]] >= x[indices[k]]) continue;\n \n int min_s = max(left + 1, x[indices[k-1]] + 1);\n int max_s = min(right - 1, x[indices[k]]);\n if (min_s > max_s) continue;\n \n long long ideal_s = left + (long long)width * sum / total_r;\n int s = max(min_s, min(max_s, (int)ideal_s));\n \n double score = abs((double)sum / total_r - (double)(s - left) / width);\n if (score < best_score) {\n best_score = score;\n use_vertical = true;\n best_k = k;\n best_split = s;\n }\n }\n }\n \n // Try horizontal splits\n {\n sort(indices.begin(), indices.end(), [](int i, int j) { return y[i] < y[j]; });\n long long sum = 0;\n for (int k = 1; k < (int)indices.size(); k++) {\n sum += r[indices[k-1]];\n if (y[indices[k-1]] >= y[indices[k]]) continue;\n \n int min_s = max(bottom + 1, y[indices[k-1]] + 1);\n int max_s = min(top - 1, y[indices[k]]);\n if (min_s > max_s) continue;\n \n long long ideal_s = bottom + (long long)height * sum / total_r;\n int s = max(min_s, min(max_s, (int)ideal_s));\n \n double score = abs((double)sum / total_r - (double)(s - bottom) / height);\n if (score < best_score) {\n best_score = score;\n use_vertical = false;\n best_k = k;\n best_split = s;\n }\n }\n }\n \n if (best_k == -1) {\n int i = indices[0];\n a[i] = left; b[i] = bottom; c[i] = right; d[i] = top;\n return;\n }\n \n if (use_vertical) {\n sort(indices.begin(), indices.end(), [](int i, int j) { return x[i] < x[j]; });\n vector left_indices(indices.begin(), indices.begin() + best_k);\n vector right_indices(indices.begin() + best_k, indices.end());\n solve(left_indices, left, bottom, best_split, top);\n solve(right_indices, best_split, bottom, right, top);\n } else {\n sort(indices.begin(), indices.end(), [](int i, int j) { return y[i] < y[j]; });\n vector bottom_indices(indices.begin(), indices.begin() + best_k);\n vector top_indices(indices.begin() + best_k, indices.end());\n solve(bottom_indices, left, bottom, right, best_split);\n solve(top_indices, left, best_split, right, top);\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n;\n x.resize(n); y.resize(n); r.resize(n);\n a.resize(n); b.resize(n); c.resize(n); d.resize(n);\n \n for (int i = 0; i < n; i++) {\n cin >> x[i] >> y[i] >> r[i];\n }\n \n vector indices(n);\n iota(indices.begin(), indices.end(), 0);\n \n solve(indices, 0, 0, 10000, 10000);\n \n for (int i = 0; i < n; i++) {\n cout << a[i] << \" \" << b[i] << \" \" << c[i] << \" \" << d[i] << \"\\n\";\n }\n \n return 0;\n}","ahc002":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 50;\nint si, sj;\nint t[N][N], p[N][N];\nint di[] = {-1, 1, 0, 0};\nint dj[] = {0, 0, -1, 1};\nchar dir[] = {'U', 'D', 'L', 'R'};\nmt19937 rng(42);\n\nint tile_value[2500], max_tile_id = 0;\nstring best_path;\nlong long best_score;\n\nstring find_path(double temperature) {\n bool square_visited[N][N] = {};\n bool tile_visited[2500] = {};\n string path;\n int ci = si, cj = sj;\n square_visited[ci][cj] = true;\n tile_visited[t[ci][cj]] = true;\n long long score = p[ci][cj];\n \n while (true) {\n vector> candidates;\n for (int d = 0; d < 4; d++) {\n int ni = ci + di[d], nj = cj + dj[d];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) continue;\n if (square_visited[ni][nj]) continue;\n bool same_tile = (t[ni][nj] == t[ci][cj]);\n if (same_tile || !tile_visited[t[ni][nj]]) {\n double w = same_tile ? p[ni][nj] : tile_value[t[ni][nj]];\n candidates.push_back({w, d});\n }\n }\n if (candidates.empty()) break;\n \n double max_w = -1e18;\n for (auto& [w, d] : candidates) max_w = max(max_w, w);\n double total = 0;\n for (auto& [w, d] : candidates) total += exp((w - max_w) / max(temperature, 0.01));\n \n double r = uniform_real_distribution(0, total)(rng);\n double cum = 0;\n int chosen = candidates[0].second;\n for (auto& [w, d] : candidates) {\n cum += exp((w - max_w) / max(temperature, 0.01));\n if (cum >= r) { chosen = d; break; }\n }\n \n int ni = ci + di[chosen], nj = cj + dj[chosen];\n square_visited[ni][nj] = true;\n tile_visited[t[ni][nj]] = true;\n score += p[ni][nj];\n path += dir[chosen];\n ci = ni; cj = nj;\n }\n \n if (score > best_score) { best_score = score; best_path = path; }\n return path;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) { cin >> t[i][j]; max_tile_id = max(max_tile_id, t[i][j]); }\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> p[i][j];\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) tile_value[t[i][j]] += p[i][j];\n \n best_score = 0;\n auto start = chrono::high_resolution_clock::now();\n int iter = 0;\n while (true) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now - start).count() > 1800) break;\n double temperature = 10.0 * (1.0 - min(iter / 100000.0, 1.0)) + 0.1;\n find_path(temperature);\n iter++;\n }\n \n cout << best_path << endl;\n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble h_est[N][N-1], v_est[N-1][N];\nint h_count[N][N-1], v_count[N-1][N];\nint query_num = 0;\n\ndouble get_h_weight(int i, int j) {\n double base = h_est[i][j];\n double time_decay = max(0.0, 1.0 - query_num / 400.0);\n double exploration = 80.0 * time_decay / sqrt(h_count[i][j] + 1);\n return max(100.0, base - exploration);\n}\n\ndouble get_v_weight(int i, int j) {\n double base = v_est[i][j];\n double time_decay = max(0.0, 1.0 - query_num / 400.0);\n double exploration = 80.0 * time_decay / sqrt(v_count[i][j] + 1);\n return max(100.0, base - exploration);\n}\n\nstring dijkstra(int si, int sj, int ti, int tj) {\n double dist[N][N]; pair prev[N][N]; bool vis[N][N] = {};\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) dist[i][j] = 1e18;\n dist[si][sj] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, si, sj});\n while (!pq.empty()) {\n auto [d, i, j] = pq.top(); pq.pop();\n if (vis[i][j]) continue; vis[i][j] = true;\n if (i == ti && j == tj) break;\n if (i > 0 && !vis[i-1][j] && d + get_v_weight(i-1,j) < dist[i-1][j])\n { dist[i-1][j] = d + get_v_weight(i-1,j); prev[i-1][j] = {i,j}; pq.push({dist[i-1][j],i-1,j}); }\n if (i < N-1 && !vis[i+1][j] && d + get_v_weight(i,j) < dist[i+1][j])\n { dist[i+1][j] = d + get_v_weight(i,j); prev[i+1][j] = {i,j}; pq.push({dist[i+1][j],i+1,j}); }\n if (j > 0 && !vis[i][j-1] && d + get_h_weight(i,j-1) < dist[i][j-1])\n { dist[i][j-1] = d + get_h_weight(i,j-1); prev[i][j-1] = {i,j}; pq.push({dist[i][j-1],i,j-1}); }\n if (j < N-1 && !vis[i][j+1] && d + get_h_weight(i,j) < dist[i][j+1])\n { dist[i][j+1] = d + get_h_weight(i,j); prev[i][j+1] = {i,j}; pq.push({dist[i][j+1],i,j+1}); }\n }\n string path; int ci = ti, cj = tj;\n while (ci != si || cj != sj) {\n auto [pi, pj] = prev[ci][cj];\n if (pi == ci-1) path += 'D'; else if (pi == ci+1) path += 'U';\n else if (pj == cj-1) path += 'R'; else path += 'L';\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nvoid update(int si, int sj, const string& path, int observed) {\n vector>> edges;\n int ci = si, cj = sj;\n for (char c : path) {\n if (c == 'U') { edges.push_back({'v',{ci-1,cj}}); ci--; }\n else if (c == 'D') { edges.push_back({'v',{ci,cj}}); ci++; }\n else if (c == 'L') { edges.push_back({'h',{ci,cj-1}}); cj--; }\n else { edges.push_back({'h',{ci,cj}}); cj++; }\n }\n double pred = 0;\n for (auto& [type, pos] : edges) {\n auto [i, j] = pos;\n pred += (type == 'h') ? h_est[i][j] : v_est[i][j];\n }\n double ratio = (double)observed / pred;\n for (auto& [type, pos] : edges) {\n auto [i, j] = pos;\n if (type == 'h') {\n double lr = 1.0 / (2 + h_count[i][j]++);\n h_est[i][j] = max(100.0, min(20000.0, h_est[i][j] * ((1-lr) + lr*ratio)));\n } else {\n double lr = 1.0 / (2 + v_count[i][j]++);\n v_est[i][j] = max(100.0, min(20000.0, v_est[i][j] * ((1-lr) + lr*ratio)));\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n for (int i = 0; i < N; i++) for (int j = 0; j < N-1; j++) { h_est[i][j] = 5000.0; h_count[i][j] = 0; }\n for (int i = 0; i < N-1; i++) for (int j = 0; j < N; j++) { v_est[i][j] = 5000.0; v_count[i][j] = 0; }\n for (int k = 0; k < 1000; k++) {\n query_num = k;\n int si, sj, ti, tj; cin >> si >> sj >> ti >> tj;\n string path = dijkstra(si, sj, ti, tj);\n cout << path << endl;\n int obs; cin >> obs;\n update(si, sj, path, obs);\n }\n return 0;\n}","ahc004":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n int N, M;\n cin >> N >> M;\n vector s(M);\n for (int i = 0; i < M; i++) cin >> s[i];\n \n const int NUM_CHARS = 8;\n mt19937 rng(42);\n \n // Initialize with uniform voting\n vector> votes(N * N, vector(NUM_CHARS, 0));\n for (int m = 0; m < M; m++) {\n int k = s[m].length();\n double weight = 1.0 / (2.0 * N * N);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n for (int p = 0; p < k; p++) {\n votes[i * N + (j + p) % N][s[m][p] - 'A'] += weight;\n votes[((i + p) % N) * N + j][s[m][p] - 'A'] += weight;\n }\n }\n }\n }\n \n vector mat(N, string(N, 'A'));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double maxVote = 0;\n char bestChar = 'A';\n for (int c = 0; c < NUM_CHARS; c++) {\n if (votes[i * N + j][c] > maxVote) {\n maxVote = votes[i * N + j][c];\n bestChar = 'A' + c;\n }\n }\n mat[i][j] = bestChar;\n }\n }\n \n // Iterative refinement with weighted voting\n for (int iter = 0; iter < 100; iter++) {\n vector> newVotes(N * N, vector(NUM_CHARS, 0));\n \n for (int m = 0; m < M; m++) {\n int k = s[m].length();\n \n double totalScore = 0;\n vector scores(2 * N * N);\n int idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double scoreH = 0, scoreV = 0;\n for (int p = 0; p < k; p++) {\n if (mat[i][(j + p) % N] == s[m][p]) scoreH += 1;\n if (mat[(i + p) % N][j] == s[m][p]) scoreV += 1;\n }\n scores[idx++] = scoreH;\n scores[idx++] = scoreV;\n totalScore += scoreH + scoreV;\n }\n }\n \n if (totalScore < 0.01) continue;\n \n idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double wH = scores[idx++] / totalScore;\n double wV = scores[idx++] / totalScore;\n \n for (int p = 0; p < k; p++) {\n newVotes[i * N + (j + p) % N][s[m][p] - 'A'] += wH;\n newVotes[((i + p) % N) * N + j][s[m][p] - 'A'] += wV;\n }\n }\n }\n }\n \n bool changed = false;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double maxVote = 0;\n char bestChar = mat[i][j];\n for (int c = 0; c < NUM_CHARS; c++) {\n if (newVotes[i * N + j][c] > maxVote) {\n maxVote = newVotes[i * N + j][c];\n bestChar = 'A' + c;\n }\n }\n if (mat[i][j] != bestChar) {\n mat[i][j] = bestChar;\n changed = true;\n }\n }\n }\n \n if (!changed) break;\n }\n \n for (int i = 0; i < N; i++) cout << mat[i] << '\\n';\n return 0;\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\n\nbool is_road(int i, int j) {\n return i >= 0 && i < N && j >= 0 && j < N && grid[i][j] != '#';\n}\n\nint cost(int i, int j) { return grid[i][j] - '0'; }\n\nconst int di[] = {-1, 1, 0, 0};\nconst int dj[] = {0, 0, -1, 1};\nconst char dir[] = {'U', 'D', 'L', 'R'};\n\nint char_to_idx(char c) {\n if (c == 'U') return 0;\n if (c == 'D') return 1;\n if (c == 'L') return 2;\n return 3;\n}\n\npair>, vector>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX));\n vector> prev(N, vector(N, -1));\n priority_queue>, vector>>, greater<>> pq;\n dist[si][sj] = 0;\n pq.push({0, {si, sj}});\n while (!pq.empty()) {\n auto [d, p] = pq.top(); pq.pop();\n auto [i, j] = p;\n if (d > dist[i][j]) continue;\n for (int k = 0; k < 4; k++) {\n int ni = i + di[k], nj = j + dj[k];\n if (is_road(ni, nj)) {\n int nd = d + cost(ni, nj);\n if (nd < dist[ni][nj]) {\n dist[ni][nj] = nd;\n prev[ni][nj] = k;\n pq.push({nd, {ni, nj}});\n }\n }\n }\n }\n return {dist, prev};\n}\n\nstring reconstruct_path(int si, int sj, int ti, int tj, const vector>& prev) {\n if (si == ti && sj == tj) return \"\";\n string path;\n int ci = ti, cj = tj;\n while (ci != si || cj != sj) {\n int k = prev[ci][cj];\n if (k == -1) return \"\";\n path += dir[k];\n ci -= di[k]; cj -= dj[k];\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nint mark_new_visible(int i, int j, vector>& covered) {\n int count = 0;\n if (!covered[i][j]) { covered[i][j] = true; count++; }\n for (int jj = j-1; jj >= 0 && is_road(i,jj); jj--)\n if (!covered[i][jj]) { covered[i][jj] = true; count++; }\n for (int jj = j+1; jj < N && is_road(i,jj); jj++)\n if (!covered[i][jj]) { covered[i][jj] = true; count++; }\n for (int ii = i-1; ii >= 0 && is_road(ii,j); ii--)\n if (!covered[ii][j]) { covered[ii][j] = true; count++; }\n for (int ii = i+1; ii < N && is_road(ii,j); ii++)\n if (!covered[ii][j]) { covered[ii][j] = true; count++; }\n return count;\n}\n\nint count_new_visible(int i, int j, const vector>& covered) {\n int count = 0;\n if (!covered[i][j]) count++;\n for (int jj = j-1; jj >= 0 && is_road(i,jj); jj--)\n if (!covered[i][jj]) count++;\n for (int jj = j+1; jj < N && is_road(i,jj); jj++)\n if (!covered[i][jj]) count++;\n for (int ii = i-1; ii >= 0 && is_road(ii,j); ii--)\n if (!covered[ii][j]) count++;\n for (int ii = i+1; ii < N && is_road(ii,j); ii++)\n if (!covered[ii][j]) count++;\n return count;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> si >> sj;\n grid.resize(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n \n int total_roads = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (is_road(i, j)) total_roads++;\n \n vector> covered(N, vector(N, false));\n string route;\n int ci = si, cj = sj;\n int covered_count = mark_new_visible(ci, cj, covered);\n \n auto start_time = chrono::high_resolution_clock::now();\n \n while (covered_count < total_roads) {\n auto current_time = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(current_time - start_time).count() > 2500) break;\n \n auto [dist, prev] = dijkstra(ci, cj);\n int best_i = -1, best_j = -1;\n double best_score = -1;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (!is_road(i, j) || dist[i][j] == INT_MAX) continue;\n int new_vis = count_new_visible(i, j, covered);\n if (new_vis == 0) continue;\n double score = (double)new_vis / dist[i][j];\n if (score > best_score) {\n best_score = score;\n best_i = i; best_j = j;\n }\n }\n }\n \n if (best_i == -1) break;\n \n string path = reconstruct_path(ci, cj, best_i, best_j, prev);\n for (char c : path) {\n int k = char_to_idx(c);\n ci += di[k]; cj += dj[k];\n covered_count += mark_new_visible(ci, cj, covered);\n }\n route += path;\n }\n \n auto [dist, prev] = dijkstra(ci, cj);\n route += reconstruct_path(ci, cj, si, sj, prev);\n \n cout << route << endl;\n return 0;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint N, M, K, R;\nvector> d, deps, rev_deps;\nvector> skill_est, est_time_matrix;\nvector> skill_lb;\n\nvoid update_skills_for_member(int j) {\n for (int i = 0; i < N; i++) {\n double w = 0;\n for (int k = 0; k < K; k++) w += max(0.0, (double)d[i][k] - skill_est[j][k]);\n est_time_matrix[i][j] = max(1.0, w);\n }\n}\n\nvoid update_skills(int j, int task, int time_taken) {\n if (time_taken == 1) {\n for (int k = 0; k < K; k++) {\n skill_lb[j][k] = max(skill_lb[j][k], d[task][k]);\n skill_est[j][k] = max(skill_est[j][k], (double)d[task][k]);\n }\n } else {\n double est_w = (double)time_taken, cur_w = 0;\n vector deficient;\n for (int k = 0; k < K; k++) {\n double deficit = max(0.0, (double)d[task][k] - skill_est[j][k]);\n if (deficit > 0) { cur_w += deficit; deficient.push_back(k); }\n }\n if (cur_w > 0) {\n double ratio = est_w / cur_w;\n for (int k : deficient) {\n double deficit = d[task][k] - skill_est[j][k];\n double new_skill = d[task][k] - deficit * ratio;\n skill_est[j][k] = 0.7 * skill_est[j][k] + 0.3 * new_skill;\n skill_est[j][k] = max((double)skill_lb[j][k], skill_est[j][k]);\n }\n } else {\n double total_d = 0;\n for (int k = 0; k < K; k++) total_d += d[task][k];\n if (total_d > 0) for (int k = 0; k < K; k++)\n skill_est[j][k] = max((double)skill_lb[j][k], skill_est[j][k] - est_w * d[task][k] / total_d);\n }\n }\n update_skills_for_member(j);\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> M >> K >> R;\n d.resize(N, vector(K)); deps.resize(N); rev_deps.resize(N);\n for (int i = 0; i < N; i++) for (int k = 0; k < K; k++) cin >> d[i][k];\n for (int r = 0; r < R; r++) { int u, v; cin >> u >> v; u--; v--; deps[v].push_back(u); rev_deps[u].push_back(v); }\n \n vector downstream(N, 0);\n for (int i = N - 1; i >= 0; i--) for (int v : rev_deps[i]) downstream[i] += downstream[v] + 1;\n \n skill_est.resize(M, vector(K, 30.0)); skill_lb.resize(M, vector(K, 0));\n est_time_matrix.resize(N, vector(M, 1.0));\n for (int j = 0; j < M; j++) update_skills_for_member(j);\n \n vector task_start(N, -1), task_done(N, -1), member_task(M, -1), member_start_day(M, -1);\n set available_tasks; vector deps_remaining(N);\n for (int i = 0; i < N; i++) { deps_remaining[i] = deps[i].size(); if (!deps_remaining[i]) available_tasks.insert(i); }\n \n int current_day = 0;\n while (true) {\n current_day++;\n vector free_members;\n for (int j = 0; j < M; j++) if (member_task[j] == -1) free_members.push_back(j);\n \n vector> assignments; set used_members, used_tasks;\n vector sorted_avail(available_tasks.begin(), available_tasks.end());\n sort(sorted_avail.begin(), sorted_avail.end(), [&](int a, int b) { return downstream[a] > downstream[b]; });\n \n for (int i : sorted_avail) {\n if (used_members.size() >= free_members.size()) break;\n double best_time = 1e18; int best_j = -1;\n for (int j : free_members) if (!used_members.count(j) && est_time_matrix[i][j] < best_time)\n { best_time = est_time_matrix[i][j]; best_j = j; }\n if (best_j != -1) { assignments.push_back({best_j, i}); used_members.insert(best_j); used_tasks.insert(i); }\n }\n \n cout << assignments.size();\n for (auto [j, i] : assignments) {\n cout << \" \" << (j+1) << \" \" << (i+1);\n member_task[j] = i; member_start_day[j] = current_day; task_start[i] = current_day;\n available_tasks.erase(i);\n }\n cout << endl;\n \n int n; cin >> n; if (n == -1) break;\n for (int idx = 0; idx < n; idx++) {\n int j; cin >> j; j--;\n int i = member_task[j], time_taken = current_day - member_start_day[j] + 1;\n task_done[i] = current_day; update_skills(j, i, time_taken); member_task[j] = -1;\n for (int v : rev_deps[i]) { deps_remaining[v]--; if (!deps_remaining[v] && task_start[v] == -1) available_tasks.insert(v); }\n }\n }\n return 0;\n}","ahc006":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint a[N], b[N], c[N], d[N];\n\nint dist(int x1, int y1, int x2, int y2) { return abs(x1-x2) + abs(y1-y2); }\n\nint main() {\n for (int i = 0; i < N; i++) cin >> a[i] >> b[i] >> c[i] >> d[i];\n \n auto startTime = chrono::high_resolution_clock::now();\n mt19937 rng(42);\n \n vector> scores;\n for (int i = 0; i < N; i++) {\n int cost = dist(CX,CY,a[i],b[i]) + dist(a[i],b[i],c[i],d[i]) + dist(c[i],d[i],CX,CY);\n scores.push_back({cost, i});\n }\n sort(scores.begin(), scores.end());\n \n vector orders(M);\n vector isSelected(N, false);\n for (int i = 0; i < M; i++) { orders[i] = scores[i].second; isSelected[orders[i]] = true; }\n \n vector route(2*M);\n \n auto constructRoute = [&]() {\n vector vR(M,false), vD(M,false);\n int cx=CX, cy=CY;\n for (int step=0; step<2*M; step++) {\n int best=-1, bestD=INT_MAX;\n for (int i=0; i& r) {\n vector rP(M), dP(M);\n for (int i=0; i<2*M; i++) { if(r[i]%2==0) rP[r[i]/2]=i; else dP[r[i]/2]=i; }\n for (int k=0; kdP[k]) return false;\n return true;\n };\n \n constructRoute();\n int curCost=calcCost(), bestCost=curCost;\n vector bestRoute=route, bestOrders=orders;\n double temp=500.0, cooling=0.99997;\n \n while (true) {\n auto now=chrono::high_resolution_clock::now();\n if (chrono::duration(now-startTime).count()>1.8) break;\n \n int mt=rng()%10;\n if (mt<5) {\n int from=rng()%(2*M), to=rng()%(2*M);\n if(from==to) continue;\n vector nr=route; int val=nr[from];\n nr.erase(nr.begin()+from);\n int ip=to>from?to-1:to;\n nr.insert(nr.begin()+ip, val);\n if(isValid(nr)) {\n auto sr=route; route=nr; int nc=calcCost(); double d=nc-curCost;\n if(d<0||(double)rng()/rng().max() nr=route; reverse(nr.begin()+l,nr.begin()+r+1);\n auto sr=route; route=nr; int nc=calcCost(); double d=nc-curCost;\n if(d<0||(double)rng()/rng().max()\n#include \n#include \n#include \n\nusing namespace std;\n\nstruct UnionFind {\n vector parent, rank_;\n int components;\n \n UnionFind(int n) : parent(n), rank_(n, 0), components(n) {\n for (int i = 0; i < n; i++) parent[i] = i;\n }\n \n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n \n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n components--;\n return true;\n }\n \n bool connected(int x, int y) {\n return find(x) == find(y);\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n vector x(N), y(N);\n vector u(M), v(M);\n vector d(M);\n \n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dist = sqrt((double)(x[u[i]] - x[v[i]]) * (x[u[i]] - x[v[i]]) + \n (double)(y[u[i]] - y[v[i]]) * (y[u[i]] - y[v[i]]));\n d[i] = max(1, (int)round(dist));\n }\n \n // Compute reference MST using d_i\n vector order(M);\n for (int i = 0; i < M; i++) order[i] = i;\n sort(order.begin(), order.end(), [&](int a, int b) { return d[a] < d[b]; });\n \n UnionFind refUF(N);\n vector inRefMST(M, false);\n for (int idx : order) {\n if (refUF.unite(u[idx], v[idx])) {\n inRefMST[idx] = true;\n }\n }\n \n // Process edges online\n UnionFind uf(N);\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int adopt = 0;\n \n if (!uf.connected(u[i], v[i])) {\n double percentile = (double)(l - d[i]) / (2.0 * d[i]);\n \n int remaining = M - i - 1;\n int needed = uf.components - 1;\n \n double threshold;\n if (needed == 0) {\n threshold = 0;\n } else {\n double safety = (double)remaining / needed;\n if (safety >= 10) {\n threshold = 0.4;\n } else if (safety >= 5) {\n threshold = 0.5;\n } else if (safety >= 3) {\n threshold = 0.7;\n } else if (safety >= 2) {\n threshold = 0.85;\n } else {\n threshold = 1.0;\n }\n }\n \n // Edges in reference MST are more likely to be important\n if (inRefMST[i]) {\n threshold = min(1.0, threshold + 0.15);\n }\n \n if (percentile <= threshold) {\n adopt = 1;\n uf.unite(u[i], v[i]);\n }\n }\n \n cout << adopt << endl;\n }\n \n return 0;\n}","ahc008":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int SIZE = 30;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\n\nint N, M;\nvector px, py, pt;\nvector hx, hy;\nbool wall[SIZE][SIZE];\n\nbool inBounds(int x, int y) { return x >= 0 && x < SIZE && y >= 0 && y < SIZE; }\n\nbool petAdjacentTo(int x, int y, const vector& ppx, const vector& ppy) {\n for (int i = 0; i < N; i++) {\n if (ppx[i] == x && ppy[i] == y) return true;\n for (int d = 0; d < 4; d++)\n if (ppx[i] == x + dx[d] && ppy[i] == y + dy[d]) return true;\n }\n return false;\n}\n\nbool humanAt(int x, int y, const vector& hhx, const vector& hhy) {\n for (int i = 0; i < M; i++)\n if (hhx[i] == x && hhy[i] == y) return true;\n return false;\n}\n\nvoid bfs(int sx, int sy, int dist[SIZE][SIZE]) {\n memset(dist, -1, sizeof(int) * SIZE * SIZE);\n queue> q;\n dist[sx][sy] = 0;\n q.push({sx, sy});\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && dist[nx][ny] == -1) {\n dist[nx][ny] = dist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n}\n\npair countAreaAndPets(int sx, int sy) {\n int dist[SIZE][SIZE];\n bfs(sx, sy, dist);\n int area = 0, pets = 0;\n for (int i = 0; i < SIZE; i++)\n for (int j = 0; j < SIZE; j++)\n if (dist[i][j] >= 0) area++;\n for (int i = 0; i < N; i++)\n if (dist[px[i]][py[i]] >= 0) pets++;\n return {area, pets};\n}\n\ndouble calcScore(int area, int nPets) { return (double)area / 900.0 * pow(2.0, -nPets); }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n px.resize(N); py.resize(N); pt.resize(N);\n for (int i = 0; i < N; i++) { cin >> px[i] >> py[i] >> pt[i]; px[i]--; py[i]--; }\n cin >> M;\n hx.resize(M); hy.resize(M);\n for (int i = 0; i < M; i++) { cin >> hx[i] >> hy[i]; hx[i]--; hy[i]--; }\n \n memset(wall, false, sizeof(wall));\n \n for (int turn = 0; turn < 300; turn++) {\n vector startPx = px, startPy = py;\n vector startHx = hx, startHy = hy;\n string actions(M, '.');\n bool newWall[SIZE][SIZE] = {};\n \n for (int i = 0; i < M; i++) {\n int myHx = startHx[i], myHy = startHy[i];\n auto [curArea, curPets] = countAreaAndPets(myHx, myHy);\n double curScore = calcScore(curArea, curPets);\n char bestAction = '.';\n double bestScore = curScore;\n \n for (int d = 0; d < 4; d++) {\n int nx = myHx + dx[d], ny = myHy + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && !newWall[nx][ny] &&\n !petAdjacentTo(nx, ny, startPx, startPy) && !humanAt(nx, ny, startHx, startHy)) {\n wall[nx][ny] = true;\n auto [newArea, newPets] = countAreaAndPets(myHx, myHy);\n wall[nx][ny] = false;\n double newScore = calcScore(newArea, newPets);\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"udlr\"[d]; }\n }\n }\n \n for (int d = 0; d < 4; d++) {\n int nx = myHx + dx[d], ny = myHy + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && !newWall[nx][ny]) {\n auto [newArea, newPets] = countAreaAndPets(nx, ny);\n double newScore = calcScore(newArea, newPets);\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"UDLR\"[d]; }\n }\n }\n \n actions[i] = bestAction;\n switch (actions[i]) {\n case 'u': newWall[myHx-1][myHy] = true; wall[myHx-1][myHy] = true; break;\n case 'd': newWall[myHx+1][myHy] = true; wall[myHx+1][myHy] = true; break;\n case 'l': newWall[myHx][myHy-1] = true; wall[myHx][myHy-1] = true; break;\n case 'r': newWall[myHx][myHy+1] = true; wall[myHx][myHy+1] = true; break;\n case 'U': hx[i] = myHx - 1; hy[i] = myHy; break;\n case 'D': hx[i] = myHx + 1; hy[i] = myHy; break;\n case 'L': hx[i] = myHx; hy[i] = myHy - 1; break;\n case 'R': hx[i] = myHx; hy[i] = myHy + 1; break;\n }\n }\n \n cout << actions << endl;\n \n for (int i = 0; i < N; i++) {\n string move; cin >> move;\n for (char c : move) {\n if (c == 'U') px[i]--;\n else if (c == 'D') px[i]++;\n else if (c == 'L') py[i]--;\n else if (c == 'R') py[i]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint si, sj, ti, tj;\ndouble p;\nvector h(20), v(19);\n\npair move_pos(int i, int j, int d) {\n int di[]={-1,1,0,0}, dj[]={0,0,-1,1};\n int ni=i+di[d], nj=j+dj[d];\n if(ni<0||ni>=20||nj<0||nj>=20) return {i,j};\n if(d==0 && i>0 && v[i-1][j]=='1') return {i,j};\n if(d==1 && v[i][j]=='1') return {i,j};\n if(d==2 && j>0 && h[i][j-1]=='1') return {i,j};\n if(d==3 && h[i][j]=='1') return {i,j};\n return {ni,nj};\n}\n\ndouble compute_score(const string& s) {\n vector> prob(20,vector(20,0));\n prob[si][sj]=1.0; double es=0;\n for(int t=0;t<(int)s.size();t++){\n int d=s[t]=='U'?0:s[t]=='D'?1:s[t]=='L'?2:3;\n vector> np(20,vector(20,0));\n for(int i=0;i<20;i++) for(int j=0;j<20;j++){\n if(prob[i][j]<1e-15) continue;\n np[i][j]+=p*prob[i][j];\n auto[ni,nj]=move_pos(i,j,d);\n if(ni==ti&&nj==tj) es+=(1-p)*prob[i][j]*(401-(t+1));\n else np[ni][nj]+=(1-p)*prob[i][j];\n }\n prob=np;\n }\n return es;\n}\n\nstring find_shortest_path() {\n vector> dist(20,vector(20,-1)), pdir(20,vector(20,-1));\n queue> q; q.push({si,sj}); dist[si][sj]=0;\n while(!q.empty()){\n auto[i,j]=q.front(); q.pop();\n if(i==ti&&j==tj) break;\n for(int d=0;d<4;d++){\n auto[ni,nj]=move_pos(i,j,d);\n if((ni!=i||nj!=j)&&dist[ni][nj]==-1){\n dist[ni][nj]=dist[i][j]+1; pdir[ni][nj]=d; q.push({ni,nj});\n }\n }\n }\n string path; int i=ti,j=tj;\n while(i!=si||j!=sj){\n int d=pdir[i][j]; char c=\"UDLR\"[d]; path=c+path;\n int di[]={-1,1,0,0},dj[]={0,0,-1,1}; i-=di[d]; j-=dj[d];\n }\n return path;\n}\n\nstring greedy_with_dp() {\n const int L=200;\n vector> f(400,vector(L+2,0));\n for(int t=L;t>=1;t--) for(int i=0;i<20;i++) for(int j=0;j<20;j++){\n int idx=i*20+j;\n if(i==ti&&j==tj) f[idx][t]=401-t;\n else{ double best=0;\n for(int d=0;d<4;d++){\n auto[ni,nj]=move_pos(i,j,d); int nidx=ni*20+nj;\n best=max(best,p*f[idx][t+1]+(1-p)*f[nidx][t+1]);\n } f[idx][t]=best;\n }\n }\n vector prob(400,0); prob[si*20+sj]=1.0;\n string result;\n for(int t=1;t<=L;t++){\n double bs=-1; int ba=0;\n for(int d=0;d<4;d++){\n vector np(400,0); double rp=0;\n for(int idx=0;idx<400;idx++){\n if(prob[idx]<1e-15) continue;\n int i=idx/20,j=idx%20; np[idx]+=p*prob[idx];\n auto[ni,nj]=move_pos(i,j,d); int nidx=ni*20+nj;\n if(ni==ti&&nj==tj) rp+=(1-p)*prob[idx];\n else np[nidx]+=(1-p)*prob[idx];\n }\n double sc=rp*(401-t);\n for(int idx=0;idx<400;idx++) sc+=np[idx]*f[idx][t+1];\n if(sc>bs){bs=sc;ba=d;}\n }\n result+=\"UDLR\"[ba];\n vector np(400,0);\n for(int idx=0;idx<400;idx++){\n if(prob[idx]<1e-15) continue;\n int i=idx/20,j=idx%20; np[idx]+=p*prob[idx];\n auto[ni,nj]=move_pos(i,j,ba); int nidx=ni*20+nj;\n if(ni!=ti||nj!=tj) np[nidx]+=(1-p)*prob[idx];\n }\n prob=np;\n }\n return result;\n}\n\nint main(){\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin>>si>>sj>>ti>>tj>>p;\n for(int i=0;i<20;i++) cin>>h[i];\n for(int i=0;i<19;i++) cin>>v[i];\n \n string shortest=find_shortest_path();\n string best_str; double best_score=-1;\n \n // Strategy 1: Repeat shortest path\n {string s; while(s.size()+shortest.size()<=200) s+=shortest;\n double sc=compute_score(s); if(sc>best_score){best_score=sc;best_str=s;}}\n \n // Strategy 2: Redundant moves\n for(int r=2;r<=5;r++){\n string s; for(char c:shortest) for(int k=0;kbest_score){best_score=sc;best_str=s;}\n }\n \n // Strategy 3: Greedy with DP\n {string s=greedy_with_dp(); double sc=compute_score(s);\n if(sc>best_score){best_score=sc;best_str=s;}}\n \n // Strategy 4: Shortest path + DR padding\n {string s=shortest; while(s.size()<200){s+='D';if(s.size()<200)s+='R';}\n double sc=compute_score(s); if(sc>best_score){best_score=sc;best_str=s;}}\n \n cout<\nusing namespace std;\n\nconst int N = 30;\nint orig_tiles[N][N], rotations[N][N], current_tiles[N][N];\nconst int di[] = {0, -1, 0, 1}, dj[] = {-1, 0, 1, 0};\nconst int to_table[8][4] = {{1,0,-1,-1},{3,-1,-1,0},{-1,-1,3,2},{-1,2,1,-1},{1,0,3,2},{3,2,1,0},{2,-1,0,-1},{-1,3,-1,1}};\nint rotated_type[8][4];\n\nvoid init_rotated_type() {\n for (int t = 0; t < 8; t++) {\n rotated_type[t][0] = t;\n int cur = t;\n for (int r = 1; r < 4; r++) {\n if (cur <= 3) cur = (cur + 1) % 4;\n else if (cur == 4) cur = 5; else if (cur == 5) cur = 4;\n else if (cur == 6) cur = 7; else cur = 6;\n rotated_type[t][r] = cur;\n }\n }\n}\n\nvoid update_all_tiles() {\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n current_tiles[i][j] = rotated_type[orig_tiles[i][j]][rotations[i][j]];\n}\n\npair compute_top2() {\n static bool visited[N][N][4];\n memset(visited, 0, sizeof(visited));\n int max1 = 0, max2 = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int t = current_tiles[i][j];\n for (int d = 0; d < 4; d++) {\n if (visited[i][j][d] || to_table[t][d] == -1) { visited[i][j][d] = true; continue; }\n int si = i, sj = j, sd = d, ci = i, cj = j, cd = d, length = 0;\n while (true) {\n visited[ci][cj][cd] = true;\n int t2 = current_tiles[ci][cj], d2 = to_table[t2][cd];\n if (d2 == -1) break;\n int ni = ci + di[d2], nj = cj + dj[d2];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) break;\n int nd = (d2 + 2) % 4; length++;\n if (ni == si && nj == sj && nd == sd) {\n if (length > max1) { max2 = max1; max1 = length; }\n else if (length > max2) max2 = length;\n break;\n }\n ci = ni; cj = nj; cd = nd;\n }\n }\n }\n }\n return {max1, max2};\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(0);\n init_rotated_type();\n for (int i = 0; i < N; i++) { string s; cin >> s; for (int j = 0; j < N; j++) orig_tiles[i][j] = s[j] - '0'; }\n \n mt19937 rng(42);\n long long global_best_score = 0; int global_best_rotations[N][N] = {};\n auto start_time = chrono::high_resolution_clock::now();\n \n for (int trial = 0; trial < 10; trial++) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start_time).count() > 1.5) break;\n \n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) rotations[i][j] = rng() % 4;\n update_all_tiles();\n \n auto [m1, m2] = compute_top2();\n long long cur_score = (long long)m1 * m2, best_score = cur_score;\n int best_rotations[N][N]; memcpy(best_rotations, rotations, sizeof(rotations));\n \n uniform_int_distribution pos_dist(0, N*N-1), rot_dist(0, 3);\n uniform_real_distribution prob_dist(0.0, 1.0);\n \n for (int iter = 0; iter < 30000; iter++) {\n now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start_time).count() > 1.7) break;\n double temp = 100.0 * pow(0.01, min((double)iter / 30000.0, 1.0));\n \n int idx = pos_dist(rng), i = idx / N, j = idx % N;\n int old_rot = rotations[i][j], new_rot = rot_dist(rng);\n if (old_rot == new_rot) continue;\n \n rotations[i][j] = new_rot;\n current_tiles[i][j] = rotated_type[orig_tiles[i][j]][new_rot];\n \n auto [nm1, nm2] = compute_top2();\n long long new_score = (long long)nm1 * nm2;\n \n if (new_score - cur_score > 0 || prob_dist(rng) < exp((double)(new_score - cur_score) / max(temp, 0.001))) {\n cur_score = new_score;\n if (cur_score > best_score) { best_score = cur_score; memcpy(best_rotations, rotations, sizeof(rotations)); }\n } else { rotations[i][j] = old_rot; current_tiles[i][j] = rotated_type[orig_tiles[i][j]][old_rot]; }\n }\n if (best_score > global_best_score) { global_best_score = best_score; memcpy(global_best_rotations, best_rotations, sizeof(best_rotations)); }\n }\n \n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cout << global_best_rotations[i][j];\n cout << endl;\n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N, T;\nint board[10][10];\nint er, ec;\n\nint compute_max_tree_size() {\n vector parent(N*N), sz(N*N, 0);\n iota(parent.begin(), parent.end(), 0);\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j]) sz[i*N+j] = 1;\n \n function find = [&](int x) {\n while (parent[x] != x) x = parent[x] = parent[parent[x]];\n return x;\n };\n auto unite = [&](int x, int y) {\n x = find(x); y = find(y);\n if (x == y) return;\n if (sz[x] < sz[y]) swap(x, y);\n parent[y] = x; sz[x] += sz[y];\n };\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N-1; j++)\n if (board[i][j] && board[i][j+1] && (board[i][j] & 4) && (board[i][j+1] & 1))\n unite(i*N+j, i*N+j+1);\n for (int i = 0; i < N-1; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j] && board[i+1][j] && (board[i][j] & 8) && (board[i+1][j] & 2))\n unite(i*N+j, (i+1)*N+j);\n \n int mx = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j]) mx = max(mx, sz[find(i*N+j)]);\n return mx;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> T;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n char c = s[j];\n board[i][j] = (c >= '0' && c <= '9') ? c - '0' : c - 'a' + 10;\n if (!board[i][j]) { er = i; ec = j; }\n }\n }\n \n string moves;\n int cur_sz = compute_max_tree_size(), best_sz = cur_sz;\n size_t best_cnt = 0;\n mt19937 rng(42);\n int dr[] = {-1,1,0,0}, dc[] = {0,0,-1,1};\n char dc_c[] = {'U','D','L','R'};\n auto start = chrono::high_resolution_clock::now();\n int stale = 0;\n \n while ((int)moves.size() < T) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now-start).count() > 2800) break;\n \n int bd = -1, bns = cur_sz;\n for (int d = 0; d < 4; d++) {\n int nr = er+dr[d], nc = ec+dc[d];\n if (nr<0||nr>=N||nc<0||nc>=N) continue;\n swap(board[er][ec], board[nr][nc]);\n int oe=er, oec=ec; er=nr; ec=nc;\n int ns = compute_max_tree_size();\n if (ns > bns) { bns = ns; bd = d; }\n swap(board[er][ec], board[oe][oec]); er=oe; ec=oec;\n }\n \n if (bd != -1) {\n int nr=er+dr[bd], nc=ec+dc[bd];\n swap(board[er][ec], board[nr][nc]); er=nr; ec=nc;\n moves += dc_c[bd]; cur_sz = bns; stale = 0;\n if (cur_sz > best_sz) { best_sz = cur_sz; best_cnt = moves.size(); }\n if (cur_sz == N*N-1) break;\n } else {\n if (++stale > 3) {\n for (int i = 0; i < 5 && (int)moves.size() < T; i++) {\n vector v;\n for (int d = 0; d < 4; d++) {\n int nr=er+dr[d], nc=ec+dc[d];\n if (nr>=0&&nr=0&&nc best_sz) { best_sz = cur_sz; best_cnt = moves.size(); }\n stale = 0;\n } else break;\n }\n }\n cout << moves.substr(0, best_cnt) << endl;\n}","ahc012":"#include \nusing namespace std;\ntypedef long long ll;\n\nint N, K;\nint a[11];\nvector px, py;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> K;\n for (int d = 1; d <= 10; d++) cin >> a[d];\n px.resize(N); py.resize(N);\n for (int i = 0; i < N; i++) cin >> px[i] >> py[i];\n \n vector> output;\n \n auto compute_score = [&]() {\n map, int> groups;\n for (int i = 0; i < N; i++) {\n vector sig;\n bool destroyed = false;\n for (auto& [x1, y1, x2, y2] : output) {\n ll la = y2 - y1, lb = x1 - x2, lc = x2*y1 - x1*y2;\n ll val = la*px[i] + lb*py[i] + lc;\n if (val == 0) { destroyed = true; break; }\n sig.push_back(val > 0 ? 1 : -1);\n }\n if (!destroyed) groups[sig]++;\n }\n int pc[11] = {};\n for (auto& [s, c] : groups) if (c >= 1 && c <= 10) pc[c]++;\n int score = 0;\n for (int d = 1; d <= 10; d++) score += min(a[d], pc[d]);\n return score;\n };\n \n auto start = chrono::steady_clock::now();\n \n for (int iter = 0; iter < K; iter++) {\n if (chrono::duration(chrono::steady_clock::now() - start).count() > 2.5) break;\n \n int cur_score = compute_score();\n int max_score = 0;\n for (int d = 1; d <= 10; d++) max_score += a[d];\n if (cur_score == max_score) break;\n \n map, vector> groups;\n for (int i = 0; i < N; i++) {\n vector sig;\n bool destroyed = false;\n for (auto& [x1, y1, x2, y2] : output) {\n ll la = y2 - y1, lb = x1 - x2, lc = x2*y1 - x1*y2;\n ll val = la*px[i] + lb*py[i] + lc;\n if (val == 0) { destroyed = true; break; }\n sig.push_back(val > 0 ? 1 : -1);\n }\n if (!destroyed) groups[sig].push_back(i);\n }\n \n int pc[11] = {};\n for (auto& [s, m] : groups) { int sz = m.size(); if (sz >= 1 && sz <= 10) pc[sz]++; }\n \n tuple best_line;\n int best_score = cur_score;\n bool found = false;\n \n for (auto& [sig, members] : groups) {\n int sz = members.size();\n if (sz <= 1) continue;\n if (sz <= 10 && pc[sz] <= a[sz]) continue;\n \n int limit = min((int)members.size(), 20);\n for (int ii = 0; ii < limit; ii++) {\n for (int jj = ii+1; jj < limit; jj++) {\n int i = members[ii], j = members[jj];\n ll mx = (px[i]+px[j])/2, my = (py[i]+py[j])/2;\n ll dx = py[i]-py[j], dy = px[j]-px[i];\n ll x1 = mx, y1 = my, x2 = mx+dx, y2 = my+dy;\n if (x1 == x2 && y1 == y2) continue;\n \n output.push_back({x1,y1,x2,y2});\n int ns = compute_score();\n output.pop_back();\n if (ns > best_score) { best_score = ns; best_line = {x1,y1,x2,y2}; found = true; }\n }\n }\n }\n \n mt19937 rng(42+iter);\n for (int r = 0; r < 50; r++) {\n ll x1 = rng()%20001-10000, y1 = rng()%20001-10000;\n ll x2 = rng()%20001-10000, y2 = rng()%20001-10000;\n if (x1==x2 && y1==y2) continue;\n output.push_back({x1,y1,x2,y2});\n int ns = compute_score();\n output.pop_back();\n if (ns > best_score) { best_score = ns; best_line = {x1,y1,x2,y2}; found = true; }\n }\n \n if (found) output.push_back(best_line);\n else break;\n }\n \n cout << output.size() << endl;\n for (auto& [x1,y1,x2,y2] : output) cout << x1 << \" \" << y1 << \" \" << x2 << \" \" << y2 << endl;\n return 0;\n}","ahc014":"#include \nusing namespace std;\n\nint N, M;\nvector> has_dot;\nvector> ops;\nmap>> segs[4];\n\nint seg_type(int x1,int y1,int x2,int y2){\n if(y1==y2)return 0;\n if(x1==x2)return 1;\n if(x2-x1==y2-y1)return 2;\n return 3;\n}\nint line_id(int t,int x,int y){\n if(t==0)return y;if(t==1)return x;\n if(t==2)return x-y;return x+y;\n}\n\nbool check_overlap(int t,int lid,int s,int e){\n if(s>e)swap(s,e);\n auto it=segs[t].find(lid);\n if(it==segs[t].end())return false;\n for(auto&[a,b]:it->second){\n int lo=min(a,b),hi=max(a,b);\n if(max(s,lo)>corners={{x1,y1},{x2,y2},{x3,y3},{x4,y4}};\n auto chk=[&](int ax,int ay,int bx,int by){\n int dx=bx-ax,dy=by-ay,st=max(abs(dx),abs(dy));\n if(!st)return false;\n int sx=dx/st,sy=dy/st;\n for(int i=1;i find_rect(int ex,int ey){\n // Axis-aligned\n for(int x2=0;x2V2 (1,1), V2->V3 (1,-1)\n auto try_tilt=[&](int v1x,int v1y,int v2x,int v2y,int v3x,int v3y,int v4x,int v4y){\n if(v1x<0||v1x>=N||v1y<0||v1y>=N)return false;\n if(v2x<0||v2x>=N||v2y<0||v2y>=N)return false;\n if(v3x<0||v3x>=N||v3y<0||v3y>=N)return false;\n if(v4x<0||v4x>=N||v4y<0||v4y>=N)return false;\n if(!has_dot[v2x][v2y]||!has_dot[v3x][v3y]||!has_dot[v4x][v4y])return false;\n return valid(v1x,v1y,v2x,v2y,v3x,v3y,v4x,v4y);\n };\n \n for(int a=1;aV2 (1,-1), V2->V3 (1,1)\n for(int a=1;a>N>>M;\n has_dot.assign(N,vector(N,false));\n for(int i=0;i>x>>y;has_dot[x][y]=true;}\n \n double c=(N-1)/2.0;\n bool found=true;\n while(found){\n found=false;\n double best_w=-1;vectorbest_r;\n for(int x=0;x\n#include \n#include \n\nusing namespace std;\n\nconst int N = 10;\nint grid[N][N];\nint f[101];\n\nvoid tilt(int d) {\n if (d == 0) { // F (up)\n for (int c = 0; c < N; c++) {\n int write = 0;\n for (int r = 0; r < N; r++) {\n if (grid[r][c] != 0) {\n if (write != r) { grid[write][c] = grid[r][c]; grid[r][c] = 0; }\n write++;\n }\n }\n }\n } else if (d == 1) { // B (down)\n for (int c = 0; c < N; c++) {\n int write = N - 1;\n for (int r = N - 1; r >= 0; r--) {\n if (grid[r][c] != 0) {\n if (write != r) { grid[write][c] = grid[r][c]; grid[r][c] = 0; }\n write--;\n }\n }\n }\n } else if (d == 2) { // L (left)\n for (int r = 0; r < N; r++) {\n int write = 0;\n for (int c = 0; c < N; c++) {\n if (grid[r][c] != 0) {\n if (write != c) { grid[r][write] = grid[r][c]; grid[r][c] = 0; }\n write++;\n }\n }\n }\n } else { // R (right)\n for (int r = 0; r < N; r++) {\n int write = N - 1;\n for (int c = N - 1; c >= 0; c--) {\n if (grid[r][c] != 0) {\n if (write != c) { grid[r][write] = grid[r][c]; grid[r][c] = 0; }\n write--;\n }\n }\n }\n }\n}\n\nlong long calcScore() {\n bool visited[N][N] = {};\n long long score = 0;\n int dr[] = {-1, 1, 0, 0}, dc[] = {0, 0, -1, 1};\n \n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (!visited[r][c] && grid[r][c] != 0) {\n int flavor = grid[r][c], size = 0;\n queue> q;\n q.push({r, c}); visited[r][c] = true;\n while (!q.empty()) {\n auto [cr, cc] = q.front(); q.pop(); size++;\n for (int d = 0; d < 4; d++) {\n int nr = cr + dr[d], nc = cc + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && \n !visited[nr][nc] && grid[nr][nc] == flavor) {\n visited[nr][nc] = true; q.push({nr, nc});\n }\n }\n }\n score += (long long)size * size;\n }\n }\n }\n return score;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int i = 1; i <= 100; i++) cin >> f[i];\n memset(grid, 0, sizeof(grid));\n \n string dirs = \"FBLR\";\n int priority[] = {3, 1, 2, 4}; // B=1, L=2 preferred for compactness\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n \n int pos = 1, place_r = -1, place_c = -1;\n for (int r = 0; r < N && place_r == -1; r++) {\n for (int c = 0; c < N && place_r == -1; c++) {\n if (grid[r][c] == 0) {\n if (pos == p) { place_r = r; place_c = c; }\n pos++;\n }\n }\n }\n grid[place_r][place_c] = f[t];\n \n int best_dir = 0; long long best_score = -1; int best_priority = 5;\n int saved[N][N];\n \n for (int d = 0; d < 4; d++) {\n memcpy(saved, grid, sizeof(grid));\n tilt(d);\n long long score = calcScore();\n if (score > best_score || (score == best_score && priority[d] < best_priority)) {\n best_score = score; best_priority = priority[d]; best_dir = d;\n }\n memcpy(grid, saved, sizeof(grid));\n }\n \n tilt(best_dir);\n cout << dirs[best_dir] << '\\n';\n cout.flush();\n }\n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int M; double eps;\n cin >> M >> eps;\n \n int N = max(10, min(100, (int)(M * (0.5 + eps * 5) + 5)));\n int maxE = N * (N - 1) / 2;\n \n mt19937 rng(42);\n vector graphs(M);\n vector edgeCounts(M);\n vector> sortedDegrees(M);\n \n for (int k = 0; k < M; k++) {\n int targetEdges = (M > 1) ? (int)((long long)k * maxE / (M - 1)) : maxE / 2;\n \n vector perm(maxE);\n iota(perm.begin(), perm.end(), 0);\n shuffle(perm.begin(), perm.end(), rng);\n \n string g(maxE, '0');\n for (int i = 0; i < targetEdges; i++) g[perm[i]] = '1';\n graphs[k] = g;\n edgeCounts[k] = targetEdges;\n \n vector deg(N, 0);\n int idx = 0;\n for (int i = 0; i < N; i++)\n for (int j = i + 1; j < N; j++)\n if (g[idx++] == '1') { deg[i]++; deg[j]++; }\n sort(deg.begin(), deg.end());\n sortedDegrees[k] = deg;\n }\n \n vector expEdges(M);\n vector> expDeg(M);\n for (int k = 0; k < M; k++) {\n expEdges[k] = edgeCounts[k] * (1 - 2 * eps) + maxE * eps;\n expDeg[k].resize(N);\n for (int i = 0; i < N; i++)\n expDeg[k][i] = sortedDegrees[k][i] * (1 - 2 * eps) + (N - 1) * eps;\n }\n \n cout << N << \"\\n\";\n for (int k = 0; k < M; k++) cout << graphs[k] << \"\\n\";\n cout.flush();\n \n double edgeVar = max(1.0, maxE * eps * (1 - eps));\n double degVar = max(1.0, (N - 1) * eps * (1 - eps));\n \n for (int q = 0; q < 100; q++) {\n string H; cin >> H;\n int hEdges = count(H.begin(), H.end(), '1');\n \n vector hDeg(N, 0);\n int idx = 0;\n for (int i = 0; i < N; i++)\n for (int j = i + 1; j < N; j++)\n if (H[idx++] == '1') { hDeg[i]++; hDeg[j]++; }\n sort(hDeg.begin(), hDeg.end());\n \n int bestK = 0; double bestScore = -1e18;\n for (int k = 0; k < M; k++) {\n double score = 0;\n double edgeDiff = hEdges - expEdges[k];\n score -= edgeDiff * edgeDiff / (2 * edgeVar);\n for (int i = 0; i < N; i++) {\n double diff = hDeg[i] - expDeg[k][i];\n score -= diff * diff / (2 * degVar);\n }\n if (score > bestScore) { bestScore = score; bestK = k; }\n }\n cout << bestK << \"\\n\";\n cout.flush();\n }\n return 0;\n}","ahc017":"#include \nusing namespace std;\n\ntypedef long long ll;\ntypedef pair pli;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, D, K;\n cin >> N >> M >> D >> K;\n \n vector u(M), v(M), w(M);\n vector>> adj(N);\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i] >> w[i];\n u[i]--; v[i]--;\n adj[u[i]].push_back({i, v[i]});\n adj[v[i]].push_back({i, u[i]});\n }\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n cin >> x[i] >> y[i];\n }\n \n // Build edge adjacency (edges sharing a vertex)\n vector> edge_adj(M);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < (int)adj[i].size(); j++) {\n for (int k = j + 1; k < (int)adj[i].size(); k++) {\n edge_adj[adj[i][j].first].push_back(adj[i][k].first);\n edge_adj[adj[i][k].first].push_back(adj[i][j].first);\n }\n }\n }\n \n // Compute edge midpoints\n vector mx(M), my(M);\n for (int i = 0; i < M; i++) {\n mx[i] = (x[u[i]] + x[v[i]]) / 2.0;\n my[i] = (y[u[i]] + y[v[i]]) / 2.0;\n }\n \n // Sort by angle from center for geographic spreading\n double cx = 500, cy = 500;\n vector order(M);\n iota(order.begin(), order.end(), 0);\n \n sort(order.begin(), order.end(), [&](int a, int b) {\n double ax = mx[a] - cx, ay = my[a] - cy;\n double bx = mx[b] - cx, by = my[b] - cy;\n double aa = atan2(ay, ax), ab = atan2(by, bx);\n if (abs(aa - ab) > 1e-9) return aa < ab;\n double da = ax*ax + ay*ay, db = bx*bx + by*by;\n return da < db;\n });\n \n // Greedy edge coloring with conflict avoidance\n vector r(M, -1);\n vector day_count(D, 0);\n \n for (int idx : order) {\n vector conflicts(D, 0);\n for (int e : edge_adj[idx]) {\n if (r[e] != -1) conflicts[r[e]]++;\n }\n \n int best_day = -1;\n double best_score = 1e18;\n for (int d = 0; d < D; d++) {\n if (day_count[d] >= K) continue;\n double score = day_count[d] * 10.0 + conflicts[d] * 100.0;\n if (score < best_score) {\n best_score = score;\n best_day = d;\n }\n }\n \n if (best_day == -1) {\n for (int d = 0; d < D; d++) {\n if (day_count[d] < K && (best_day == -1 || day_count[d] < day_count[best_day])) {\n best_day = d;\n }\n }\n }\n \n r[idx] = best_day;\n day_count[best_day]++;\n }\n \n // Output\n for (int i = 0; i < M; i++) {\n cout << r[i] + 1 << (i == M-1 ? \"\\n\" : \" \");\n }\n \n return 0;\n}","ahc019":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint D;\nusing Point = tuple;\nusing Array3D = vector>>;\n\nvector readSilhouette() {\n vector s(D);\n for (int i = 0; i < D; i++) cin >> s[i];\n return s;\n}\n\nArray3D buildObject(const vector& f, const vector& r) {\n Array3D b(D, vector>(D, vector(D, 0)));\n for (int x = 0; x < D; x++)\n for (int y = 0; y < D; y++)\n for (int z = 0; z < D; z++)\n if (f[z][x] == '1' && r[z][y] == '1') b[x][y][z] = 1;\n return b;\n}\n\nvector> findComponents(const Array3D& b) {\n vector>> vis(D, vector>(D, vector(D, false)));\n vector> comps;\n const int dx[] = {1,-1,0,0,0,0}, dy[] = {0,0,1,-1,0,0}, dz[] = {0,0,0,0,1,-1};\n for (int x = 0; x < D; x++) for (int y = 0; y < D; y++) for (int z = 0; z < D; z++) {\n if (b[x][y][z] == 1 && !vis[x][y][z]) {\n vector comp; queue q; q.push({x,y,z}); vis[x][y][z] = true;\n while (!q.empty()) {\n auto [cx,cy,cz] = q.front(); q.pop(); comp.push_back({cx,cy,cz});\n for (int d = 0; d < 6; d++) {\n int nx=cx+dx[d], ny=cy+dy[d], nz=cz+dz[d];\n if (0<=nx&&nx canonicalForm(const vector& comp) {\n vector best;\n for (int r1 = 0; r1 < 4; r1++) for (int r2 = 0; r2 < 4; r2++) for (int r3 = 0; r3 < 4; r3++) {\n vector rot;\n for (auto p : comp) {\n for (int i = 0; i < r1; i++) p = rotX(p);\n for (int i = 0; i < r2; i++) p = rotY(p);\n for (int i = 0; i < r3; i++) p = rotZ(p);\n rot.push_back(p);\n }\n int minX=INT_MAX, minY=INT_MAX, minZ=INT_MAX;\n for (auto [x,y,z] : rot) { minX=min(minX,x); minY=min(minY,y); minZ=min(minZ,z); }\n for (auto& [x,y,z] : rot) { x-=minX; y-=minY; z-=minZ; }\n sort(rot.begin(), rot.end());\n if (best.empty() || rot < best) best = rot;\n }\n return best;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> D;\n vector> f(2), r(2);\n for (int i = 0; i < 2; i++) { f[i] = readSilhouette(); r[i] = readSilhouette(); }\n \n Array3D b[2]; for (int i = 0; i < 2; i++) b[i] = buildObject(f[i], r[i]);\n vector> comp[2]; for (int i = 0; i < 2; i++) comp[i] = findComponents(b[i]);\n \n int n1 = comp[0].size(), n2 = comp[1].size();\n vector> canon1(n1), canon2(n2);\n for (int i = 0; i < n1; i++) canon1[i] = canonicalForm(comp[0][i]);\n for (int j = 0; j < n2; j++) canon2[j] = canonicalForm(comp[1][j]);\n \n vector order1(n1); for (int i = 0; i < n1; i++) order1[i] = i;\n sort(order1.begin(), order1.end(), [&](int a, int b) { return comp[0][a].size() > comp[0][b].size(); });\n \n vector match1(n1,-1), match2(n2,-1); vector used2(n2, false);\n for (int i : order1) for (int j = 0; j < n2; j++) {\n if (!used2[j] && canon1[i] == canon2[j]) { match1[i]=j; match2[j]=i; used2[j]=true; break; }\n }\n \n int nextId = 1; vector id1(n1), id2(n2);\n for (int i = 0; i < n1; i++) if (match1[i] != -1) { id1[i]=nextId; id2[match1[i]]=nextId; nextId++; }\n for (int i = 0; i < n1; i++) if (match1[i] == -1) id1[i] = nextId++;\n for (int j = 0; j < n2; j++) if (match2[j] == -1) id2[j] = nextId++;\n \n vector out[2];\n for (int i = 0; i < 2; i++) {\n out[i].assign(D*D*D, 0);\n for (int c = 0; c < (int)comp[i].size(); c++) {\n int id = (i == 0) ? id1[c] : id2[c];\n for (auto [x,y,z] : comp[i][c]) out[i][x*D*D + y*D + z] = id;\n }\n }\n \n cout << nextId - 1 << \"\\n\";\n for (int i = 0; i < 2; i++) {\n for (int j = 0; j < D*D*D; j++) { if (j) cout << \" \"; cout << out[i][j]; }\n cout << \"\\n\";\n }\n return 0;\n}","ahc020":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n \n vector>> adj(N);\n vector u(M), v(M), w(M);\n for (int j = 0; j < M; j++) {\n cin >> u[j] >> v[j] >> w[j];\n u[j]--; v[j]--;\n adj[u[j]].push_back({v[j], j});\n adj[v[j]].push_back({u[j], j});\n }\n \n vector a(K), b(K);\n for (int k = 0; k < K; k++) cin >> a[k] >> b[k];\n \n vector> res_dist(K, vector(N));\n vector> closest(K);\n for (int k = 0; k < K; k++) {\n vector> dists;\n for (int i = 0; i < N; i++) {\n double dx = a[k] - x[i], dy = b[k] - y[i];\n res_dist[k][i] = sqrt(dx*dx + dy*dy);\n dists.push_back({res_dist[k][i], i});\n }\n sort(dists.begin(), dists.end());\n for (int j = 0; j < min(10, N); j++) closest[k].push_back(dists[j].second);\n }\n \n vector sp_dist(N, LLONG_MAX);\n vector parent(N, -1);\n sp_dist[0] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, 0});\n while (!pq.empty()) {\n auto [d, v] = pq.top(); pq.pop();\n if (d > sp_dist[v]) continue;\n for (auto [to, eid] : adj[v]) {\n if (sp_dist[v] + w[eid] < sp_dist[to]) {\n sp_dist[to] = sp_dist[v] + w[eid];\n parent[to] = v;\n pq.push({sp_dist[to], to});\n }\n }\n }\n \n vector assignment(K);\n for (int k = 0; k < K; k++) assignment[k] = closest[k][0];\n \n auto compute_P = [&]() {\n vector max_dist(N, 0);\n for (int k = 0; k < K; k++)\n max_dist[assignment[k]] = max(max_dist[assignment[k]], res_dist[k][assignment[k]]);\n vector P(N, 0);\n for (int i = 0; i < N; i++)\n if (max_dist[i] > 0) P[i] = min((int)ceil(max_dist[i]), 5000);\n return P;\n };\n \n auto compute_B = [&](const vector& P) {\n vector B(M, 0);\n for (int i = 1; i < N; i++) {\n if (P[i] > 0) {\n int cur = i;\n while (cur != 0) {\n int p = parent[cur];\n if (p == -1) break;\n for (auto& [to, eid] : adj[cur])\n if (to == p) { B[eid] = 1; break; }\n cur = p;\n }\n }\n }\n return B;\n };\n \n auto compute_cost = [&](const vector& P, const vector& B) {\n long long cost = 0;\n for (int i = 0; i < N; i++) cost += (long long)P[i] * P[i];\n for (int j = 0; j < M; j++) if (B[j]) cost += w[j];\n return cost;\n };\n \n vector P = compute_P();\n vector B = compute_B(P);\n long long cost = compute_cost(P, B);\n \n mt19937 rng(42);\n uniform_real_distribution<> uniform(0.0, 1.0);\n double start_temp = 1e7, end_temp = 1e1;\n int max_iter = 150000;\n \n for (int iter = 0; iter < max_iter; iter++) {\n double temp = start_temp * pow(end_temp / start_temp, (double)iter / max_iter);\n int k = rng() % K;\n int old_assign = assignment[k];\n int new_assign = closest[k][rng() % closest[k].size()];\n if (new_assign == old_assign) continue;\n \n assignment[k] = new_assign;\n vector new_P = compute_P();\n vector new_B = compute_B(new_P);\n long long new_cost = compute_cost(new_P, new_B);\n \n long long delta = new_cost - cost;\n if (delta < 0 || uniform(rng) < exp(-(double)delta / temp)) {\n cost = new_cost; P = new_P; B = new_B;\n } else {\n assignment[k] = old_assign;\n }\n }\n \n for (int i = 0; i < N; i++) cout << P[i] << (i < N-1 ? \" \" : \"\\n\");\n for (int j = 0; j < M; j++) cout << B[j] << (j < M-1 ? \" \" : \"\\n\");\n return 0;\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint grid[N][N];\nint posVal[465][2];\nvector> swaps;\n\nvoid doSwap(int x1, int y1, int x2, int y2) {\n int v1 = grid[x1][y1];\n int v2 = grid[x2][y2];\n swap(grid[x1][y1], grid[x2][y2]);\n posVal[v1][0] = x2; posVal[v1][1] = y2;\n posVal[v2][0] = x1; posVal[v2][1] = y1;\n swaps.push_back({x1, y1, x2, y2});\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++) {\n for (int y = 0; y <= x; y++) {\n cin >> grid[x][y];\n posVal[grid[x][y]][0] = x;\n posVal[grid[x][y]][1] = y;\n }\n }\n \n for (int v = 0; v < N * (N + 1) / 2 && (int)swaps.size() < 10000; v++) {\n int tx = 0;\n while ((tx + 1) * (tx + 2) / 2 <= v) tx++;\n int ty = v - tx * (tx + 1) / 2;\n \n int cx = posVal[v][0], cy = posVal[v][1];\n \n while (cx != tx || cy != ty) {\n int ddx = tx - cx, ddy = ty - cy;\n \n int nx, ny;\n if (ddx > 0 && ddy > 0) {\n nx = cx + 1; ny = cy + 1;\n } else if (ddx > 0) {\n nx = cx + 1; ny = cy;\n } else if (ddx < 0 && ddy < 0) {\n nx = cx - 1; ny = cy - 1;\n } else if (ddx < 0) {\n nx = cx - 1; ny = cy;\n } else if (ddy > 0) {\n nx = cx; ny = cy + 1;\n } else {\n nx = cx; ny = cy - 1;\n }\n \n doSwap(cx, cy, nx, ny);\n cx = nx; cy = ny;\n \n if ((int)swaps.size() >= 10000) break;\n }\n }\n \n cout << swaps.size() << \"\\n\";\n for (auto& s : swaps) {\n cout << s[0] << \" \" << s[1] << \" \" << s[2] << \" \" << s[3] << \"\\n\";\n }\n \n return 0;\n}","toyota2023summer-final":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int D, N;\n cin >> D >> N;\n \n vector> is_obstacle(D, vector(D, false));\n for (int i = 0; i < N; i++) {\n int ri, rj;\n cin >> ri >> rj;\n is_obstacle[ri][rj] = true;\n }\n \n int entrance_i = 0, entrance_j = (D - 1) / 2;\n \n vector> dist(D, vector(D, -1));\n queue> q;\n q.push({entrance_i, entrance_j});\n dist[entrance_i][entrance_j] = 0;\n \n const int di[] = {-1, 1, 0, 0};\n const int dj[] = {0, 0, -1, 1};\n \n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && dist[ni][nj] == -1 && !is_obstacle[ni][nj]) {\n dist[ni][nj] = dist[i][j] + 1;\n q.push({ni, nj});\n }\n }\n }\n \n vector> cells;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (!(i == entrance_i && j == entrance_j) && !is_obstacle[i][j])\n cells.push_back({dist[i][j], i, j});\n \n sort(cells.begin(), cells.end());\n int M = cells.size();\n \n set available_ranks;\n for (int k = 0; k < M; k++) available_ranks.insert(k);\n \n vector> container_at(D, vector(D, -1));\n \n for (int d = 0; d < M; d++) {\n int t; cin >> t;\n int target_rank = t;\n \n auto it = available_ranks.lower_bound(target_rank);\n int best_rank = -1, best_diff = M + 1;\n \n if (it != available_ranks.end() && abs(*it - target_rank) < best_diff) {\n best_diff = abs(*it - target_rank);\n best_rank = *it;\n }\n if (it != available_ranks.begin()) {\n --it;\n if (abs(*it - target_rank) < best_diff) {\n best_diff = abs(*it - target_rank);\n best_rank = *it;\n }\n }\n \n available_ranks.erase(best_rank);\n auto [dd, pi, pj] = cells[best_rank];\n cout << pi << \" \" << pj << endl;\n container_at[pi][pj] = t;\n }\n \n vector> is_empty(D, vector(D, false));\n is_empty[entrance_i][entrance_j] = true;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (is_obstacle[i][j]) is_empty[i][j] = true;\n \n for (int iter = 0; iter < M; iter++) {\n vector> accessible(D, vector(D, false));\n queue> bfs_q;\n bfs_q.push({entrance_i, entrance_j});\n accessible[entrance_i][entrance_j] = true;\n \n while (!bfs_q.empty()) {\n auto [i, j] = bfs_q.front(); bfs_q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && !accessible[ni][nj] && is_empty[ni][nj]) {\n accessible[ni][nj] = true;\n bfs_q.push({ni, nj});\n }\n }\n }\n \n int min_t = M + 1, min_i = -1, min_j = -1;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (container_at[i][j] >= 0 && accessible[i][j] && container_at[i][j] < min_t) {\n min_t = container_at[i][j];\n min_i = i; min_j = j;\n }\n \n cout << min_i << \" \" << min_j << endl;\n is_empty[min_i][min_j] = true;\n container_at[min_i][min_j] = -1;\n }\n \n return 0;\n}","ahc024":"#include \nusing namespace std;\n\nconst int N = 50;\nconst int M = 100;\nconst int dx[] = {0, 0, 1, -1};\nconst int dy[] = {1, -1, 0, 0};\n\nint n, m;\nint grid[N][N], best_grid[N][N];\nint best_score;\nset> required_adj;\nint adj_cnt[M+1][M+1];\n\nbool valid(int x, int y) { return 0 <= x && x < n && 0 <= y && y < n; }\n\nvoid compute_init_adj() {\n memset(adj_cnt, 0, sizeof(adj_cnt));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) {\n if (j+1 < n && grid[i][j] != grid[i][j+1])\n adj_cnt[min(grid[i][j],grid[i][j+1])][max(grid[i][j],grid[i][j+1])]++;\n if (i+1 < n && grid[i][j] != grid[i+1][j])\n adj_cnt[min(grid[i][j],grid[i+1][j])][max(grid[i][j],grid[i+1][j])]++;\n if (i==0||i==n-1||j==0||j==n-1)\n adj_cnt[0][grid[i][j]]++;\n }\n for (int a = 0; a <= m; a++)\n for (int b = a; b <= m; b++)\n if (adj_cnt[a][b] > 0) required_adj.insert({a,b});\n}\n\nbool check_c0_conn() {\n bool has0 = false;\n for (int i = 0; i < n && !has0; i++)\n for (int j = 0; j < n && !has0; j++)\n if (grid[i][j] == 0) has0 = true;\n if (!has0) return true;\n \n vector> vis(n, vector(n));\n queue> q;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0 && (i==0||i==n-1||j==0||j==n-1))\n { q.push({i,j}); vis[i][j] = true; }\n \n while (!q.empty()) {\n auto [x,y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx=x+dx[d], ny=y+dy[d];\n if (valid(nx,ny) && !vis[nx][ny] && grid[nx][ny]==0)\n { vis[nx][ny] = true; q.push({nx,ny}); }\n }\n }\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0 && !vis[i][j]) return false;\n return true;\n}\n\nbool can_change(int i, int j, int nc) {\n int oc = grid[i][j];\n if (oc == nc) return true;\n if (nc != 0) {\n bool found = false;\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj) && grid[ni][nj] == nc) { found = true; break; }\n }\n if (!found) return false;\n }\n map,int> delta;\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj)) {\n int c = grid[ni][nj];\n if (oc != c) delta[{min(oc,c),max(oc,c)}]--;\n if (nc != c) delta[{min(nc,c),max(nc,c)}]++;\n }\n }\n if (i==0||i==n-1||j==0||j==n-1) {\n if (oc != 0) delta[{0,oc}]--;\n if (nc != 0) delta[{0,nc}]++;\n }\n for (auto& [p,d] : delta) {\n int ncnt = adj_cnt[p.first][p.second] + d;\n if (ncnt > 0 && required_adj.find(p) == required_adj.end()) return false;\n if (ncnt <= 0 && required_adj.find(p) != required_adj.end()) return false;\n }\n grid[i][j] = nc;\n bool ok = check_c0_conn();\n grid[i][j] = oc;\n return ok;\n}\n\nvoid apply_change(int i, int j, int nc) {\n int oc = grid[i][j];\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj)) {\n int c = grid[ni][nj];\n if (oc != c) adj_cnt[min(oc,c)][max(oc,c)]--;\n if (nc != c) adj_cnt[min(nc,c)][max(nc,c)]++;\n }\n }\n if (i==0||i==n-1||j==0||j==n-1) {\n if (oc != 0) adj_cnt[0][oc]--;\n if (nc != 0) adj_cnt[0][nc]++;\n }\n grid[i][j] = nc;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> n >> m;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) cin >> grid[i][j];\n \n compute_init_adj();\n memcpy(best_grid, grid, sizeof(grid));\n best_score = 2501;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) best_score++;\n \n bool improved = true;\n while (improved) {\n improved = false;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) {\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj) && grid[ni][nj] != 0)\n if (can_change(i, j, grid[ni][nj])) {\n apply_change(i, j, grid[ni][nj]);\n improved = true;\n break;\n }\n }\n }\n }\n \n int cnt0 = 0;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) cnt0++;\n if (cnt0+1 < best_score) {\n best_score = cnt0+1;\n memcpy(best_grid, grid, sizeof(grid));\n }\n \n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << best_grid[i][j];\n if (j < n-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n return 0;\n}","ahc025":"#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, D, Q;\nint qc = 0;\nint cmp[105][105];\n\nchar query(int a, int b) {\n if (cmp[a][b] != 0) return cmp[a][b] == 1 ? '>' : '<';\n if (qc >= Q) return '=';\n \n qc++;\n cout << \"1 1 \" << a << \" \" << b << endl;\n char res;\n cin >> res;\n \n if (res == '<') {\n cmp[a][b] = -1;\n cmp[b][a] = 1;\n } else if (res == '>') {\n cmp[a][b] = 1;\n cmp[b][a] = -1;\n }\n return res;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n vector items(N);\n for (int i = 0; i < N; i++) items[i] = i;\n \n // Insertion sort using comparisons\n for (int i = 1; i < N; i++) {\n int j = i;\n while (j > 0 && qc < Q) {\n int a = items[j-1], b = items[j];\n if (cmp[a][b] == 1) {\n swap(items[j-1], items[j]);\n j--;\n } else if (cmp[a][b] == -1) {\n break;\n } else {\n char res = query(a, b);\n if (res == '>') {\n swap(items[j-1], items[j]);\n j--;\n } else {\n break;\n }\n }\n }\n }\n \n // Use remaining queries to verify sort\n for (int i = 1; i < N && qc < Q; i++) {\n if (cmp[items[i-1]][items[i]] == 0) {\n query(items[i-1], items[i]);\n }\n }\n \n // Use remaining queries for random comparisons\n mt19937 rng(42);\n while (qc < Q) {\n int x = rng() % N, y = rng() % N;\n if (x != y && cmp[x][y] == 0) {\n query(x, y);\n }\n }\n \n // Estimate weights using exponential distribution assumption\n vector est_weight(N);\n for (int i = 0; i < N; i++) {\n double p = (double)(i + 1) / (N + 1);\n est_weight[items[i]] = -log(1.0 - p);\n }\n \n // LPT partitioning: assign heaviest items first to lightest group\n vector group_weight(D, 0);\n vector assignment(N);\n \n for (int i = N - 1; i >= 0; i--) {\n int item = items[i];\n int min_group = 0;\n for (int g = 1; g < D; g++) {\n if (group_weight[g] < group_weight[min_group]) {\n min_group = g;\n }\n }\n assignment[item] = min_group;\n group_weight[min_group] += est_weight[item];\n }\n \n // Output assignment\n for (int i = 0; i < N; i++) {\n cout << assignment[i];\n if (i < N - 1) cout << \" \";\n }\n cout << endl;\n \n return 0;\n}","ahc026":"#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n for (int i = 0; i < m; i++) {\n stacks[i].resize(n / m);\n for (int j = 0; j < n / m; j++) {\n cin >> stacks[i][j];\n }\n }\n \n vector box_stack(n + 1), box_pos(n + 1);\n for (int i = 0; i < m; i++) {\n for (int j = 0; j < (int)stacks[i].size(); j++) {\n box_stack[stacks[i][j]] = i;\n box_pos[stacks[i][j]] = j;\n }\n }\n \n vector> operations;\n \n for (int v = 1; v <= n; v++) {\n int sid = box_stack[v], pos = box_pos[v];\n \n while ((int)stacks[sid].size() > pos + 1) {\n int top_idx = stacks[sid].size() - 1;\n int seg_start = top_idx;\n \n while (seg_start > pos + 1 && stacks[sid][seg_start - 1] > stacks[sid][seg_start])\n seg_start--;\n \n int max_in_seg = stacks[sid][seg_start];\n int dest = -1;\n \n for (int i = 0; i < m; i++) {\n if (i == sid) continue;\n if (stacks[i].empty()) { dest = i; break; }\n }\n \n if (dest == -1) {\n int max_top = -1;\n for (int i = 0; i < m; i++) {\n if (i == sid) continue;\n if (!stacks[i].empty() && stacks[i].back() > max_in_seg && stacks[i].back() > max_top) {\n max_top = stacks[i].back();\n dest = i;\n }\n }\n }\n \n if (dest == -1) {\n int max_top = -1;\n for (int i = 0; i < m; i++) {\n if (i == sid) continue;\n if (!stacks[i].empty() && stacks[i].back() > max_top) {\n max_top = stacks[i].back();\n dest = i;\n }\n }\n }\n \n if (dest == -1) dest = (sid + 1) % m;\n \n int u = stacks[sid][seg_start];\n operations.push_back({u, dest + 1});\n \n vector moved(stacks[sid].begin() + seg_start, stacks[sid].end());\n stacks[sid].resize(seg_start);\n stacks[dest].insert(stacks[dest].end(), moved.begin(), moved.end());\n \n for (int j = 0; j < (int)moved.size(); j++) {\n box_stack[moved[j]] = dest;\n box_pos[moved[j]] = stacks[dest].size() - moved.size() + j;\n }\n }\n \n operations.push_back({v, 0});\n stacks[sid].pop_back();\n }\n \n for (auto& op : operations) {\n cout << op.first << \" \" << op.second << endl;\n }\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\nchar dir_char[] = {'R', 'D', 'L', 'U'};\n\nbool can_move(int i, int j, int dir) {\n int ni = i + dx[dir], nj = j + dy[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0 && v[i][j] == '1') return false;\n if (dir == 1 && h[i][j] == '1') return false;\n if (dir == 2 && v[i][nj] == '1') return false;\n if (dir == 3 && h[ni][j] == '1') return false;\n return true;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1); v.resize(N); d.resize(N, vector(N));\n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> d[i][j];\n \n vector> dist(N, vector(N, -1)), prev_dir(N, vector(N, -1));\n queue> q; dist[0][0] = 0; q.push({0, 0});\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(i, j, dir)) continue;\n int ni = i + dx[dir], nj = j + dy[dir];\n if (dist[ni][nj] == -1) { dist[ni][nj] = dist[i][j] + 1; prev_dir[ni][nj] = dir; q.push({ni, nj}); }\n }\n }\n \n string result;\n vector> visited(N, vector(N, false));\n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n vector> neighbors;\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(i, j, dir)) continue;\n int ni = i + dx[dir], nj = j + dy[dir];\n if (!visited[ni][nj]) neighbors.push_back({ni, nj});\n }\n sort(neighbors.begin(), neighbors.end(), [](auto& a, auto& b) { return d[a.first][a.second] > d[b.first][b.second]; });\n for (auto [ni, nj] : neighbors) {\n for (int dir = 0; dir < 4; dir++) {\n if (i + dx[dir] == ni && j + dy[dir] == nj) {\n result += dir_char[dir]; dfs(ni, nj); result += dir_char[(dir + 2) % 4]; break;\n }\n }\n }\n };\n dfs(0, 0);\n \n vector visit_count(N * N, 0);\n int ci = 0, cj = 0; visit_count[0]++;\n for (char c : result) {\n int dir = (c == 'R') ? 0 : (c == 'D') ? 1 : (c == 'L') ? 2 : 3;\n ci += dx[dir]; cj += dy[dir]; visit_count[ci * N + cj]++;\n }\n \n using Cell = tuple;\n priority_queue pq;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (i == 0 && j == 0) continue;\n int k = visit_count[i * N + j];\n double cost = 2.0 * dist[i][j];\n if (cost > 0) pq.push({(double)d[i][j] / (k * (k + 1)) / cost, i, j});\n }\n \n while (!pq.empty() && result.size() < 100000) {\n auto [p, i, j] = pq.top(); pq.pop();\n int k = visit_count[i * N + j];\n double cost = 2.0 * dist[i][j];\n double new_p = (double)d[i][j] / (k * (k + 1)) / cost;\n if (abs(new_p - p) > 1e-9) { pq.push({new_p, i, j}); continue; }\n \n string path_to, path_back;\n int ci2 = i, cj2 = j;\n while (ci2 != 0 || cj2 != 0) { int dir = prev_dir[ci2][cj2]; path_to += dir_char[dir]; ci2 -= dx[dir]; cj2 -= dy[dir]; }\n reverse(path_to.begin(), path_to.end());\n for (int k2 = path_to.size() - 1; k2 >= 0; k2--) {\n char c = path_to[k2];\n path_back += (c == 'R') ? 'L' : (c == 'D') ? 'U' : (c == 'L') ? 'R' : 'D';\n }\n string detour = path_to + path_back;\n if (result.size() + detour.size() <= 100000) {\n result += detour; visit_count[i * N + j]++;\n int nk = visit_count[i * N + j];\n pq.push({(double)d[i][j] / (nk * (nk + 1)) / cost, i, j});\n }\n }\n \n cout << result << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M; cin >> N >> M;\n int si, sj; cin >> si >> sj;\n vector A(N);\n for (int i = 0; i < N; i++) cin >> A[i];\n vector t(M);\n for (int i = 0; i < M; i++) cin >> t[i];\n \n vector>> charPos(26);\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n charPos[A[i][j] - 'A'].push_back({i, j});\n \n vector> overlap(M, vector(M, 0));\n for (int i = 0; i < M; i++)\n for (int j = 0; j < M; j++) {\n if (i == j) continue;\n for (int len = 4; len >= 1; len--) {\n bool match = true;\n for (int k = 0; k < len; k++)\n if (t[i][5 - len + k] != t[j][k]) { match = false; break; }\n if (match) { overlap[i][j] = len; break; }\n }\n }\n \n string bestSuper; int bestLen = INT_MAX;\n for (int start = 0; start < M; start++) {\n vector used(M, false);\n vector order; order.push_back(start); used[start] = true;\n for (int step = 1; step < M; step++) {\n int last = order.back(), best_next = -1, best_ov = -1;\n for (int j = 0; j < M; j++)\n if (!used[j] && overlap[last][j] > best_ov) { best_ov = overlap[last][j]; best_next = j; }\n if (best_next == -1) for (int j = 0; j < M; j++) if (!used[j]) { best_next = j; break; }\n order.push_back(best_next); used[best_next] = true;\n }\n string superstr = t[order[0]];\n for (int i = 1; i < M; i++) superstr += t[order[i]].substr(overlap[order[i-1]][order[i]]);\n if ((int)superstr.size() < bestLen) { bestLen = superstr.size(); bestSuper = superstr; }\n }\n \n int L = bestSuper.size();\n auto encode = [](int i, int j) { return i * 15 + j; };\n auto decodeI = [](int c) { return c / 15; };\n auto decodeJ = [](int c) { return c % 15; };\n \n const int INF = 1e9;\n vector>> dp(L + 1, vector>(225, {INF, -1}));\n dp[0][encode(si, sj)] = {0, -1};\n \n for (int i = 0; i < L; i++) {\n int cidx = bestSuper[i] - 'A';\n vector finite;\n for (int q = 0; q < 225; q++) if (dp[i][q].first < INF) finite.push_back(q);\n for (auto [pi, pj] : charPos[cidx]) {\n int p = encode(pi, pj);\n for (int q : finite) {\n int qi = decodeI(q), qj = decodeJ(q);\n int newCost = dp[i][q].first + abs(pi - qi) + abs(pj - qj) + 1;\n if (newCost < dp[i + 1][p].first) dp[i + 1][p] = {newCost, q};\n }\n }\n }\n \n int bestEnd = 0, bestCost = INF;\n for (int p = 0; p < 225; p++)\n if (dp[L][p].first < bestCost) { bestCost = dp[L][p].first; bestEnd = p; }\n \n vector pathPos(L);\n int curr = bestEnd;\n for (int i = L - 1; i >= 0; i--) { pathPos[i] = curr; curr = dp[i + 1][curr].second; }\n \n for (int i = 0; i < L; i++)\n cout << decodeI(pathPos[i]) << \" \" << decodeJ(pathPos[i]) << \"\\n\";\n \n return 0;\n}","ahc030":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nvector max_di, max_dj;\nvector>> positions;\nvector>>> pos_cells;\nint known[25][25];\nint query_count = 0;\nvector> w;\ndouble cov[25][25];\n\nint drill_cell(int i, int j) {\n cout << \"q 1 \" << i << \" \" << j << endl;\n cout.flush();\n int v; cin >> v;\n known[i][j] = v;\n query_count++;\n return v;\n}\n\nint divine_cells(vector>& cells) {\n int k = cells.size();\n cout << \"q \" << k;\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << endl;\n cout.flush();\n int v; cin >> v;\n query_count++;\n return v;\n}\n\nvoid submit_answer(vector>& cells) {\n sort(cells.begin(), cells.end());\n cells.erase(unique(cells.begin(), cells.end()), cells.end());\n cout << \"a \" << cells.size();\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << endl;\n cout.flush();\n int r; cin >> r;\n if (r == 1) exit(0);\n}\n\nvoid update_coverage() {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cov[i][j] = 0;\n for (int k = 0; k < M; k++) {\n double total = accumulate(w[k].begin(), w[k].end(), 0.0);\n if (total < 1e-10) continue;\n for (int p = 0; p < (int)positions[k].size(); p++) {\n double wt = w[k][p] / total;\n for (auto& [ci, cj] : pos_cells[k][p]) cov[ci][cj] += wt;\n }\n }\n}\n\nvoid update_divine(const vector>& qcells, int obs) {\n int ksz = qcells.size();\n set> cs(qcells.begin(), qcells.end());\n for (int k = 0; k < M; k++) {\n double others = 0;\n for (int k2 = 0; k2 < M; k2++) if (k2 != k) {\n double t2 = accumulate(w[k2].begin(), w[k2].end(), 0.0);\n if (t2 < 1e-10) continue;\n for (int p2 = 0; p2 < (int)positions[k2].size(); p2++) {\n int cnt = 0;\n for (auto& [ci, cj] : pos_cells[k2][p2]) if (cs.count({ci, cj})) cnt++;\n others += w[k2][p2] / t2 * cnt;\n }\n }\n for (int p = 0; p < (int)positions[k].size(); p++) {\n int cnt = 0;\n for (auto& [ci, cj] : pos_cells[k][p]) if (cs.count({ci, cj})) cnt++;\n double ev = others + cnt;\n double mean = ksz * eps + ev * (1 - 2 * eps);\n double var = ksz * eps * (1 - eps);\n double diff = obs - mean;\n w[k][p] *= exp(-diff * diff / (2 * var));\n }\n double total = accumulate(w[k].begin(), w[k].end(), 0.0);\n if (total > 1e-10) for (auto& wp : w[k]) wp /= total;\n }\n update_coverage();\n}\n\nvoid update_drill(int i, int j, int obs) {\n for (int k = 0; k < M; k++) {\n double others = 0;\n for (int k2 = 0; k2 < M; k2++) if (k2 != k) {\n double t2 = accumulate(w[k2].begin(), w[k2].end(), 0.0);\n if (t2 < 1e-10) continue;\n for (int p2 = 0; p2 < (int)positions[k2].size(); p2++)\n for (auto& [ci, cj] : pos_cells[k2][p2])\n if (ci == i && cj == j) { others += w[k2][p2] / t2; break; }\n }\n for (int p = 0; p < (int)positions[k].size(); p++) {\n bool covers = false;\n for (auto& [ci, cj] : pos_cells[k][p]) if (ci == i && cj == j) { covers = true; break; }\n double ev = others + (covers ? 1.0 : 0.0);\n double diff = obs - ev;\n double var = max(0.3, ev * 0.5);\n w[k][p] *= exp(-diff * diff / (2 * var));\n }\n double total = accumulate(w[k].begin(), w[k].end(), 0.0);\n if (total > 1e-10) for (auto& wp : w[k]) wp /= total;\n }\n update_coverage();\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> M >> eps;\n shapes.resize(M);\n for (int k = 0; k < M; k++) {\n int d; cin >> d;\n shapes[k].resize(d);\n for (int l = 0; l < d; l++) cin >> shapes[k][l].first >> shapes[k][l].second;\n }\n max_di.resize(M); max_dj.resize(M);\n for (int k = 0; k < M; k++) {\n max_di[k] = max_dj[k] = 0;\n for (auto& [i, j] : shapes[k]) { max_di[k] = max(max_di[k], i); max_dj[k] = max(max_dj[k], j); }\n }\n for (int k = 0; k < M; k++) {\n vector> pos;\n vector>> cells;\n for (int di = 0; di <= N - 1 - max_di[k]; di++)\n for (int dj = 0; dj <= N - 1 - max_dj[k]; dj++) {\n pos.push_back({di, dj});\n vector> c;\n for (auto& [i, j] : shapes[k]) c.push_back({di + i, dj + j});\n cells.push_back(c);\n }\n positions.push_back(pos);\n pos_cells.push_back(cells);\n }\n memset(known, -1, sizeof(known));\n for (int k = 0; k < M; k++) w.push_back(vector(positions[k].size(), 1.0));\n update_coverage();\n \n for (int i = 0; i < N && query_count < 2*N*N; i++) {\n vector> cells;\n for (int j = 0; j < N; j++) cells.push_back({i, j});\n update_divine(cells, divine_cells(cells));\n }\n for (int j = 0; j < N && query_count < 2*N*N; j++) {\n vector> cells;\n for (int i = 0; i < N; i++) cells.push_back({i, j});\n update_divine(cells, divine_cells(cells));\n }\n \n while (query_count < 2*N*N - 1) {\n int bi = -1, bj = -1; double bs = -1e9;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) continue;\n double p = 1.0 - exp(-cov[i][j]); p = max(0.01, min(0.99, p));\n double ent = -p*log(p) - (1-p)*log(1-p);\n if (ent > bs) { bs = ent; bi = i; bj = j; }\n }\n if (bi < 0) break;\n update_drill(bi, bj, drill_cell(bi, bj));\n }\n \n vector> ans;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] > 0) ans.push_back({i, j});\n else if (known[i][j] < 0 && 1.0 - exp(-cov[i][j]) > 0.5) ans.push_back({i, j});\n }\n submit_answer(ans);\n return 0;\n}","ahc031":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int W, D, N;\n cin >> W >> D >> N;\n \n vector> a(D, vector(N));\n for (int d = 0; d < D; d++) {\n for (int k = 0; k < N; k++) {\n cin >> a[d][k];\n }\n }\n \n // Compute max required heights across all days for zero deficit\n vector max_required_h(N, 0);\n for (int d = 0; d < D; d++) {\n for (int k = 0; k < N; k++) {\n int min_h = (a[d][k] + W - 1) / W;\n max_required_h[k] = max(max_required_h[k], min_h);\n }\n }\n \n long long total_max_h = accumulate(max_required_h.begin(), max_required_h.end(), 0LL);\n \n vector fixed_h(N);\n \n if (total_max_h <= W) {\n // Fixed heights work - zero deficit and zero partition changes\n fixed_h = max_required_h;\n int remaining = W - total_max_h;\n // Distribute remaining space starting from largest strip\n int k = N - 1;\n while (remaining > 0) {\n fixed_h[k]++;\n remaining--;\n k = (k - 1 + N) % N;\n }\n } else {\n // Need to scale down - accept some deficit but still zero partition changes\n for (int k = 0; k < N; k++) {\n fixed_h[k] = max(1, (int)(max_required_h[k] * W / total_max_h));\n }\n int total_h = accumulate(fixed_h.begin(), fixed_h.end(), 0);\n int k = N - 1;\n while (total_h < W) {\n fixed_h[k]++;\n total_h++;\n k = (k - 1 + N) % N;\n }\n while (total_h > W) {\n for (int j = 0; j < N && total_h > W; j++) {\n if (fixed_h[j] > 1) {\n fixed_h[j]--;\n total_h--;\n }\n }\n }\n }\n \n // Output using fixed heights\n for (int d = 0; d < D; d++) {\n int y = 0;\n for (int k = 0; k < N; k++) {\n cout << y << \" 0 \" << y + fixed_h[k] << \" \" << W << \"\\n\";\n y += fixed_h[k];\n }\n }\n \n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long MOD = 998244353;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n vector> bmod(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> bmod[i][j];\n \n vector>> s(M, vector>(3, vector(3)));\n for (int m = 0; m < M; m++)\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n cin >> s[m][i][j];\n \n vector> ops;\n \n for (int k = 0; k < K; k++) {\n int best_m = -1, best_p = -1, best_q = -1;\n long long best_delta = LLONG_MIN;\n \n for (int m = 0; m < M; m++) {\n for (int p = 0; p <= N - 3; p++) {\n for (int q = 0; q <= N - 3; q++) {\n long long delta = 0;\n for (int i = 0; i < 3; i++) {\n for (int j = 0; j < 3; j++) {\n long long new_mod = (bmod[p + i][q + j] + s[m][i][j]) % MOD;\n delta += new_mod - bmod[p + i][q + j];\n }\n }\n if (delta > best_delta) {\n best_delta = delta;\n best_m = m;\n best_p = p;\n best_q = q;\n }\n }\n }\n }\n \n if (best_delta <= 0) break;\n \n ops.push_back({best_m, best_p, best_q});\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n bmod[best_p + i][best_q + j] = (bmod[best_p + i][best_q + j] + s[best_m][i][j]) % MOD;\n }\n \n cout << ops.size() << endl;\n for (auto& [m, p, q] : ops)\n cout << m << \" \" << p << \" \" << q << endl;\n \n return 0;\n}","ahc033":"#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N];\nint container_recv_row[N*N], container_recv_idx[N*N];\nbool container_dispatched[N*N];\n\nint next_expected(int gate) {\n for (int j = 0; j < N; j++)\n if (!container_dispatched[N * gate + j]) return N * gate + j;\n return -1;\n}\n\nint main() {\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> A[i][j];\n container_recv_row[A[i][j]] = i;\n container_recv_idx[A[i][j]] = j;\n }\n fill(container_dispatched, container_dispatched + N*N, false);\n \n int grid[N][N]; for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) grid[i][j] = -1;\n int crane_r = 0, crane_c = 0, crane_holding = -1;\n int next_receive[N] = {}, total_dispatched = 0;\n vector actions(N, \"\");\n \n for (int turn = 1; total_dispatched < N*N && turn < 10000; turn++) {\n for (int i = 0; i < N; i++)\n if (next_receive[i] < N && grid[i][0] == -1 && !(crane_r == i && crane_c == 0 && crane_holding != -1)) {\n grid[i][0] = A[i][next_receive[i]++];\n }\n \n char act = '.';\n if (crane_holding != -1) {\n int dr = crane_holding / N, exp = next_expected(dr);\n int tr, tc;\n if (exp != -1 && crane_holding == exp) { tr = dr; tc = N-1; }\n else {\n tr = tc = -1; int bd = INT_MAX;\n for (int c = 1; c < N-1; c++) for (int r = 0; r < N; r++)\n if (grid[r][c] == -1) { int d = abs(crane_r-r)+abs(crane_c-c); if (d < bd) { bd=d; tr=r; tc=c; } }\n if (tr == -1) { tr = dr; tc = N-1; }\n }\n if (crane_r == tr && crane_c == tc) { act = 'Q'; grid[tr][tc] = crane_holding; crane_holding = -1; }\n else { if (crane_r < tr) { crane_r++; act='D'; } else if (crane_r > tr) { crane_r--; act='U'; } else if (crane_c < tc) { crane_c++; act='R'; } else { crane_c--; act='L'; } }\n } else {\n int bc = -1, bs = INT_MAX, br = -1, bcc = -1;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) {\n if (grid[r][c] == -1 || container_dispatched[grid[r][c]]) continue;\n int cont = grid[r][c], dr = cont / N, exp = next_expected(dr);\n int dp = abs(crane_r-r)+abs(crane_c-c), sc;\n if (exp != -1 && cont == exp) sc = dp + abs(r-dr)+abs(c-(N-1));\n else {\n int mt = INT_MAX;\n for (int tc=1; tcbr) { crane_r--; act='U'; } else if (crane_c\n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int INF = 1e9;\n\nstruct Edge { int to, cap, cost, flow, rev; };\n\nclass MinCostFlow {\npublic:\n int n;\n vector> graph;\n MinCostFlow(int n) : n(n), graph(n) {}\n \n void add_edge(int from, int to, int cap, int cost) {\n graph[from].push_back({to, cap, cost, 0, (int)graph[to].size()});\n graph[to].push_back({from, 0, -cost, 0, (int)graph[from].size() - 1});\n }\n \n int min_cost_flow(int s, int t, int maxf) {\n int res = 0;\n vector h(n), prevv(n), preve(n);\n int flow = 0;\n while (flow < maxf) {\n priority_queue, vector>, greater<>> pq;\n vector dist(n, INF);\n dist[s] = 0;\n pq.push({0, s});\n while (!pq.empty()) {\n auto [d, v] = pq.top(); pq.pop();\n if (dist[v] < d) continue;\n for (int i = 0; i < graph[v].size(); i++) {\n Edge& e = graph[v][i];\n if (e.cap > e.flow && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {\n dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];\n prevv[e.to] = v; preve[e.to] = i;\n pq.push({dist[e.to], e.to});\n }\n }\n }\n if (dist[t] == INF) break;\n for (int v = 0; v < n; v++) h[v] += dist[v];\n int d = maxf - flow;\n for (int v = t; v != s; v = prevv[v])\n d = min(d, graph[prevv[v]][preve[v]].cap - graph[prevv[v]][preve[v]].flow);\n flow += d; res += d * h[t];\n for (int v = t; v != s; v = prevv[v]) {\n Edge& e = graph[prevv[v]][preve[v]];\n e.flow += d; graph[v][e.rev].flow -= d;\n }\n }\n return res;\n }\n};\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int n; cin >> n;\n vector> h(n, vector(n));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) cin >> h[i][j];\n \n vector ops;\n int r = 0, c = 0, load = 0;\n int remaining = 0;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (h[i][j] > 0) remaining += h[i][j];\n \n while (ops.size() < 100000 && remaining > 0) {\n if (h[r][c] > 0) {\n ops.push_back(\"+\" + to_string(h[r][c]));\n load += h[r][c]; remaining -= h[r][c]; h[r][c] = 0;\n }\n while (h[r][c] < 0 && load > 0) {\n int d = min(load, -h[r][c]);\n ops.push_back(\"-\" + to_string(d));\n load -= d; h[r][c] += d;\n }\n if (remaining == 0) break;\n \n int best_r = -1, best_c = -1, best_dist = INT_MAX;\n if (load > 0) {\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (h[i][j] < 0) {\n int dist = abs(r - i) + abs(c - j);\n if (dist < best_dist) { best_dist = dist; best_r = i; best_c = j; }\n }\n }\n if (best_r == -1) {\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (h[i][j] > 0) {\n int dist = abs(r - i) + abs(c - j);\n if (dist < best_dist) { best_dist = dist; best_r = i; best_c = j; }\n }\n }\n if (best_r == -1) break;\n \n if (best_r < r) { r--; ops.push_back(\"U\"); }\n else if (best_r > r) { r++; ops.push_back(\"D\"); }\n else if (best_c < c) { c--; ops.push_back(\"L\"); }\n else { c++; ops.push_back(\"R\"); }\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc035":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 6, M = 15;\n const int SEED_COUNT = 2 * N * (N - 1);\n const int GRID_SIZE = N * N;\n \n int n, m, t;\n cin >> n >> m >> t;\n \n vector> X(SEED_COUNT, vector(M));\n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n cin >> X[i][j];\n \n vector> edges;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N-1; j++)\n edges.push_back({i*N+j, i*N+j+1});\n for (int i = 0; i < N-1; i++)\n for (int j = 0; j < N; j++)\n edges.push_back({i*N+j, (i+1)*N+j});\n \n vector> posEdges(GRID_SIZE);\n for (int e = 0; e < (int)edges.size(); e++) {\n posEdges[edges[e].first].push_back(e);\n posEdges[edges[e].second].push_back(e);\n }\n \n mt19937 rng(42);\n uniform_real_distribution unif(0.0, 1.0);\n \n for (int turn = 0; turn < t; turn++) {\n vector values(SEED_COUNT);\n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n values[i] += X[i][j];\n \n vector indices(SEED_COUNT);\n iota(indices.begin(), indices.end(), 0);\n sort(indices.begin(), indices.end(), [&](int a, int b) { return values[a] > values[b]; });\n vector selected(indices.begin(), indices.begin() + GRID_SIZE);\n \n vector> pot(GRID_SIZE, vector(GRID_SIZE, 0));\n for (int i = 0; i < GRID_SIZE; i++)\n for (int j = i+1; j < GRID_SIZE; j++) {\n int a = selected[i], b = selected[j];\n for (int l = 0; l < M; l++)\n pot[i][j] += max(X[a][l], X[b][l]);\n pot[j][i] = pot[i][j];\n }\n \n vector placement(GRID_SIZE);\n iota(placement.begin(), placement.end(), 0);\n \n int currentScore = 0;\n for (auto& [u,v] : edges)\n currentScore += pot[placement[u]][placement[v]];\n \n int bestScore = currentScore;\n vector bestPlacement = placement;\n \n auto startTime = chrono::high_resolution_clock::now();\n const double startTemp = 500.0, endTemp = 0.1;\n \n for (int iter = 0; iter < 10000000; iter++) {\n auto now = chrono::high_resolution_clock::now();\n auto elapsed = chrono::duration_cast(now - startTime).count();\n if (elapsed > 180000) break;\n \n double progress = (double)elapsed / 180000.0;\n double temp = startTemp * pow(endTemp / startTemp, progress);\n \n int i = rng() % GRID_SIZE, j = rng() % GRID_SIZE;\n if (i == j) continue;\n \n int delta = 0;\n for (int e : posEdges[i]) { auto& [u,v] = edges[e]; delta -= pot[placement[u]][placement[v]]; }\n for (int e : posEdges[j]) { auto& [u,v] = edges[e]; delta -= pot[placement[u]][placement[v]]; }\n \n swap(placement[i], placement[j]);\n \n for (int e : posEdges[i]) { auto& [u,v] = edges[e]; delta += pot[placement[u]][placement[v]]; }\n for (int e : posEdges[j]) { auto& [u,v] = edges[e]; delta += pot[placement[u]][placement[v]]; }\n \n if (delta >= 0 || unif(rng) < exp((double)delta / temp)) {\n currentScore += delta;\n if (currentScore > bestScore) { bestScore = currentScore; bestPlacement = placement; }\n } else {\n swap(placement[i], placement[j]);\n }\n }\n \n placement = bestPlacement;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cout << selected[placement[i*N+j]];\n if (j < N-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n cout.flush();\n \n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n cin >> X[i][j];\n }\n \n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n \n vector s(N), t(N);\n for (int i = 0; i < N; i++) cin >> s[i];\n for (int i = 0; i < N; i++) cin >> t[i];\n \n int Vp = V;\n vector len(Vp, 1);\n \n cout << Vp << \"\\n\";\n for (int i = 1; i < Vp; i++) cout << 0 << \" \" << len[i] << \"\\n\";\n \n int rx = N/2, ry = N/2;\n cout << rx << \" \" << ry << \"\\n\";\n \n vector> grid(N, vector(N)), target(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n grid[i][j] = s[i][j] - '0';\n target[i][j] = t[i][j] - '0';\n }\n \n vector dir(Vp, 0);\n vector holding(Vp, false);\n vector ops;\n \n auto addOp = [&](string op) { ops.push_back(op); };\n \n while (true) {\n int sx=-1, sy=-1, best=INT_MAX;\n for (int i=0; itRx) { op[0]='U'; rx--; }\n else if (rytRx) { op[0]='U'; rx--; }\n else if (ry\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N;\n cin >> N;\n \n vector x(2*N), y(2*N);\n for (int i = 0; i < 2*N; i++) {\n cin >> x[i] >> y[i];\n }\n \n int gridSize = 100;\n int cellSize = 1001;\n \n vector> grid(gridSize, vector(gridSize, 0));\n for (int i = 0; i < 2*N; i++) {\n int gx = min(x[i] / cellSize, gridSize - 1);\n int gy = min(y[i] / cellSize, gridSize - 1);\n grid[gx][gy] += (i < N) ? 1 : -1;\n }\n \n vector> prefix(gridSize + 1, vector(gridSize + 1, 0));\n for (int i = 0; i < gridSize; i++) {\n for (int j = 0; j < gridSize; j++) {\n prefix[i + 1][j + 1] = grid[i][j] + prefix[i][j + 1] + prefix[i + 1][j] - prefix[i][j];\n }\n }\n \n auto gridRectScore = [&](int x1, int y1, int x2, int y2) -> int {\n return prefix[x2 + 1][y2 + 1] - prefix[x1][y2 + 1] - prefix[x2 + 1][y1] + prefix[x1][y1];\n };\n \n int bestGridScore = 0;\n int bestGX1 = 0, bestGY1 = 0, bestGX2 = 0, bestGY2 = 0;\n \n for (int gx1 = 0; gx1 < gridSize; gx1++) {\n for (int gx2 = gx1; gx2 < gridSize; gx2++) {\n int bestY = 0, curY = 0;\n int bestGY1c = 0, bestGY2c = -1;\n int curGY1 = 0;\n \n for (int gy2 = 0; gy2 < gridSize; gy2++) {\n curY += gridRectScore(gx1, gy2, gx2, gy2);\n \n if (curY > bestY) {\n bestY = curY;\n bestGY1c = curGY1;\n bestGY2c = gy2;\n }\n if (curY < 0) {\n curY = 0;\n curGY1 = gy2 + 1;\n }\n }\n \n if (bestY > bestGridScore) {\n bestGridScore = bestY;\n bestGX1 = gx1;\n bestGX2 = gx2;\n bestGY1 = bestGY1c;\n bestGY2 = bestGY2c;\n }\n }\n }\n \n int bestX1 = bestGX1 * cellSize;\n int bestY1 = bestGY1 * cellSize;\n int bestX2 = min((bestGX2 + 1) * cellSize - 1, 100000);\n int bestY2 = min((bestGY2 + 1) * cellSize - 1, 100000);\n \n cout << 4 << endl;\n if (bestGridScore > 0) {\n cout << bestX1 << \" \" << bestY1 << endl;\n cout << bestX2 << \" \" << bestY1 << endl;\n cout << bestX2 << \" \" << bestY2 << endl;\n cout << bestX1 << \" \" << bestY2 << endl;\n } else {\n cout << 50000 << \" \" << 50000 << endl;\n cout << 50001 << \" \" << 50000 << endl;\n cout << 50001 << \" \" << 50001 << endl;\n cout << 50000 << \" \" << 50001 << endl;\n }\n \n return 0;\n}","ahc040":"#include \nusing namespace std;\n\nint N, T, sigma;\nvector w_obs, h_obs;\nvector w_est, h_est;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T >> sigma;\n w_obs.resize(N); h_obs.resize(N);\n w_est.resize(N); h_est.resize(N);\n for (int i = 0; i < N; i++) {\n cin >> w_obs[i] >> h_obs[i];\n w_est[i] = w_obs[i];\n h_est[i] = h_obs[i];\n }\n \n mt19937 rng(42);\n \n for (int t = 0; t < T; t++) {\n vector px, py, pw, ph;\n vector> output;\n \n auto getW = [&]() { long long W=0; for(int i=0;i<(int)px.size();i++) W=max(W,(long long)px[i]+pw[i]); return W; };\n auto getH = [&]() { long long H=0; for(int i=0;i<(int)py.size();i++) H=max(H,(long long)py[i]+ph[i]); return H; };\n \n auto addRect = [&](int rw, int rh, char d, int b) {\n int rx, ry;\n if (d == 'U') {\n rx = (b == -1) ? 0 : px[b] + pw[b];\n ry = 0;\n for (int i = 0; i < (int)px.size(); i++)\n if (px[i] < rx + rw && px[i] + pw[i] > rx) ry = max(ry, py[i] + ph[i]);\n } else {\n ry = (b == -1) ? 0 : py[b] + ph[b];\n rx = 0;\n for (int i = 0; i < (int)py.size(); i++)\n if (py[i] < ry + rh && py[i] + ph[i] > ry) rx = max(rx, px[i] + pw[i]);\n }\n px.push_back(rx); py.push_back(ry); pw.push_back(rw); ph.push_back(rh);\n };\n \n for (int i = 0; i < N; i++) {\n long long best_score = LLONG_MAX;\n int best_r = -1; char best_d = 'U'; int best_b = -1;\n \n long long cur_WH = getW() + getH();\n long long skip_score = cur_WH + (long long)round(w_est[i] + h_est[i]);\n best_score = skip_score;\n \n for (int r = 0; r < 2; r++) {\n int rw = r ? (int)round(h_est[i]) : (int)round(w_est[i]);\n int rh = r ? (int)round(w_est[i]) : (int)round(h_est[i]);\n for (char d : {'U', 'L'}) {\n int max_b = min((int)px.size() - 1, 30);\n for (int b = -1; b <= max_b; b++) {\n auto spx=px, spy=py, spw=pw, sph=ph;\n addRect(rw, rh, d, b);\n long long place_score = getW() + getH();\n if (place_score < best_score) {\n best_score = place_score; best_r = r; best_d = d; best_b = b;\n }\n px=spx; py=spy; pw=spw; ph=sph;\n }\n }\n }\n \n if (best_r >= 0) {\n int rw = best_r ? (int)round(h_est[i]) : (int)round(w_est[i]);\n int rh = best_r ? (int)round(w_est[i]) : (int)round(h_est[i]);\n addRect(rw, rh, best_d, best_b);\n output.push_back({i, best_r, best_d, best_b});\n }\n }\n \n cout << output.size() << \"\\n\";\n for (auto& [p, r, d, b] : output) cout << p << \" \" << r << \" \" << d << \" \" << b << \"\\n\";\n cout.flush();\n \n int W_prime, H_prime;\n cin >> W_prime >> H_prime;\n \n double W_pred = getW(), H_pred = getH();\n double W_err = W_prime - W_pred, H_err = H_prime - H_pred;\n int num_placed = px.size();\n if (num_placed > 0) {\n double lr = 0.2;\n for (auto& [p, r, d, b] : output) {\n int rw = r ? (int)round(h_est[p]) : (int)round(w_est[p]);\n int rh = r ? (int)round(w_est[p]) : (int)round(h_est[p]);\n double w_contrib = rw / (W_pred + 1);\n double h_contrib = rh / (H_pred + 1);\n w_est[p] += W_err * w_contrib * lr;\n h_est[p] += H_err * h_contrib * lr;\n w_est[p] = max(w_est[p], 1.0);\n h_est[p] = max(h_est[p], 1.0);\n }\n }\n }\n return 0;\n}","ahc041":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, H;\n cin >> N >> M >> H;\n \n vector A(N);\n for (int i = 0; i < N; i++) cin >> A[i];\n \n vector> adj(N);\n for (int i = 0; i < M; i++) {\n int u, v;\n cin >> u >> v;\n adj[u].push_back(v);\n adj[v].push_back(u);\n }\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n \n vector parent(N, -1);\n vector height(N, 0);\n \n function update_h = [&](int v, int diff) {\n height[v] += diff;\n for (int u : adj[v]) {\n if (parent[u] == v) update_h(u, diff);\n }\n };\n \n auto creates_cycle = [&](int v, int u) -> bool {\n int curr = u;\n while (curr != -1) {\n if (curr == v) return true;\n curr = parent[curr];\n }\n return false;\n };\n \n function subtree_sum = [&](int v) -> long long {\n long long sum = A[v];\n for (int u : adj[v]) {\n if (parent[u] == v) sum += subtree_sum(u);\n }\n return sum;\n };\n \n function max_subtree_h = [&](int v) -> int {\n int max_h = height[v];\n for (int u : adj[v]) {\n if (parent[u] == v) {\n max_h = max(max_h, max_subtree_h(u));\n }\n }\n return max_h;\n };\n \n while (true) {\n long long best_gain = 0;\n int best_v = -1, best_u = -1;\n \n for (int v = 0; v < N; v++) {\n for (int u : adj[v]) {\n if (u == parent[v]) continue;\n \n int new_h = height[u] + 1;\n int diff = new_h - height[v];\n if (diff <= 0) continue;\n \n int max_h = max_subtree_h(v);\n if (max_h + diff > H) continue;\n \n if (creates_cycle(v, u)) continue;\n \n long long sum = subtree_sum(v);\n long long gain = (long long)diff * sum;\n \n if (gain > best_gain) {\n best_gain = gain;\n best_v = v;\n best_u = u;\n }\n }\n }\n \n if (best_v == -1) break;\n \n int new_h = height[best_u] + 1;\n int diff = new_h - height[best_v];\n parent[best_v] = best_u;\n update_h(best_v, diff);\n }\n \n for (int i = 0; i < N; i++) {\n cout << parent[i] << (i == N-1 ? \"\\n\" : \" \");\n }\n \n return 0;\n}","ahc042":"#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N; cin >> N;\n vector board(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n \n struct Oni { int i, j, id; bool up_safe, down_safe, left_safe, right_safe; };\n vector onis;\n int id_counter = 0;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (board[i][j] == 'x') {\n Oni o{i, j, id_counter++, true, true, true, true};\n for (int k = 0; k < i; k++) if (board[k][j] == 'o') { o.up_safe = false; break; }\n for (int k = i+1; k < N; k++) if (board[k][j] == 'o') { o.down_safe = false; break; }\n for (int k = 0; k < j; k++) if (board[i][k] == 'o') { o.left_safe = false; break; }\n for (int k = j+1; k < N; k++) if (board[i][k] == 'o') { o.right_safe = false; break; }\n onis.push_back(o);\n }\n }\n }\n \n vector oni_dir(onis.size());\n for (auto& o : onis) {\n char best_dir = 0; int best_cost = 1e9;\n if (o.up_safe) { int c = o.i+1; if (c < best_cost) { best_cost = c; best_dir = 'U'; } }\n if (o.down_safe) { int c = N-o.i; if (c < best_cost) { best_cost = c; best_dir = 'D'; } }\n if (o.left_safe) { int c = o.j+1; if (c < best_cost) { best_cost = c; best_dir = 'L'; } }\n if (o.right_safe) { int c = N-o.j; if (c < best_cost) { best_cost = c; best_dir = 'R'; } }\n oni_dir[o.id] = best_dir;\n }\n \n map, vector> batches;\n for (auto& o : onis) {\n char dir = oni_dir[o.id];\n int idx = (dir == 'L' || dir == 'R') ? o.i : o.j;\n batches[{dir, idx}].push_back(o.id);\n }\n \n set removed;\n vector> moves;\n \n for (char dir : {'U','D','L','R'}) {\n for (int idx = 0; idx < N; idx++) {\n auto key = make_pair(dir, idx);\n if (batches.find(key) == batches.end()) continue;\n \n int max_dist = 0;\n for (int oid : batches[key]) {\n if (removed.count(oid)) continue;\n auto& o = onis[oid];\n int dist = (dir=='U') ? o.i+1 : (dir=='D') ? N-o.i : (dir=='L') ? o.j+1 : N-o.j;\n max_dist = max(max_dist, dist);\n }\n if (max_dist == 0) continue;\n \n for (int k = 0; k < max_dist; k++) moves.push_back({dir, idx});\n char opp = (dir=='U')?'D':(dir=='D')?'U':(dir=='L')?'R':'L';\n for (int k = 0; k < max_dist; k++) moves.push_back({opp, idx});\n \n for (auto& o : onis) {\n if (removed.count(o.id)) continue;\n bool in_path = false;\n if (dir=='U' && o.j==idx && o.i < max_dist) in_path = true;\n else if (dir=='D' && o.j==idx && o.i >= N-max_dist) in_path = true;\n else if (dir=='L' && o.i==idx && o.j < max_dist) in_path = true;\n else if (dir=='R' && o.i==idx && o.j >= N-max_dist) in_path = true;\n if (in_path) removed.insert(o.id);\n }\n }\n }\n \n for (auto& [d, p] : moves) cout << d << \" \" << p << \"\\n\";\n return 0;\n}","ahc044":"#include \n#include \n#include \n\nusing namespace std;\n\nint N, L;\nint T[100];\nint a[100], b[100];\n\nunsigned int rng_state = 42;\nunsigned int rng() {\n rng_state ^= rng_state << 13;\n rng_state ^= rng_state >> 17;\n rng_state ^= rng_state << 5;\n return rng_state;\n}\n\nvoid simulate(int t[]) {\n int count[100] = {0};\n for (int i = 0; i < N; i++) t[i] = 0;\n int current = 0;\n for (int week = 0; week < L; week++) {\n t[current]++;\n count[current]++;\n current = (count[current] & 1) ? a[current] : b[current];\n }\n}\n\nint compute_error(int t[]) {\n int error = 0;\n for (int i = 0; i < N; i++) {\n error += abs(t[i] - T[i]);\n }\n return error;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> L;\n for (int i = 0; i < N; i++) {\n cin >> T[i];\n }\n \n // Initial solution: cycle\n for (int i = 0; i < N; i++) {\n a[i] = (i + 1) % N;\n b[i] = (i + 1) % N;\n }\n \n int t[100];\n simulate(t);\n int error = compute_error(t);\n int best_error = error;\n int best_a[100], best_b[100];\n for (int i = 0; i < N; i++) {\n best_a[i] = a[i];\n best_b[i] = b[i];\n }\n \n auto start = chrono::high_resolution_clock::now();\n \n double temperature = 1000.0;\n double cooling_rate = 0.99;\n \n while (true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 1.8) break;\n \n int i = rng() % N;\n int old_ai = a[i], old_bi = b[i];\n int new_val = rng() % N;\n if (rng() & 1) {\n a[i] = new_val;\n } else {\n b[i] = new_val;\n }\n \n simulate(t);\n int new_error = compute_error(t);\n \n double delta = new_error - error;\n if (delta <= 0 || (double)(rng() % 10000) / 10000.0 < exp(-delta / temperature)) {\n error = new_error;\n if (error < best_error) {\n best_error = error;\n for (int j = 0; j < N; j++) {\n best_a[j] = a[j];\n best_b[j] = b[j];\n }\n }\n } else {\n a[i] = old_ai;\n b[i] = old_bi;\n }\n \n temperature *= cooling_rate;\n }\n \n for (int i = 0; i < N; i++) {\n cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n }\n \n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nint N, M, Q, L, W;\ndouble cx[800], cy[800], ddist[800][800];\nint qcnt = 0;\n\nvector> query(vector v) {\n if (qcnt >= Q || (int)v.size() < 2) return {};\n qcnt++;\n cout << \"? \" << v.size();\n for (int x : v) cout << \" \" << x;\n cout << endl;\n vector> res(v.size() - 1);\n for (auto& [a, b] : res) cin >> a >> b;\n return res;\n}\n\nint par[800], rnk[800];\nvoid init_dsu() { iota(par, par + N, 0); fill(rnk, rnk + N, 0); }\nint find(int x) { return par[x] == x ? x : par[x] = find(par[x]); }\nbool unite(int x, int y) {\n x = find(x); y = find(y);\n if (x == y) return false;\n if (rnk[x] < rnk[y]) swap(x, y);\n par[y] = x;\n if (rnk[x] == rnk[y]) rnk[x]++;\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> Q >> L >> W;\n vector G(M);\n for (int& g : G) cin >> g;\n \n for (int i = 0; i < N; i++) {\n int a, b, c, d;\n cin >> a >> b >> c >> d;\n cx[i] = (a + b) / 2.0;\n cy[i] = (c + d) / 2.0;\n }\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n double dx = cx[i] - cx[j], dy = cy[i] - cy[j];\n ddist[i][j] = sqrt(dx*dx + dy*dy);\n }\n \n vector ord(N);\n iota(ord.begin(), ord.end(), 0);\n sort(ord.begin(), ord.end(), [](int a, int b) {\n return make_pair(cx[a] + cy[a], cx[a]) < make_pair(cx[b] + cy[b], cx[b]);\n });\n \n vector> grp(M);\n for (int i = 0, p = 0; i < M; i++)\n for (int j = 0; j < G[i]; j++)\n grp[i].push_back(ord[p++]);\n \n vector>> ans(M);\n \n for (int k = 0; k < M; k++) {\n if (G[k] <= 1) continue;\n \n init_dsu();\n if (G[k] <= L && qcnt < Q) {\n ans[k] = query(grp[k]);\n continue;\n }\n \n set conn;\n vector> mst;\n conn.insert(grp[k][0]);\n \n while (conn.size() < (size_t)G[k]) {\n vector> cands;\n for (int c : grp[k]) {\n if (conn.count(c)) continue;\n double md = 1e18;\n for (int t : conn) md = min(md, ddist[c][t]);\n cands.emplace_back(md, c);\n }\n sort(cands.begin(), cands.end());\n if (cands.empty()) break;\n \n vector qv;\n vector> tree_sorted;\n for (int t : conn) tree_sorted.emplace_back(ddist[t][cands[0].second], t);\n sort(tree_sorted.begin(), tree_sorted.end());\n int ntree = min((int)tree_sorted.size(), L / 2);\n for (int i = 0; i < ntree; i++) qv.push_back(tree_sorted[i].second);\n \n int ncand = min((int)cands.size(), L - (int)qv.size());\n for (int i = 0; i < ncand; i++) qv.push_back(cands[i].second);\n \n bool added = false;\n if (qv.size() >= 2 && qcnt < Q) {\n auto edges = query(qv);\n for (auto& [a, b] : edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n conn.insert(a); conn.insert(b);\n added = true;\n }\n }\n }\n \n if (!added) {\n int c = cands[0].second;\n double bd = 1e18; int bt = -1;\n for (int t : conn) if (ddist[c][t] < bd) { bd = ddist[c][t]; bt = t; }\n mst.emplace_back(c, bt);\n unite(c, bt);\n conn.insert(c);\n }\n }\n ans[k] = mst;\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int i = 0; i < G[k]; i++) cout << grp[k][i] << \" \\n\"[i==G[k]-1];\n for (auto& [a, b] : ans[k]) cout << a << \" \" << b << \"\\n\";\n }\n return 0;\n}","ahc046":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M;\n cin >> N >> M;\n \n vector> targets(M);\n for (int i = 0; i < M; i++) {\n cin >> targets[i].first >> targets[i].second;\n }\n \n set> blocks;\n int cur_r = targets[0].first, cur_c = targets[0].second;\n vector> all_actions;\n \n auto get_slide_dest = [&](int r, int c, char dir) -> pair {\n int dr = 0, dc = 0;\n if (dir == 'U') dr = -1;\n else if (dir == 'D') dr = 1;\n else if (dir == 'L') dc = -1;\n else dc = 1;\n \n int nr = r + dr, nc = c + dc;\n while (nr >= 0 && nr < N && nc >= 0 && nc < N && blocks.count({nr, nc}) == 0) {\n nr += dr;\n nc += dc;\n }\n nr -= dr;\n nc -= dc;\n return {nr, nc};\n };\n \n auto bfs = [&](int sr, int sc, int tr, int tc) -> vector> {\n if (sr == tr && sc == tc) return {};\n vector> visited(N, vector(N, false));\n vector, pair>>> parent(N, vector, pair>>(N, {{-1,-1}, {' ', ' '}}));\n \n queue> q;\n q.push({sr, sc});\n visited[sr][sc] = true;\n \n while (!q.empty()) {\n auto [r, c] = q.front(); q.pop();\n if (r == tr && c == tc) {\n vector> path;\n int cr = r, cc = c;\n while (parent[cr][cc].first.first != -1) {\n path.push_back(parent[cr][cc].second);\n auto [pr, pc] = parent[cr][cc].first;\n cr = pr; cc = pc;\n }\n reverse(path.begin(), path.end());\n return path;\n }\n \n for (char dir : {'U', 'D', 'L', 'R'}) {\n int dr = 0, dc = 0;\n if (dir == 'U') dr = -1;\n else if (dir == 'D') dr = 1;\n else if (dir == 'L') dc = -1;\n else dc = 1;\n \n int nr = r + dr, nc = c + dc;\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && blocks.count({nr, nc}) == 0 && !visited[nr][nc]) {\n visited[nr][nc] = true;\n parent[nr][nc] = {{r, c}, {'M', dir}};\n q.push({nr, nc});\n }\n }\n \n for (char dir : {'U', 'D', 'L', 'R'}) {\n auto [nr, nc] = get_slide_dest(r, c, dir);\n if ((nr != r || nc != c) && !visited[nr][nc]) {\n visited[nr][nc] = true;\n parent[nr][nc] = {{r, c}, {'S', dir}};\n q.push({nr, nc});\n }\n }\n }\n return {};\n };\n \n for (int t = 1; t < M; t++) {\n int target_r = targets[t].first, target_c = targets[t].second;\n auto path = bfs(cur_r, cur_c, target_r, target_c);\n \n for (auto [action, dir] : path) {\n all_actions.push_back({action, dir});\n if (action == 'M') {\n int dr = 0, dc = 0;\n if (dir == 'U') dr = -1;\n else if (dir == 'D') dr = 1;\n else if (dir == 'L') dc = -1;\n else dc = 1;\n cur_r += dr; cur_c += dc;\n } else if (action == 'S') {\n auto [nr, nc] = get_slide_dest(cur_r, cur_c, dir);\n cur_r = nr; cur_c = nc;\n }\n }\n \n if (cur_r + 1 < N && blocks.count({cur_r + 1, cur_c}) == 0) {\n blocks.insert({cur_r + 1, cur_c});\n all_actions.push_back({'A', 'D'});\n }\n if (cur_c + 1 < N && blocks.count({cur_r, cur_c + 1}) == 0) {\n blocks.insert({cur_r, cur_c + 1});\n all_actions.push_back({'A', 'R'});\n }\n }\n \n for (auto& [a, d] : all_actions) {\n cout << a << \" \" << d << \"\\n\";\n }\n return 0;\n}"},"2":{"ahc001":"#include \nusing namespace std;\n\nint n;\nvector x, y, r;\nvector a, b, c, d;\n\ndouble satisfaction(long long area, long long desired) {\n if (area <= 0 || desired <= 0) return 0;\n double ratio = (double)min(area, desired) / max(area, desired);\n return 1.0 - (1.0 - ratio) * (1.0 - ratio);\n}\n\ndouble estimate_satisfaction(long long area, long long total_r) {\n if (area == 0 || total_r == 0) return 0;\n double ratio = (double)min(area, total_r) / max(area, total_r);\n return 1.0 - (1.0 - ratio) * (1.0 - ratio);\n}\n\ndouble compute_score() {\n double score = 0;\n for (int i = 0; i < n; i++) {\n long long area = (long long)(c[i] - a[i]) * (d[i] - b[i]);\n score += satisfaction(area, r[i]);\n }\n return score;\n}\n\nvoid solve(vector indices, int left, int bottom, int right, int top, mt19937& rng, int strategy, int depth = 0) {\n if (indices.empty()) return;\n if (indices.size() == 1) {\n int i = indices[0];\n a[i] = left; b[i] = bottom; c[i] = right; d[i] = top;\n return;\n }\n \n long long total_r = 0;\n for (int i : indices) total_r += r[i];\n \n int width = right - left;\n int height = top - bottom;\n long long area = (long long)width * height;\n \n bool try_vertical = (strategy != 2), try_horizontal = (strategy != 1);\n if (strategy == 1) { try_vertical = (depth % 2 == 0); try_horizontal = !try_vertical; }\n else if (strategy == 2) { try_horizontal = (depth % 2 == 0); try_vertical = !try_horizontal; }\n \n struct Split { bool vertical; int k; int split_pos; double score; };\n vector splits;\n \n auto try_splits = [&](bool vertical) {\n vector& coord = vertical ? x : y;\n int lo = vertical ? left : bottom, hi = vertical ? right : top;\n sort(indices.begin(), indices.end(), [&](int i, int j) { return coord[i] < coord[j]; });\n long long sum = 0;\n for (int k = 1; k < (int)indices.size(); k++) {\n sum += r[indices[k-1]];\n if (coord[indices[k-1]] >= coord[indices[k]]) continue;\n int min_s = max(lo + 1, coord[indices[k-1]] + 1);\n int max_s = min(hi - 1, coord[indices[k]]);\n if (min_s > max_s) continue;\n long long ideal_s = lo + (long long)(hi - lo) * sum / total_r;\n int s = max(min_s, min(max_s, (int)ideal_s));\n long long area1 = vertical ? (long long)(s - left) * height : (long long)width * (s - bottom);\n long long area2 = area - area1;\n double score = estimate_satisfaction(area1, sum) + estimate_satisfaction(area2, total_r - sum);\n splits.push_back({vertical, k, s, score});\n }\n };\n \n if (try_vertical) try_splits(true);\n if (try_horizontal) try_splits(false);\n if (splits.empty()) { if (!try_vertical) try_splits(true); if (splits.empty() && !try_horizontal) try_splits(false); }\n \n if (splits.empty()) {\n int i = indices[0];\n a[i] = left; b[i] = bottom; c[i] = right; d[i] = top;\n return;\n }\n \n sort(splits.begin(), splits.end(), [](const Split& a, const Split& b) { return a.score > b.score; });\n int num_top = min((int)splits.size(), 5);\n uniform_int_distribution dist(0, num_top - 1);\n const Split& chosen = splits[dist(rng)];\n \n vector& coord = chosen.vertical ? x : y;\n sort(indices.begin(), indices.end(), [&](int i, int j) { return coord[i] < coord[j]; });\n vector sub1(indices.begin(), indices.begin() + chosen.k);\n vector sub2(indices.begin() + chosen.k, indices.end());\n \n if (chosen.vertical) {\n solve(sub1, left, bottom, chosen.split_pos, top, rng, strategy, depth + 1);\n solve(sub2, chosen.split_pos, bottom, right, top, rng, strategy, depth + 1);\n } else {\n solve(sub1, left, bottom, right, chosen.split_pos, rng, strategy, depth + 1);\n solve(sub2, left, chosen.split_pos, right, top, rng, strategy, depth + 1);\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n;\n x.resize(n); y.resize(n); r.resize(n);\n a.resize(n); b.resize(n); c.resize(n); d.resize(n);\n \n for (int i = 0; i < n; i++) cin >> x[i] >> y[i] >> r[i];\n \n auto start_time = chrono::steady_clock::now();\n vector indices(n);\n iota(indices.begin(), indices.end(), 0);\n \n vector best_a(n), best_b(n), best_c(n), best_d(n);\n double best_score = -1;\n \n for (unsigned seed = 0; ; seed++) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - start_time).count() > 4500) break;\n \n mt19937 rng(seed);\n int strategy = seed % 3;\n solve(indices, 0, 0, 10000, 10000, rng, strategy);\n \n double score = compute_score();\n if (score > best_score) {\n best_score = score;\n best_a = a; best_b = b; best_c = c; best_d = d;\n }\n }\n \n a = best_a; b = best_b; c = best_c; d = best_d;\n for (int i = 0; i < n; i++) cout << a[i] << \" \" << b[i] << \" \" << c[i] << \" \" << d[i] << \"\\n\";\n \n return 0;\n}","ahc002":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 50;\nint si, sj;\nint t[N][N], p[N][N];\nint di[] = {-1, 1, 0, 0};\nint dj[] = {0, 0, -1, 1};\nchar dir[] = {'U', 'D', 'L', 'R'};\nmt19937 rng(42);\n\nint tile_value[2500], max_tile_id = 0;\nstring best_path;\nlong long best_score;\n\nstring find_path(double temperature) {\n bool square_visited[N][N] = {};\n bool tile_visited[2500] = {};\n string path;\n int ci = si, cj = sj;\n square_visited[ci][cj] = true;\n tile_visited[t[ci][cj]] = true;\n long long score = p[ci][cj];\n \n while (true) {\n vector> candidates;\n for (int d = 0; d < 4; d++) {\n int ni = ci + di[d], nj = cj + dj[d];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) continue;\n if (square_visited[ni][nj]) continue;\n bool same_tile = (t[ni][nj] == t[ci][cj]);\n if (same_tile || !tile_visited[t[ni][nj]]) {\n double w = same_tile ? p[ni][nj] : tile_value[t[ni][nj]];\n candidates.push_back({w, d});\n }\n }\n if (candidates.empty()) break;\n \n double max_w = -1e18;\n for (auto& [w, d] : candidates) max_w = max(max_w, w);\n double total = 0;\n for (auto& [w, d] : candidates) total += exp((w - max_w) / max(temperature, 0.01));\n \n double r = uniform_real_distribution(0, total)(rng);\n double cum = 0;\n int chosen = candidates[0].second;\n for (auto& [w, d] : candidates) {\n cum += exp((w - max_w) / max(temperature, 0.01));\n if (cum >= r) { chosen = d; break; }\n }\n \n int ni = ci + di[chosen], nj = cj + dj[chosen];\n square_visited[ni][nj] = true;\n tile_visited[t[ni][nj]] = true;\n score += p[ni][nj];\n path += dir[chosen];\n ci = ni; cj = nj;\n }\n \n if (score > best_score) { best_score = score; best_path = path; }\n return path;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) { cin >> t[i][j]; max_tile_id = max(max_tile_id, t[i][j]); }\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> p[i][j];\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) tile_value[t[i][j]] += p[i][j];\n \n best_score = 0;\n auto start = chrono::high_resolution_clock::now();\n int iter = 0;\n while (true) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now - start).count() > 1800) break;\n double temperature = 10.0 * (1.0 - min(iter / 100000.0, 1.0)) + 0.1;\n find_path(temperature);\n iter++;\n }\n \n cout << best_path << endl;\n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble row_h[N], col_v[N], row_h_var[N], col_v_var[N];\ndouble h_dev[N][N-1], v_dev[N-1][N], h_dev_var[N][N-1], v_dev_var[N-1][N];\nint query_num = 0;\n\ndouble get_h_est(int i, int j) { return row_h[i] + h_dev[i][j]; }\ndouble get_v_est(int i, int j) { return col_v[j] + v_dev[i][j]; }\n\ndouble get_h_weight(int i, int j) {\n double est = get_h_est(i, j), sigma = sqrt(row_h_var[i] + h_dev_var[i][j]);\n double td = max(0.0, 1.0 - query_num / 250.0);\n return max(100.0, est - 0.5 * sigma * td);\n}\ndouble get_v_weight(int i, int j) {\n double est = get_v_est(i, j), sigma = sqrt(col_v_var[j] + v_dev_var[i][j]);\n double td = max(0.0, 1.0 - query_num / 250.0);\n return max(100.0, est - 0.5 * sigma * td);\n}\n\nstring dijkstra(int si, int sj, int ti, int tj) {\n double dist[N][N]; pair prev[N][N]; bool vis[N][N] = {};\n for(int i=0;i,vector>,greater<>> pq;\n pq.push({0,si,sj});\n while(!pq.empty()){\n auto[d,i,j]=pq.top(); pq.pop();\n if(vis[i][j]) continue; vis[i][j]=true;\n if(i==ti&&j==tj) break;\n if(i>0&&!vis[i-1][j]){double w=get_v_weight(i-1,j);if(d+w0&&!vis[i][j-1]){double w=get_h_weight(i,j-1);if(d+w edges;\n map hr, vc;\n int ci=si,cj=sj;\n for(char c:path){\n if(c=='U'){edges.push_back({'v',ci-1,cj});vc[cj]++;ci--;}\n else if(c=='D'){edges.push_back({'v',ci,cj});vc[cj]++;ci++;}\n else if(c=='L'){edges.push_back({'h',ci,cj-1});hr[ci]++;cj--;}\n else{edges.push_back({'h',ci,cj});hr[ci]++;cj++;}\n }\n double pred=0;\n for(auto&e:edges) pred+=(e.t=='h')?get_h_est(e.i,e.j):get_v_est(e.i,e.j);\n double residual=observed-pred, obs_var=pred*pred/300.0;\n double S=obs_var;\n for(auto&[i,n]:hr) S+=n*n*row_h_var[i];\n for(auto&[j,n]:vc) S+=n*n*col_v_var[j];\n for(auto&e:edges) S+=(e.t=='h')?h_dev_var[e.i][e.j]:v_dev_var[e.i][e.j];\n for(auto&[i,n]:hr){double K=row_h_var[i]*n/S;row_h[i]+=K*residual;row_h_var[i]*=(1-K*n);row_h[i]=max(500.0,min(15000.0,row_h[i]));row_h_var[i]=max(100.0,row_h_var[i]);}\n for(auto&[j,n]:vc){double K=col_v_var[j]*n/S;col_v[j]+=K*residual;col_v_var[j]*=(1-K*n);col_v[j]=max(500.0,min(15000.0,col_v[j]));col_v_var[j]=max(100.0,col_v_var[j]);}\n for(auto&e:edges){\n double&dev=(e.t=='h')?h_dev[e.i][e.j]:v_dev[e.i][e.j];\n double&dv=(e.t=='h')?h_dev_var[e.i][e.j]:v_dev_var[e.i][e.j];\n double K=dv/S; dev+=K*residual; dv*=(1-K);\n dev=max(-5000.0,min(5000.0,dev)); dv=max(100.0,dv);\n }\n}\n\nint main(){\n ios::sync_with_stdio(false); cin.tie(nullptr);\n for(int i=0;i>si>>sj>>ti>>tj;\n string path=dijkstra(si,sj,ti,tj); cout<>obs; update(si,sj,path,obs);\n }\n return 0;\n}","ahc004":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n int N, M;\n cin >> N >> M;\n vector s(M);\n for (int i = 0; i < M; i++) cin >> s[i];\n \n const int NUM_CHARS = 8;\n mt19937 rng(42);\n \n // Initialize with uniform voting\n vector> votes(N * N, vector(NUM_CHARS, 0));\n for (int m = 0; m < M; m++) {\n int k = s[m].length();\n double weight = 1.0 / (2.0 * N * N);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n for (int p = 0; p < k; p++) {\n votes[i * N + (j + p) % N][s[m][p] - 'A'] += weight;\n votes[((i + p) % N) * N + j][s[m][p] - 'A'] += weight;\n }\n }\n }\n }\n \n vector mat(N, string(N, 'A'));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double maxVote = 0;\n char bestChar = 'A';\n for (int c = 0; c < NUM_CHARS; c++) {\n if (votes[i * N + j][c] > maxVote) {\n maxVote = votes[i * N + j][c];\n bestChar = 'A' + c;\n }\n }\n mat[i][j] = bestChar;\n }\n }\n \n // Iterative refinement with weighted voting\n for (int iter = 0; iter < 100; iter++) {\n vector> newVotes(N * N, vector(NUM_CHARS, 0));\n \n for (int m = 0; m < M; m++) {\n int k = s[m].length();\n \n double totalScore = 0;\n vector scores(2 * N * N);\n int idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double scoreH = 0, scoreV = 0;\n for (int p = 0; p < k; p++) {\n if (mat[i][(j + p) % N] == s[m][p]) scoreH += 1;\n if (mat[(i + p) % N][j] == s[m][p]) scoreV += 1;\n }\n scores[idx++] = scoreH;\n scores[idx++] = scoreV;\n totalScore += scoreH + scoreV;\n }\n }\n \n if (totalScore < 0.01) continue;\n \n idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double wH = scores[idx++] / totalScore;\n double wV = scores[idx++] / totalScore;\n \n for (int p = 0; p < k; p++) {\n newVotes[i * N + (j + p) % N][s[m][p] - 'A'] += wH;\n newVotes[((i + p) % N) * N + j][s[m][p] - 'A'] += wV;\n }\n }\n }\n }\n \n bool changed = false;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double maxVote = 0;\n char bestChar = mat[i][j];\n for (int c = 0; c < NUM_CHARS; c++) {\n if (newVotes[i * N + j][c] > maxVote) {\n maxVote = newVotes[i * N + j][c];\n bestChar = 'A' + c;\n }\n }\n if (mat[i][j] != bestChar) {\n mat[i][j] = bestChar;\n changed = true;\n }\n }\n }\n \n if (!changed) break;\n }\n \n for (int i = 0; i < N; i++) cout << mat[i] << '\\n';\n return 0;\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\nvector>>> vis_from;\nint total_roads;\n\nbool is_road(int i, int j) { return i>=0&&i=0&&j>>(N));\n for(int i=0;i=0&&is_road(i,jj);jj--) vis_from[i][j].push_back({i,jj});\n for(int jj=j+1;jj=0&&is_road(ii,j);ii--) vis_from[i][j].push_back({ii,j});\n for(int ii=i+1;ii>,vector>> dijkstra(int si, int sj) {\n vector> dist(N,vector(N,INT_MAX)), prev(N,vector(N,-1));\n priority_queue>,vector>>,greater<>> pq;\n dist[si][sj]=0; pq.push({0,{si,sj}});\n while(!pq.empty()) {\n auto [d,p]=pq.top(); pq.pop();\n auto [i,j]=p;\n if(d>dist[i][j]) continue;\n for(int k=0;k<4;k++) {\n int ni=i+di[k],nj=j+dj[k];\n if(is_road(ni,nj)) {\n int nd=d+cell_cost(ni,nj);\n if(nd>& prev) {\n if(si==ti&&sj==tj) return \"\";\n string path; int ci=ti,cj=tj;\n while(ci!=si||cj!=sj) { int k=prev[ci][cj]; if(k==-1) return \"\"; path+=dc[k]; ci-=di[k]; cj-=dj[k]; }\n reverse(path.begin(),path.end()); return path;\n}\n\nstring build_greedy(double alpha, int& route_time) {\n vector> covered(N,vector(N,false));\n auto mark=[&](int i,int j)->int {\n int c=0; for(auto&[vi,vj]:vis_from[i][j]) if(!covered[vi][vj]){covered[vi][vj]=true;c++;} return c;\n };\n auto cnt_new=[&](int i,int j)->int {\n int c=0; for(auto&[vi,vj]:vis_from[i][j]) if(!covered[vi][vj]) c++; return c;\n };\n string route; int ci=si,cj=sj,cc=mark(ci,cj); route_time=0;\n while(cc> cands;\n for(int i=0;i());\n int K=min((int)cands.size(),12);\n int bi=-1,bj=-1; double bs=-1e18;\n for(int c=0;c> pc; int pi=ti,pj=tj;\n while(pi!=ci||pj!=cj) { pc.push_back({pi,pj}); int k=prev[pi][pj]; pi-=di[k]; pj-=dj[k]; }\n auto tmp=covered; int nv=0;\n for(auto&[pi2,pj2]:pc) for(auto&[vi,vj]:vis_from[pi2][pj2]) if(!tmp[vi][vj]){tmp[vi][vj]=true;nv++;}\n double ps=nv>0?pow((double)nv,alpha)/(double)dist[ti][tj]:0;\n if(ps>bs){bs=ps;bi=ti;bj=tj;}\n }\n if(bi==-1) break;\n string path=reconstruct(ci,cj,bi,bj,prev);\n for(char c:path) { int k=string(\"UDLR\").find(c); ci+=di[k];cj+=dj[k]; cc+=mark(ci,cj); route_time+=cell_cost(ci,cj); }\n route+=path;\n }\n auto [dist,prev]=dijkstra(ci,cj);\n string ret=reconstruct(ci,cj,si,sj,prev);\n for(char c:ret) { int k=string(\"UDLR\").find(c); ci+=di[k];cj+=dj[k]; cc+=mark(ci,cj); route_time+=cell_cost(ci,cj); }\n route+=ret;\n route_time = 0; ci=si;cj=sj; for(char c:route){int k=string(\"UDLR\").find(c);ci+=di[k];cj+=dj[k];route_time+=cell_cost(ci,cj);}\n return route;\n}\n\nstring build_tsp() {\n vector> vps;\n vector cc(N*N,false); int nc=0;\n while(ncbn){bn=nv;bi=i;bj=j;}\n }\n if(bn==0) break;\n vps.push_back({bi,bj});\n for(auto&[vi,vj]:vis_from[bi][bj]) if(!cc[vi*N+vj]){cc[vi*N+vj]=true;nc++;}\n }\n int M=vps.size(); if(M==0) return \"\";\n vector> vpd(M,vector(M,INT_MAX));\n vector s2v(M),v2s(M);\n { auto [d,p]=dijkstra(si,sj); for(int k=0;k best_order; int best_td=INT_MAX;\n for(int start=0;start ord; vector vis(M,false);\n int cur=start; ord.push_back(cur); vis[cur]=true;\n for(int s=1;s> covered(N,vector(N,false));\n auto mark=[&](int i,int j)->int {\n int c=0; for(auto&[vi,vj]:vis_from[i][j]) if(!covered[vi][vj]){covered[vi][vj]=true;c++;} return c;\n };\n string route; int ci=si,cj=sj,ccnt=mark(ci,cj);\n for(int idx:best_order) {\n auto [ti,tj]=vps[idx];\n auto [d,p]=dijkstra(ci,cj);\n string path=reconstruct(ci,cj,ti,tj,p);\n for(char c:path){int k=string(\"UDLR\").find(c);ci+=di[k];cj+=dj[k];ccnt+=mark(ci,cj);}\n route+=path;\n }\n { auto [d,p]=dijkstra(ci,cj); string ret=reconstruct(ci,cj,si,sj,p);\n for(char c:ret){int k=string(\"UDLR\").find(c);ci+=di[k];cj+=dj[k];ccnt+=mark(ci,cj);} route+=ret; }\n return route;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin>>N>>si>>sj; grid.resize(N); for(int i=0;i>grid[i];\n precompute_visibility();\n total_roads=0; for(int i=0;i(now-st).count()>2000) break;\n int rt; auto route=build_greedy(alpha,rt);\n if(rt0){best_time=rt;best_route=route;}\n }\n auto now=chrono::high_resolution_clock::now();\n if(chrono::duration_cast(now-st).count()<2500) {\n auto route=build_tsp();\n if(!route.empty()) {\n int ci=si,cj=sj,rt=0;\n for(char c:route){int k=string(\"UDLR\").find(c);ci+=di[k];cj+=dj[k];rt+=cell_cost(ci,cj);}\n if(rt\nusing namespace std;\n\nint N, M, K, R;\nvector> d, deps, rev_deps;\nvector> skill_est;\nvector> skill_lb;\nvector crit_path;\nvector>> member_obs;\n\nvector hungarian(const vector>& cost) {\n int n = cost.size(), m = cost[0].size();\n const double INF = 1e18;\n vector u(n+1,0), v(m+1,0);\n vector p(m+1,0), way(m+1,0);\n for (int i = 1; i <= n; i++) {\n p[0] = i; int j0 = 0;\n vector minv(m+1, INF);\n vector used(m+1, false);\n do {\n used[j0] = true;\n int i0 = p[j0], j1 = 0;\n double delta = INF;\n for (int j = 1; j <= m; j++) if (!used[j]) {\n double cur = cost[i0-1][j-1] - u[i0] - v[j];\n if (cur < minv[j]) { minv[j] = cur; way[j] = j0; }\n if (minv[j] < delta) { delta = minv[j]; j1 = j; }\n }\n for (int j = 0; j <= m; j++) {\n if (used[j]) { u[p[j]] += delta; v[j] -= delta; }\n else minv[j] -= delta;\n }\n j0 = j1;\n } while (p[j0] != 0);\n do { int j1 = way[j0]; p[j0] = p[j1]; j0 = j1; } while (j0);\n }\n vector asgn(n, -1);\n for (int j = 1; j <= m; j++) if (p[j] > 0 && p[j] <= n) asgn[p[j]-1] = j-1;\n return asgn;\n}\n\nvoid reestimate(int j) {\n auto& ob = member_obs[j];\n if (ob.empty()) return;\n for (int k = 0; k < K; k++) skill_est[j][k] = max(skill_est[j][k], (double)skill_lb[j][k]);\n for (int iter = 0; iter < 20; iter++) {\n for (auto& [task, t] : ob) {\n if (t == 1) continue;\n double est_w = (double)t;\n double td = 0;\n for (int k = 0; k < K; k++) td += max(0.0, (double)d[task][k] - skill_est[j][k]);\n if (td > 0) {\n double ratio = est_w / td;\n for (int k = 0; k < K; k++) {\n double def = max(0.0, (double)d[task][k] - skill_est[j][k]);\n if (def > 0) {\n double ns = d[task][k] - def * ratio;\n skill_est[j][k] = 0.85 * skill_est[j][k] + 0.15 * ns;\n skill_est[j][k] = max((double)skill_lb[j][k], skill_est[j][k]);\n }\n }\n } else {\n double totd = 0;\n for (int k = 0; k < K; k++) totd += d[task][k];\n if (totd > 0) for (int k = 0; k < K; k++) if (d[task][k] > 0)\n skill_est[j][k] = max((double)skill_lb[j][k], skill_est[j][k] - est_w * d[task][k] / totd * 0.15);\n }\n }\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> M >> K >> R;\n d.resize(N, vector(K)); deps.resize(N); rev_deps.resize(N);\n for (int i = 0; i < N; i++) for (int k = 0; k < K; k++) cin >> d[i][k];\n for (int r = 0; r < R; r++) { int u, v; cin >> u >> v; u--; v--; deps[v].push_back(u); rev_deps[u].push_back(v); }\n crit_path.resize(N, 0);\n for (int i = N-1; i >= 0; i--) for (int v : rev_deps[i]) crit_path[i] = max(crit_path[i], crit_path[v]+1);\n skill_est.resize(M, vector(K)); skill_lb.resize(M, vector(K, 0)); member_obs.resize(M);\n for (int k = 0; k < K; k++) {\n vector dk(N); for (int i = 0; i < N; i++) dk[i] = d[i][k];\n sort(dk.begin(), dk.end());\n double init = dk[N/2];\n for (int j = 0; j < M; j++) skill_est[j][k] = init;\n }\n vector task_start(N,-1), task_done(N,-1), member_task(M,-1), member_start_day(M,-1);\n set available_tasks; vector deps_rem(N);\n for (int i = 0; i < N; i++) { deps_rem[i] = deps[i].size(); if (!deps_rem[i]) available_tasks.insert(i); }\n int current_day = 0;\n while (true) {\n current_day++;\n vector free_members;\n for (int j = 0; j < M; j++) if (member_task[j] == -1) free_members.push_back(j);\n int fm = free_members.size();\n if (fm > 0 && !available_tasks.empty()) {\n vector av(available_tasks.begin(), available_tasks.end());\n sort(av.begin(), av.end(), [&](int a, int b){ return crit_path[a] > crit_path[b]; });\n int nr = min((int)av.size(), fm*4), na = max(nr, fm);\n vector> cost(fm, vector(na, 1e9));\n for (int mi = 0; mi < fm; mi++) { int j = free_members[mi];\n for (int ti = 0; ti < nr; ti++) { int i = av[ti];\n double w = 0; for (int k = 0; k < K; k++) w += max(0.0, (double)d[i][k]-skill_est[j][k]);\n cost[mi][ti] = max(1.0, w) - crit_path[i]*0.15;\n }\n }\n auto asgn = hungarian(cost);\n vector> assigns;\n for (int mi = 0; mi < fm; mi++) { int ti = asgn[mi];\n if (ti >= 0 && ti < nr) assigns.push_back({free_members[mi], av[ti]});\n }\n cout << assigns.size();\n for (auto [j,i] : assigns) {\n cout << \" \" << (j+1) << \" \" << (i+1);\n member_task[j]=i; member_start_day[j]=current_day; task_start[i]=current_day;\n available_tasks.erase(i);\n }\n cout << endl;\n } else cout << 0 << endl;\n int n; cin >> n; if (n == -1) break;\n for (int idx = 0; idx < n; idx++) {\n int j; cin >> j; j--;\n int i = member_task[j], tt = current_day - member_start_day[j] + 1;\n task_done[i] = current_day;\n if (tt == 1) for (int k = 0; k < K; k++) {\n skill_lb[j][k] = max(skill_lb[j][k], d[i][k]);\n skill_est[j][k] = max(skill_est[j][k], (double)d[i][k]);\n }\n member_obs[j].push_back({i, tt});\n int oc = member_obs[j].size();\n if (oc <= 5 || oc % 5 == 0) reestimate(j);\n member_task[j] = -1;\n for (int v : rev_deps[i]) { deps_rem[v]--; if (!deps_rem[v] && task_start[v]==-1) available_tasks.insert(v); }\n }\n }\n return 0;\n}","ahc006":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint a[N], b[N], c[N], d[N];\n\ninline int dist(int x1, int y1, int x2, int y2) { return abs(x1-x2) + abs(y1-y2); }\n\nstruct Xor128 {\n unsigned x = 123456789, y = 362436069, z = 521288629, w = 88675123;\n unsigned next() {\n unsigned t = x ^ (x << 11);\n x = y; y = z; z = w;\n return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));\n }\n double nextDouble() {\n return next() / 4294967295.0;\n }\n int nextInt(int n) {\n return next() % n;\n }\n};\n\nXor128 rng;\n\nint route[100];\nint bestRouteArr[100];\nint orders[M];\nint bestOrders[M];\nbool isSelected[N];\n\nint calcCost() {\n int cost = 0, x = CX, y = CY;\n for (int i = 0; i < 2 * M; i++) {\n int ord = orders[route[i] / 2]; \n bool isD = route[i] % 2;\n int nx = isD ? c[ord] : a[ord], ny = isD ? d[ord] : b[ord];\n cost += dist(x, y, nx, ny); \n x = nx; y = ny;\n }\n return cost + dist(x, y, CX, CY);\n}\n\nbool isValidForInsert(int ip) {\n int k = route[ip] / 2;\n bool isD = route[ip] % 2;\n if (!isD) { // It's a restaurant\n for (int i = ip + 1; i < 2 * M; i++) {\n if (route[i] == k * 2 + 1) return true;\n }\n return false;\n } else { // It's a delivery\n for (int i = 0; i < ip; i++) {\n if (route[i] == k * 2) return true;\n }\n return false;\n }\n}\n\nvoid constructRoute() {\n bool vR[M], vD[M];\n memset(vR, 0, sizeof vR);\n memset(vD, 0, sizeof vD);\n int cx = CX, cy = CY;\n for (int step = 0; step < 2 * M; step++) {\n int best = -1, bestD = INT_MAX;\n for (int i = 0; i < M; i++) {\n if (!vR[i]) { \n int d2 = dist(cx, cy, a[orders[i]], b[orders[i]]); \n if (d2 < bestD) { bestD = d2; best = i * 2; } \n }\n if (vR[i] && !vD[i]) { \n int d2 = dist(cx, cy, c[orders[i]], d[orders[i]]); \n if (d2 < bestD) { bestD = d2; best = i * 2 + 1; } \n }\n }\n route[step] = best;\n if (best % 2 == 0) { vR[best / 2] = true; cx = a[orders[best / 2]]; cy = b[orders[best / 2]]; }\n else { vD[best / 2] = true; cx = c[orders[best / 2]]; cy = d[orders[best / 2]]; }\n }\n}\n\npair getCoord(int idx) {\n if (idx < 0 || idx >= 2 * M) return {CX, CY};\n int ord = orders[route[idx] / 2];\n bool isD = route[idx] % 2;\n if (isD) return {c[ord], d[ord]};\n else return {a[ord], b[ord]};\n}\n\nint distByIdx(int i, int j) {\n auto [x1, y1] = getCoord(i);\n auto [x2, y2] = getCoord(j);\n return abs(x1 - x2) + abs(y1 - y2);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n for (int i = 0; i < N; i++) cin >> a[i] >> b[i] >> c[i] >> d[i];\n \n auto startTime = chrono::high_resolution_clock::now();\n \n vector> scores;\n for (int i = 0; i < N; i++) {\n int cost = dist(CX, CY, a[i], b[i]) + dist(a[i], b[i], c[i], d[i]) + dist(c[i], d[i], CX, CY);\n scores.push_back({cost, i});\n }\n sort(scores.begin(), scores.end());\n \n for (int i = 0; i < M; i++) { orders[i] = scores[i].second; isSelected[orders[i]] = true; }\n \n constructRoute();\n int curCost = calcCost(), bestCost = curCost;\n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n \n double temp = 100.0, cooling = 0.99999;\n int iter = 0;\n \n while (true) {\n if (iter % 1000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - startTime).count() > 1.8) break;\n }\n iter++;\n \n int mt = rng.nextInt(10);\n if (mt < 5) {\n int from = rng.nextInt(2 * M), to = rng.nextInt(2 * M);\n if (from == to) continue;\n \n int savedRoute[100];\n memcpy(savedRoute, route, sizeof(route));\n \n int val = route[from];\n for (int i = from; i < 2 * M - 1; i++) route[i] = route[i + 1];\n int ip = to > from ? to - 1 : to;\n for (int i = 2 * M - 1; i > ip; i--) route[i] = route[i - 1];\n route[ip] = val;\n \n if (isValidForInsert(ip)) {\n int nc = calcCost(); double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n } else {\n memcpy(route, savedRoute, sizeof(route));\n }\n } else {\n memcpy(route, savedRoute, sizeof(route));\n }\n } else if (mt < 8) {\n int ii = rng.nextInt(M), oi = rng.nextInt(N);\n if (isSelected[oi]) continue;\n \n int savedOrders[50];\n memcpy(savedOrders, orders, sizeof(orders));\n int savedRoute[100];\n memcpy(savedRoute, route, sizeof(route));\n \n int oo = orders[ii]; \n orders[ii] = oi; \n isSelected[oo] = false; \n isSelected[oi] = true;\n \n constructRoute(); \n int nc = calcCost(); \n double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n } else { \n memcpy(orders, savedOrders, sizeof(orders));\n isSelected[oi] = false; \n isSelected[oo] = true; \n memcpy(route, savedRoute, sizeof(route));\n }\n } else {\n int l = rng.nextInt(2 * M - 1), r = l + 1 + rng.nextInt(2 * M - 1 - l);\n bool valid = true;\n bool inSegment[50] = {false};\n for (int i = l; i <= r; i++) {\n int k = route[i] / 2;\n if (inSegment[k]) { valid = false; break; }\n inSegment[k] = true;\n }\n if (valid) {\n int delta = distByIdx(l - 1, r) + distByIdx(l, r + 1) - distByIdx(l - 1, l) - distByIdx(r, r + 1);\n int nc = curCost + delta;\n double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n reverse(route + l, route + r + 1);\n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n }\n }\n }\n temp *= cooling;\n }\n \n cout << M;\n for(int i = 0; i < M; i++) cout << \" \" << bestOrders[i] + 1;\n cout << endl;\n cout << 2 * M + 2 << \" \" << CX << \" \" << CY;\n for(int i = 0; i < 2 * M; i++) {\n int ord = bestOrders[bestRouteArr[i] / 2]; bool isD = bestRouteArr[i] % 2;\n cout << \" \" << (isD ? c[ord] : a[ord]) << \" \" << (isD ? d[ord] : b[ord]);\n }\n cout << \" \" << CX << \" \" << CY << endl;\n}","ahc007":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct UnionFind {\n vector parent, rank_;\n int components;\n \n UnionFind(int n) : parent(n), rank_(n, 0), components(n) {\n for (int i = 0; i < n; i++) parent[i] = i;\n }\n \n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n \n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n components--;\n return true;\n }\n \n bool connected(int x, int y) {\n return find(x) == find(y);\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n vector x(N), y(N);\n vector u(M), v(M);\n vector d(M);\n \n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dist = sqrt((double)(x[u[i]] - x[v[i]]) * (x[u[i]] - x[v[i]]) + \n (double)(y[u[i]] - y[v[i]]) * (y[u[i]] - y[v[i]]));\n d[i] = max(1, (int)round(dist));\n }\n \n // Compute reference MST using d_i\n vector order(M);\n for (int i = 0; i < M; i++) order[i] = i;\n sort(order.begin(), order.end(), [&](int a, int b) { return d[a] < d[b]; });\n \n UnionFind refUF(N);\n vector inRefMST(M, false);\n for (int idx : order) {\n if (refUF.unite(u[idx], v[idx])) {\n inRefMST[idx] = true;\n }\n }\n \n // Process edges online\n UnionFind uf(N);\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int adopt = 0;\n \n if (!uf.connected(u[i], v[i])) {\n if (inRefMST[i]) {\n // Always accept reference MST edges - guarantees connectivity\n adopt = 1;\n uf.unite(u[i], v[i]);\n } else {\n // Accept non-MST edges only if they're cheap enough\n // to potentially replace expensive MST edges\n double percentile = (double)(l - d[i]) / (2.0 * d[i]);\n percentile = max(0.0, min(1.0, percentile));\n \n int remaining = M - i - 1;\n int needed = uf.components - 1;\n double safety = (needed > 0) ? (double)remaining / needed : 999.0;\n \n double threshold;\n if (safety >= 5) threshold = 0.3;\n else if (safety >= 3) threshold = 0.4;\n else if (safety >= 2) threshold = 0.5;\n else threshold = 0.65;\n \n if (percentile <= threshold) {\n adopt = 1;\n uf.unite(u[i], v[i]);\n }\n }\n }\n \n cout << adopt << endl;\n }\n \n return 0;\n}","ahc008":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int SIZE = 30;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\n\nint N, M;\nvector px, py, pt;\nvector hx, hy;\nbool wall[SIZE][SIZE];\n\nbool inBounds(int x, int y) { return x >= 0 && x < SIZE && y >= 0 && y < SIZE; }\n\nvoid bfs(int sx, int sy, int dist[SIZE][SIZE]) {\n memset(dist, -1, sizeof(int) * SIZE * SIZE);\n if (!inBounds(sx, sy) || wall[sx][sy]) return;\n queue> q;\n dist[sx][sy] = 0;\n q.push({sx, sy});\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && dist[nx][ny] == -1) {\n dist[nx][ny] = dist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n}\n\ndouble petThreatWeight(int t) {\n switch(t) { case 1: return 1.0; case 2: return 1.5; case 3: return 2.0; case 4: return 2.5; case 5: return 2.0; default: return 1.0; }\n}\n\ndouble computeScoreWithDist(int dist[SIZE][SIZE]) {\n int area = 0;\n double effectivePets = 0;\n for (int i = 0; i < SIZE; i++)\n for (int j = 0; j < SIZE; j++)\n if (dist[i][j] >= 0) area++;\n for (int i = 0; i < N; i++)\n if (dist[px[i]][py[i]] >= 0) effectivePets += 1.0;\n\n int boundaryDist[SIZE][SIZE];\n memset(boundaryDist, -1, sizeof(int) * SIZE * SIZE);\n queue> q;\n for (int x = 0; x < SIZE; x++)\n for (int y = 0; y < SIZE; y++)\n if (dist[x][y] < 0 && !wall[x][y]) {\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && dist[nx][ny] >= 0) {\n if (boundaryDist[x][y] == -1) { boundaryDist[x][y] = 1; q.push({x, y}); }\n break;\n }\n }\n }\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && boundaryDist[nx][ny] == -1 && dist[nx][ny] < 0) {\n boundaryDist[nx][ny] = boundaryDist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n for (int i = 0; i < N; i++) {\n if (dist[px[i]][py[i]] >= 0) continue;\n int d = boundaryDist[px[i]][py[i]];\n if (d >= 1 && d <= 10) effectivePets += petThreatWeight(pt[i]) * 0.2 * exp(-0.2 * d);\n }\n return (double)area / 900.0 * pow(2.0, -effectivePets);\n}\n\nbool petAdjacentTo(int x, int y, const vector& ppx, const vector& ppy) {\n for (int i = 0; i < N; i++) {\n if (ppx[i] == x && ppy[i] == y) return true;\n for (int d = 0; d < 4; d++)\n if (ppx[i] == x + dx[d] && ppy[i] == y + dy[d]) return true;\n }\n return false;\n}\n\nbool humanAt(int x, int y, const vector& hhx, const vector& hhy) {\n for (int i = 0; i < M; i++) if (hhx[i] == x && hhy[i] == y) return true;\n return false;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N;\n px.resize(N); py.resize(N); pt.resize(N);\n for (int i = 0; i < N; i++) { cin >> px[i] >> py[i] >> pt[i]; px[i]--; py[i]--; }\n cin >> M;\n hx.resize(M); hy.resize(M);\n for (int i = 0; i < M; i++) { cin >> hx[i] >> hy[i]; hx[i]--; hy[i]--; }\n memset(wall, false, sizeof(wall));\n\n for (int turn = 0; turn < 300; turn++) {\n vector startPx = px, startPy = py, startHx = hx, startHy = hy;\n string actions(M, '.');\n bool newWall[SIZE][SIZE] = {};\n\n for (int i = 0; i < M; i++) {\n int myHx = startHx[i], myHy = startHy[i];\n int distBefore[SIZE][SIZE];\n bfs(myHx, myHy, distBefore);\n double bestScore = computeScoreWithDist(distBefore);\n char bestAction = '.';\n\n for (int d = 0; d < 4; d++) {\n int wx = myHx + dx[d], wy = myHy + dy[d];\n if (inBounds(wx, wy) && !wall[wx][wy] && !newWall[wx][wy] &&\n !petAdjacentTo(wx, wy, startPx, startPy) && !humanAt(wx, wy, startHx, startHy)) {\n wall[wx][wy] = true;\n int distAfter[SIZE][SIZE];\n bfs(myHx, myHy, distAfter);\n double newScore = computeScoreWithDist(distAfter);\n for (int j = 0; j < N; j++)\n if (distBefore[startPx[j]][startPy[j]] >= 0 && distAfter[startPx[j]][startPy[j]] < 0)\n newScore += 0.05;\n for (int dd = 0; dd < 4; dd++) {\n int nx = wx + dx[dd], ny = wy + dy[dd];\n if (!inBounds(nx, ny) || wall[nx][ny]) newScore += 0.003;\n }\n newScore += 0.001;\n wall[wx][wy] = false;\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"udlr\"[d]; }\n }\n }\n for (int d = 0; d < 4; d++) {\n int nx = myHx + dx[d], ny = myHy + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && !newWall[nx][ny]) {\n int distAfter[SIZE][SIZE];\n bfs(nx, ny, distAfter);\n double newScore = computeScoreWithDist(distAfter);\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"UDLR\"[d]; }\n }\n }\n actions[i] = bestAction;\n switch (actions[i]) {\n case 'u': newWall[myHx-1][myHy]=true; wall[myHx-1][myHy]=true; break;\n case 'd': newWall[myHx+1][myHy]=true; wall[myHx+1][myHy]=true; break;\n case 'l': newWall[myHx][myHy-1]=true; wall[myHx][myHy-1]=true; break;\n case 'r': newWall[myHx][myHy+1]=true; wall[myHx][myHy+1]=true; break;\n case 'U': hx[i]=myHx-1; hy[i]=myHy; break;\n case 'D': hx[i]=myHx+1; hy[i]=myHy; break;\n case 'L': hx[i]=myHx; hy[i]=myHy-1; break;\n case 'R': hx[i]=myHx; hy[i]=myHy+1; break;\n }\n }\n cout << actions << endl;\n for (int i = 0; i < N; i++) {\n string move; cin >> move;\n for (char c : move) {\n if (c=='U') px[i]--; else if (c=='D') px[i]++;\n else if (c=='L') py[i]--; else if (c=='R') py[i]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint si,sj,ti,tj;double p;int ti_idx;\nint md[400][4];bool itm[400][4];double fv[400][202];int c2d[256];\n\nvoid init(const vector& h,const vector& v){\n ti_idx=ti*20+tj;\n int di[]={-1,1,0,0},dj[]={0,0,-1,1};\n for(int i=0;i<20;i++)for(int j=0;j<20;j++){int idx=i*20+j;\n for(int d=0;d<4;d++){int ni=i+di[d],nj=j+dj[d];bool bl=false;\n if(ni<0||ni>=20||nj<0||nj>=20)bl=true;\n else if(d==0&&i>0&&v[i-1][j]=='1')bl=true;\n else if(d==1&&v[i][j]=='1')bl=true;\n else if(d==2&&j>0&&h[i][j-1]=='1')bl=true;\n else if(d==3&&h[i][j]=='1')bl=true;\n if(bl){ni=i;nj=j;}md[idx][d]=ni*20+nj;itm[idx][d]=(ni==ti&&nj==tj);}}\n memset(fv,0,sizeof(fv));\n for(int t=200;t>=1;t--)for(int i=0;i<400;i++){\n if(i==ti_idx)fv[i][t]=401-t;\n else{double b=0;for(int d=0;d<4;d++)b=max(b,p*fv[i][t+1]+(1-p)*fv[md[i][d]][t+1]);fv[i][t]=b;}}\n}\n\ndouble score(const string& s){double pr[400]={},np[400];pr[si*20+sj]=1;double es=0;\n for(int t=0;t<(int)s.size();t++){int d=c2d[(unsigned char)s[t]];memset(np,0,sizeof(np));\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;np[i]+=p*pr[i];int ni=md[i][d];\n if(itm[i][d])es+=(1-p)*pr[i]*(401-t-1);else np[ni]+=(1-p)*pr[i];}\n memcpy(pr,np,sizeof(pr));}return es;}\n\nstring bfs_path(){int dist[20][20],pd[20][20];memset(dist,-1,sizeof(dist));\n queue>q;q.push({si,sj});dist[si][sj]=0;\n while(!q.empty()){auto[i,j]=q.front();q.pop();if(i==ti&&j==tj)break;\n for(int d=0;d<4;d++){int ni=md[i*20+j][d]/20,nj=md[i*20+j][d]%20;\n if((ni!=i||nj!=j)&&dist[ni][nj]==-1){dist[ni][nj]=dist[i][j]+1;pd[ni][nj]=d;q.push({ni,nj});}}}\n string path;int ci=ti,cj=tj;int di[]={-1,1,0,0},dj[]={0,0,-1,1};\n while(ci!=si||cj!=sj){int d=pd[ci][cj];path=\"UDLR\"[d]+path;ci-=di[d];cj-=dj[d];}return path;}\n\nstring greedy(){double pr[400]={},np[400];pr[si*20+sj]=1;string res;\n for(int t=1;t<=200;t++){double bs=-1;int ba=0;\n for(int d=0;d<4;d++){double rp=0;memset(np,0,sizeof(np));\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;np[i]+=p*pr[i];\n if(itm[i][d])rp+=(1-p)*pr[i];else np[md[i][d]]+=(1-p)*pr[i];}\n double sc=rp*(401-t);for(int i=0;i<400;i++)sc+=np[i]*fv[i][t+1];\n if(sc>bs){bs=sc;ba=d;}}\n res+=\"UDLR\"[ba];memset(np,0,sizeof(np));\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;np[i]+=p*pr[i];\n if(!itm[i][ba])np[md[i][ba]]+=(1-p)*pr[i];}memcpy(pr,np,sizeof(pr));}return res;}\n\nstring beam(int B){struct S{double pr[400];double acc,te;string s;};\n vectorbm(1);memset(bm[0].pr,0,sizeof(bm[0].pr));bm[0].pr[si*20+sj]=1;bm[0].acc=0;bm[0].te=0;\n for(int i=0;i<400;i++)bm[0].te+=bm[0].pr[i]*fv[i][1];\n for(int t=1;t<=200;t++){vector>sc;vectorcand;\n for(int bi=0;bi<(int)bm.size();bi++){for(int d=0;d<4;d++){S ns;memset(ns.pr,0,sizeof(ns.pr));ns.acc=bm[bi].acc;\n for(int i=0;i<400;i++){if(bm[bi].pr[i]<1e-18)continue;ns.pr[i]+=p*bm[bi].pr[i];\n if(itm[i][d])ns.acc+=(1-p)*bm[bi].pr[i]*(401-t);else ns.pr[md[i][d]]+=(1-p)*bm[bi].pr[i];}\n ns.s=bm[bi].s+\"UDLR\"[d];ns.te=ns.acc;for(int i=0;i<400;i++)ns.te+=ns.pr[i]*fv[i][t+1];\n sc.push_back({ns.te,(int)cand.size()});cand.push_back(move(ns));}}\n int k=min(B,(int)sc.size());\n if((int)sc.size()>k)partial_sort(sc.begin(),sc.begin()+k,sc.end(),[](auto&a,auto&b){return a.first>b.first;});\n vectornb(k);for(int i=0;ibs){bs=s;br=st.s;}}return br;}\n\nvoid suffix_opt(string&best,double&bs){auto ts=[&](const string&s){double sc=score(s);if(sc>bs){bs=sc;best=s;}};\n for(int k:vector{50,100,150}){if(k>=(int)best.size())continue;\n double pr[400]={};pr[si*20+sj]=1;\n for(int t=0;tbsc){bsc=sc;ba=d;}}\n ns+=\"UDLR\"[ba];double np[400]={};\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;np[i]+=p*pr[i];\n if(!itm[i][ba])np[md[i][ba]]+=(1-p)*pr[i];}memcpy(pr,np,sizeof(pr));}\n ts(ns);}}\n\nint main(){ios_base::sync_with_stdio(false);cin.tie(nullptr);\n c2d['U']=0;c2d['D']=1;c2d['L']=2;c2d['R']=3;\n cin>>si>>sj>>ti>>tj>>p;vectorh(20),v(19);\n for(int i=0;i<20;i++)cin>>h[i];for(int i=0;i<19;i++)cin>>v[i];init(h,v);\n string best;double bs=-1;auto ts=[&](const string&s){double sc=score(s);if(sc>bs){bs=sc;best=s;}};\n string sp=bfs_path();\n {string s;while((int)(s.size()+sp.size())<=200)s+=sp;ts(s);}\n for(int r=2;r<=5;r++){string s;for(char c:sp)for(int k=0;k(0,(int)ns.size()-1)(rng);\n ns[pos]=\"UDLR\"[uniform_int_distribution(0,3)(rng)];\n double sc=score(ns);if(sc>bs){bs=sc;best=ns;}}\n suffix_opt(best,bs);\n for(int len=100;len<200;len+=25)ts(best.substr(0,len));\n cout<\nusing namespace std;\n\nconst int N = 30;\nint orig_tiles[N][N], rotations[N][N], current_tiles[N][N];\nconst int di[] = {0, -1, 0, 1}, dj[] = {-1, 0, 1, 0};\nconst int to_table[8][4] = {{1,0,-1,-1},{3,-1,-1,0},{-1,-1,3,2},{-1,2,1,-1},{1,0,3,2},{3,2,1,0},{2,-1,0,-1},{-1,3,-1,1}};\nint rotated_type[8][4];\n\nvoid init_rotated_type() {\n for (int t = 0; t < 8; t++) {\n rotated_type[t][0] = t;\n int cur = t;\n for (int r = 1; r < 4; r++) {\n if (cur <= 3) cur = (cur + 1) % 4;\n else if (cur == 4) cur = 5; else if (cur == 5) cur = 4;\n else if (cur == 6) cur = 7; else cur = 6;\n rotated_type[t][r] = cur;\n }\n }\n}\n\nvoid update_all_tiles() {\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n current_tiles[i][j] = rotated_type[orig_tiles[i][j]][rotations[i][j]];\n}\n\npair compute_top2() {\n static bool visited[N][N][4];\n memset(visited, 0, sizeof(visited));\n int max1 = 0, max2 = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int t = current_tiles[i][j];\n for (int d = 0; d < 4; d++) {\n if (visited[i][j][d] || to_table[t][d] == -1) { visited[i][j][d] = true; continue; }\n int si = i, sj = j, sd = d, ci = i, cj = j, cd = d, length = 0;\n while (true) {\n visited[ci][cj][cd] = true;\n int t2 = current_tiles[ci][cj], d2 = to_table[t2][cd];\n if (d2 == -1) break;\n int ni = ci + di[d2], nj = cj + dj[d2];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) break;\n int nd = (d2 + 2) % 4; length++;\n if (ni == si && nj == sj && nd == sd) {\n if (length > max1) { max2 = max1; max1 = length; }\n else if (length > max2) max2 = length;\n break;\n }\n ci = ni; cj = nj; cd = nd;\n }\n }\n }\n }\n return {max1, max2};\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(0);\n init_rotated_type();\n for (int i = 0; i < N; i++) { string s; cin >> s; for (int j = 0; j < N; j++) orig_tiles[i][j] = s[j] - '0'; }\n \n mt19937 rng(42);\n long long global_best_score = 0; int global_best_rotations[N][N] = {};\n auto start_time = chrono::high_resolution_clock::now();\n \n for (int trial = 0; trial < 10; trial++) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start_time).count() > 1.5) break;\n \n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) rotations[i][j] = rng() % 4;\n update_all_tiles();\n \n auto [m1, m2] = compute_top2();\n long long cur_score = (long long)m1 * m2, best_score = cur_score;\n int best_rotations[N][N]; memcpy(best_rotations, rotations, sizeof(rotations));\n \n uniform_int_distribution pos_dist(0, N*N-1), rot_dist(0, 3);\n uniform_real_distribution prob_dist(0.0, 1.0);\n \n for (int iter = 0; iter < 30000; iter++) {\n now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start_time).count() > 1.7) break;\n double temp = 100.0 * pow(0.01, min((double)iter / 30000.0, 1.0));\n \n int idx = pos_dist(rng), i = idx / N, j = idx % N;\n int old_rot = rotations[i][j], new_rot = rot_dist(rng);\n if (old_rot == new_rot) continue;\n \n rotations[i][j] = new_rot;\n current_tiles[i][j] = rotated_type[orig_tiles[i][j]][new_rot];\n \n auto [nm1, nm2] = compute_top2();\n long long new_score = (long long)nm1 * nm2;\n \n if (new_score - cur_score > 0 || prob_dist(rng) < exp((double)(new_score - cur_score) / max(temp, 0.001))) {\n cur_score = new_score;\n if (cur_score > best_score) { best_score = cur_score; memcpy(best_rotations, rotations, sizeof(rotations)); }\n } else { rotations[i][j] = old_rot; current_tiles[i][j] = rotated_type[orig_tiles[i][j]][old_rot]; }\n }\n if (best_score > global_best_score) { global_best_score = best_score; memcpy(global_best_rotations, best_rotations, sizeof(best_rotations)); }\n }\n \n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cout << global_best_rotations[i][j];\n cout << endl;\n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N, T;\nint board[10][10];\nint er, ec;\nint par[100], gsz[100];\n\nint find_root(int x) {\n while (par[x] != x) x = par[x] = par[par[x]];\n return x;\n}\n\nvoid unite(int x, int y) {\n x = find_root(x); y = find_root(y);\n if (x == y) return;\n if (gsz[x] < gsz[y]) swap(x, y);\n par[y] = x; gsz[x] += gsz[y];\n}\n\nint compute_max_tree_size() {\n for (int i = 0; i < N*N; i++) { par[i] = i; gsz[i] = 0; }\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j]) gsz[i*N+j] = 1;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N-1; j++)\n if (board[i][j] && board[i][j+1] && (board[i][j] & 4) && (board[i][j+1] & 1))\n unite(i*N+j, i*N+j+1);\n for (int i = 0; i < N-1; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j] && board[i+1][j] && (board[i][j] & 8) && (board[i+1][j] & 2))\n unite(i*N+j, (i+1)*N+j);\n int mx = 0;\n for (int i = 0; i < N*N; i++) mx = max(mx, gsz[i]);\n return mx;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> T;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n char c = s[j];\n board[i][j] = (c >= '0' && c <= '9') ? c - '0' : c - 'a' + 10;\n if (!board[i][j]) { er = i; ec = j; }\n }\n }\n \n string moves; moves.reserve(T);\n int cur_sz = compute_max_tree_size();\n int best_sz = cur_sz, best_idx = 0;\n mt19937 rng(42);\n constexpr int dr[] = {-1,1,0,0}, dc[] = {0,0,-1,1};\n constexpr char dc_c[] = {'U','D','L','R'};\n constexpr int rev_dir[] = {1,0,3,2};\n int last_d = -1;\n auto start = chrono::high_resolution_clock::now();\n double temp = 2.5;\n int no_improve = 0;\n \n while ((int)moves.size() < T) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now-start).count() > 2900) break;\n \n int ns[4];\n for (int d = 0; d < 4; d++) {\n int nr = er+dr[d], nc = ec+dc[d];\n if (nr<0||nr>=N||nc<0||nc>=N) { ns[d] = -1; continue; }\n swap(board[er][ec], board[nr][nc]);\n int oer=er, oec=ec; er=nr; ec=nc;\n ns[d] = compute_max_tree_size();\n swap(board[er][ec], board[oer][oec]); er=oer; ec=oec;\n }\n \n int best_d = -1, best_ns = -1;\n for (int d = 0; d < 4; d++)\n if (ns[d] > best_ns) { best_ns = ns[d]; best_d = d; }\n if (best_d == -1) break;\n \n int chosen;\n if (best_ns > cur_sz) {\n chosen = best_d;\n no_improve = 0;\n } else {\n no_improve++;\n double delta = best_ns - cur_sz;\n double prob = exp(delta / max(temp, 0.001));\n if ((double)rng() / (double)UINT32_MAX < prob) {\n chosen = best_d;\n } else {\n int valid[4], nv = 0;\n for (int d = 0; d < 4; d++) {\n if (ns[d] < 0) continue;\n if (last_d >= 0 && d == rev_dir[last_d]) continue;\n valid[nv++] = d;\n }\n if (nv == 0)\n for (int d = 0; d < 4; d++)\n if (ns[d] >= 0) valid[nv++] = d;\n if (nv == 0) break;\n chosen = valid[rng() % nv];\n }\n }\n \n int nr = er+dr[chosen], nc = ec+dc[chosen];\n swap(board[er][ec], board[nr][nc]);\n er = nr; ec = nc;\n moves += dc_c[chosen];\n cur_sz = ns[chosen];\n last_d = chosen;\n \n if (cur_sz > best_sz) { best_sz = cur_sz; best_idx = moves.size(); }\n \n temp *= 0.9997;\n if (no_improve > 40) { temp = min(temp * 1.8, 6.0); no_improve = 20; }\n if (best_sz == N*N-1) break;\n }\n \n cout << moves.substr(0, best_idx) << endl;\n}","ahc012":"#include \nusing namespace std;\ntypedef long long ll;\n\nint N, K;\nint a[11];\nvector px, py;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> K;\n for (int d = 1; d <= 10; d++) cin >> a[d];\n px.resize(N); py.resize(N);\n for (int i = 0; i < N; i++) cin >> px[i] >> py[i];\n \n vector> lines;\n auto start = chrono::steady_clock::now();\n \n for (int iter = 0; iter < K; iter++) {\n if (chrono::duration(chrono::steady_clock::now() - start).count() > 2.0) break;\n \n map, vector> groups;\n for (int i = 0; i < N; i++) {\n vector sig; bool dead = false;\n for (auto& L : lines) {\n ll la = L[3]-L[1], lb = L[0]-L[2], lc = L[2]*L[1]-L[0]*L[3];\n ll val = la*px[i] + lb*py[i] + lc;\n if (val == 0) { dead = true; break; }\n sig.push_back(val > 0 ? 1 : -1);\n }\n if (!dead) groups[sig].push_back(i);\n }\n \n int pc[11] = {};\n for (auto& [s, m] : groups) { int sz = m.size(); if (sz >= 1 && sz <= 10) pc[sz]++; }\n int cur_score = 0;\n for (int d = 1; d <= 10; d++) cur_score += min(a[d], pc[d]);\n int max_score = 0;\n for (int d = 1; d <= 10; d++) max_score += a[d];\n if (cur_score == max_score) break;\n \n vector>> cands;\n auto try_line = [&](ll x1, ll y1, ll x2, ll y2) {\n if (x1 == x2 && y1 == y2) return;\n ll la = y2-y1, lb = x1-x2, lc = x2*y1-x1*y2;\n int new_pc[11] = {};\n for (auto& [sig, members] : groups) {\n int pos = 0, neg = 0;\n for (int i : members) {\n ll val = la*px[i] + lb*py[i] + lc;\n if (val > 0) pos++; else if (val < 0) neg++;\n }\n if (pos >= 1 && pos <= 10) new_pc[pos]++;\n if (neg >= 1 && neg <= 10) new_pc[neg]++;\n }\n int score = 0;\n for (int d = 1; d <= 10; d++) score += min(a[d], new_pc[d]);\n cands.push_back({score, {x1, y1, x2, y2}});\n };\n \n for (auto& [sig, members] : groups) {\n int sz = members.size();\n if (sz <= 1) continue;\n if (sz <= 10 && pc[sz] <= a[sz]) continue;\n int lim = min((int)members.size(), 20);\n for (int ii = 0; ii < lim; ii++)\n for (int jj = ii+1; jj < lim; jj++) {\n int i = members[ii], j = members[jj];\n ll sx = px[i]+px[j], sy = py[i]+py[j];\n ll dx = 2*(py[i]-py[j]), dy = 2*(px[j]-px[i]);\n try_line(sx, sy, sx+dx, sy+dy);\n }\n ll cx = 0, cy = 0;\n for (int i : members) { cx += px[i]; cy += py[i]; }\n for (int angle = 0; angle < 18; angle++) {\n double a_rad = angle * M_PI / 9;\n ll dx = (ll)round(10000*cos(a_rad)), dy = (ll)round(10000*sin(a_rad));\n if (dx == 0 && dy == 0) continue;\n try_line(cx, cy, cx + dx*sz, cy + dy*sz);\n }\n }\n \n mt19937 rng(iter*12345+67890);\n for (int r = 0; r < 50; r++) {\n ll x1 = rng()%20001-10000, y1 = rng()%20001-10000;\n ll x2 = rng()%20001-10000, y2 = rng()%20001-10000;\n try_line(x1, y1, x2, y2);\n }\n \n if (cands.empty()) break;\n int best = 0;\n for (int i = 1; i < (int)cands.size(); i++)\n if (cands[i].first > cands[best].first) best = i;\n lines.push_back(cands[best].second);\n }\n \n cout << lines.size() << \"\\n\";\n for (auto& L : lines)\n cout << L[0] << \" \" << L[1] << \" \" << L[2] << \" \" << L[3] << \"\\n\";\n return 0;\n}","ahc014":"#include \nusing namespace std;\n\nint N, M;\nvector> has_dot;\nvector> ops;\nmap>> segs[4];\n\nint seg_type(int x1,int y1,int x2,int y2){\n if(y1==y2)return 0;\n if(x1==x2)return 1;\n if(x2-x1==y2-y1)return 2;\n return 3;\n}\nint line_id(int t,int x,int y){\n if(t==0)return y;if(t==1)return x;\n if(t==2)return x-y;return x+y;\n}\n\nbool check_overlap(int t,int lid,int s,int e){\n if(s>e)swap(s,e);\n auto it=segs[t].find(lid);\n if(it==segs[t].end())return false;\n for(auto&[a,b]:it->second){\n int lo=min(a,b),hi=max(a,b);\n if(max(s,lo)>corners={{x1,y1},{x2,y2},{x3,y3},{x4,y4}};\n auto chk=[&](int ax,int ay,int bx,int by){\n int dx=bx-ax,dy=by-ay,st=max(abs(dx),abs(dy));\n if(!st)return false;\n int sx=dx/st,sy=dy/st;\n for(int i=1;i find_rect(int ex,int ey){\n // Axis-aligned\n for(int x2=0;x2V2 (1,1), V2->V3 (1,-1)\n auto try_tilt=[&](int v1x,int v1y,int v2x,int v2y,int v3x,int v3y,int v4x,int v4y){\n if(v1x<0||v1x>=N||v1y<0||v1y>=N)return false;\n if(v2x<0||v2x>=N||v2y<0||v2y>=N)return false;\n if(v3x<0||v3x>=N||v3y<0||v3y>=N)return false;\n if(v4x<0||v4x>=N||v4y<0||v4y>=N)return false;\n if(!has_dot[v2x][v2y]||!has_dot[v3x][v3y]||!has_dot[v4x][v4y])return false;\n return valid(v1x,v1y,v2x,v2y,v3x,v3y,v4x,v4y);\n };\n \n for(int a=1;aV2 (1,-1), V2->V3 (1,1)\n for(int a=1;a>N>>M;\n has_dot.assign(N,vector(N,false));\n for(int i=0;i>x>>y;has_dot[x][y]=true;}\n \n double c=(N-1)/2.0;\n bool found=true;\n while(found){\n found=false;\n double best_w=-1;vectorbest_r;\n for(int x=0;x\n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 10;\nint grid[N][N];\nint f[101];\nmt19937 rng(42);\n\nvoid tiltGrid(int g[N][N], int d) {\n if (d == 0) {\n for (int c = 0; c < N; c++) {\n int w = 0;\n for (int r = 0; r < N; r++) {\n if (g[r][c]) { if (w != r) { g[w][c] = g[r][c]; g[r][c] = 0; } w++; }\n }\n }\n } else if (d == 1) {\n for (int c = 0; c < N; c++) {\n int w = N - 1;\n for (int r = N - 1; r >= 0; r--) {\n if (g[r][c]) { if (w != r) { g[w][c] = g[r][c]; g[r][c] = 0; } w--; }\n }\n }\n } else if (d == 2) {\n for (int r = 0; r < N; r++) {\n int w = 0;\n for (int c = 0; c < N; c++) {\n if (g[r][c]) { if (w != c) { g[r][w] = g[r][c]; g[r][c] = 0; } w++; }\n }\n }\n } else {\n for (int r = 0; r < N; r++) {\n int w = N - 1;\n for (int c = N - 1; c >= 0; c--) {\n if (g[r][c]) { if (w != c) { g[r][w] = g[r][c]; g[r][c] = 0; } w--; }\n }\n }\n }\n}\n\nlong long calcScore(int g[N][N]) {\n bool visited[N][N] = {};\n long long score = 0;\n int dr[] = {-1, 1, 0, 0}, dc[] = {0, 0, -1, 1};\n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (!visited[r][c] && g[r][c]) {\n int flavor = g[r][c], size = 0;\n queue> q;\n q.push({r, c}); visited[r][c] = true;\n while (!q.empty()) {\n auto [cr, cc] = q.front(); q.pop(); size++;\n for (int d = 0; d < 4; d++) {\n int nr = cr + dr[d], nc = cc + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !visited[nr][nc] && g[nr][nc] == flavor) {\n visited[nr][nc] = true; q.push({nr, nc});\n }\n }\n }\n score += (long long)size * size;\n }\n }\n }\n return score;\n}\n\nlong long calcPotential(int g[N][N], int turn) {\n if (turn >= 100) return 0;\n int nextFlavor = f[turn + 1];\n long long potential = 0;\n int dr[] = {-1, 1, 0, 0}, dc[] = {0, 0, -1, 1};\n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (g[r][c] == 0) {\n for (int d = 0; d < 4; d++) {\n int nr = r + dr[d], nc = c + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && g[nr][nc] == nextFlavor) {\n potential++; break;\n }\n }\n }\n }\n }\n // Also count adjacency within same flavor groups\n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (g[r][c]) {\n if (r + 1 < N && g[r+1][c] == g[r][c]) potential++;\n if (c + 1 < N && g[r][c+1] == g[r][c]) potential++;\n }\n }\n }\n return potential;\n}\n\nlong long simulate(int start_t, int orig_g[N][N]) {\n int g[N][N];\n memcpy(g, orig_g, sizeof(g));\n for (int t = start_t; t <= 100; t++) {\n pair empty_cells[100];\n int cnt = 0;\n for (int r = 0; r < N; r++)\n for (int c = 0; c < N; c++)\n if (g[r][c] == 0) empty_cells[cnt++] = {r, c};\n if (cnt == 0) break;\n int idx = rng() % cnt;\n g[empty_cells[idx].first][empty_cells[idx].second] = f[t];\n // Greedy tilt in simulation\n long long best = -1; int best_d = 1;\n int saved[N][N];\n for (int d = 0; d < 4; d++) {\n memcpy(saved, g, sizeof(g));\n tiltGrid(g, d);\n long long sc = calcScore(g);\n if (sc > best) { best = sc; best_d = d; }\n memcpy(g, saved, sizeof(g));\n }\n tiltGrid(g, best_d);\n }\n return calcScore(g);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int i = 1; i <= 100; i++) cin >> f[i];\n memset(grid, 0, sizeof(grid));\n \n string dirs = \"FBLR\";\n int priority[] = {4, 1, 2, 3}; // B > L > R > F\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n int pos = 1, pr = -1, pc = -1;\n for (int r = 0; r < N && pr == -1; r++)\n for (int c = 0; c < N && pr == -1; c++)\n if (grid[r][c] == 0) { if (pos == p) { pr = r; pc = c; } pos++; }\n grid[pr][pc] = f[t];\n \n long long scores[4], pot[4];\n int saved[N][N];\n for (int d = 0; d < 4; d++) {\n memcpy(saved, grid, sizeof(grid));\n tiltGrid(grid, d);\n scores[d] = calcScore(grid);\n pot[d] = calcPotential(grid, t);\n memcpy(grid, saved, sizeof(grid));\n }\n \n long long maxScore = *max_element(scores, scores + 4);\n vector cands;\n for (int d = 0; d < 4; d++) if (scores[d] == maxScore) cands.push_back(d);\n \n int best_dir;\n if (cands.size() == 1) {\n best_dir = cands[0];\n } else {\n // Use potential to narrow down\n long long maxPot = -1;\n for (int d : cands) maxPot = max(maxPot, pot[d]);\n vector cands2;\n for (int d : cands) if (pot[d] == maxPot) cands2.push_back(d);\n \n if (cands2.size() == 1) {\n best_dir = cands2[0];\n } else if (t < 85) {\n // Monte Carlo tiebreak\n int num_sims = max(10, 50 - t / 3);\n long long mc[4] = {};\n for (int d : cands2) {\n int temp[N][N];\n memcpy(temp, grid, sizeof(grid));\n tiltGrid(temp, d);\n for (int s = 0; s < num_sims; s++) mc[d] += simulate(t + 1, temp);\n }\n best_dir = cands2[0];\n for (int d : cands2) if (mc[d] > mc[best_dir]) best_dir = d;\n } else {\n best_dir = *min_element(cands2.begin(), cands2.end(), [&](int a, int b) { return priority[a] < priority[b]; });\n }\n }\n \n tiltGrid(grid, best_dir);\n cout << dirs[best_dir] << '\\n';\n cout.flush();\n }\n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int M; double eps;\n cin >> M >> eps;\n \n int N;\n {\n double f = sqrt(max(eps * (1.0 - eps), 0.001));\n N = (int)round(2.5 * M * f + sqrt(2.0 * M) + 3);\n N = max(4, min(100, N));\n }\n \n int maxE = N * (N - 1) / 2;\n mt19937 rng(42);\n \n auto eidx = [&](int i, int j) -> int {\n if (i > j) swap(i, j);\n return i * (2 * N - i - 1) / 2 + (j - i - 1);\n };\n \n auto sortedDeg = [&](const string& g) -> vector {\n vector d(N, 0);\n for (int i = 0; i < N; i++)\n for (int j = i + 1; j < N; j++) {\n if (g[i * (2*N-i-1)/2 + (j-i-1)] == '1') { d[i]++; d[j]++; }\n }\n sort(d.begin(), d.end());\n return d;\n };\n \n int NC = min(2000, max(M * 10, 500));\n vector cands(NC, string(maxE, '0'));\n vector> cdeg(NC);\n \n for (int c = 0; c < NC; c++) {\n string g(maxE, '0');\n if (c < NC / 3) {\n double dens = (c + 1.0) / (NC / 3 + 1);\n int te = max(0, min(maxE, (int)round(dens * maxE)));\n vector p(maxE); iota(p.begin(), p.end(), 0);\n shuffle(p.begin(), p.end(), rng);\n for (int i = 0; i < te; i++) g[p[i]] = '1';\n } else if (c < 2 * NC / 3) {\n int code = c - NC / 3;\n vector b(N, 0);\n int numOnes = code / max(1, (NC / 3 / N)) + 1;\n int offset = code % max(1, (NC / 3 / N));\n for (int i = 0; i < min(numOnes, N); i++) {\n int pos = (offset + i * (N / max(numOnes, 1))) % N;\n b[pos] = 1;\n }\n for (int j = 0; j < N; j++)\n if (b[j])\n for (int i = 0; i < j; i++)\n g[eidx(i, j)] = '1';\n } else {\n int code = c - 2 * NC / 3;\n int cliqueSz = (code / max(1, NC / 3 / N)) + 1;\n cliqueSz = min(cliqueSz, N);\n int crossE = code % max(1, NC / 3 / N);\n for (int i = 0; i < cliqueSz; i++)\n for (int j = i + 1; j < cliqueSz; j++)\n g[eidx(i, j)] = '1';\n int added = 0;\n for (int i = 0; i < cliqueSz && added < crossE; i++)\n for (int j = cliqueSz; j < N && added < crossE; j++) {\n g[eidx(i, j)] = '1'; added++;\n }\n }\n cands[c] = g;\n cdeg[c] = sortedDeg(g);\n }\n \n vector> fp(NC, vector(N));\n for (int c = 0; c < NC; c++)\n for (int i = 0; i < N; i++)\n fp[c][i] = cdeg[c][i] * (1.0 - 2.0 * eps) + (N - 1) * eps;\n \n vector sel;\n vector minD(NC, 1e18);\n vector used(NC, false);\n \n sel.push_back(0); used[0] = true;\n for (int c = 0; c < NC; c++) {\n double d = 0;\n for (int i = 0; i < N; i++) { double df = fp[c][i] - fp[0][i]; d += df * df; }\n minD[c] = d;\n }\n \n for (int k = 1; k < M; k++) {\n int best = -1; double bestD = -1;\n for (int c = 0; c < NC; c++) {\n if (used[c]) continue;\n if (minD[c] > bestD) { bestD = minD[c]; best = c; }\n }\n sel.push_back(best); used[best] = true;\n for (int c = 0; c < NC; c++) {\n if (used[c]) continue;\n double d = 0;\n for (int i = 0; i < N; i++) { double df = fp[c][i] - fp[best][i]; d += df * df; }\n minD[c] = min(minD[c], d);\n }\n }\n \n // Precompute adjacency matrices for Hamming distance decoding\n vector> adjM(M, vector(maxE));\n vector> gfp(M, vector(N));\n for (int k = 0; k < M; k++) {\n gfp[k] = fp[sel[k]];\n for (int e = 0; e < maxE; e++) adjM[k][e] = (cands[sel[k]][e] == '1') ? 1 : 0;\n }\n \n cout << N << \"\\n\";\n for (int k = 0; k < M; k++) cout << cands[sel[k]] << \"\\n\";\n cout.flush();\n \n double dVar = max(1.0, (N - 1.0) * eps * (1.0 - eps));\n \n for (int q = 0; q < 100; q++) {\n string H; cin >> H;\n vector hd = sortedDeg(H);\n \n // Primary: fingerprint distance\n int bestK = 0; double bestS = -1e18;\n for (int k = 0; k < M; k++) {\n double s = 0;\n for (int i = 0; i < N; i++) {\n double diff = hd[i] - gfp[k][i];\n s -= diff * diff / (2.0 * dVar);\n }\n if (s > bestS) { bestS = s; bestK = k; }\n }\n \n cout << bestK << \"\\n\";\n cout.flush();\n }\n return 0;\n}","ahc017":"#include \nusing namespace std;\n\ntypedef long long ll;\ntypedef pair pli;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, D, K;\n cin >> N >> M >> D >> K;\n \n vector u(M), v(M), w(M);\n vector>> adj(N);\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i] >> w[i];\n u[i]--; v[i]--;\n adj[u[i]].push_back({i, v[i]});\n adj[v[i]].push_back({i, u[i]});\n }\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n cin >> x[i] >> y[i];\n }\n \n // Build edge adjacency (edges sharing a vertex)\n vector> edge_adj(M);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < (int)adj[i].size(); j++) {\n for (int k = j + 1; k < (int)adj[i].size(); k++) {\n edge_adj[adj[i][j].first].push_back(adj[i][k].first);\n edge_adj[adj[i][k].first].push_back(adj[i][j].first);\n }\n }\n }\n \n // Compute edge midpoints\n vector mx(M), my(M);\n for (int i = 0; i < M; i++) {\n mx[i] = (x[u[i]] + x[v[i]]) / 2.0;\n my[i] = (y[u[i]] + y[v[i]]) / 2.0;\n }\n \n // Sort by angle from center for geographic spreading\n double cx = 500, cy = 500;\n vector order(M);\n iota(order.begin(), order.end(), 0);\n \n sort(order.begin(), order.end(), [&](int a, int b) {\n double ax = mx[a] - cx, ay = my[a] - cy;\n double bx = mx[b] - cx, by = my[b] - cy;\n double aa = atan2(ay, ax), ab = atan2(by, bx);\n if (abs(aa - ab) > 1e-9) return aa < ab;\n double da = ax*ax + ay*ay, db = bx*bx + by*by;\n return da < db;\n });\n \n // Greedy edge coloring with conflict avoidance\n vector r(M, -1);\n vector day_count(D, 0);\n \n for (int idx : order) {\n vector conflicts(D, 0);\n for (int e : edge_adj[idx]) {\n if (r[e] != -1) conflicts[r[e]]++;\n }\n \n int best_day = -1;\n double best_score = 1e18;\n for (int d = 0; d < D; d++) {\n if (day_count[d] >= K) continue;\n double score = day_count[d] * 10.0 + conflicts[d] * 100.0;\n if (score < best_score) {\n best_score = score;\n best_day = d;\n }\n }\n \n if (best_day == -1) {\n for (int d = 0; d < D; d++) {\n if (day_count[d] < K && (best_day == -1 || day_count[d] < day_count[best_day])) {\n best_day = d;\n }\n }\n }\n \n r[idx] = best_day;\n day_count[best_day]++;\n }\n \n // Output\n for (int i = 0; i < M; i++) {\n cout << r[i] + 1 << (i == M-1 ? \"\\n\" : \" \");\n }\n \n return 0;\n}","ahc019":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint D;\nusing Point = tuple;\nusing Array3D = vector>>;\n\nvector readSilhouette() {\n vector s(D);\n for (int i = 0; i < D; i++) cin >> s[i];\n return s;\n}\n\nArray3D buildMaxFill(const vector& f, const vector& r) {\n Array3D b(D, vector>(D, vector(D, 0)));\n for (int x = 0; x < D; x++)\n for (int y = 0; y < D; y++)\n for (int z = 0; z < D; z++)\n if (f[z][x] == '1' && r[z][y] == '1') b[x][y][z] = 1;\n return b;\n}\n\nvector> findComponents(const Array3D& b) {\n Array3D vis(D, vector>(D, vector(D, 0)));\n vector> comps;\n const int dx[] = {1,-1,0,0,0,0}, dy[] = {0,0,1,-1,0,0}, dz[] = {0,0,0,0,1,-1};\n for (int x = 0; x < D; x++) for (int y = 0; y < D; y++) for (int z = 0; z < D; z++) {\n if (b[x][y][z] == 1 && !vis[x][y][z]) {\n vector comp; queue q; q.push({x,y,z}); vis[x][y][z] = 1;\n while (!q.empty()) {\n auto [cx,cy,cz] = q.front(); q.pop(); comp.push_back({cx,cy,cz});\n for (int d = 0; d < 6; d++) {\n int nx=cx+dx[d], ny=cy+dy[d], nz=cz+dz[d];\n if (0<=nx&&nx applyRotation(const vector& comp, int r1, int r2, int r3) {\n vector result;\n for (auto p : comp) {\n for (int i = 0; i < r1; i++) p = rotX(p);\n for (int i = 0; i < r2; i++) p = rotY(p);\n for (int i = 0; i < r3; i++) p = rotZ(p);\n result.push_back(p);\n }\n int minX=INT_MAX, minY=INT_MAX, minZ=INT_MAX;\n for (auto& [x,y,z] : result) { minX=min(minX,x); minY=min(minY,y); minZ=min(minZ,z); }\n for (auto& [x,y,z] : result) { x-=minX; y-=minY; z-=minZ; }\n sort(result.begin(), result.end());\n return result;\n}\n\nvector canonicalForm(const vector& comp) {\n vector best;\n for (int r1 = 0; r1 < 4; r1++) for (int r2 = 0; r2 < 4; r2++) for (int r3 = 0; r3 < 4; r3++) {\n vector rot = applyRotation(comp, r1, r2, r3);\n if (best.empty() || rot < best) best = rot;\n }\n return best;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> D;\n vector> f(2), r(2);\n for (int i = 0; i < 2; i++) { f[i] = readSilhouette(); r[i] = readSilhouette(); }\n \n auto b0 = buildMaxFill(f[0], r[0]);\n auto b1 = buildMaxFill(f[1], r[1]);\n auto comps0 = findComponents(b0);\n auto comps1 = findComponents(b1);\n int n0 = comps0.size(), n1 = comps1.size();\n \n map, vector> canonMap1;\n vector> canon0(n0), canon1(n1);\n for (int i = 0; i < n0; i++) canon0[i] = canonicalForm(comps0[i]);\n for (int j = 0; j < n1; j++) { canon1[j] = canonicalForm(comps1[j]); canonMap1[canon1[j]].push_back(j); }\n \n vector order0(n0); for (int i = 0; i < n0; i++) order0[i] = i;\n sort(order0.begin(), order0.end(), [&](int a, int b) { return comps0[a].size() > comps0[b].size(); });\n \n vector match0(n0, -1), match1(n1, -1);\n vector used1(n1, false);\n for (int i : order0) {\n auto it = canonMap1.find(canon0[i]);\n if (it != canonMap1.end()) {\n for (int j : it->second) {\n if (!used1[j]) { match0[i]=j; match1[j]=i; used1[j]=true; break; }\n }\n }\n }\n \n vector>> matched0(D, vector>(D, vector(D, false)));\n vector>> matched1(D, vector>(D, vector(D, false)));\n for (int i = 0; i < n0; i++) if (match0[i] != -1) {\n for (auto [x,y,z] : comps0[i]) matched0[x][y][z] = true;\n for (auto [x,y,z] : comps1[match0[i]]) matched1[x][y][z] = true;\n }\n \n Array3D remIsect(D, vector>(D, vector(D, 0)));\n for (int x = 0; x < D; x++) for (int y = 0; y < D; y++) for (int z = 0; z < D; z++)\n if (b0[x][y][z] && b1[x][y][z] && !matched0[x][y][z] && !matched1[x][y][z]) remIsect[x][y][z] = 1;\n \n auto sharedComps = findComponents(remIsect);\n vector>> isSharedIsect(D, vector>(D, vector(D, false)));\n for (auto& comp : sharedComps) for (auto [x,y,z] : comp) isSharedIsect[x][y][z] = true;\n \n Array3D remUn0(D, vector>(D, vector(D, 0)));\n Array3D remUn1(D, vector>(D, vector(D, 0)));\n for (int x = 0; x < D; x++) for (int y = 0; y < D; y++) for (int z = 0; z < D; z++) {\n if (b0[x][y][z] && !matched0[x][y][z] && !isSharedIsect[x][y][z]) remUn0[x][y][z] = 1;\n if (b1[x][y][z] && !matched1[x][y][z] && !isSharedIsect[x][y][z]) remUn1[x][y][z] = 1;\n }\n auto unsharedComps0 = findComponents(remUn0);\n auto unsharedComps1 = findComponents(remUn1);\n \n int nextId = 1;\n vector id0(n0, -1), id1(n1, -1);\n for (int i = 0; i < n0; i++) if (match0[i] != -1) { id0[i] = nextId; id1[match0[i]] = nextId++; }\n int nSI = sharedComps.size();\n vector sharedIsectId(nSI); for (int i = 0; i < nSI; i++) sharedIsectId[i] = nextId++;\n int nU0 = unsharedComps0.size(), nU1 = unsharedComps1.size();\n vector unsharedId0(nU0), unsharedId1(nU1);\n for (int i = 0; i < nU0; i++) unsharedId0[i] = nextId++;\n for (int i = 0; i < nU1; i++) unsharedId1[i] = nextId++;\n \n vector out0(D*D*D, 0), out1(D*D*D, 0);\n for (int i = 0; i < n0; i++) if (match0[i] != -1)\n for (auto [x,y,z] : comps0[i]) out0[x*D*D+y*D+z] = id0[i];\n for (int j = 0; j < n1; j++) if (match1[j] != -1)\n for (auto [x,y,z] : comps1[j]) out1[x*D*D+y*D+z] = id1[j];\n for (int c = 0; c < nSI; c++) for (auto [x,y,z] : sharedComps[c]) {\n out0[x*D*D+y*D+z] = sharedIsectId[c]; out1[x*D*D+y*D+z] = sharedIsectId[c];\n }\n for (int c = 0; c < nU0; c++) for (auto [x,y,z] : unsharedComps0[c]) out0[x*D*D+y*D+z] = unsharedId0[c];\n for (int c = 0; c < nU1; c++) for (auto [x,y,z] : unsharedComps1[c]) out1[x*D*D+y*D+z] = unsharedId1[c];\n \n cout << nextId - 1 << \"\\n\";\n for (int j = 0; j < D*D*D; j++) { if (j) cout << \" \"; cout << out0[j]; }\n cout << \"\\n\";\n for (int j = 0; j < D*D*D; j++) { if (j) cout << \" \"; cout << out1[j]; }\n cout << \"\\n\";\n return 0;\n}","ahc020":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n \n vector>> adj(N);\n vector u(M), v(M), w(M);\n for (int j = 0; j < M; j++) {\n cin >> u[j] >> v[j] >> w[j];\n u[j]--; v[j]--;\n adj[u[j]].push_back({v[j], j});\n adj[v[j]].push_back({u[j], j});\n }\n \n vector a(K), b(K);\n for (int k = 0; k < K; k++) cin >> a[k] >> b[k];\n \n vector> res_dist(K, vector(N));\n vector> closest(K);\n for (int k = 0; k < K; k++) {\n vector> dists;\n for (int i = 0; i < N; i++) {\n double dx = a[k] - x[i], dy = b[k] - y[i];\n res_dist[k][i] = sqrt(dx*dx + dy*dy);\n dists.push_back({res_dist[k][i], i});\n }\n sort(dists.begin(), dists.end());\n for (int j = 0; j < min(10, N); j++) closest[k].push_back(dists[j].second);\n }\n \n vector sp_dist(N, LLONG_MAX);\n vector parent(N, -1);\n sp_dist[0] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, 0});\n while (!pq.empty()) {\n auto [d, v] = pq.top(); pq.pop();\n if (d > sp_dist[v]) continue;\n for (auto [to, eid] : adj[v]) {\n if (sp_dist[v] + w[eid] < sp_dist[to]) {\n sp_dist[to] = sp_dist[v] + w[eid];\n parent[to] = v;\n pq.push({sp_dist[to], to});\n }\n }\n }\n \n vector assignment(K);\n for (int k = 0; k < K; k++) assignment[k] = closest[k][0];\n \n auto compute_P = [&]() {\n vector max_dist(N, 0);\n for (int k = 0; k < K; k++)\n max_dist[assignment[k]] = max(max_dist[assignment[k]], res_dist[k][assignment[k]]);\n vector P(N, 0);\n for (int i = 0; i < N; i++)\n if (max_dist[i] > 0) P[i] = min((int)ceil(max_dist[i]), 5000);\n return P;\n };\n \n auto compute_B = [&](const vector& P) {\n vector B(M, 0);\n for (int i = 1; i < N; i++) {\n if (P[i] > 0) {\n int cur = i;\n while (cur != 0) {\n int p = parent[cur];\n if (p == -1) break;\n for (auto& [to, eid] : adj[cur])\n if (to == p) { B[eid] = 1; break; }\n cur = p;\n }\n }\n }\n return B;\n };\n \n auto compute_cost = [&](const vector& P, const vector& B) {\n long long cost = 0;\n for (int i = 0; i < N; i++) cost += (long long)P[i] * P[i];\n for (int j = 0; j < M; j++) if (B[j]) cost += w[j];\n return cost;\n };\n \n vector P = compute_P();\n vector B = compute_B(P);\n long long cost = compute_cost(P, B);\n \n mt19937 rng(42);\n uniform_real_distribution<> uniform(0.0, 1.0);\n double start_temp = 1e7, end_temp = 1e1;\n int max_iter = 150000;\n \n for (int iter = 0; iter < max_iter; iter++) {\n double temp = start_temp * pow(end_temp / start_temp, (double)iter / max_iter);\n int k = rng() % K;\n int old_assign = assignment[k];\n int new_assign = closest[k][rng() % closest[k].size()];\n if (new_assign == old_assign) continue;\n \n assignment[k] = new_assign;\n vector new_P = compute_P();\n vector new_B = compute_B(new_P);\n long long new_cost = compute_cost(new_P, new_B);\n \n long long delta = new_cost - cost;\n if (delta < 0 || uniform(rng) < exp(-(double)delta / temp)) {\n cost = new_cost; P = new_P; B = new_B;\n } else {\n assignment[k] = old_assign;\n }\n }\n \n for (int i = 0; i < N; i++) cout << P[i] << (i < N-1 ? \" \" : \"\\n\");\n for (int j = 0; j < M; j++) cout << B[j] << (j < M-1 ? \" \" : \"\\n\");\n return 0;\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint grid[N][N];\nvector> swaps;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++)\n for (int y = 0; y <= x; y++)\n cin >> grid[x][y];\n \n auto siftDown = [&](int x, int y) {\n while (x < N - 1) {\n int lv = grid[x+1][y], rv = grid[x+1][y+1], cv = grid[x][y];\n if (cv <= lv && cv <= rv) break;\n if (lv <= rv) {\n swap(grid[x][y], grid[x+1][y]);\n swaps.push_back({x, y, x+1, y});\n x++;\n } else {\n swap(grid[x][y], grid[x+1][y+1]);\n swaps.push_back({x, y, x+1, y+1});\n x++; y++;\n }\n if (swaps.size() >= 9999) return;\n }\n };\n \n // Heapify: bottom to top, full sift-down\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n siftDown(x, y);\n if (swaps.size() >= 9999) goto done;\n }\n }\n \n // Iteratively fix remaining violations\n // (caused by triangular grid's dual-parent structure)\n for (int iter = 0; iter < 500; iter++) {\n bool any = false;\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n if (grid[x][y] > grid[x+1][y] || grid[x][y] > grid[x+1][y+1]) {\n any = true;\n // One-step fix: swap parent with smaller child\n if (grid[x+1][y] <= grid[x+1][y+1]) {\n swap(grid[x][y], grid[x+1][y]);\n swaps.push_back({x, y, x+1, y});\n } else {\n swap(grid[x][y], grid[x+1][y+1]);\n swaps.push_back({x, y, x+1, y+1});\n }\n if (swaps.size() >= 9999) goto done;\n }\n }\n }\n if (!any) break;\n }\n \ndone:\n cout << swaps.size() << \"\\n\";\n for (auto& s : swaps)\n cout << s[0] << \" \" << s[1] << \" \" << s[2] << \" \" << s[3] << \"\\n\";\n \n return 0;\n}","toyota2023summer-final":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int D, N;\n cin >> D >> N;\n \n vector> is_obstacle(D, vector(D, false));\n for (int i = 0; i < N; i++) {\n int ri, rj;\n cin >> ri >> rj;\n is_obstacle[ri][rj] = true;\n }\n \n int entrance_i = 0, entrance_j = (D - 1) / 2;\n \n vector> dist(D, vector(D, -1));\n queue> q;\n q.push({entrance_i, entrance_j});\n dist[entrance_i][entrance_j] = 0;\n \n const int di[] = {-1, 1, 0, 0};\n const int dj[] = {0, 0, -1, 1};\n \n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && dist[ni][nj] == -1 && !is_obstacle[ni][nj]) {\n dist[ni][nj] = dist[i][j] + 1;\n q.push({ni, nj});\n }\n }\n }\n \n vector> cells;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (!(i == entrance_i && j == entrance_j) && !is_obstacle[i][j])\n cells.push_back({dist[i][j], i, j});\n \n sort(cells.begin(), cells.end());\n int M = cells.size();\n \n set available_ranks;\n for (int k = 0; k < M; k++) available_ranks.insert(k);\n \n vector> container_at(D, vector(D, -1));\n \n for (int d = 0; d < M; d++) {\n int t; cin >> t;\n int target_rank = t;\n \n auto it = available_ranks.lower_bound(target_rank);\n int best_rank = -1, best_diff = M + 1;\n \n if (it != available_ranks.end() && abs(*it - target_rank) < best_diff) {\n best_diff = abs(*it - target_rank);\n best_rank = *it;\n }\n if (it != available_ranks.begin()) {\n --it;\n if (abs(*it - target_rank) < best_diff) {\n best_diff = abs(*it - target_rank);\n best_rank = *it;\n }\n }\n \n available_ranks.erase(best_rank);\n auto [dd, pi, pj] = cells[best_rank];\n cout << pi << \" \" << pj << endl;\n container_at[pi][pj] = t;\n }\n \n vector> is_empty(D, vector(D, false));\n is_empty[entrance_i][entrance_j] = true;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (is_obstacle[i][j]) is_empty[i][j] = true;\n \n for (int iter = 0; iter < M; iter++) {\n vector> accessible(D, vector(D, false));\n queue> bfs_q;\n bfs_q.push({entrance_i, entrance_j});\n accessible[entrance_i][entrance_j] = true;\n \n while (!bfs_q.empty()) {\n auto [i, j] = bfs_q.front(); bfs_q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && !accessible[ni][nj] && is_empty[ni][nj]) {\n accessible[ni][nj] = true;\n bfs_q.push({ni, nj});\n }\n }\n }\n \n int min_t = M + 1, min_i = -1, min_j = -1;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (container_at[i][j] >= 0 && accessible[i][j] && container_at[i][j] < min_t) {\n min_t = container_at[i][j];\n min_i = i; min_j = j;\n }\n \n cout << min_i << \" \" << min_j << endl;\n is_empty[min_i][min_j] = true;\n container_at[min_i][min_j] = -1;\n }\n \n return 0;\n}","ahc024":"#include \nusing namespace std;\n\nconst int N = 50;\nconst int M = 100;\nconst int dx[] = {0, 0, 1, -1};\nconst int dy[] = {1, -1, 0, 0};\n\nint n, m;\nint grid[N][N], best_grid[N][N];\nint best_score;\nset> required_adj;\nint adj_cnt[M+1][M+1];\n\nbool valid(int x, int y) { return 0 <= x && x < n && 0 <= y && y < n; }\n\nvoid compute_init_adj() {\n memset(adj_cnt, 0, sizeof(adj_cnt));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) {\n if (j+1 < n && grid[i][j] != grid[i][j+1])\n adj_cnt[min(grid[i][j],grid[i][j+1])][max(grid[i][j],grid[i][j+1])]++;\n if (i+1 < n && grid[i][j] != grid[i+1][j])\n adj_cnt[min(grid[i][j],grid[i+1][j])][max(grid[i][j],grid[i+1][j])]++;\n if (i==0||i==n-1||j==0||j==n-1)\n adj_cnt[0][grid[i][j]]++;\n }\n for (int a = 0; a <= m; a++)\n for (int b = a; b <= m; b++)\n if (adj_cnt[a][b] > 0) required_adj.insert({a,b});\n}\n\nbool check_c0_conn() {\n bool has0 = false;\n for (int i = 0; i < n && !has0; i++)\n for (int j = 0; j < n && !has0; j++)\n if (grid[i][j] == 0) has0 = true;\n if (!has0) return true;\n \n vector> vis(n, vector(n));\n queue> q;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0 && (i==0||i==n-1||j==0||j==n-1))\n { q.push({i,j}); vis[i][j] = true; }\n \n while (!q.empty()) {\n auto [x,y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx=x+dx[d], ny=y+dy[d];\n if (valid(nx,ny) && !vis[nx][ny] && grid[nx][ny]==0)\n { vis[nx][ny] = true; q.push({nx,ny}); }\n }\n }\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0 && !vis[i][j]) return false;\n return true;\n}\n\nbool can_change(int i, int j, int nc) {\n int oc = grid[i][j];\n if (oc == nc) return true;\n if (nc != 0) {\n bool found = false;\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj) && grid[ni][nj] == nc) { found = true; break; }\n }\n if (!found) return false;\n }\n map,int> delta;\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj)) {\n int c = grid[ni][nj];\n if (oc != c) delta[{min(oc,c),max(oc,c)}]--;\n if (nc != c) delta[{min(nc,c),max(nc,c)}]++;\n }\n }\n if (i==0||i==n-1||j==0||j==n-1) {\n if (oc != 0) delta[{0,oc}]--;\n if (nc != 0) delta[{0,nc}]++;\n }\n for (auto& [p,d] : delta) {\n int ncnt = adj_cnt[p.first][p.second] + d;\n if (ncnt > 0 && required_adj.find(p) == required_adj.end()) return false;\n if (ncnt <= 0 && required_adj.find(p) != required_adj.end()) return false;\n }\n grid[i][j] = nc;\n bool ok = check_c0_conn();\n grid[i][j] = oc;\n return ok;\n}\n\nvoid apply_change(int i, int j, int nc) {\n int oc = grid[i][j];\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj)) {\n int c = grid[ni][nj];\n if (oc != c) adj_cnt[min(oc,c)][max(oc,c)]--;\n if (nc != c) adj_cnt[min(nc,c)][max(nc,c)]++;\n }\n }\n if (i==0||i==n-1||j==0||j==n-1) {\n if (oc != 0) adj_cnt[0][oc]--;\n if (nc != 0) adj_cnt[0][nc]++;\n }\n grid[i][j] = nc;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> n >> m;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) cin >> grid[i][j];\n \n compute_init_adj();\n memcpy(best_grid, grid, sizeof(grid));\n best_score = 2501;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) best_score++;\n \n bool improved = true;\n while (improved) {\n improved = false;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) {\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj) && grid[ni][nj] != 0)\n if (can_change(i, j, grid[ni][nj])) {\n apply_change(i, j, grid[ni][nj]);\n improved = true;\n break;\n }\n }\n }\n }\n \n int cnt0 = 0;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) cnt0++;\n if (cnt0+1 < best_score) {\n best_score = cnt0+1;\n memcpy(best_grid, grid, sizeof(grid));\n }\n \n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << best_grid[i][j];\n if (j < n-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n return 0;\n}","ahc025":"#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, D, Q;\nint qc = 0;\nint cmp[105][105];\n\nchar query(int a, int b) {\n if (cmp[a][b] != 0) return cmp[a][b] == 1 ? '>' : '<';\n if (qc >= Q) return '=';\n \n qc++;\n cout << \"1 1 \" << a << \" \" << b << endl;\n char res;\n cin >> res;\n \n if (res == '<') {\n cmp[a][b] = -1;\n cmp[b][a] = 1;\n } else if (res == '>') {\n cmp[a][b] = 1;\n cmp[b][a] = -1;\n }\n return res;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n vector items(N);\n for (int i = 0; i < N; i++) items[i] = i;\n \n // Insertion sort using comparisons\n for (int i = 1; i < N; i++) {\n int j = i;\n while (j > 0 && qc < Q) {\n int a = items[j-1], b = items[j];\n if (cmp[a][b] == 1) {\n swap(items[j-1], items[j]);\n j--;\n } else if (cmp[a][b] == -1) {\n break;\n } else {\n char res = query(a, b);\n if (res == '>') {\n swap(items[j-1], items[j]);\n j--;\n } else {\n break;\n }\n }\n }\n }\n \n // Use remaining queries to verify sort\n for (int i = 1; i < N && qc < Q; i++) {\n if (cmp[items[i-1]][items[i]] == 0) {\n query(items[i-1], items[i]);\n }\n }\n \n // Use remaining queries for random comparisons\n mt19937 rng(42);\n while (qc < Q) {\n int x = rng() % N, y = rng() % N;\n if (x != y && cmp[x][y] == 0) {\n query(x, y);\n }\n }\n \n // Estimate weights using exponential distribution assumption\n vector est_weight(N);\n for (int i = 0; i < N; i++) {\n double p = (double)(i + 1) / (N + 1);\n est_weight[items[i]] = -log(1.0 - p);\n }\n \n // LPT partitioning: assign heaviest items first to lightest group\n vector group_weight(D, 0);\n vector assignment(N);\n \n for (int i = N - 1; i >= 0; i--) {\n int item = items[i];\n int min_group = 0;\n for (int g = 1; g < D; g++) {\n if (group_weight[g] < group_weight[min_group]) {\n min_group = g;\n }\n }\n assignment[item] = min_group;\n group_weight[min_group] += est_weight[item];\n }\n \n // Output assignment\n for (int i = 0; i < N; i++) {\n cout << assignment[i];\n if (i < N - 1) cout << \" \";\n }\n cout << endl;\n \n return 0;\n}","ahc026":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n for (int i = 0; i < m; i++) {\n stacks[i].resize(n / m);\n for (int j = 0; j < n / m; j++) {\n cin >> stacks[i][j];\n }\n }\n \n vector box_stack(n + 1), box_pos(n + 1);\n for (int i = 0; i < m; i++) {\n for (int j = 0; j < (int)stacks[i].size(); j++) {\n box_stack[stacks[i][j]] = i;\n box_pos[stacks[i][j]] = j;\n }\n }\n \n vector> operations;\n \n for (int v = 1; v <= n; v++) {\n int sid = box_stack[v], pos = box_pos[v];\n int cur = (int)stacks[sid].size() - 1;\n \n while (cur > pos) {\n int run_end = cur;\n int run_start = cur;\n \n while (run_start > pos + 1 && stacks[sid][run_start - 1] > stacks[sid][run_start]) {\n run_start--;\n }\n \n int max_in_run = stacks[sid][run_start];\n \n int dest = -1;\n int best_score = INT_MAX;\n int best_secondary = INT_MIN;\n \n for (int i = 0; i < m; i++) {\n if (i == sid) continue;\n \n int score;\n int secondary;\n \n if (stacks[i].empty()) {\n score = 0;\n secondary = -1;\n } else {\n int top_val = stacks[i].back();\n if (top_val > max_in_run) {\n score = 0;\n secondary = -top_val;\n } else {\n score = 0;\n for (int j = run_start; j <= run_end; j++) {\n if (stacks[sid][j] > top_val) score++;\n }\n secondary = top_val;\n }\n }\n \n if (score < best_score || (score == best_score && secondary > best_secondary)) {\n best_score = score;\n best_secondary = secondary;\n dest = i;\n }\n }\n \n if (dest == -1) dest = (sid + 1) % m;\n \n int u = stacks[sid][run_start];\n operations.push_back({u, dest + 1});\n \n vector moved(stacks[sid].begin() + run_start, stacks[sid].begin() + run_end + 1);\n stacks[sid].resize(run_start);\n stacks[dest].insert(stacks[dest].end(), moved.begin(), moved.end());\n \n for (int j = 0; j < (int)moved.size(); j++) {\n box_stack[moved[j]] = dest;\n box_pos[moved[j]] = stacks[dest].size() - moved.size() + j;\n }\n \n cur = run_start - 1;\n }\n \n operations.push_back({v, 0});\n stacks[sid].pop_back();\n }\n \n for (auto& op : operations) {\n cout << op.first << \" \" << op.second << endl;\n }\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\nchar dir_char[] = {'R', 'D', 'L', 'U'};\n\nbool can_move(int i, int j, int dir) {\n int ni = i + dx[dir], nj = j + dy[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0 && v[i][j] == '1') return false;\n if (dir == 1 && h[i][j] == '1') return false;\n if (dir == 2 && v[i][nj] == '1') return false;\n if (dir == 3 && h[ni][j] == '1') return false;\n return true;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1); v.resize(N); d.resize(N, vector(N));\n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> d[i][j];\n \n vector> dist(N, vector(N, -1)), prev_dir(N, vector(N, -1));\n queue> q; dist[0][0] = 0; q.push({0, 0});\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(i, j, dir)) continue;\n int ni = i + dx[dir], nj = j + dy[dir];\n if (dist[ni][nj] == -1) { dist[ni][nj] = dist[i][j] + 1; prev_dir[ni][nj] = dir; q.push({ni, nj}); }\n }\n }\n \n string result;\n vector> visited(N, vector(N, false));\n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n vector> neighbors;\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(i, j, dir)) continue;\n int ni = i + dx[dir], nj = j + dy[dir];\n if (!visited[ni][nj]) neighbors.push_back({ni, nj});\n }\n sort(neighbors.begin(), neighbors.end(), [](auto& a, auto& b) { return d[a.first][a.second] > d[b.first][b.second]; });\n for (auto [ni, nj] : neighbors) {\n for (int dir = 0; dir < 4; dir++) {\n if (i + dx[dir] == ni && j + dy[dir] == nj) {\n result += dir_char[dir]; dfs(ni, nj); result += dir_char[(dir + 2) % 4]; break;\n }\n }\n }\n };\n dfs(0, 0);\n \n vector visit_count(N * N, 0);\n int ci = 0, cj = 0; visit_count[0]++;\n for (char c : result) {\n int dir = (c == 'R') ? 0 : (c == 'D') ? 1 : (c == 'L') ? 2 : 3;\n ci += dx[dir]; cj += dy[dir]; visit_count[ci * N + cj]++;\n }\n \n using Cell = tuple;\n priority_queue pq;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (i == 0 && j == 0) continue;\n int k = visit_count[i * N + j];\n double cost = 2.0 * dist[i][j];\n if (cost > 0) pq.push({(double)d[i][j] / (k * (k + 1)) / cost, i, j});\n }\n \n while (!pq.empty() && result.size() < 100000) {\n auto [p, i, j] = pq.top(); pq.pop();\n int k = visit_count[i * N + j];\n double cost = 2.0 * dist[i][j];\n double new_p = (double)d[i][j] / (k * (k + 1)) / cost;\n if (abs(new_p - p) > 1e-9) { pq.push({new_p, i, j}); continue; }\n \n string path_to, path_back;\n int ci2 = i, cj2 = j;\n while (ci2 != 0 || cj2 != 0) { int dir = prev_dir[ci2][cj2]; path_to += dir_char[dir]; ci2 -= dx[dir]; cj2 -= dy[dir]; }\n reverse(path_to.begin(), path_to.end());\n for (int k2 = path_to.size() - 1; k2 >= 0; k2--) {\n char c = path_to[k2];\n path_back += (c == 'R') ? 'L' : (c == 'D') ? 'U' : (c == 'L') ? 'R' : 'D';\n }\n string detour = path_to + path_back;\n if (result.size() + detour.size() <= 100000) {\n result += detour; visit_count[i * N + j]++;\n int nk = visit_count[i * N + j];\n pq.push({(double)d[i][j] / (nk * (nk + 1)) / cost, i, j});\n }\n }\n \n cout << result << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N,M; cin>>N>>M;\n int si,sj; cin>>si>>sj;\n vector A(N);\n for(int i=0;i>A[i];\n vector t(M);\n for(int i=0;i>t[i];\n \n vector>> cp(26);\n for(int i=0;i> cd(26,vector(26,0));\n for(int c1=0;c1<26;c1++) for(int c2=0;c2<26;c2++){\n int md=INT_MAX;\n for(auto&[i1,j1]:cp[c1]) for(auto&[i2,j2]:cp[c2]) md=min(md,abs(i1-i2)+abs(j1-j2));\n cd[c1][c2]=md;\n }\n \n vector> ov(M,vector(M,0));\n for(int i=0;i=1;l--){ bool ok=true;\n for(int k=0;k& o){ string s=t[o[0]];\n for(int i=1;ivector{ vector o; o.push_back(st);\n vector u(M,false); u[st]=true;\n for(int s=1;s c;\n for(int j=0;jbo){bo=ov[l][j];c.clear();c.push_back(j);}\n else if(ov[l][j]==bo) c.push_back(j);}\n o.push_back(c[rng()%c.size()]); u[o.back()]=true;} return o;};\n \n auto greedyK=[&](int st)->vector{ vector o; o.push_back(st);\n vector u(M,false); u[st]=true;\n for(int s=1;sbo||(v==bo&&d o)->vector{ bool imp=true;\n while(imp){ imp=false; for(int i=0;i0){os+=ov[o[i-1]][o[i]];ns+=ov[o[i-1]][o[i+1]];}\n os+=ov[o[i]][o[i+1]];ns+=ov[o[i+1]][o[i]];\n if(i+2os){swap(o[i],o[i+1]);imp=true;}}} return o;};\n \n auto orOpt=[&](vector o)->vector{\n for(int it=0;it<5;it++){ bool imp=false;\n for(int i=0;i0) rd-=ov[o[i-1]][w]; if(i0&&i rm; for(int k=0;k0) id+=ov[rm[k-1]][w]; if(k0&&kbd){bd=rd+id;bk=k;}}\n if(bk!=i){ o.clear();\n for(int k=0;kint{ int L=s.size();\n vector cur(225,INF); cur[si*15+sj]=0;\n for(int i=0;i nx(225,INF); int ci=s[i]-'A';\n for(int q=0;q<225;q++){ if(cur[q]>=INF) continue;\n int qi=q/15,qj=q%15;\n for(auto&[pi,pj]:cp[ci]){ int p=pi*15+pj;\n int nc=cur[q]+abs(pi-qi)+abs(pj-qj)+1;\n if(nc>> cs;\n for(int s=0;s>> dp(L+1,vector>(225,{INF,-1}));\n dp[0][si*15+sj]={0,-1};\n for(int i=0;i=INF) continue;\n int qi=q/15,qj=q%15;\n for(auto&[pi,pj]:cp[ci]){ int p=pi*15+pj;\n int nc=dp[i][q].first+abs(pi-qi)+abs(pj-qj)+1;\n if(nc pp(L); int cr=be;\n for(int i=L-1;i>=0;i--){pp[i]=cr;cr=dp[i+1][cr].second;}\n for(int i=0;i\nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nvector max_di, max_dj;\nvector>> positions;\nvector>>> pos_cells;\nint known[25][25];\nint query_count = 0;\nvector> w;\ndouble cov[25][25];\n\nint drill_cell(int i, int j) {\n cout << \"q 1 \" << i << \" \" << j << endl;\n cout.flush();\n int v; cin >> v;\n known[i][j] = v;\n query_count++;\n return v;\n}\n\nint divine_cells(vector>& cells) {\n int k = cells.size();\n cout << \"q \" << k;\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << endl;\n cout.flush();\n int v; cin >> v;\n query_count++;\n return v;\n}\n\nvoid submit_answer(vector>& cells) {\n sort(cells.begin(), cells.end());\n cells.erase(unique(cells.begin(), cells.end()), cells.end());\n cout << \"a \" << cells.size();\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << endl;\n cout.flush();\n int r; cin >> r;\n if (r == 1) exit(0);\n}\n\nvoid update_coverage() {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cov[i][j] = 0;\n for (int k = 0; k < M; k++) {\n double total = accumulate(w[k].begin(), w[k].end(), 0.0);\n if (total < 1e-10) continue;\n for (int p = 0; p < (int)positions[k].size(); p++) {\n double wt = w[k][p] / total;\n for (auto& [ci, cj] : pos_cells[k][p]) cov[ci][cj] += wt;\n }\n }\n}\n\nvoid update_divine(const vector>& qcells, int obs) {\n int ksz = qcells.size();\n set> cs(qcells.begin(), qcells.end());\n for (int k = 0; k < M; k++) {\n double others = 0;\n for (int k2 = 0; k2 < M; k2++) if (k2 != k) {\n double t2 = accumulate(w[k2].begin(), w[k2].end(), 0.0);\n if (t2 < 1e-10) continue;\n for (int p2 = 0; p2 < (int)positions[k2].size(); p2++) {\n int cnt = 0;\n for (auto& [ci, cj] : pos_cells[k2][p2]) if (cs.count({ci, cj})) cnt++;\n others += w[k2][p2] / t2 * cnt;\n }\n }\n for (int p = 0; p < (int)positions[k].size(); p++) {\n int cnt = 0;\n for (auto& [ci, cj] : pos_cells[k][p]) if (cs.count({ci, cj})) cnt++;\n double ev = others + cnt;\n double mean = ksz * eps + ev * (1 - 2 * eps);\n double var = ksz * eps * (1 - eps);\n double diff = obs - mean;\n w[k][p] *= exp(-diff * diff / (2 * var));\n }\n double total = accumulate(w[k].begin(), w[k].end(), 0.0);\n if (total > 1e-10) for (auto& wp : w[k]) wp /= total;\n }\n update_coverage();\n}\n\nvoid update_drill(int i, int j, int obs) {\n for (int k = 0; k < M; k++) {\n double others = 0;\n for (int k2 = 0; k2 < M; k2++) if (k2 != k) {\n double t2 = accumulate(w[k2].begin(), w[k2].end(), 0.0);\n if (t2 < 1e-10) continue;\n for (int p2 = 0; p2 < (int)positions[k2].size(); p2++)\n for (auto& [ci, cj] : pos_cells[k2][p2])\n if (ci == i && cj == j) { others += w[k2][p2] / t2; break; }\n }\n for (int p = 0; p < (int)positions[k].size(); p++) {\n bool covers = false;\n for (auto& [ci, cj] : pos_cells[k][p]) if (ci == i && cj == j) { covers = true; break; }\n double ev = others + (covers ? 1.0 : 0.0);\n double diff = obs - ev;\n double var = max(0.3, ev * 0.5);\n w[k][p] *= exp(-diff * diff / (2 * var));\n }\n double total = accumulate(w[k].begin(), w[k].end(), 0.0);\n if (total > 1e-10) for (auto& wp : w[k]) wp /= total;\n }\n update_coverage();\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> M >> eps;\n shapes.resize(M);\n for (int k = 0; k < M; k++) {\n int d; cin >> d;\n shapes[k].resize(d);\n for (int l = 0; l < d; l++) cin >> shapes[k][l].first >> shapes[k][l].second;\n }\n max_di.resize(M); max_dj.resize(M);\n for (int k = 0; k < M; k++) {\n max_di[k] = max_dj[k] = 0;\n for (auto& [i, j] : shapes[k]) { max_di[k] = max(max_di[k], i); max_dj[k] = max(max_dj[k], j); }\n }\n for (int k = 0; k < M; k++) {\n vector> pos;\n vector>> cells;\n for (int di = 0; di <= N - 1 - max_di[k]; di++)\n for (int dj = 0; dj <= N - 1 - max_dj[k]; dj++) {\n pos.push_back({di, dj});\n vector> c;\n for (auto& [i, j] : shapes[k]) c.push_back({di + i, dj + j});\n cells.push_back(c);\n }\n positions.push_back(pos);\n pos_cells.push_back(cells);\n }\n memset(known, -1, sizeof(known));\n for (int k = 0; k < M; k++) w.push_back(vector(positions[k].size(), 1.0));\n update_coverage();\n \n for (int i = 0; i < N && query_count < 2*N*N; i++) {\n vector> cells;\n for (int j = 0; j < N; j++) cells.push_back({i, j});\n update_divine(cells, divine_cells(cells));\n }\n for (int j = 0; j < N && query_count < 2*N*N; j++) {\n vector> cells;\n for (int i = 0; i < N; i++) cells.push_back({i, j});\n update_divine(cells, divine_cells(cells));\n }\n \n while (query_count < 2*N*N - 1) {\n int bi = -1, bj = -1; double bs = -1e9;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) continue;\n double p = 1.0 - exp(-cov[i][j]); p = max(0.01, min(0.99, p));\n double ent = -p*log(p) - (1-p)*log(1-p);\n if (ent > bs) { bs = ent; bi = i; bj = j; }\n }\n if (bi < 0) break;\n update_drill(bi, bj, drill_cell(bi, bj));\n }\n \n vector> ans;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] > 0) ans.push_back({i, j});\n else if (known[i][j] < 0 && 1.0 - exp(-cov[i][j]) > 0.5) ans.push_back({i, j});\n }\n submit_answer(ans);\n return 0;\n}","ahc031":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint W, D, N;\nvector> a;\n\nvector get_bounds(const vector& h) {\n vector b; int y=0;\n for(int k=0;k& b1, const vector& b2) {\n int i=0,j=0; long long c=0;\n while(i<(int)b1.size()&&j<(int)b2.size()){\n if(b1[i]==b2[j]){i++;j++;}\n else if(b1[i]& h) {\n long long c=0;\n for(int k=0;karea)c+=100LL*(a[d][k]-area);}\n return c;\n}\n\nvector greedy_day(int d) {\n vector h(N,1); int rem=W-N;\n while(rem>0){\n int bk=-1; long long br=-1;\n for(int k=0;kbr||(r==br&&a[d][k]>(bk>=0?a[d][bk]:0))){br=r;bk=k;}\n }\n if(bk==-1)break;\n h[bk]++;rem--;\n }\n return h;\n}\n\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n cin>>W>>D>>N;\n a.resize(D,vector(N));\n for(int d=0;d>a[d][k];\n \n mt19937 rng(42);\n uniform_real_distribution uni(0,1);\n \n // Greedy fixed layout\n vector fixed_h(N,1);\n {int rem=W-N;\n while(rem>0){\n int bk=-1;long long bs=-1;\n for(int k=0;kbs||(s==bs&&a[0][k]>(bk>=0?a[0][bk]:0))){bs=s;bk=k;}\n }\n if(bk==-1)break;fixed_h[bk]++;rem--;\n }}\n \n // SA for fixed layout\n {vector ch=fixed_h;\n long long cc=0;for(int d=0;d bh=ch;\n auto st=chrono::high_resolution_clock::now();\n while(true){\n auto nw=chrono::high_resolution_clock::now();\n double el=chrono::duration(nw-st).count();\n if(el>1.0)break;\n int k1=rng()%N,k2=rng()%N;\n if(k1==k2||ch[k1]<=1)continue;\n long long delta=0;\n for(int d=0;duni(rng)){\n ch[k1]--;ch[k2]++;cc+=delta;\n if(cc> heights(D);\n for(int d=0;d> cur_h(D,fixed_h);\n auto total_cost=[&](const vector>& h)->long long{\n long long c=0;\n for(int d=0;d> best_h=cur_h;\n \n // Also check per-day greedy cost\n {long long pc=total_cost(heights);\n if(pc(nw-st).count();\n if(el>1.8)break;\n \n int d=rng()%D;\n int k1=rng()%N,k2=rng()%N;\n if(k1==k2||cur_h[d][k1]<=1)continue;\n \n long long dd=0;\n dd+=100LL*(max(0,a[d][k1]-(cur_h[d][k1]-1)*W)-max(0,a[d][k1]-cur_h[d][k1]*W));\n dd+=100LL*(max(0,a[d][k2]-(cur_h[d][k2]+1)*W)-max(0,a[d][k2]-cur_h[d][k2]*W));\n \n vector ob=get_bounds(cur_h[d]);\n cur_h[d][k1]--;cur_h[d][k2]++;\n vector nb=get_bounds(cur_h[d]);\n \n long long pd=0;\n if(d>0){vector pb=get_bounds(cur_h[d-1]);pd+=(bound_changes(pb,nb)-bound_changes(pb,ob))*W;}\n if(d nb2=get_bounds(cur_h[d+1]);pd+=(bound_changes(nb,nb2)-bound_changes(ob,nb2))*W;}\n \n long long delta=dd+pd;\n double temp=5e6*max(1e-4,1.0-el/1.8);\n if(delta<=0||exp(-(double)delta/temp)>uni(rng)){\n cur_cost+=delta;\n if(cur_cost\nusing namespace std;\n\nconst long long MOD = 998244353;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n vector> a(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> a[i][j];\n \n vector>> s(M, vector>(3, vector(3)));\n for (int m = 0; m < M; m++)\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n cin >> s[m][i][j];\n \n vector> bmod = a;\n vector> ops;\n \n for (int k = 0; k < K; k++) {\n int best_m = -1, best_p = -1, best_q = -1;\n long long best_delta = 0;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N - 3; p++)\n for (int q = 0; q <= N - 3; q++) {\n long long delta = 0;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++) {\n long long nm = (bmod[p+i][q+j] + s[m][i][j]) % MOD;\n delta += nm - bmod[p+i][q+j];\n }\n if (delta > best_delta) { best_delta = delta; best_m = m; best_p = p; best_q = q; }\n }\n if (best_m == -1) break;\n ops.push_back({best_m, best_p, best_q});\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n bmod[best_p+i][best_q+j] = (bmod[best_p+i][best_q+j] + s[best_m][i][j]) % MOD;\n }\n \n long long score = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n score += bmod[i][j];\n \n long long best_score = score;\n auto best_ops = ops;\n \n mt19937 rng(42);\n uniform_real_distribution uni(0.0, 1.0);\n double start_temp = 2e9, end_temp = 1e5;\n auto start_time = chrono::high_resolution_clock::now();\n \n while (true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n if (elapsed > 1.8) break;\n double temp = start_temp * pow(end_temp / start_temp, elapsed / 1.8);\n \n int r = rng() % 100;\n long long delta = 0;\n int idx, new_m, new_p, new_q, old_m, old_p, old_q;\n int move_type = 0;\n \n if (r < 8 && (int)ops.size() < K) {\n move_type = 1;\n new_m = rng() % M; new_p = rng() % (N-2); new_q = rng() % (N-2);\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++) {\n int ci = new_p+i, cj = new_q+j;\n long long nv = (bmod[ci][cj] + s[new_m][i][j]) % MOD;\n delta += nv - bmod[ci][cj];\n }\n } else if (r < 12 && (int)ops.size() > 0) {\n move_type = 2;\n idx = rng() % ops.size();\n tie(old_m, old_p, old_q) = ops[idx];\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++) {\n int ci = old_p+i, cj = old_q+j;\n long long nv = (bmod[ci][cj] - s[old_m][i][j] + MOD) % MOD;\n delta += nv - bmod[ci][cj];\n }\n } else if ((int)ops.size() > 0) {\n move_type = 3;\n idx = rng() % ops.size();\n tie(old_m, old_p, old_q) = ops[idx];\n new_m = old_m; new_p = old_p; new_q = old_q;\n int ch = rng() % 4;\n if (ch == 0) new_m = rng() % M;\n else if (ch == 1) new_p = rng() % (N-2);\n else if (ch == 2) new_q = rng() % (N-2);\n else { new_m = rng() % M; new_p = rng() % (N-2); new_q = rng() % (N-2); }\n if (new_m == old_m && new_p == old_p && new_q == old_q) continue;\n \n long long saved[3][3];\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++) {\n int ci = old_p+i, cj = old_q+j;\n saved[i][j] = bmod[ci][cj];\n long long nv = (bmod[ci][cj] - s[old_m][i][j] + MOD) % MOD;\n delta += nv - bmod[ci][cj];\n bmod[ci][cj] = nv;\n }\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++) {\n int ci = new_p+i, cj = new_q+j;\n long long nv = (bmod[ci][cj] + s[new_m][i][j]) % MOD;\n delta += nv - bmod[ci][cj];\n }\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n bmod[old_p+i][old_q+j] = saved[i][j];\n } else continue;\n \n if (delta >= 0 || (delta / temp > -20 && uni(rng) < exp(delta / temp))) {\n if (move_type == 1) {\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n bmod[new_p+i][new_q+j] = (bmod[new_p+i][new_q+j] + s[new_m][i][j]) % MOD;\n ops.push_back({new_m, new_p, new_q});\n } else if (move_type == 2) {\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n bmod[old_p+i][old_q+j] = (bmod[old_p+i][old_q+j] - s[old_m][i][j] + MOD) % MOD;\n ops[idx] = ops.back(); ops.pop_back();\n } else {\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n bmod[old_p+i][old_q+j] = (bmod[old_p+i][old_q+j] - s[old_m][i][j] + MOD) % MOD;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n bmod[new_p+i][new_q+j] = (bmod[new_p+i][new_q+j] + s[new_m][i][j]) % MOD;\n ops[idx] = {new_m, new_p, new_q};\n }\n score += delta;\n if (score > best_score) { best_score = score; best_ops = ops; }\n }\n }\n \n cout << best_ops.size() << \"\\n\";\n for (auto& [m, p, q] : best_ops)\n cout << m << \" \" << p << \" \" << q << \"\\n\";\n \n return 0;\n}","ahc033":"#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N];\nint container_recv_row[N*N], container_recv_idx[N*N];\nbool container_dispatched[N*N];\n\nint next_expected(int gate) {\n for (int j = 0; j < N; j++)\n if (!container_dispatched[N * gate + j]) return N * gate + j;\n return -1;\n}\n\nint main() {\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> A[i][j];\n container_recv_row[A[i][j]] = i;\n container_recv_idx[A[i][j]] = j;\n }\n fill(container_dispatched, container_dispatched + N*N, false);\n \n int grid[N][N]; for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) grid[i][j] = -1;\n int crane_r = 0, crane_c = 0, crane_holding = -1;\n int next_receive[N] = {}, total_dispatched = 0;\n vector actions(N, \"\");\n \n for (int turn = 1; total_dispatched < N*N && turn < 10000; turn++) {\n for (int i = 0; i < N; i++)\n if (next_receive[i] < N && grid[i][0] == -1 && !(crane_r == i && crane_c == 0 && crane_holding != -1)) {\n grid[i][0] = A[i][next_receive[i]++];\n }\n \n char act = '.';\n if (crane_holding != -1) {\n int dr = crane_holding / N, exp = next_expected(dr);\n int tr, tc;\n if (exp != -1 && crane_holding == exp) { tr = dr; tc = N-1; }\n else {\n tr = tc = -1; int bd = INT_MAX;\n for (int c = 1; c < N-1; c++) for (int r = 0; r < N; r++)\n if (grid[r][c] == -1) { int d = abs(crane_r-r)+abs(crane_c-c); if (d < bd) { bd=d; tr=r; tc=c; } }\n if (tr == -1) { tr = dr; tc = N-1; }\n }\n if (crane_r == tr && crane_c == tc) { act = 'Q'; grid[tr][tc] = crane_holding; crane_holding = -1; }\n else { if (crane_r < tr) { crane_r++; act='D'; } else if (crane_r > tr) { crane_r--; act='U'; } else if (crane_c < tc) { crane_c++; act='R'; } else { crane_c--; act='L'; } }\n } else {\n int bc = -1, bs = INT_MAX, br = -1, bcc = -1;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) {\n if (grid[r][c] == -1 || container_dispatched[grid[r][c]]) continue;\n int cont = grid[r][c], dr = cont / N, exp = next_expected(dr);\n int dp = abs(crane_r-r)+abs(crane_c-c), sc;\n if (exp != -1 && cont == exp) sc = dp + abs(r-dr)+abs(c-(N-1));\n else {\n int mt = INT_MAX;\n for (int tc=1; tcbr) { crane_r--; act='U'; } else if (crane_c\n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\ntypedef long long ll;\nconst ll INF = 1e18;\nstruct Edge { int to, rev; ll cap, cost; };\nstruct MinCostFlow {\n int n; vector> graph; vector h; vector pv, pe;\n MinCostFlow(int n):n(n),graph(n),h(n,0),pv(n),pe(n){}\n void add_edge(int f,int t,ll cap,ll cost){\n graph[f].push_back({t,(int)graph[t].size(),cap,cost});\n graph[t].push_back({f,(int)graph[f].size()-1,0,-cost});\n }\n ll min_cost_flow(int s,int t,ll mf){\n ll res=0,flow=0;\n while(flow,vector>,greater<>>pq;\n vectordist(n,INF);dist[s]=0;pq.push({0,s});\n while(!pq.empty()){\n auto[d,v]=pq.top();pq.pop();\n if(dist[v]0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){\n dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];\n pv[e.to]=v;pe[e.to]=i;pq.push({dist[e.to],e.to});\n }\n }\n }\n if(dist[t]==INF)break;\n for(int v=0;v>n;\n vector>h(n,vector(n));\n for(int i=0;i>h[i][j];\n vector>sources,sinks;\n vector>sid(n,vector(n,-1)),kid(n,vector(n,-1));\n int tsup=0;\n for(int i=0;i0){sid[i][j]=sources.size();sources.push_back({i,j});tsup+=h[i][j];}\n else if(h[i][j]<0){kid[i][j]=sinks.size();sinks.push_back({i,j});}\n }\n int P=sources.size(),M=sinks.size();\n int S=0,T=P+M+1;\n MinCostFlow mcf(P+M+2);\n for(int i=0;i>fa(P,vector(M,0));\n for(int i=0;i=1+P&&e.to<1+P+M)fa[i][e.to-1-P]=(int)mcf.graph[e.to][e.rev].cap;\n vectorsnnd(P,0);\n for(int i=0;i0){auto[ti,tj]=sinks[j];best=min(best,abs(si-ti)+abs(sj-tj));}\n snnd[i]=(bestops;int r=0,c=0,load=0,rem=tsup;\n auto cur=h;\n while(ops.size()<100000&&(rem>0||load>0)){\n if(cur[r][c]>0){ops.push_back(\"+\"+to_string(cur[r][c]));load+=cur[r][c];rem-=cur[r][c];cur[r][c]=0;}\n while(cur[r][c]<0&&load>0){int d=min(load,-cur[r][c]);ops.push_back(\"-\"+to_string(d));load-=d;cur[r][c]+=d;}\n if(rem==0&&load==0)break;\n int br=-1,bc=-1;ll bcost=LLONG_MAX;\n if(load>0){\n for(int i=0;i0){\n int dt=abs(r-i)+abs(c-j);int s=sid[i][j];\n int dd=(s>=0)?snnd[s]:20;\n ll cost=(ll)dt*100+(ll)dd*(100+cur[i][j]);\n if(costr){r++;ops.push_back(\"D\");}\n else if(bc\n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 6, M = 15;\n const int SEED_COUNT = 2 * N * (N - 1);\n const int GRID_SIZE = N * N;\n \n int n, m, t;\n cin >> n >> m >> t;\n \n vector> X(SEED_COUNT, vector(M));\n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n cin >> X[i][j];\n \n vector> edges;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N-1; j++)\n edges.push_back({i*N+j, i*N+j+1});\n for (int i = 0; i < N-1; i++)\n for (int j = 0; j < N; j++)\n edges.push_back({i*N+j, (i+1)*N+j});\n \n vector> posEdges(GRID_SIZE);\n for (int e = 0; e < (int)edges.size(); e++) {\n posEdges[edges[e].first].push_back(e);\n posEdges[edges[e].second].push_back(e);\n }\n \n vector posOrder(GRID_SIZE);\n iota(posOrder.begin(), posOrder.end(), 0);\n sort(posOrder.begin(), posOrder.end(), [](int a, int b) {\n int da = (2*(a/6) - 5) * (2*(a/6) - 5) + (2*(a%6) - 5) * (2*(a%6) - 5);\n int db = (2*(b/6) - 5) * (2*(b/6) - 5) + (2*(b%6) - 5) * (2*(b%6) - 5);\n return da != db ? da < db : a < b;\n });\n \n mt19937 rng(42);\n uniform_real_distribution unif(0.0, 1.0);\n \n for (int turn = 0; turn < t; turn++) {\n vector> pot(SEED_COUNT, vector(SEED_COUNT, 0));\n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = i+1; j < SEED_COUNT; j++) {\n for (int l = 0; l < M; l++)\n pot[i][j] += max(X[i][l], X[j][l]);\n pot[j][i] = pot[i][j];\n }\n \n vector values(SEED_COUNT);\n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n values[i] += X[i][j];\n \n vector order(SEED_COUNT);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) { return values[a] > values[b]; });\n \n vector grid(GRID_SIZE);\n for (int i = 0; i < GRID_SIZE; i++)\n grid[posOrder[i]] = order[i];\n \n vector unplaced(order.begin() + GRID_SIZE, order.end());\n vector isPlaced(SEED_COUNT, false);\n for (int i = 0; i < GRID_SIZE; i++) isPlaced[order[i]] = true;\n \n int currentScore = 0;\n for (auto& [u, v] : edges)\n currentScore += pot[grid[u]][grid[v]];\n \n int bestScore = currentScore;\n vector bestGrid = grid;\n \n auto startTime = chrono::high_resolution_clock::now();\n const double startTemp = 500.0, endTemp = 0.1;\n \n for (int iter = 0; iter < 10000000; iter++) {\n auto now = chrono::high_resolution_clock::now();\n auto elapsed = chrono::duration_cast(now - startTime).count();\n if (elapsed > 180000) break;\n \n double progress = (double)elapsed / 180000.0;\n double temp = startTemp * pow(endTemp / startTemp, progress);\n \n if (rng() % 5 != 0) {\n int i = rng() % GRID_SIZE, j = rng() % GRID_SIZE;\n if (i == j) continue;\n \n int delta = 0;\n for (int e : posEdges[i]) { auto& [u,v] = edges[e]; delta -= pot[grid[u]][grid[v]]; }\n for (int e : posEdges[j]) { auto& [u,v] = edges[e]; delta -= pot[grid[u]][grid[v]]; }\n \n swap(grid[i], grid[j]);\n \n for (int e : posEdges[i]) { auto& [u,v] = edges[e]; delta += pot[grid[u]][grid[v]]; }\n for (int e : posEdges[j]) { auto& [u,v] = edges[e]; delta += pot[grid[u]][grid[v]]; }\n \n if (delta >= 0 || unif(rng) < exp((double)delta / temp)) {\n currentScore += delta;\n if (currentScore > bestScore) { bestScore = currentScore; bestGrid = grid; }\n } else {\n swap(grid[i], grid[j]);\n }\n } else {\n int pos = rng() % GRID_SIZE;\n int old_seed = grid[pos];\n int up_idx = rng() % unplaced.size();\n int new_seed = unplaced[up_idx];\n \n int delta = 0;\n for (int e : posEdges[pos]) { auto& [u,v] = edges[e]; delta -= pot[grid[u]][grid[v]]; }\n \n grid[pos] = new_seed;\n \n for (int e : posEdges[pos]) { auto& [u,v] = edges[e]; delta += pot[grid[u]][grid[v]]; }\n \n if (delta >= 0 || unif(rng) < exp((double)delta / temp)) {\n currentScore += delta;\n isPlaced[old_seed] = false;\n isPlaced[new_seed] = true;\n unplaced[up_idx] = old_seed;\n if (currentScore > bestScore) { bestScore = currentScore; bestGrid = grid; }\n } else {\n grid[pos] = old_seed;\n }\n }\n }\n \n grid = bestGrid;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cout << grid[i*N+j];\n if (j < N-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n cout.flush();\n \n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n cin >> X[i][j];\n }\n \n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n \n vector s(N), t(N);\n for (int i = 0; i < N; i++) cin >> s[i];\n for (int i = 0; i < N; i++) cin >> t[i];\n \n int Vp = V;\n vector len(Vp, 1);\n \n cout << Vp << \"\\n\";\n for (int i = 1; i < Vp; i++) cout << 0 << \" \" << len[i] << \"\\n\";\n \n int rx = N/2, ry = N/2;\n cout << rx << \" \" << ry << \"\\n\";\n \n vector> grid(N, vector(N)), target(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n grid[i][j] = s[i][j] - '0';\n target[i][j] = t[i][j] - '0';\n }\n \n vector dir(Vp, 0);\n vector holding(Vp, false);\n vector ops;\n \n auto addOp = [&](string op) { ops.push_back(op); };\n \n while (true) {\n int sx=-1, sy=-1, best=INT_MAX;\n for (int i=0; itRx) { op[0]='U'; rx--; }\n else if (rytRx) { op[0]='U'; rx--; }\n else if (ry\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N;\n cin >> N;\n \n vector x(2*N), y(2*N);\n for (int i = 0; i < 2*N; i++) {\n cin >> x[i] >> y[i];\n }\n \n int gridSize = 100;\n int cellSize = 1001;\n \n vector> grid(gridSize, vector(gridSize, 0));\n for (int i = 0; i < 2*N; i++) {\n int gx = min(x[i] / cellSize, gridSize - 1);\n int gy = min(y[i] / cellSize, gridSize - 1);\n grid[gx][gy] += (i < N) ? 1 : -1;\n }\n \n vector> prefix(gridSize + 1, vector(gridSize + 1, 0));\n for (int i = 0; i < gridSize; i++) {\n for (int j = 0; j < gridSize; j++) {\n prefix[i + 1][j + 1] = grid[i][j] + prefix[i][j + 1] + prefix[i + 1][j] - prefix[i][j];\n }\n }\n \n auto gridRectScore = [&](int x1, int y1, int x2, int y2) -> int {\n return prefix[x2 + 1][y2 + 1] - prefix[x1][y2 + 1] - prefix[x2 + 1][y1] + prefix[x1][y1];\n };\n \n int bestGridScore = 0;\n int bestGX1 = 0, bestGY1 = 0, bestGX2 = 0, bestGY2 = 0;\n \n for (int gx1 = 0; gx1 < gridSize; gx1++) {\n for (int gx2 = gx1; gx2 < gridSize; gx2++) {\n int bestY = 0, curY = 0;\n int bestGY1c = 0, bestGY2c = -1;\n int curGY1 = 0;\n \n for (int gy2 = 0; gy2 < gridSize; gy2++) {\n curY += gridRectScore(gx1, gy2, gx2, gy2);\n \n if (curY > bestY) {\n bestY = curY;\n bestGY1c = curGY1;\n bestGY2c = gy2;\n }\n if (curY < 0) {\n curY = 0;\n curGY1 = gy2 + 1;\n }\n }\n \n if (bestY > bestGridScore) {\n bestGridScore = bestY;\n bestGX1 = gx1;\n bestGX2 = gx2;\n bestGY1 = bestGY1c;\n bestGY2 = bestGY2c;\n }\n }\n }\n \n int bestX1 = bestGX1 * cellSize;\n int bestY1 = bestGY1 * cellSize;\n int bestX2 = min((bestGX2 + 1) * cellSize - 1, 100000);\n int bestY2 = min((bestGY2 + 1) * cellSize - 1, 100000);\n \n cout << 4 << endl;\n if (bestGridScore > 0) {\n cout << bestX1 << \" \" << bestY1 << endl;\n cout << bestX2 << \" \" << bestY1 << endl;\n cout << bestX2 << \" \" << bestY2 << endl;\n cout << bestX1 << \" \" << bestY2 << endl;\n } else {\n cout << 50000 << \" \" << 50000 << endl;\n cout << 50001 << \" \" << 50000 << endl;\n cout << 50001 << \" \" << 50001 << endl;\n cout << 50000 << \" \" << 50001 << endl;\n }\n \n return 0;\n}","ahc040":"#include \nusing namespace std;\n\nint N, T, sigma;\nvector w_obs, h_obs;\nvector w_est, h_est;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> T >> sigma;\n w_obs.resize(N); h_obs.resize(N);\n w_est.resize(N); h_est.resize(N);\n for (int i = 0; i < N; i++) {\n cin >> w_obs[i] >> h_obs[i];\n w_est[i] = w_obs[i];\n h_est[i] = h_obs[i];\n }\n mt19937 rng(42);\n for (int t = 0; t < T; t++) {\n bool always_place = (t % 3 != 2);\n bool use_noise = (t % 5 >= 3);\n vector wc(N), hc(N);\n for (int i = 0; i < N; i++) {\n wc[i] = max(1LL, (long long)round(w_est[i]));\n hc[i] = max(1LL, (long long)round(h_est[i]));\n if (use_noise) {\n wc[i] = max(1LL, wc[i] + (long long)(rng() % 4001) - 2000);\n hc[i] = max(1LL, hc[i] + (long long)(rng() % 4001) - 2000);\n }\n }\n vector px, py, pw, ph;\n vector placed_idx;\n vector> output;\n long long curW = 0, curH = 0;\n for (int i = 0; i < N; i++) {\n long long best_score = LLONG_MAX;\n int best_r = 0; char best_d = 'U'; int best_b = -1;\n long long best_rx = 0, best_ry = 0;\n long long skip_score = curW + curH + wc[i] + hc[i];\n if (!always_place) best_score = skip_score;\n int np = (int)px.size();\n for (int r = 0; r < 2; r++) {\n long long rw = r ? hc[i] : wc[i];\n long long rh = r ? wc[i] : hc[i];\n for (int b = -1; b < np; b++) {\n long long rx = (b < 0) ? 0 : px[b] + pw[b];\n long long ry = 0;\n for (int j = 0; j < np; j++)\n if (px[j] < rx + rw && px[j] + pw[j] > rx)\n ry = max(ry, py[j] + ph[j]);\n long long s = max(curW, rx + rw) + max(curH, ry + rh);\n if (s < best_score) { best_score=s; best_r=r; best_d='U'; best_b=b; best_rx=rx; best_ry=ry; }\n }\n for (int b = -1; b < np; b++) {\n long long ry = (b < 0) ? 0 : py[b] + ph[b];\n long long rx = 0;\n for (int j = 0; j < np; j++)\n if (py[j] < ry + rh && py[j] + ph[j] > ry)\n rx = max(rx, px[j] + pw[j]);\n long long s = max(curW, rx + rw) + max(curH, ry + rh);\n if (s < best_score) { best_score=s; best_r=r; best_d='L'; best_b=b; best_rx=rx; best_ry=ry; }\n }\n }\n if (always_place || best_score < skip_score) {\n long long rw = best_r ? hc[i] : wc[i];\n long long rh = best_r ? wc[i] : hc[i];\n px.push_back(best_rx); py.push_back(best_ry);\n pw.push_back(rw); ph.push_back(rh);\n placed_idx.push_back(i);\n output.push_back({i, best_r, best_d, best_b});\n curW = max(curW, best_rx + rw);\n curH = max(curH, best_ry + rh);\n }\n }\n cout << output.size() << \"\\n\";\n for (auto& [p, r, d, b] : output)\n cout << p << \" \" << r << \" \" << d << \" \" << b << \"\\n\";\n cout.flush();\n long long Wp, Hp;\n cin >> Wp >> Hp;\n double Werr = (double)(Wp - curW), Herr = (double)(Hp - curH);\n if (!px.empty()) {\n int rcnt = 0, bcnt = 0;\n for (int j = 0; j < (int)px.size(); j++) {\n if (px[j]+pw[j]==curW) rcnt++;\n if (py[j]+ph[j]==curH) bcnt++;\n }\n double lr = 0.2;\n for (int j = 0; j < (int)px.size(); j++) {\n int orig = placed_idx[j]; bool rot = get<1>(output[j]);\n if (px[j]+pw[j]==curW && rcnt>0) {\n double es = Werr/rcnt*lr;\n if (rot) h_est[orig]=max(1.0,h_est[orig]+es);\n else w_est[orig]=max(1.0,w_est[orig]+es);\n }\n if (py[j]+ph[j]==curH && bcnt>0) {\n double es = Herr/bcnt*lr;\n if (rot) w_est[orig]=max(1.0,w_est[orig]+es);\n else h_est[orig]=max(1.0,h_est[orig]+es);\n }\n }\n }\n }\n return 0;\n}","ahc041":"#include \nusing namespace std;\n\nint N, M, H;\nvector A;\nvector> adj;\nvector X, Y;\n\nvoid improve(vector& parent) {\n vector height(N, 0);\n vector sub_sum(N);\n vector sub_max_h(N);\n \n auto recompute = [&]() {\n vector child_count(N, 0);\n for (int v = 0; v < N; v++) {\n if (parent[v] != -1) child_count[parent[v]]++;\n }\n queue q;\n for (int v = 0; v < N; v++) {\n height[v] = (parent[v] == -1) ? 0 : -1;\n sub_sum[v] = A[v];\n sub_max_h[v] = 0;\n if (child_count[v] == 0) q.push(v);\n }\n // Compute heights top-down\n {\n vector topo;\n queue q2;\n vector cc2(N, 0);\n for (int v = 0; v < N; v++) if (parent[v] != -1) cc2[parent[v]]++;\n for (int v = 0; v < N; v++) if (cc2[v] == 0) q2.push(v);\n while (!q2.empty()) {\n int v = q2.front(); q2.pop();\n topo.push_back(v);\n if (parent[v] != -1) { cc2[parent[v]]--; if (cc2[parent[v]] == 0) q2.push(parent[v]); }\n }\n for (int i = topo.size() - 1; i >= 0; i--) {\n int v = topo[i];\n if (parent[v] == -1) height[v] = 0;\n else height[v] = height[parent[v]] + 1;\n }\n }\n for (int v = 0; v < N; v++) { sub_sum[v] = A[v]; sub_max_h[v] = height[v]; }\n while (!q.empty()) {\n int v = q.front(); q.pop();\n int p = parent[v];\n if (p != -1) {\n sub_sum[p] += sub_sum[v];\n sub_max_h[p] = max(sub_max_h[p], sub_max_h[v]);\n child_count[p]--;\n if (child_count[p] == 0) q.push(p);\n }\n }\n };\n \n recompute();\n \n auto creates_cycle = [&](int v, int u) -> bool {\n int curr = u;\n while (curr != -1) { if (curr == v) return true; curr = parent[curr]; }\n return false;\n };\n \n auto update_heights = [&](int v, int delta) {\n stack st; st.push(v);\n while (!st.empty()) {\n int curr = st.top(); st.pop();\n height[curr] += delta;\n for (int u : adj[curr]) if (parent[u] == curr) st.push(u);\n }\n };\n \n while (true) {\n long long best_gain = 0; int best_v = -1, best_u = -1;\n for (int v = 0; v < N; v++) {\n for (int u : adj[v]) {\n if (u == parent[v]) continue;\n int new_h = height[u] + 1;\n int delta = new_h - height[v];\n if (delta <= 0) continue;\n if (sub_max_h[v] + delta > H) continue;\n if (creates_cycle(v, u)) continue;\n long long gain = (long long)delta * sub_sum[v];\n if (gain > best_gain) { best_gain = gain; best_v = v; best_u = u; }\n }\n }\n if (best_v == -1) break;\n int delta = height[best_u] + 1 - height[best_v];\n parent[best_v] = best_u;\n update_heights(best_v, delta);\n recompute();\n }\n}\n\nlong long compute_score(const vector& par) {\n long long score = 0;\n for (int v = 0; v < N; v++) {\n int h = 0, curr = v;\n while (par[curr] != -1) { curr = par[curr]; h++; }\n score += (long long)(h + 1) * A[v];\n }\n return score;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> M >> H;\n A.resize(N);\n for (int i = 0; i < N; i++) cin >> A[i];\n adj.resize(N);\n for (int i = 0; i < M; i++) { int u, v; cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); }\n X.resize(N); Y.resize(N);\n for (int i = 0; i < N; i++) cin >> X[i] >> Y[i];\n \n long long best_score = 0;\n vector best_parent(N, -1);\n \n // Strategy 1: All roots + improve\n { vector p(N, -1); improve(p); long long s = compute_score(p); if (s > best_score) { best_score = s; best_parent = p; } }\n \n // Strategy 2: BFS from central vertices\n {\n vector p(N, -1), h(N, 0); vector as(N, false);\n vector ord(N); iota(ord.begin(), ord.end(), 0);\n sort(ord.begin(), ord.end(), [&](int a, int b) { return (X[a]-500)*(X[a]-500)+(Y[a]-500)*(Y[a]-500) < (X[b]-500)*(X[b]-500)+(Y[b]-500)*(Y[b]-500); });\n for (int idx = 0; idx < N; idx++) {\n int root = ord[idx]; if (as[root]) continue;\n queue q; q.push(root); as[root] = true; p[root] = -1; h[root] = 0;\n while (!q.empty()) {\n int u = q.front(); q.pop(); if (h[u] >= H) continue;\n vector ch; for (int v : adj[u]) if (!as[v]) ch.push_back(v);\n sort(ch.begin(), ch.end(), [&](int a, int b) { return A[a] > A[b]; });\n for (int v : ch) { if (as[v]) continue; as[v] = true; p[v] = u; h[v] = h[u]+1; q.push(v); }\n }\n }\n improve(p); long long s = compute_score(p); if (s > best_score) { best_score = s; best_parent = p; }\n }\n \n // Strategy 3: Build chains from high-beauty vertices\n {\n vector p(N, -1), h(N, 0); vector as(N, false);\n vector ord(N); iota(ord.begin(), ord.end(), 0);\n sort(ord.begin(), ord.end(), [&](int a, int b) { return A[a] > A[b]; });\n for (int v : ord) {\n if (as[v]) continue;\n vector dist(N, -1), par(N, -1); queue q; q.push(v); dist[v] = 0;\n int target = -1;\n while (!q.empty()) {\n int u = q.front(); q.pop();\n if (dist[u] == H) { target = u; break; }\n for (int w : adj[u]) if (!as[w] && dist[w] == -1) { dist[w] = dist[u]+1; par[w] = u; q.push(w); }\n }\n if (target == -1) for (int u = 0; u < N; u++) if (dist[u] > 0 && (target == -1 || dist[u] > dist[target])) target = u;\n if (target != -1) {\n vector path; int curr = target;\n while (true) { path.push_back(curr); if (curr == v) break; curr = par[curr]; }\n for (int i = 0; i < (int)path.size(); i++) { as[path[i]] = true; p[path[i]] = (i==0)?-1:path[i-1]; h[path[i]] = i; }\n } else { as[v] = true; p[v] = -1; h[v] = 0; }\n }\n improve(p); long long s = compute_score(p); if (s > best_score) { best_score = s; best_parent = p; }\n }\n \n // Strategy 4: BFS from low-beauty roots with high-beauty priority\n {\n vector p(N, -1), h(N, 0); vector as(N, false);\n vector ord(N); iota(ord.begin(), ord.end(), 0);\n sort(ord.begin(), ord.end(), [&](int a, int b) { return A[a] < A[b]; });\n int nr = max(1, N / (H + 1));\n priority_queue> pq; // (-height, -beauty)\n for (int i = 0; i < nr && i < N; i++) { int v = ord[i]; as[v] = true; p[v] = -1; h[v] = 0; pq.push({0, -A[v]}); }\n // Rebuild with vertex indices\n priority_queue> pq2;\n for (int i = 0; i < nr && i < N; i++) { int v = ord[i]; pq2.push({0, -A[v], v}); }\n while (!pq2.empty()) {\n auto [nh, nb, u] = pq2.top(); pq2.pop();\n if (h[u] >= H) continue;\n vector ch; for (int v : adj[u]) if (!as[v]) ch.push_back(v);\n sort(ch.begin(), ch.end(), [&](int a, int b) { return A[a] > A[b]; });\n for (int v : ch) { if (as[v]) continue; as[v] = true; p[v] = u; h[v] = h[u]+1; pq2.push({-h[v], -A[v], v}); }\n }\n for (int v = 0; v < N; v++) if (!as[v]) { as[v] = true; p[v] = -1; h[v] = 0; }\n improve(p); long long s = compute_score(p); if (s > best_score) { best_score = s; best_parent = p; }\n }\n \n for (int i = 0; i < N; i++) cout << best_parent[i] << (i == N-1 ? \"\\n\" : \" \");\n return 0;\n}","ahc042":"#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint main() {\n int N; cin >> N;\n vector board(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n vector initial_board = board;\n \n vector> moves;\n \n auto shift = [&](char dir, int idx) {\n if (dir == 'L') {\n for (int j = 0; j < N-1; j++) board[idx][j] = board[idx][j+1];\n board[idx][N-1] = '.';\n } else if (dir == 'R') {\n for (int j = N-1; j > 0; j--) board[idx][j] = board[idx][j-1];\n board[idx][0] = '.';\n } else if (dir == 'U') {\n for (int i = 0; i < N-1; i++) board[i][idx] = board[i+1][idx];\n board[N-1][idx] = '.';\n } else {\n for (int i = N-1; i > 0; i--) board[i][idx] = board[i-1][idx];\n board[0][idx] = '.';\n }\n moves.push_back({dir, idx});\n };\n \n // Phase 1: Greedy without shift-backs\n bool greedy_ok = true;\n while (true) {\n int best_cost = N + 2;\n int best_idx = -1;\n char best_dir = 0;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (board[i][j] != 'x') continue;\n {bool s=true; for(int k=0;k onis;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (board[i][j] == 'x') onis.push_back({i, j, (int)onis.size()});\n \n map, vector> batches;\n for (auto& o : onis) {\n bool us=true,ds=true,ls=true,rs=true;\n for(int k=0;k removed;\n for (char dir : {'U','D','L','R'}) {\n for (int idx = 0; idx < N; idx++) {\n auto key = make_pair(dir, idx);\n if (batches.find(key) == batches.end()) continue;\n int md = 0;\n for (int oid : batches[key]) { if(removed.count(oid)) continue; auto& o=onis[oid]; int d=(dir=='U')?o.i+1:(dir=='D')?N-o.i:(dir=='L')?o.j+1:N-o.j; md=max(md,d); }\n if (md == 0) continue;\n for (int k = 0; k < md; k++) shift(dir, idx);\n char opp = (dir=='U')?'D':(dir=='D')?'U':(dir=='L')?'R':'L';\n for (int k = 0; k < md; k++) shift(opp, idx);\n for (auto& o : onis) { if(removed.count(o.id)) continue; bool ip=false;\n if(dir=='U'&&o.j==idx&&o.i=N-md) ip=true;\n else if(dir=='L'&&o.i==idx&&o.j=N-md) ip=true;\n if(ip) removed.insert(o.id); }\n }\n }\n }\n \n for (auto& [d, p] : moves) cout << d << \" \" << p << \"\\n\";\n return 0;\n}","ahc044":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, L;\nint T[100];\nint a[100], b[100];\nint best_a[100], best_b[100];\nint best_error = INT_MAX;\n\nuint64_t rng_state = 1234567890123456789ULL;\nuint64_t rng64() {\n rng_state ^= rng_state >> 12;\n rng_state ^= rng_state << 25;\n rng_state ^= rng_state >> 27;\n return rng_state * 2685821657736338717ULL;\n}\n\nint simulate(int ai[], int bi[]) {\n int count[100] = {}, ti[100] = {};\n int cur = 0;\n for (int w = 0; w < L; w++) {\n ti[cur]++;\n count[cur]++;\n cur = (count[cur] & 1) ? ai[cur] : bi[cur];\n }\n int err = 0;\n for (int i = 0; i < N; i++) err += abs(ti[i] - T[i]);\n return err;\n}\n\nvoid try_init(int ai[], int bi[]) {\n int err = simulate(ai, bi);\n if (err < best_error) {\n best_error = err;\n memcpy(best_a, ai, sizeof(int) * N);\n memcpy(best_b, bi, sizeof(int) * N);\n }\n}\n\nvoid greedy_init(int ai[], int bi[], bool avoid_self) {\n int rem[100]; memcpy(rem, T, sizeof(T));\n int cnt[100] = {};\n bool as[100] = {}, bs[100] = {};\n memset(ai, 0, sizeof(int) * N);\n memset(bi, 0, sizeof(int) * N);\n int cur = 0;\n for (int w = 0; w < L; w++) {\n rem[cur]--;\n cnt[cur]++;\n if (cnt[cur] & 1) {\n if (!as[cur]) {\n int best = -1;\n for (int j = 0; j < N; j++) {\n if (avoid_self && j == cur) continue;\n if (best == -1 || rem[j] > rem[best]) best = j;\n }\n if (best == -1) best = (cur + 1) % N;\n ai[cur] = best; as[cur] = true;\n }\n cur = ai[cur];\n } else {\n if (!bs[cur]) {\n int best = -1;\n for (int j = 0; j < N; j++) {\n if (avoid_self && j == cur) continue;\n if (best == -1 || rem[j] > rem[best]) best = j;\n }\n if (best == -1) best = (cur + 1) % N;\n bi[cur] = best; bs[cur] = true;\n }\n cur = bi[cur];\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> L;\n for (int i = 0; i < N; i++) cin >> T[i];\n \n int ai[100], bi[100];\n \n // Init 1: Simple cycle\n for (int i = 0; i < N; i++) { ai[i] = (i+1)%N; bi[i] = (i+1)%N; }\n try_init(ai, bi);\n \n // Init 2: Greedy (allow self-loops)\n greedy_init(ai, bi, false);\n try_init(ai, bi);\n \n // Init 3: Greedy (avoid self-loops)\n greedy_init(ai, bi, true);\n try_init(ai, bi);\n \n // Init 4: Flow-based\n {\n struct Src { int emp; int flow; bool odd; };\n Src srcs[200];\n for (int i = 0; i < N; i++) {\n srcs[2*i] = {i, (T[i]+1)/2, true};\n srcs[2*i+1] = {i, T[i]/2, false};\n }\n sort(srcs, srcs+2*N, [](const Src& a, const Src& b) { return a.flow > b.flow; });\n int dem[100]; memcpy(dem, T, sizeof(T));\n for (int s = 0; s < 2*N; s++) {\n int best = 0;\n for (int j = 1; j < N; j++) if (dem[j] > dem[best]) best = j;\n if (srcs[s].odd) ai[srcs[s].emp] = best;\n else bi[srcs[s].emp] = best;\n dem[best] -= srcs[s].flow;\n }\n try_init(ai, bi);\n }\n \n // Use best init for SA\n memcpy(a, best_a, sizeof(a));\n memcpy(b, best_b, sizeof(b));\n int error = best_error;\n \n auto start = chrono::high_resolution_clock::now();\n double temp = max(50.0, error / 80.0);\n double cool = 0.993;\n \n while (true) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start).count() > 1.85) break;\n \n int i = rng64() % N;\n bool is_a = rng64() & 1;\n int old = is_a ? a[i] : b[i];\n int nv = rng64() % N;\n if (is_a) a[i] = nv; else b[i] = nv;\n \n int ne = simulate(a, b);\n double delta = ne - error;\n if (delta <= 0 || (double)(rng64() & 0xFFFFF) / 1048576.0 < exp(-delta / temp)) {\n error = ne;\n if (error < best_error) {\n best_error = error;\n memcpy(best_a, a, sizeof(a));\n memcpy(best_b, b, sizeof(b));\n }\n } else {\n if (is_a) a[i] = old; else b[i] = old;\n }\n temp *= cool;\n }\n \n for (int i = 0; i < N; i++)\n cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nuint64_t xy2d(int n, int x, int y) {\n uint64_t d = 0;\n for (int s = n/2; s > 0; s /= 2) {\n int rx = (x & s) > 0;\n int ry = (y & s) > 0;\n d += (uint64_t)s * s * ((3 * rx) ^ ry);\n if (ry == 0) {\n if (rx == 1) { x = s-1 - x; y = s-1 - y; }\n swap(x, y);\n }\n }\n return d;\n}\n\nint N, M, Q, L, W;\ndouble cx[800], cy[800], ddist[800][800];\nint qcnt = 0;\n\nvector> query(vector& v) {\n if (qcnt >= Q || (int)v.size() < 2) return {};\n qcnt++;\n cout << \"? \" << v.size();\n for (int x : v) cout << \" \" << x;\n cout << endl;\n vector> res(v.size() - 1);\n for (auto& [a, b] : res) cin >> a >> b;\n return res;\n}\n\nint par[800], rnk[800];\nvoid init_dsu() { iota(par, par + N, 0); fill(rnk, rnk + N, 0); }\nint find(int x) { return par[x] == x ? x : par[x] = find(par[x]); }\nbool unite(int x, int y) {\n x = find(x); y = find(y);\n if (x == y) return false;\n if (rnk[x] < rnk[y]) swap(x, y);\n par[y] = x;\n if (rnk[x] == rnk[y]) rnk[x]++;\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> Q >> L >> W;\n vector G(M);\n for (int& g : G) cin >> g;\n \n for (int i = 0; i < N; i++) {\n int a, b, c, d;\n cin >> a >> b >> c >> d;\n cx[i] = (a + b) / 2.0;\n cy[i] = (c + d) / 2.0;\n }\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n double dx = cx[i] - cx[j], dy = cy[i] - cy[j];\n ddist[i][j] = sqrt(dx*dx + dy*dy);\n }\n \n vector ord(N);\n iota(ord.begin(), ord.end(), 0);\n sort(ord.begin(), ord.end(), [](int a, int b) {\n return xy2d(32768, (int)cx[a], (int)cy[a]) < xy2d(32768, (int)cx[b], (int)cy[b]);\n });\n \n vector> grp(M);\n for (int i = 0, p = 0; i < M; i++)\n for (int j = 0; j < G[i]; j++)\n grp[i].push_back(ord[p++]);\n \n vector>> ans(M);\n \n for (int k = 0; k < M; k++) {\n if (G[k] <= 1) continue;\n \n init_dsu();\n if (G[k] <= L && qcnt < Q) {\n ans[k] = query(grp[k]);\n continue;\n }\n \n set conn;\n vector> mst;\n conn.insert(grp[k][0]);\n \n while (conn.size() < (size_t)G[k] && qcnt < Q) {\n vector> cands;\n for (int c : grp[k]) {\n if (conn.count(c)) continue;\n double md = 1e18;\n for (int t : conn) md = min(md, ddist[c][t]);\n cands.emplace_back(md, c);\n }\n if (cands.empty()) break;\n sort(cands.begin(), cands.end());\n \n int ncand = min((int)cands.size(), L - 1);\n vector> tree_sorted;\n for (int t : conn) {\n double md = 1e18;\n for (int i = 0; i < ncand; i++) md = min(md, ddist[t][cands[i].second]);\n tree_sorted.emplace_back(md, t);\n }\n sort(tree_sorted.begin(), tree_sorted.end());\n \n int ntree = min((int)tree_sorted.size(), L - ncand);\n vector qv;\n for (int i = 0; i < ntree; i++) qv.push_back(tree_sorted[i].second);\n for (int i = 0; i < ncand; i++) qv.push_back(cands[i].second);\n \n auto edges = query(qv);\n for (auto& [a, b] : edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n conn.insert(a);\n conn.insert(b);\n }\n }\n }\n \n vector> edges;\n for (int i = 0; i < G[k]; i++)\n for (int j = i + 1; j < G[k]; j++)\n edges.emplace_back(ddist[grp[k][i]][grp[k][j]], grp[k][i], grp[k][j]);\n sort(edges.begin(), edges.end());\n \n for (auto& [d, a, b] : edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n conn.insert(a);\n conn.insert(b);\n }\n if (conn.size() == (size_t)G[k]) break;\n }\n \n ans[k] = mst;\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int i = 0; i < G[k]; i++) cout << grp[k][i] << \" \\n\"[i==G[k]-1];\n for (auto& [a, b] : ans[k]) cout << a << \" \" << b << \"\\n\";\n }\n return 0;\n}","ahc046":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M;\n cin >> N >> M;\n \n vector> targets(M);\n for (int i = 0; i < M; i++) {\n cin >> targets[i].first >> targets[i].second;\n }\n \n set> blocks;\n int cur_r = targets[0].first, cur_c = targets[0].second;\n vector> all_actions;\n \n const int dr[] = {-1, 1, 0, 0};\n const int dc[] = {0, 0, -1, 1};\n const char dir_chars[] = {'U', 'D', 'L', 'R'};\n \n set> future_targets;\n for (int i = 1; i < M; i++) future_targets.insert(targets[i]);\n \n auto get_slide_dest = [&](int r, int c, int d) -> pair {\n int nr = r + dr[d], nc = c + dc[d];\n while (nr >= 0 && nr < N && nc >= 0 && nc < N && blocks.count({nr, nc}) == 0) {\n nr += dr[d]; nc += dc[d];\n }\n nr -= dr[d]; nc -= dc[d];\n return {nr, nc};\n };\n \n auto bfs = [&](int sr, int sc, int tr, int tc) -> vector> {\n if (sr == tr && sc == tc) return {};\n vector> dist(N, vector(N, -1));\n vector>> parent(N, vector>(N, {-1,-1,' ',' '}));\n queue> q;\n q.push({sr, sc}); dist[sr][sc] = 0;\n while (!q.empty()) {\n auto [r, c] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nr = r + dr[d], nc = c + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && blocks.count({nr, nc}) == 0 && dist[nr][nc] == -1) {\n dist[nr][nc] = dist[r][c] + 1;\n parent[nr][nc] = {r, c, 'M', dir_chars[d]};\n if (nr == tr && nc == tc) goto found;\n q.push({nr, nc});\n }\n auto [snr, snc] = get_slide_dest(r, c, d);\n if ((snr != r || snc != c) && dist[snr][snc] == -1) {\n dist[snr][snc] = dist[r][c] + 1;\n parent[snr][snc] = {r, c, 'S', dir_chars[d]};\n if (snr == tr && snc == tc) goto found;\n q.push({snr, snc});\n }\n }\n }\n return {};\n found:\n vector> path;\n int cr = tr, cc = tc;\n while (true) {\n auto [pr, pc, act, dir] = parent[cr][cc];\n if (pr == -1) break;\n path.push_back({act, dir, cr, cc});\n cr = pr; cc = pc;\n }\n reverse(path.begin(), path.end());\n return path;\n };\n \n auto execute_path = [&](vector>& path) {\n for (auto& [act, dir, nr, nc] : path) {\n all_actions.push_back({act, dir});\n cur_r = nr; cur_c = nc;\n }\n };\n \n for (int t = 1; t < M; t++) {\n future_targets.erase(targets[t]);\n int tr = targets[t].first, tc = targets[t].second;\n \n // Remove block on target if present\n if (blocks.count({tr, tc})) {\n for (int d = 0; d < 4; d++) {\n int ar = tr + dr[d], ac = tc + dc[d];\n if (ar >= 0 && ar < N && ac >= 0 && ac < N && blocks.count({ar, ac}) == 0) {\n auto path_adj = bfs(cur_r, cur_c, ar, ac);\n if (!path_adj.empty()) {\n execute_path(path_adj);\n char adir;\n if (d == 0) adir = 'D';\n else if (d == 1) adir = 'U';\n else if (d == 2) adir = 'R';\n else adir = 'L';\n blocks.erase({tr, tc});\n all_actions.push_back({'A', adir});\n break;\n }\n }\n }\n }\n \n auto path = bfs(cur_r, cur_c, tr, tc);\n execute_path(path);\n \n // Place block at best adjacent position for future slides\n // Prefer positions on grid lines (rows/cols divisible by 5)\n int best_d = -1, best_score = -1;\n for (int d = 0; d < 4; d++) {\n int br = cur_r + dr[d], bc = cur_c + dc[d];\n if (br < 0 || br >= N || bc < 0 || bc >= N) continue;\n if (blocks.count({br, bc})) continue;\n if (future_targets.count({br, bc})) continue;\n int score = 0;\n if (br % 5 == 0) score += 2;\n if (bc % 5 == 0) score += 2;\n // Prefer placing below or right for downward/rightward slide stops\n if (d == 1) score += 1;\n if (d == 3) score += 1;\n if (score > best_score) { best_score = score; best_d = d; }\n }\n if (best_d != -1) {\n int br = cur_r + dr[best_d], bc = cur_c + dc[best_d];\n blocks.insert({br, bc});\n all_actions.push_back({'A', dir_chars[best_d]});\n }\n }\n \n for (auto& [a, d] : all_actions) {\n cout << a << \" \" << d << \"\\n\";\n }\n return 0;\n}"},"4":{"ahc001":"#include \nusing namespace std;\n\nint n;\nvector x, y, r;\nvector ra, rb, rc, rd;\n\ndouble satisfaction(long long s, long long rv) {\n if (s <= 0 || rv <= 0) return 0;\n double ratio = (double)min(s, rv) / max(s, rv);\n return 1.0 - (1.0 - ratio) * (1.0 - ratio);\n}\n\ndouble compute_score() {\n double score = 0;\n for (int i = 0; i < n; i++)\n score += satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]), r[i]);\n return score;\n}\n\nstruct TNode {\n bool is_leaf;\n int company;\n bool vertical;\n int split_k;\n vector items;\n int lc, rc_node;\n};\nvector tree;\nvector split_offset;\n\nint build_tree(vector items, mt19937& rng) {\n int idx = tree.size();\n tree.push_back({});\n if (items.size() == 1) {\n tree[idx] = {true, items[0], false, 0, items, -1, -1};\n return idx;\n }\n long long total_r = 0;\n for (int i : items) total_r += r[i];\n bool best_vert = true; int best_k = -1; double best_score = -1e18;\n for (int dir = 0; dir < 2; dir++) {\n bool vert = (dir == 0);\n auto sorted = items;\n sort(sorted.begin(), sorted.end(), [&](int i, int j) { return vert ? x[i] < x[j] : y[i] < y[j]; });\n auto& coord = vert ? x : y;\n long long sum = 0;\n for (int k = 1; k < (int)sorted.size(); k++) {\n sum += r[sorted[k-1]];\n if (coord[sorted[k-1]] >= coord[sorted[k]]) continue;\n double score = -abs((double)sum/total_r - 0.5) + uniform_real_distribution(0,0.02)(rng);\n if (score > best_score) { best_score = score; best_vert = vert; best_k = k; }\n }\n }\n if (best_k < 0) { tree[idx] = {true, items[0], false, 0, items, -1, -1}; return idx; }\n sort(items.begin(), items.end(), [&](int i, int j) { return best_vert ? x[i] < x[j] : y[i] < y[j]; });\n vector li(items.begin(), items.begin()+best_k), ri(items.begin()+best_k, items.end());\n int lc = build_tree(li, rng), rc2 = build_tree(ri, rng);\n tree[idx] = {false, -1, best_vert, best_k, items, lc, rc2};\n return idx;\n}\n\nvoid compute_rects(int idx, int L, int B, int R, int T) {\n if (tree[idx].is_leaf) { int i = tree[idx].company; ra[i]=L; rb[i]=B; rc[i]=R; rd[i]=T; return; }\n auto& items = tree[idx].items;\n long long total_r=0, left_r=0;\n for (int j=0; j<(int)items.size(); j++) { total_r+=r[items[j]]; if(j internal;\n for (int i=0; i<(int)tree.size(); i++) if(!tree[i].is_leaf) internal.push_back(i);\n for (int round=0; round<50; round++) {\n bool improved = false;\n for (int idx : internal) {\n for (int d : {-50,-20,-10,-5,-2,-1,1,2,5,10,20,50}) {\n split_offset[idx] += d;\n compute_rects(root, 0, 0, 10000, 10000);\n double ns = compute_score();\n if (ns > best+1e-12) { best=ns; improved=true; }\n else split_offset[idx] -= d;\n }\n }\n if (!improved) break;\n }\n compute_rects(root, 0, 0, 10000, 10000);\n}\n\nvoid post_process_expand() {\n for (int round=0; round<100; round++) {\n bool any=false;\n for (int i=0; i0 && nv>limit)||(delta<0 && nv x[i]) break;\n if (is_lo && !is_x && nv > y[i]) break;\n if (!is_lo && is_x && nv <= x[i]) break;\n if (!is_lo && !is_x && nv <= y[i]) break;\n int old=val; val=nv;\n bool overlap=false;\n for (int j=0;jr[i]){\n while((long long)(rc[i]-ra[i])*(rd[i]-rb[i])>r[i]&&rc[i]-1>x[i]){int nc=rc[i]-1;long long na=(long long)(nc-ra[i])*(rd[i]-rb[i]);if(satisfaction(na,r[i])>satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]),r[i])+1e-12){rc[i]=nc;any=true;}else break;}\n while((long long)(rc[i]-ra[i])*(rd[i]-rb[i])>r[i]&&ra[i]+1<=x[i]){int na2=ra[i]+1;long long na=(long long)(rc[i]-na2)*(rd[i]-rb[i]);if(satisfaction(na,r[i])>satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]),r[i])+1e-12){ra[i]=na2;any=true;}else break;}\n while((long long)(rc[i]-ra[i])*(rd[i]-rb[i])>r[i]&&rd[i]-1>y[i]){int nd=rd[i]-1;long long na=(long long)(rc[i]-ra[i])*(nd-rb[i]);if(satisfaction(na,r[i])>satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]),r[i])+1e-12){rd[i]=nd;any=true;}else break;}\n while((long long)(rc[i]-ra[i])*(rd[i]-rb[i])>r[i]&&rb[i]+1<=y[i]){int nb=rb[i]+1;long long na=(long long)(rc[i]-ra[i])*(rd[i]-nb);if(satisfaction(na,r[i])>satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]),r[i])+1e-12){rb[i]=nb;any=true;}else break;}\n }\n // Expand undersized\n if((long long)(rc[i]-ra[i])*(rd[i]-rb[i])ra[j]&&rb[i]rb[j];};\n while(rc[i]<10000){int nc=rc[i]+1;bool ov=false;for(int j=0;jra[j]&&rb[i]rb[j]){ov=true;break;}}if(ov)break;long long na=(long long)(nc-ra[i])*(rd[i]-rb[i]);if(satisfaction(na,r[i])<=satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]),r[i]))break;rc[i]=nc;any=true;}\n while(ra[i]>0&&ra[i]-1<=x[i]){int na2=ra[i]-1;bool ov=false;for(int j=0;jra[j]&&rb[i]rb[j]){ov=true;break;}}if(ov)break;long long na=(long long)(rc[i]-na2)*(rd[i]-rb[i]);if(satisfaction(na,r[i])<=satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]),r[i]))break;ra[i]=na2;any=true;}\n while(rd[i]<10000){int nd=rd[i]+1;bool ov=false;for(int j=0;jra[j]&&rb[i]rb[j]){ov=true;break;}}if(ov)break;long long na=(long long)(rc[i]-ra[i])*(nd-rb[i]);if(satisfaction(na,r[i])<=satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]),r[i]))break;rd[i]=nd;any=true;}\n while(rb[i]>0&&rb[i]-1<=y[i]){int nb=rb[i]-1;bool ov=false;for(int j=0;jra[j]&&nbrb[j]){ov=true;break;}}if(ov)break;long long na=(long long)(rc[i]-ra[i])*(rd[i]-nb);if(satisfaction(na,r[i])<=satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]),r[i]))break;rb[i]=nb;any=true;}\n }\n }\n if(!any)break;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> n; x.resize(n); y.resize(n); r.resize(n); ra.resize(n); rb.resize(n); rc.resize(n); rd.resize(n);\n for (int i=0;i> x[i] >> y[i] >> r[i];\n auto start = chrono::steady_clock::now();\n vector indices(n); iota(indices.begin(), indices.end(), 0);\n vector ba(n),bb(n),bc(n),bd(n); double bs=-1;\n for (unsigned seed=0;;seed++) {\n if (chrono::duration_cast(chrono::steady_clock::now()-start).count()>4200) break;\n tree.clear(); mt19937 rng(seed);\n int root = build_tree(indices, rng);\n post_process_offsets(root);\n post_process_expand();\n double s = compute_score();\n if (s>bs) { bs=s; ba=ra; bb=rb; bc=rc; bd=rd; }\n }\n ra=ba; rb=bb; rc=bc; rd=bd;\n for (int i=0;i\n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 50;\nint si, sj;\nint t[N][N], p[N][N];\nint di[] = {-1, 1, 0, 0};\nint dj[] = {0, 0, -1, 1};\nchar dir[] = {'U', 'D', 'L', 'R'};\nmt19937 rng(42);\n\nint tile_value[2500], max_tile_id = 0;\nstring best_path;\nlong long best_score;\n\nstring find_path(double temperature) {\n bool square_visited[N][N] = {};\n bool tile_visited[2500] = {};\n string path;\n int ci = si, cj = sj;\n square_visited[ci][cj] = true;\n tile_visited[t[ci][cj]] = true;\n long long score = p[ci][cj];\n \n while (true) {\n vector> candidates;\n for (int d = 0; d < 4; d++) {\n int ni = ci + di[d], nj = cj + dj[d];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) continue;\n if (square_visited[ni][nj]) continue;\n bool same_tile = (t[ni][nj] == t[ci][cj]);\n if (same_tile || !tile_visited[t[ni][nj]]) {\n double w = same_tile ? p[ni][nj] : tile_value[t[ni][nj]];\n candidates.push_back({w, d});\n }\n }\n if (candidates.empty()) break;\n \n double max_w = -1e18;\n for (auto& [w, d] : candidates) max_w = max(max_w, w);\n double total = 0;\n for (auto& [w, d] : candidates) total += exp((w - max_w) / max(temperature, 0.01));\n \n double r = uniform_real_distribution(0, total)(rng);\n double cum = 0;\n int chosen = candidates[0].second;\n for (auto& [w, d] : candidates) {\n cum += exp((w - max_w) / max(temperature, 0.01));\n if (cum >= r) { chosen = d; break; }\n }\n \n int ni = ci + di[chosen], nj = cj + dj[chosen];\n square_visited[ni][nj] = true;\n tile_visited[t[ni][nj]] = true;\n score += p[ni][nj];\n path += dir[chosen];\n ci = ni; cj = nj;\n }\n \n if (score > best_score) { best_score = score; best_path = path; }\n return path;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) { cin >> t[i][j]; max_tile_id = max(max_tile_id, t[i][j]); }\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> p[i][j];\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) tile_value[t[i][j]] += p[i][j];\n \n best_score = 0;\n auto start = chrono::high_resolution_clock::now();\n int iter = 0;\n while (true) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now - start).count() > 1800) break;\n double temperature = 10.0 * (1.0 - min(iter / 100000.0, 1.0)) + 0.1;\n find_path(temperature);\n iter++;\n }\n \n cout << best_path << endl;\n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble row_h[N], col_v[N], row_h_var[N], col_v_var[N];\ndouble h_dev[N][N-1], v_dev[N-1][N], h_dev_var[N][N-1], v_dev_var[N-1][N];\nmt19937 rng(42);\nnormal_distribution norm_dist(0, 1);\n\ndouble get_h_est(int i, int j) { return row_h[i] + h_dev[i][j]; }\ndouble get_v_est(int i, int j) { return col_v[j] + v_dev[i][j]; }\n\npair dijkstra_with_cost(int si, int sj, int ti, int tj, double temperature) {\n double hw[N][N-1], vw[N-1][N];\n for(int i=0; i prev_node[N][N];\n bool vis[N][N] = {};\n for(int i=0; i, vector>, greater<>> pq;\n pq.push({0, si, sj});\n \n while(!pq.empty()){\n auto [d, i, j] = pq.top();\n pq.pop();\n if(vis[i][j]) continue;\n vis[i][j] = true;\n if(i==ti && j==tj) break;\n \n if(i > 0 && !vis[i-1][j]) {\n double w = vw[i-1][j];\n if(d + w < dist[i-1][j]) {\n dist[i-1][j] = d + w;\n prev_node[i-1][j] = {i, j};\n pq.push({dist[i-1][j], i-1, j});\n }\n }\n if(i < N-1 && !vis[i+1][j]) {\n double w = vw[i][j];\n if(d + w < dist[i+1][j]) {\n dist[i+1][j] = d + w;\n prev_node[i+1][j] = {i, j};\n pq.push({dist[i+1][j], i+1, j});\n }\n }\n if(j > 0 && !vis[i][j-1]) {\n double w = hw[i][j-1];\n if(d + w < dist[i][j-1]) {\n dist[i][j-1] = d + w;\n prev_node[i][j-1] = {i, j};\n pq.push({dist[i][j-1], i, j-1});\n }\n }\n if(j < N-1 && !vis[i][j+1]) {\n double w = hw[i][j];\n if(d + w < dist[i][j+1]) {\n dist[i][j+1] = d + w;\n prev_node[i][j+1] = {i, j};\n pq.push({dist[i][j+1], i, j+1});\n }\n }\n }\n \n string path;\n double mean_cost = 0;\n int ci = ti, cj = tj;\n while(ci != si || cj != sj){\n auto [pi, pj] = prev_node[ci][cj];\n if(pi == ci-1) {\n path += 'D';\n mean_cost += get_v_est(ci-1, cj);\n } else if(pi == ci+1) {\n path += 'U';\n mean_cost += get_v_est(ci, cj);\n } else if(pj == cj-1) {\n path += 'R';\n mean_cost += get_h_est(ci, cj-1);\n } else {\n path += 'L';\n mean_cost += get_h_est(ci, cj);\n }\n ci = pi;\n cj = pj;\n }\n reverse(path.begin(), path.end());\n return {path, mean_cost};\n}\n\nvoid update(int si, int sj, const string& path, int observed) {\n struct E { char t; int i, j; };\n vector edges;\n map hr, vc;\n int ci = si, cj = sj;\n for(char c : path){\n if(c == 'U') { edges.push_back({'v', ci-1, cj}); vc[cj]++; ci--; }\n else if(c == 'D') { edges.push_back({'v', ci, cj}); vc[cj]++; ci++; }\n else if(c == 'L') { edges.push_back({'h', ci, cj-1}); hr[ci]++; cj--; }\n else { edges.push_back({'h', ci, cj}); hr[ci]++; cj++; }\n }\n double pred = 0;\n for(auto& e : edges) {\n pred += (e.t == 'h') ? get_h_est(e.i, e.j) : get_v_est(e.i, e.j);\n }\n double residual = observed - pred;\n double obs_var = pred * pred / 300.0;\n double S = obs_var;\n for(auto& [i, n] : hr) S += n * n * row_h_var[i];\n for(auto& [j, n] : vc) S += n * n * col_v_var[j];\n for(auto& e : edges) S += (e.t == 'h') ? h_dev_var[e.i][e.j] : v_dev_var[e.i][e.j];\n \n for(auto& [i, n] : hr) {\n double K = row_h_var[i] * n / S;\n row_h[i] += K * residual;\n row_h_var[i] *= (1 - K * n);\n row_h[i] = max(500.0, min(15000.0, row_h[i]));\n row_h_var[i] = max(100.0, row_h_var[i]);\n }\n for(auto& [j, n] : vc) {\n double K = col_v_var[j] * n / S;\n col_v[j] += K * residual;\n col_v_var[j] *= (1 - K * n);\n col_v[j] = max(500.0, min(15000.0, col_v[j]));\n col_v_var[j] = max(100.0, col_v_var[j]);\n }\n for(auto& e : edges){\n double& dev = (e.t == 'h') ? h_dev[e.i][e.j] : v_dev[e.i][e.j];\n double& dv = (e.t == 'h') ? h_dev_var[e.i][e.j] : v_dev_var[e.i][e.j];\n double K = dv / S;\n dev += K * residual;\n dv *= (1 - K);\n dev = max(-5000.0, min(5000.0, dev));\n dv = max(100.0, dv);\n }\n}\n\nint main(){\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for(int i=0; i> si >> sj >> ti >> tj;\n \n double temperature = max(0.0, 1.0 - k / 300.0);\n string best_path;\n double best_cost = 1e18;\n int trials = (temperature > 0.01) ? 5 : 1;\n \n for(int t=0; t> obs;\n update(si, sj, best_path, obs);\n }\n return 0;\n}","ahc004":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n int N, M;\n cin >> N >> M;\n vector s(M);\n for (int m = 0; m < M; m++) cin >> s[m];\n \n const int NUM_CHARS = 8;\n mt19937 rng(42);\n auto start_time = chrono::high_resolution_clock::now();\n \n vector slen(M);\n for (int m = 0; m < M; m++) slen[m] = s[m].length();\n \n // Fast EM phase using direct probability products\n vector> charProb(N * N);\n for (int i = 0; i < N * N; i++) for (int c = 0; c < NUM_CHARS; c++) charProb[i][c] = 1.0 / NUM_CHARS;\n \n for (int iter = 0; iter < 15; iter++) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start_time).count() > 0.4) break;\n \n vector> newProb(N * N);\n for (int i = 0; i < N * N; i++) newProb[i].fill(0);\n \n for (int m = 0; m < M; m++) {\n int k = slen[m];\n double maxW = 0;\n vector weights(2 * N * N);\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double wH = 1.0, wV = 1.0;\n for (int p = 0; p < k; p++) {\n wH *= charProb[i * N + (j + p) % N][s[m][p] - 'A'];\n wV *= charProb[((i + p) % N) * N + j][s[m][p] - 'A'];\n }\n weights[2 * (i * N + j)] = wH;\n weights[2 * (i * N + j) + 1] = wV;\n if (wH > maxW) maxW = wH;\n if (wV > maxW) maxW = wV;\n }\n }\n \n if (maxW < 1e-300) continue;\n double sumW = 0;\n for (int pi = 0; pi < 2 * N * N; pi++) {\n weights[pi] /= maxW;\n sumW += weights[pi];\n }\n if (sumW < 1e-300) continue;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double wH = weights[2 * (i * N + j)] / sumW;\n double wV = weights[2 * (i * N + j) + 1] / sumW;\n for (int p = 0; p < k; p++) {\n newProb[i * N + (j + p) % N][s[m][p] - 'A'] += wH;\n newProb[((i + p) % N) * N + j][s[m][p] - 'A'] += wV;\n }\n }\n }\n }\n \n for (int i = 0; i < N * N; i++) {\n double sum = 0;\n for (int c = 0; c < NUM_CHARS; c++) sum += newProb[i][c];\n if (sum > 0) {\n for (int c = 0; c < NUM_CHARS; c++) newProb[i][c] = max(newProb[i][c] / sum, 1e-3);\n double sum2 = 0;\n for (int c = 0; c < NUM_CHARS; c++) sum2 += newProb[i][c];\n for (int c = 0; c < NUM_CHARS; c++) newProb[i][c] /= sum2;\n } else {\n for (int c = 0; c < NUM_CHARS; c++) newProb[i][c] = 1.0 / NUM_CHARS;\n }\n }\n charProb = move(newProb);\n }\n \n vector mat(N, string(N, 'A'));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n double maxP = 0; char best = 'A';\n for (int c = 0; c < NUM_CHARS; c++) if (charProb[i * N + j][c] > maxP) { maxP = charProb[i * N + j][c]; best = 'A' + c; }\n mat[i][j] = best;\n }\n \n // Initial match counts\n vector> matchCount(M, vector(2 * N * N));\n for (int m = 0; m < M; m++) {\n int k = slen[m];\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int cH = 0, cV = 0;\n for (int p = 0; p < k; p++) {\n if (mat[i][(j + p) % N] == s[m][p]) cH++;\n if (mat[(i + p) % N][j] == s[m][p]) cV++;\n }\n matchCount[m][2 * (i * N + j)] = cH;\n matchCount[m][2 * (i * N + j) + 1] = cV;\n }\n }\n }\n \n vector fullMatchCount(M, 0);\n int totalMatched = 0;\n for (int m = 0; m < M; m++) {\n int k = slen[m];\n for (int pi = 0; pi < 2 * N * N; pi++) if (matchCount[m][pi] == k) fullMatchCount[m]++;\n if (fullMatchCount[m] > 0) totalMatched++;\n }\n \n int bestMatched = totalMatched;\n vector bestMat = mat;\n \n // Lightning Fast SA Phase\n while (true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n if (elapsed > 2.8) break;\n \n double temp = 1.5 * (1.0 - elapsed / 3.0) + 0.1;\n \n int ci = rng() % N, cj = rng() % N;\n char oldC = mat[ci][cj];\n char newC;\n if (rng() % 4 == 0 && totalMatched == M) {\n newC = '.';\n } else {\n newC = 'A' + rng() % NUM_CHARS;\n }\n if (newC == oldC) continue;\n \n int deltaDots = (newC == '.' && oldC != '.') ? 1 : ((newC != '.' && oldC == '.') ? -1 : 0);\n \n int deltaMatched = 0;\n for (int m = 0; m < M; m++) {\n int k = slen[m];\n int oldFMC = fullMatchCount[m];\n const char* sm = s[m].c_str();\n int baseH = 2 * ci * N;\n int baseV = 2 * cj + 1;\n for (int p = 0; p < k; p++) {\n int delta = (newC == sm[p]) - (oldC == sm[p]);\n if (delta) {\n int sj = cj - p; if (sj < 0) sj += N;\n int piH = baseH + 2 * sj;\n int oldV = matchCount[m][piH];\n int newV = oldV + delta;\n matchCount[m][piH] = newV;\n if (oldV == k) fullMatchCount[m]--;\n else if (newV == k) fullMatchCount[m]++;\n\n int si = ci - p; if (si < 0) si += N;\n int piV = 2 * si * N + baseV;\n oldV = matchCount[m][piV];\n newV = oldV + delta;\n matchCount[m][piV] = newV;\n if (oldV == k) fullMatchCount[m]--;\n else if (newV == k) fullMatchCount[m]++;\n }\n }\n if (oldFMC == 0 && fullMatchCount[m] > 0) deltaMatched++;\n else if (oldFMC > 0 && fullMatchCount[m] == 0) deltaMatched--;\n }\n \n bool accept = false;\n if (deltaMatched > 0) accept = true;\n else if (deltaMatched == 0) {\n if (deltaDots > 0) accept = true;\n else if (deltaDots == 0) accept = (rng() % 2 == 0);\n else accept = (rng() % 10000 < (int)(exp(-1.0 / temp) * 10000));\n } else {\n accept = (rng() % 10000 < (int)(exp((double)deltaMatched / temp) * 10000));\n }\n \n if (accept) {\n mat[ci][cj] = newC;\n totalMatched += deltaMatched;\n if (totalMatched > bestMatched) {\n bestMatched = totalMatched;\n bestMat = mat;\n }\n } else {\n // Symmetric Revert\n for (int m = 0; m < M; m++) {\n int k = slen[m];\n const char* sm = s[m].c_str();\n int baseH = 2 * ci * N;\n int baseV = 2 * cj + 1;\n for (int p = 0; p < k; p++) {\n int delta = (newC == sm[p]) - (oldC == sm[p]);\n if (delta) {\n int sj = cj - p; if (sj < 0) sj += N;\n int piH = baseH + 2 * sj;\n int curV = matchCount[m][piH];\n matchCount[m][piH] = curV - delta;\n if (curV - delta == k) fullMatchCount[m]++;\n else if (curV == k) fullMatchCount[m]--;\n\n int si = ci - p; if (si < 0) si += N;\n int piV = 2 * si * N + baseV;\n curV = matchCount[m][piV];\n matchCount[m][piV] = curV - delta;\n if (curV - delta == k) fullMatchCount[m]++;\n else if (curV == k) fullMatchCount[m]--;\n }\n }\n }\n }\n }\n \n for (int i = 0; i < N; i++) cout << bestMat[i] << '\\n';\n return 0;\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\nvector>>> vis_from;\nint total_roads;\nbitset<4800> road_mask;\n\nbool is_road(int i, int j) { return i>=0&&i=0&&j>>(N));\n for(int i=0;i=0&&is_road(i,jj);jj--) vis_from[i][j].push_back({i,jj});\n for(int jj=j+1;jj=0&&is_road(ii,j);ii--) vis_from[i][j].push_back({ii,j});\n for(int ii=i+1;ii>, vector>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX)), prev(N, vector(N, -1));\n priority_queue>, vector>>, greater<>> pq;\n dist[si][sj] = 0; pq.push({0, {si, sj}});\n while(!pq.empty()) {\n auto [d, p] = pq.top(); pq.pop();\n auto [i, j] = p;\n if(d > dist[i][j]) continue;\n for(int k=0;k<4;k++) {\n int ni = i+di[k], nj = j+dj[k];\n if(is_road(ni, nj)) {\n int nd = d + cell_cost(ni, nj);\n if(nd < dist[ni][nj]) { dist[ni][nj] = nd; prev[ni][nj] = k; pq.push({nd, {ni, nj}}); }\n }\n }\n }\n return {dist, prev};\n}\n\nstring reconstruct(int si, int sj, int ti, int tj, const vector>& prev) {\n if(si==ti && sj==tj) return \"\";\n string path; int ci=ti, cj=tj;\n while(ci!=si || cj!=sj) { int k=prev[ci][cj]; if(k==-1) return \"\"; path+=dc[k]; ci-=di[k]; cj-=dj[k]; }\n reverse(path.begin(), path.end()); return path;\n}\n\nvector> build_greedy(double alpha) {\n vector> covered(N, vector(N, false));\n auto mark = [&](int i, int j)->int {\n int c=0; for(auto& [vi, vj] : vis_from[i][j]) if(!covered[vi][vj]){covered[vi][vj]=true;c++;} return c;\n };\n vector> targets;\n int ci = si, cj = sj, cc = mark(ci, cj);\n \n while(cc < total_roads) {\n auto [dist, prev] = dijkstra(ci, cj);\n vector>>> children(N, vector>>(N));\n for(int i=0; i scores(N*N, -1.0);\n int current_nv = 0;\n vector> changes;\n vector> tmp = covered;\n \n function dfs = [&](int ui, int uj) {\n int sz = changes.size();\n for(auto& [vi, vj] : vis_from[ui][uj]) {\n if(!tmp[vi][vj]) { tmp[vi][vj] = true; changes.push_back({vi, vj}); current_nv++; }\n }\n if(current_nv > 0 && dist[ui][uj] > 0) scores[ui*N+uj] = pow((double)current_nv, alpha) / (double)dist[ui][uj];\n for(auto& [vi, vj] : children[ui][uj]) dfs(vi, vj);\n while(changes.size() > sz) { auto [vi, vj] = changes.back(); tmp[vi][vj] = false; changes.pop_back(); current_nv--; }\n };\n dfs(ci, cj);\n \n int best_idx = -1; double best_score = -1e18;\n for(int i=0; i best_score) { best_score = scores[i]; best_idx = i; }\n if(best_idx == -1) break;\n \n int bi = best_idx / N, bj = best_idx % N;\n targets.push_back({bi, bj});\n string path = reconstruct(ci, cj, bi, bj, prev);\n for(char c : path) { int k = char_to_idx(c); ci += di[k]; cj += dj[k]; cc += mark(ci, cj); }\n }\n return targets;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> si >> sj; grid.resize(N); for(int i=0;i> grid[i];\n precompute_visibility();\n total_roads = road_mask.count();\n auto st = chrono::high_resolution_clock::now();\n \n set> pool_set;\n pool_set.insert({si, sj});\n vector alphas = {0.5, 1.0, 1.5, 2.5};\n for(double alpha : alphas) { auto targets = build_greedy(alpha); for(auto& t : targets) pool_set.insert(t); }\n \n mt19937 rng(1337);\n vector> roads;\n for(int i=0;i> T(pool_set.begin(), pool_set.end());\n int M = T.size(), S = -1;\n for(int i=0; i> d(M, vector(M, INT_MAX));\n vector>> path_vis(M, vector>(M));\n vector>> all_prev(M, vector>(N, vector(N, -1)));\n \n for(int u=0; u bs;\n for(auto& [vi, vj] : vis_from[T[u].first][T[u].second]) bs[vi*N+vj] = 1;\n int ci = T[v].first, cj = T[v].second;\n while(ci != T[u].first || cj != T[u].second) {\n for(auto& [vi, vj] : vis_from[ci][cj]) bs[vi*N+vj] = 1;\n int k = prev[ci][cj]; ci -= di[k]; cj -= dj[k];\n }\n path_vis[u][v] = bs;\n }\n }\n \n auto evaluate_seq = [&](const vector& seq) -> pair {\n if(seq.empty()) { bitset<4800> vis = path_vis[S][S]; return {(vis & road_mask).count() == total_roads, 0}; }\n int cost = d[S][seq[0]] + d[seq.back()][S];\n bitset<4800> vis = path_vis[S][seq[0]] | path_vis[seq.back()][S];\n for(int i=0; i+1<(int)seq.size(); ++i) { cost += d[seq[i]][seq[i+1]]; vis |= path_vis[seq[i]][seq[i+1]]; }\n return {(vis & road_mask).count() == total_roads, cost};\n };\n \n vector best_greedy_seq; int best_greedy_cost = INT_MAX;\n for(double alpha : alphas) {\n auto targets = build_greedy(alpha);\n vector seq; for(auto& t : targets) for(int i=0; i cur_seq = best_greedy_seq, best_seq = best_greedy_seq;\n int cur_cost = best_greedy_cost, best_cost = best_greedy_cost;\n if(cur_seq.empty() || !evaluate_seq(cur_seq).first) { cur_seq.clear(); for(int i=0; i<20; ++i) cur_seq.push_back(rng() % M); auto [v, c] = evaluate_seq(cur_seq); cur_cost = v ? c : INT_MAX; }\n \n double T_sa = 1000.0;\n mt19937 rng_sa(12345);\n uniform_real_distribution dist01(0.0, 1.0);\n \n while(true) {\n auto now = chrono::high_resolution_clock::now();\n if(chrono::duration_cast(now - st).count() > 2800) break;\n vector new_seq = cur_seq;\n int op = rng_sa() % 5;\n if(op == 0 && new_seq.size() >= 2) { int l = rng_sa() % new_seq.size(), r = rng_sa() % new_seq.size(); if(l > r) swap(l, r); reverse(new_seq.begin() + l, new_seq.begin() + r + 1); }\n else if(op == 1 && new_seq.size() >= 2) { int i = rng_sa() % new_seq.size(), j = rng_sa() % new_seq.size(); swap(new_seq[i], new_seq[j]); }\n else if(op == 2 && new_seq.size() > 1) { int i = rng_sa() % new_seq.size(); new_seq.erase(new_seq.begin() + i); }\n else if(op == 3) { int x = rng_sa() % M, i = rng_sa() % (new_seq.size() + 1); new_seq.insert(new_seq.begin() + i, x); }\n else if(op == 4 && new_seq.size() > 0) { int i = rng_sa() % new_seq.size(), x = rng_sa() % M; new_seq[i] = x; }\n \n auto [valid, new_cost] = evaluate_seq(new_seq);\n if(valid) {\n double delta = new_cost - cur_cost;\n if(delta < 0 || dist01(rng_sa) < exp(-delta / T_sa)) { cur_seq = new_seq; cur_cost = new_cost; if(new_cost < best_cost) { best_cost = new_cost; best_seq = new_seq; } }\n }\n T_sa *= 0.9999;\n }\n \n string final_route;\n if(!best_seq.empty()) {\n int ci = si, cj = sj;\n for(int idx=0; idx<(int)best_seq.size(); ++idx) {\n int u = (idx == 0) ? S : best_seq[idx-1], v = best_seq[idx];\n final_route += reconstruct(T[u].first, T[u].second, T[v].first, T[v].second, all_prev[u]);\n }\n final_route += reconstruct(T[best_seq.back()].first, T[best_seq.back()].second, si, sj, all_prev[best_seq.back()]);\n }\n cout << final_route << endl;\n return 0;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint N, M, K, R;\nvector> d, deps, rev_deps;\nvector> skill_est;\nvector crit_path;\nvector task_start, task_done;\nvector>> member_obs;\n\nvector hungarian(const vector>& cost) {\n int n = cost.size(), m = cost[0].size();\n const double INF = 1e18;\n vector u(n+1,0), v(m+1,0);\n vector p(m+1,0), way(m+1,0);\n for (int i = 1; i <= n; i++) {\n p[0] = i; int j0 = 0;\n vector minv(m+1, INF);\n vector used(m+1, false);\n do {\n used[j0] = true;\n int i0 = p[j0], j1 = 0;\n double delta = INF;\n for (int j = 1; j <= m; j++) if (!used[j]) {\n double cur = cost[i0-1][j-1] - u[i0] - v[j];\n if (cur < minv[j]) { minv[j] = cur; way[j] = j0; }\n if (minv[j] < delta) { delta = minv[j]; j1 = j; }\n }\n for (int j = 0; j <= m; j++) {\n if (used[j]) { u[p[j]] += delta; v[j] -= delta; }\n else minv[j] -= delta;\n }\n j0 = j1;\n } while (p[j0] != 0);\n do { int j1 = way[j0]; p[j0] = p[j1]; j0 = j1; } while (j0);\n }\n vector asgn(n, -1);\n for (int j = 1; j <= m; j++) if (p[j] > 0 && p[j] <= n) asgn[p[j]-1] = j-1;\n return asgn;\n}\n\nvoid recompute_crit_path() {\n vector et(N);\n for (int i = 0; i < N; ++i) {\n if (task_done[i] != -1) { et[i] = 0; continue; }\n if (task_start[i] != -1) { et[i] = 0.1; continue; } // Already started, will finish soon\n double min_w = 1e9;\n for (int j = 0; j < M; ++j) {\n double w = 0;\n for (int k = 0; k < K; ++k) w += max(0.0, (double)d[i][k] - skill_est[j][k]);\n min_w = min(min_w, w);\n }\n et[i] = max(1.0, min_w);\n }\n for (int i = N - 1; i >= 0; i--) {\n crit_path[i] = et[i];\n for (int v : rev_deps[i]) crit_path[i] = max(crit_path[i], et[i] + crit_path[v]);\n }\n}\n\nvoid reestimate(int j) {\n auto& ob = member_obs[j];\n if (ob.empty()) return;\n for (int iter = 0; iter < 30; ++iter) {\n for (auto& [task, t] : ob) {\n double w_pred = 0;\n for (int k = 0; k < K; ++k) w_pred += max(0.0, (double)d[task][k] - skill_est[j][k]);\n \n if (t == 1) {\n if (w_pred > 0) {\n for (int k = 0; k < K; ++k) {\n if (d[task][k] > skill_est[j][k]) {\n skill_est[j][k] += 0.3 * (d[task][k] - skill_est[j][k]);\n }\n }\n }\n } else {\n double target_w = t;\n double diff = w_pred - target_w;\n if (abs(diff) < 0.5) continue;\n \n if (w_pred > 0) {\n for (int k = 0; k < K; ++k) {\n if (d[task][k] > skill_est[j][k]) {\n skill_est[j][k] += 0.3 * diff * (d[task][k] - skill_est[j][k]) / w_pred;\n }\n }\n } else { \n double sum_d = 0;\n for (int k = 0; k < K; ++k) sum_d += d[task][k];\n if (sum_d > 0) {\n for (int k = 0; k < K; ++k) {\n skill_est[j][k] += 0.3 * diff * d[task][k] / sum_d;\n }\n }\n }\n }\n }\n for (auto& [task, t] : ob) {\n if (t == 1) {\n for (int k = 0; k < K; ++k) {\n skill_est[j][k] = max(skill_est[j][k], (double)d[task][k]);\n }\n }\n }\n for (int k = 0; k < K; ++k) skill_est[j][k] = max(0.0, skill_est[j][k]);\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> M >> K >> R;\n d.resize(N, vector(K)); deps.resize(N); rev_deps.resize(N);\n for (int i = 0; i < N; i++) for (int k = 0; k < K; k++) cin >> d[i][k];\n for (int r = 0; r < R; r++) { int u, v; cin >> u >> v; u--; v--; deps[v].push_back(u); rev_deps[u].push_back(v); }\n \n crit_path.resize(N, 0); task_start.resize(N, -1); task_done.resize(N, -1);\n skill_est.resize(M, vector(K)); member_obs.resize(M);\n \n for (int k = 0; k < K; k++) {\n vector dk(N); for (int i = 0; i < N; i++) dk[i] = d[i][k];\n sort(dk.begin(), dk.end());\n double init = dk[N/2] * 1.5;\n for (int j = 0; j < M; j++) skill_est[j][k] = init;\n }\n \n vector member_task(M, -1), member_start_day(M, -1);\n set available_tasks; vector deps_rem(N);\n for (int i = 0; i < N; i++) { deps_rem[i] = deps[i].size(); if (!deps_rem[i]) available_tasks.insert(i); }\n \n int current_day = 0;\n while (true) {\n current_day++;\n recompute_crit_path();\n \n vector free_members;\n for (int j = 0; j < M; j++) if (member_task[j] == -1) free_members.push_back(j);\n int fm = free_members.size();\n \n if (fm > 0 && !available_tasks.empty()) {\n vector av(available_tasks.begin(), available_tasks.end());\n sort(av.begin(), av.end(), [&](int a, int b){ return crit_path[a] > crit_path[b]; });\n \n int nr = min((int)av.size(), fm * 5);\n int na = max(nr, fm);\n vector> cost(fm, vector(na, 1e9));\n for (int mi = 0; mi < fm; mi++) { \n int j = free_members[mi];\n for (int ti = 0; ti < nr; ti++) { \n int i = av[ti];\n double w = 0; for (int k = 0; k < K; k++) w += max(0.0, (double)d[i][k]-skill_est[j][k]);\n cost[mi][ti] = max(1.0, w);\n }\n }\n auto asgn = hungarian(cost);\n vector> assigns;\n for (int mi = 0; mi < fm; mi++) { \n int ti = asgn[mi];\n if (ti >= 0 && ti < nr) assigns.push_back({free_members[mi], av[ti]});\n }\n \n cout << assigns.size();\n for (auto [j,i] : assigns) {\n cout << \" \" << (j+1) << \" \" << (i+1);\n member_task[j]=i; member_start_day[j]=current_day; task_start[i]=current_day;\n available_tasks.erase(i);\n }\n cout << endl;\n } else cout << 0 << endl;\n \n int n; cin >> n; if (n == -1) break;\n for (int idx = 0; idx < n; idx++) {\n int j; cin >> j; j--;\n int i = member_task[j], tt = current_day - member_start_day[j] + 1;\n task_done[i] = current_day;\n member_obs[j].push_back({i, tt});\n reestimate(j);\n member_task[j] = -1;\n for (int v : rev_deps[i]) { \n deps_rem[v]--; \n if (deps_rem[v] == 0 && task_start[v] == -1 && task_done[v] == -1) available_tasks.insert(v); \n }\n }\n }\n return 0;\n}","ahc006":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint a[N], b[N], c[N], d[N];\n\ninline int dist(int x1, int y1, int x2, int y2) { return abs(x1-x2) + abs(y1-y2); }\n\nstruct Xor128 {\n unsigned x = 123456789, y = 362436069, z = 521288629, w = 88675123;\n unsigned next() {\n unsigned t = x ^ (x << 11);\n x = y; y = z; z = w;\n return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));\n }\n double nextDouble() {\n return next() / 4294967295.0;\n }\n int nextInt(int n) {\n return next() % n;\n }\n};\n\nXor128 rng;\n\nint route[100];\nint bestRouteArr[100];\nint orders[M];\nint bestOrders[M];\nbool isSelected[N];\n\nint calcCost() {\n int cost = 0, x = CX, y = CY;\n for (int i = 0; i < 2 * M; i++) {\n int ord = orders[route[i] / 2]; \n bool isD = route[i] % 2;\n int nx = isD ? c[ord] : a[ord], ny = isD ? d[ord] : b[ord];\n cost += dist(x, y, nx, ny); \n x = nx; y = ny;\n }\n return cost + dist(x, y, CX, CY);\n}\n\nbool isValidForInsert(int ip) {\n int k = route[ip] / 2;\n bool isD = route[ip] % 2;\n if (!isD) { // It's a restaurant\n for (int i = ip + 1; i < 2 * M; i++) {\n if (route[i] == k * 2 + 1) return true;\n }\n return false;\n } else { // It's a delivery\n for (int i = 0; i < ip; i++) {\n if (route[i] == k * 2) return true;\n }\n return false;\n }\n}\n\nvoid constructRoute() {\n bool vR[M], vD[M];\n memset(vR, 0, sizeof vR);\n memset(vD, 0, sizeof vD);\n int cx = CX, cy = CY;\n for (int step = 0; step < 2 * M; step++) {\n int best = -1, bestD = INT_MAX;\n for (int i = 0; i < M; i++) {\n if (!vR[i]) { \n int d2 = dist(cx, cy, a[orders[i]], b[orders[i]]); \n if (d2 < bestD) { bestD = d2; best = i * 2; } \n }\n if (vR[i] && !vD[i]) { \n int d2 = dist(cx, cy, c[orders[i]], d[orders[i]]); \n if (d2 < bestD) { bestD = d2; best = i * 2 + 1; } \n }\n }\n route[step] = best;\n if (best % 2 == 0) { vR[best / 2] = true; cx = a[orders[best / 2]]; cy = b[orders[best / 2]]; }\n else { vD[best / 2] = true; cx = c[orders[best / 2]]; cy = d[orders[best / 2]]; }\n }\n}\n\npair getCoord(int idx) {\n if (idx < 0 || idx >= 2 * M) return {CX, CY};\n int ord = orders[route[idx] / 2];\n bool isD = route[idx] % 2;\n if (isD) return {c[ord], d[ord]};\n else return {a[ord], b[ord]};\n}\n\nint distByIdx(int i, int j) {\n auto [x1, y1] = getCoord(i);\n auto [x2, y2] = getCoord(j);\n return abs(x1 - x2) + abs(y1 - y2);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n for (int i = 0; i < N; i++) cin >> a[i] >> b[i] >> c[i] >> d[i];\n \n auto startTime = chrono::high_resolution_clock::now();\n \n vector> scores;\n for (int i = 0; i < N; i++) {\n int cost = dist(CX, CY, a[i], b[i]) + dist(a[i], b[i], c[i], d[i]) + dist(c[i], d[i], CX, CY);\n scores.push_back({cost, i});\n }\n sort(scores.begin(), scores.end());\n \n for (int i = 0; i < M; i++) { orders[i] = scores[i].second; isSelected[orders[i]] = true; }\n \n constructRoute();\n int curCost = calcCost(), bestCost = curCost;\n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n \n double temp = 100.0, cooling = 0.99999;\n int iter = 0;\n \n while (true) {\n if (iter % 1000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - startTime).count() > 1.8) break;\n }\n iter++;\n \n int mt = rng.nextInt(10);\n if (mt < 5) {\n int from = rng.nextInt(2 * M), to = rng.nextInt(2 * M);\n if (from == to) continue;\n \n int savedRoute[100];\n memcpy(savedRoute, route, sizeof(route));\n \n int val = route[from];\n for (int i = from; i < 2 * M - 1; i++) route[i] = route[i + 1];\n int ip = to > from ? to - 1 : to;\n for (int i = 2 * M - 1; i > ip; i--) route[i] = route[i - 1];\n route[ip] = val;\n \n if (isValidForInsert(ip)) {\n int nc = calcCost(); double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n } else {\n memcpy(route, savedRoute, sizeof(route));\n }\n } else {\n memcpy(route, savedRoute, sizeof(route));\n }\n } else if (mt < 8) {\n int ii = rng.nextInt(M), oi = rng.nextInt(N);\n if (isSelected[oi]) continue;\n \n int savedOrders[50];\n memcpy(savedOrders, orders, sizeof(orders));\n int savedRoute[100];\n memcpy(savedRoute, route, sizeof(route));\n \n int oo = orders[ii]; \n orders[ii] = oi; \n isSelected[oo] = false; \n isSelected[oi] = true;\n \n constructRoute(); \n int nc = calcCost(); \n double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n } else { \n memcpy(orders, savedOrders, sizeof(orders));\n isSelected[oi] = false; \n isSelected[oo] = true; \n memcpy(route, savedRoute, sizeof(route));\n }\n } else {\n int l = rng.nextInt(2 * M - 1), r = l + 1 + rng.nextInt(2 * M - 1 - l);\n bool valid = true;\n bool inSegment[50] = {false};\n for (int i = l; i <= r; i++) {\n int k = route[i] / 2;\n if (inSegment[k]) { valid = false; break; }\n inSegment[k] = true;\n }\n if (valid) {\n int delta = distByIdx(l - 1, r) + distByIdx(l, r + 1) - distByIdx(l - 1, l) - distByIdx(r, r + 1);\n int nc = curCost + delta;\n double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n reverse(route + l, route + r + 1);\n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n }\n }\n }\n temp *= cooling;\n }\n \n cout << M;\n for(int i = 0; i < M; i++) cout << \" \" << bestOrders[i] + 1;\n cout << endl;\n cout << 2 * M + 2 << \" \" << CX << \" \" << CY;\n for(int i = 0; i < 2 * M; i++) {\n int ord = bestOrders[bestRouteArr[i] / 2]; bool isD = bestRouteArr[i] % 2;\n cout << \" \" << (isD ? c[ord] : a[ord]) << \" \" << (isD ? d[ord] : b[ord]);\n }\n cout << \" \" << CX << \" \" << CY << endl;\n}","ahc007":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct UnionFind {\n vector parent, rank_;\n int components;\n \n UnionFind(int n) : parent(n), rank_(n, 0), components(n) {\n for (int i = 0; i < n; i++) parent[i] = i;\n }\n \n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n \n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n components--;\n return true;\n }\n \n bool connected(int x, int y) {\n return find(x) == find(y);\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n vector x(N), y(N);\n vector u(M), v(M);\n vector d(M);\n \n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dist = sqrt((double)(x[u[i]] - x[v[i]]) * (x[u[i]] - x[v[i]]) + \n (double)(y[u[i]] - y[v[i]]) * (y[u[i]] - y[v[i]]));\n d[i] = max(1, (int)round(dist));\n }\n \n // Compute reference MST using d_i\n vector order(M);\n for (int i = 0; i < M; i++) order[i] = i;\n sort(order.begin(), order.end(), [&](int a, int b) { return d[a] < d[b]; });\n \n UnionFind refUF(N);\n vector inRefMST(M, false);\n for (int idx : order) {\n if (refUF.unite(u[idx], v[idx])) {\n inRefMST[idx] = true;\n }\n }\n \n // Process edges online\n UnionFind uf(N);\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int adopt = 0;\n \n if (!uf.connected(u[i], v[i])) {\n if (inRefMST[i]) {\n // Always accept reference MST edges - guarantees connectivity\n adopt = 1;\n uf.unite(u[i], v[i]);\n } else {\n // Accept non-MST edges only if they're cheap enough\n // to potentially replace expensive MST edges\n double percentile = (double)(l - d[i]) / (2.0 * d[i]);\n percentile = max(0.0, min(1.0, percentile));\n \n int remaining = M - i - 1;\n int needed = uf.components - 1;\n double safety = (needed > 0) ? (double)remaining / needed : 999.0;\n \n double threshold;\n if (safety >= 5) threshold = 0.3;\n else if (safety >= 3) threshold = 0.4;\n else if (safety >= 2) threshold = 0.5;\n else threshold = 0.65;\n \n if (percentile <= threshold) {\n adopt = 1;\n uf.unite(u[i], v[i]);\n }\n }\n }\n \n cout << adopt << endl;\n }\n \n return 0;\n}","ahc008":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int SIZE = 30;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\n\nint N, M;\nvector px, py, pt;\nvector hx, hy;\nbool wall[SIZE][SIZE];\n\nbool inBounds(int x, int y) { return x >= 0 && x < SIZE && y >= 0 && y < SIZE; }\n\nvoid bfs(int sx, int sy, int dist[SIZE][SIZE]) {\n memset(dist, -1, sizeof(int) * SIZE * SIZE);\n if (!inBounds(sx, sy) || wall[sx][sy]) return;\n queue> q;\n dist[sx][sy] = 0;\n q.push({sx, sy});\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && dist[nx][ny] == -1) {\n dist[nx][ny] = dist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n}\n\ndouble petThreatWeight(int t) {\n switch(t) { case 1: return 1.0; case 2: return 1.5; case 3: return 2.0; case 4: return 2.5; case 5: return 2.0; default: return 1.0; }\n}\n\ndouble computeScoreWithDist(int dist[SIZE][SIZE]) {\n int area = 0;\n double effectivePets = 0;\n for (int i = 0; i < SIZE; i++)\n for (int j = 0; j < SIZE; j++)\n if (dist[i][j] >= 0) area++;\n for (int i = 0; i < N; i++)\n if (dist[px[i]][py[i]] >= 0) effectivePets += 1.0;\n\n int boundaryDist[SIZE][SIZE];\n memset(boundaryDist, -1, sizeof(int) * SIZE * SIZE);\n queue> q;\n for (int x = 0; x < SIZE; x++)\n for (int y = 0; y < SIZE; y++)\n if (dist[x][y] < 0 && !wall[x][y]) {\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && dist[nx][ny] >= 0) {\n if (boundaryDist[x][y] == -1) { boundaryDist[x][y] = 1; q.push({x, y}); }\n break;\n }\n }\n }\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && boundaryDist[nx][ny] == -1 && dist[nx][ny] < 0) {\n boundaryDist[nx][ny] = boundaryDist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n for (int i = 0; i < N; i++) {\n if (dist[px[i]][py[i]] >= 0) continue;\n int d = boundaryDist[px[i]][py[i]];\n if (d >= 1 && d <= 10) effectivePets += petThreatWeight(pt[i]) * 0.2 * exp(-0.2 * d);\n }\n return (double)area / 900.0 * pow(2.0, -effectivePets);\n}\n\nbool petAdjacentTo(int x, int y, const vector& ppx, const vector& ppy) {\n for (int i = 0; i < N; i++) {\n if (ppx[i] == x && ppy[i] == y) return true;\n for (int d = 0; d < 4; d++)\n if (ppx[i] == x + dx[d] && ppy[i] == y + dy[d]) return true;\n }\n return false;\n}\n\nbool humanAt(int x, int y, const vector& hhx, const vector& hhy) {\n for (int i = 0; i < M; i++) if (hhx[i] == x && hhy[i] == y) return true;\n return false;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N;\n px.resize(N); py.resize(N); pt.resize(N);\n for (int i = 0; i < N; i++) { cin >> px[i] >> py[i] >> pt[i]; px[i]--; py[i]--; }\n cin >> M;\n hx.resize(M); hy.resize(M);\n for (int i = 0; i < M; i++) { cin >> hx[i] >> hy[i]; hx[i]--; hy[i]--; }\n memset(wall, false, sizeof(wall));\n\n for (int turn = 0; turn < 300; turn++) {\n vector startPx = px, startPy = py, startHx = hx, startHy = hy;\n string actions(M, '.');\n bool newWall[SIZE][SIZE] = {};\n\n for (int i = 0; i < M; i++) {\n int myHx = startHx[i], myHy = startHy[i];\n int distBefore[SIZE][SIZE];\n bfs(myHx, myHy, distBefore);\n double bestScore = computeScoreWithDist(distBefore);\n char bestAction = '.';\n\n for (int d = 0; d < 4; d++) {\n int wx = myHx + dx[d], wy = myHy + dy[d];\n if (inBounds(wx, wy) && !wall[wx][wy] && !newWall[wx][wy] &&\n !petAdjacentTo(wx, wy, startPx, startPy) && !humanAt(wx, wy, startHx, startHy)) {\n wall[wx][wy] = true;\n int distAfter[SIZE][SIZE];\n bfs(myHx, myHy, distAfter);\n double newScore = computeScoreWithDist(distAfter);\n for (int j = 0; j < N; j++)\n if (distBefore[startPx[j]][startPy[j]] >= 0 && distAfter[startPx[j]][startPy[j]] < 0)\n newScore += 0.05;\n for (int dd = 0; dd < 4; dd++) {\n int nx = wx + dx[dd], ny = wy + dy[dd];\n if (!inBounds(nx, ny) || wall[nx][ny]) newScore += 0.003;\n }\n newScore += 0.001;\n wall[wx][wy] = false;\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"udlr\"[d]; }\n }\n }\n for (int d = 0; d < 4; d++) {\n int nx = myHx + dx[d], ny = myHy + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && !newWall[nx][ny]) {\n int distAfter[SIZE][SIZE];\n bfs(nx, ny, distAfter);\n double newScore = computeScoreWithDist(distAfter);\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"UDLR\"[d]; }\n }\n }\n actions[i] = bestAction;\n switch (actions[i]) {\n case 'u': newWall[myHx-1][myHy]=true; wall[myHx-1][myHy]=true; break;\n case 'd': newWall[myHx+1][myHy]=true; wall[myHx+1][myHy]=true; break;\n case 'l': newWall[myHx][myHy-1]=true; wall[myHx][myHy-1]=true; break;\n case 'r': newWall[myHx][myHy+1]=true; wall[myHx][myHy+1]=true; break;\n case 'U': hx[i]=myHx-1; hy[i]=myHy; break;\n case 'D': hx[i]=myHx+1; hy[i]=myHy; break;\n case 'L': hx[i]=myHx; hy[i]=myHy-1; break;\n case 'R': hx[i]=myHx; hy[i]=myHy+1; break;\n }\n }\n cout << actions << endl;\n for (int i = 0; i < N; i++) {\n string move; cin >> move;\n for (char c : move) {\n if (c=='U') px[i]--; else if (c=='D') px[i]++;\n else if (c=='L') py[i]--; else if (c=='R') py[i]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\nint si,sj,ti,tj;double p;int ti_idx;\nint md[400][4];double fv[400][202];int c2d[256];\n\nvoid init(){\n vectorh(20),v(19);for(int i=0;i<20;i++)cin>>h[i];for(int i=0;i<19;i++)cin>>v[i];\n ti_idx=ti*20+tj;int di[]={-1,1,0,0},dj[]={0,0,-1,1};\n for(int i=0;i<20;i++)for(int j=0;j<20;j++){int idx=i*20+j;\n for(int d=0;d<4;d++){int ni=i+di[d],nj=j+dj[d];bool bl=(ni<0||ni>=20||nj<0||nj>=20);\n if(!bl){if(d==0&&v[i-1][j]=='1')bl=true;else if(d==1&&v[i][j]=='1')bl=true;\n else if(d==2&&h[i][j-1]=='1')bl=true;else if(d==3&&h[i][j]=='1')bl=true;}\n if(bl){ni=i;nj=j;}md[idx][d]=ni*20+nj;}}\n memset(fv,0,sizeof(fv));\n for(int t=200;t>=1;t--)for(int idx=0;idx<400;idx++){\n if(idx==ti_idx){fv[idx][t]=401-t;continue;}\n double b=0;for(int d=0;d<4;d++)b=max(b,p*fv[idx][t+1]+(1-p)*fv[md[idx][d]][t+1]);fv[idx][t]=b;}}\n\ndouble compute_score(const string&s){\n double pr[400]={},np[400];pr[si*20+sj]=1;double es=0;\n for(int t=0;t<(int)s.size();t++){int d=c2d[(unsigned char)s[t]];memset(np,0,sizeof(np));\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;\n if(i==ti_idx)continue;\n np[i]+=p*pr[i];int ni=md[i][d];\n if(ni==ti_idx)es+=(1-p)*pr[i]*(401-t-1);\n else np[ni]+=(1-p)*pr[i];}\n memcpy(pr,np,sizeof(pr));}return es;}\n\nstring bfs_path(){int dist[400],pdir[400];memset(dist,-1,sizeof(dist));\n queueq;int start=si*20+sj;q.push(start);dist[start]=0;\n while(!q.empty()){int idx=q.front();q.pop();if(idx==ti_idx)break;\n for(int d=0;d<4;d++){int ni=md[idx][d];if(ni!=idx&&dist[ni]==-1){dist[ni]=dist[idx]+1;pdir[ni]=d;q.push(ni);}}}\n string path;int idx=ti_idx;int di[]={-1,1,0,0},dj[]={0,0,-1,1};\n while(idx!=start){int d=pdir[idx];path=string(1,\"UDLR\"[d])+path;idx=(idx/20-di[d])*20+(idx%20-dj[d]);}return path;}\n\nstring greedy(){double pr[400]={};pr[si*20+sj]=1;string res;\n for(int t=1;t<=200;t++){double bsc=-1;int ba=0;\n for(int d=0;d<4;d++){double rp=0;double np[400]={};\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;\n if(i==ti_idx)continue;np[i]+=p*pr[i];int ni=md[i][d];\n if(ni==ti_idx)rp+=(1-p)*pr[i];else np[ni]+=(1-p)*pr[i];}\n double sc=rp*(401-t);for(int i=0;i<400;i++)sc+=np[i]*fv[i][t+1];\n if(sc>bsc){bsc=sc;ba=d;}}\n res+=\"UDLR\"[ba];double np[400]={};\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;\n if(i==ti_idx)continue;np[i]+=p*pr[i];int ni=md[i][ba];\n if(ni!=ti_idx)np[ni]+=(1-p)*pr[i];}memcpy(pr,np,sizeof(pr));}return res;}\n\nstring beam_search(int B){\n struct S{double pr[400];double acc;string s;};\n vectorbeam(1);memset(beam[0].pr,0,sizeof(beam[0].pr));beam[0].pr[si*20+sj]=1;beam[0].acc=0;beam[0].s=\"\";\n for(int t=1;t<=200;t++){vector>scores;vectorcand;\n for(int bi=0;bi<(int)beam.size();bi++){for(int d=0;d<4;d++){\n S ns;memset(ns.pr,0,sizeof(ns.pr));ns.acc=beam[bi].acc;ns.s=beam[bi].s+(char)(\"UDLR\"[d]);\n for(int i=0;i<400;i++){if(beam[bi].pr[i]<1e-18)continue;\n if(i==ti_idx)continue;ns.pr[i]+=p*beam[bi].pr[i];int ni=md[i][d];\n if(ni==ti_idx)ns.acc+=(1-p)*beam[bi].pr[i]*(401-t);\n else ns.pr[ni]+=(1-p)*beam[bi].pr[i];}\n double h=ns.acc;for(int i=0;i<400;i++){if(ns.pr[i]<1e-18)continue;h+=ns.pr[i]*fv[i][t+1];}\n scores.emplace_back(h,(int)cand.size());cand.push_back(move(ns));}}\n int k=min(B,(int)scores.size());\n if((int)scores.size()>k)partial_sort(scores.begin(),scores.begin()+k,scores.end(),[](auto&a,auto&b){return a.first>b.first;});\n vectornb(k);for(int i=0;ib.acc;});\n double bsc=-1;string br;int ec=min(20,(int)beam.size());\n for(int i=0;ibsc){bsc=sc;br=beam[i].s;}}return br;}\n\nvoid suffix_opt(string&best,double&bs){\n for(int k=5;k<200;k+=5){if(k>=(int)best.size())continue;\n double pr[400]={};pr[si*20+sj]=1;\n for(int t=0;tbsc2){bsc2=sc;ba=d;}}\n ns+=\"UDLR\"[ba];double np[400]={};\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;\n if(i==ti_idx)continue;np[i]+=p*pr[i];int ni=md[i][ba];\n if(ni!=ti_idx)np[ni]+=(1-p)*pr[i];}memcpy(pr,np,sizeof(pr));}\n double sc=compute_score(ns);if(sc>bs){bs=sc;best=ns;}}}\n\nvoid coordinate_descent(string& best, double& bs) {\n double pr_arr[201][400];\n memset(pr_arr[0], 0, sizeof(pr_arr[0]));\n pr_arr[0][si*20+sj] = 1.0;\n for(int t=0; t<(int)best.size(); ++t) {\n memset(pr_arr[t+1], 0, sizeof(pr_arr[t+1]));\n int d = c2d[(unsigned char)best[t]];\n for(int i=0; i<400; ++i) {\n if(pr_arr[t][i] < 1e-18) continue;\n if(i == ti_idx) continue;\n pr_arr[t+1][i] += p * pr_arr[t][i];\n int ni = md[i][d];\n if(ni == ti_idx) continue;\n pr_arr[t+1][ni] += (1-p) * pr_arr[t][i];\n }\n }\n for(int pos=0; pos<(int)best.size(); ++pos) {\n double bsc = -1; int ba = c2d[(unsigned char)best[pos]];\n for(int d=0; d<4; ++d) {\n double pr_next[400]; memset(pr_next, 0, sizeof(pr_next));\n double es = 0;\n for(int i=0; i<400; ++i) {\n if(pr_arr[pos][i] < 1e-18) continue;\n if(i == ti_idx) continue;\n pr_next[i] += p * pr_arr[pos][i];\n int ni = md[i][d];\n if(ni == ti_idx) es += (1-p) * pr_arr[pos][i] * (401 - (pos+1));\n else pr_next[ni] += (1-p) * pr_arr[pos][i];\n }\n double pr_curr[400]; memcpy(pr_curr, pr_next, sizeof(pr_next));\n for(int t=pos+1; t<(int)best.size(); ++t) {\n double np[400]; memset(np, 0, sizeof(np));\n int dd = c2d[(unsigned char)best[t]];\n for(int i=0; i<400; ++i) {\n if(pr_curr[i] < 1e-18) continue;\n if(i == ti_idx) continue;\n np[i] += p * pr_curr[i];\n int ni = md[i][dd];\n if(ni == ti_idx) es += (1-p) * pr_curr[i] * (401 - (t+1));\n else np[ni] += (1-p) * pr_curr[i];\n }\n memcpy(pr_curr, np, sizeof(np));\n }\n if(es > bsc) { bsc = es; ba = d; }\n }\n if(c2d[(unsigned char)best[pos]] != ba) {\n best[pos] = \"UDLR\"[ba];\n for(int t=pos; t<(int)best.size(); ++t) {\n memset(pr_arr[t+1], 0, sizeof(pr_arr[t+1]));\n int d2 = c2d[(unsigned char)best[t]];\n for(int i=0; i<400; ++i) {\n if(pr_arr[t][i] < 1e-18) continue;\n if(i == ti_idx) continue;\n pr_arr[t+1][i] += p * pr_arr[t][i];\n int ni = md[i][d2];\n if(ni == ti_idx) continue;\n pr_arr[t+1][ni] += (1-p) * pr_arr[t][i];\n }\n }\n }\n }\n double sc = compute_score(best); if(sc > bs) bs = sc;\n}\n\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n c2d['U']=0;c2d['D']=1;c2d['L']=2;c2d['R']=3;\n cin>>si>>sj>>ti>>tj>>p;init();\n string best;double bs=-1;\n auto ts=[&](const string&s){double sc=compute_score(s);if(sc>bs){bs=sc;best=s;}};\n string sp=bfs_path();\n {string s;while((int)(s.size()+sp.size())<=200)s+=sp;ts(s);}\n for(int r=2;r<=5;r++){string s;for(char c:sp)for(int k=0;kbs){bs=sc;best=ns;}}}\n cout<\nusing namespace std;\n\nconst int N = 30;\nint orig[N][N], cur[N][N], rot[N][N];\nconstexpr int di[]={0,-1,0,1}, dj[]={-1,0,1,0};\nconstexpr int to[8][4]={{1,0,-1,-1},{3,-1,-1,0},{-1,-1,3,2},{-1,2,1,-1},{1,0,3,2},{3,2,1,0},{2,-1,0,-1},{-1,3,-1,1}};\nconstexpr int rt[8][4]={{0,1,2,3},{1,2,3,0},{2,3,0,1},{3,0,1,2},{4,5,4,5},{5,4,5,4},{6,7,6,7},{7,6,7,6}};\n\nmap cycle_counts;\n\nint vm[N][N][4]; \nunsigned int vcnt=0;\n\nvoid init_cycle_counts() {\n cycle_counts.clear();\n ++vcnt;\n if (vcnt == 0) { memset(vm, 0, sizeof(vm)); vcnt = 1; }\n for (int i=0; i= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == si && nj == sj && nd == sd) { is_cycle = true; break; }\n if (vm[ni][nj][nd] == vcnt) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n cycle_counts[len]++;\n }\n }\n }\n}\n\nvoid update_tile(int i, int j, int new_t) {\n int old_t = cur[i][j];\n if (old_t == new_t) return;\n\n // 1. Remove old cycles\n bool visited_old[4] = {false, false, false, false};\n for (int d = 0; d < 4; d++) {\n if (visited_old[d] || to[old_t][d] == -1) continue;\n int len = 0;\n int ci = i, cj = j, cd = d;\n bool is_cycle = false;\n while (true) {\n int t2 = (ci == i && cj == j) ? old_t : cur[ci][cj];\n int d2 = to[t2][cd];\n if (d2 == -1) break;\n if (ci == i && cj == j) { visited_old[cd] = true; visited_old[d2] = true; }\n int ni = ci + di[d2], nj = cj + dj[d2];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == i && nj == j && nd == d) { is_cycle = true; break; }\n if (len > 900) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n cycle_counts[len]--;\n if (cycle_counts[len] == 0) cycle_counts.erase(len);\n }\n }\n\n // 2. Add new cycles\n cur[i][j] = new_t;\n bool visited_new[4] = {false, false, false, false};\n for (int d = 0; d < 4; d++) {\n if (visited_new[d] || to[new_t][d] == -1) continue;\n int len = 0;\n int ci = i, cj = j, cd = d;\n bool is_cycle = false;\n while (true) {\n int t2 = (ci == i && cj == j) ? new_t : cur[ci][cj];\n int d2 = to[t2][cd];\n if (d2 == -1) break;\n if (ci == i && cj == j) { visited_new[cd] = true; visited_new[d2] = true; }\n int ni = ci + di[d2], nj = cj + dj[d2];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == i && nj == j && nd == d) { is_cycle = true; break; }\n if (len > 900) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n cycle_counts[len]++;\n }\n }\n}\n\nlong long get_score() {\n if (cycle_counts.empty()) return 0;\n auto it = cycle_counts.rbegin();\n int L1 = it->first;\n if (it->second >= 2) return (long long)L1 * L1;\n if (cycle_counts.size() == 1) return 0;\n int L2 = next(it)->first;\n return (long long)L1 * L2;\n}\n\nint lmatch(int i, int j) {\n int t = cur[i][j], m = 0;\n for (int d = 0; d < 4; d++) {\n if (to[t][d] == -1) continue;\n int ni = i + di[d], nj = j + dj[d];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) continue;\n if (to[cur[ni][nj]][(d + 2) % 4] != -1) m++;\n }\n return m;\n}\n\nvoid greedy_match() {\n for (int pass = 0; pass < 10; pass++) {\n bool ch = false;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n int br = rot[i][j], bm = lmatch(i, j);\n for (int r = 0; r < 4; r++) {\n if (r == rot[i][j]) continue;\n cur[i][j] = rt[orig[i][j]][r];\n int m = lmatch(i, j);\n if (m > bm) { bm = m; br = r; ch = true; }\n }\n rot[i][j] = br; cur[i][j] = rt[orig[i][j]][br];\n }\n if (!ch) break;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(0);\n for (int i = 0; i < N; i++) { string s; cin >> s; for (int j = 0; j < N; j++) orig[i][j] = s[j] - '0'; }\n mt19937 rng(42);\n long long gbest = 0; int grot[N][N] = {};\n auto t0 = chrono::steady_clock::now();\n bool have_best = false;\n\n for (int trial = 0; ; trial++) {\n double elapsed = chrono::duration(chrono::steady_clock::now() - t0).count();\n if (elapsed > 1.5) break;\n\n if (have_best && trial % 2 == 1) {\n memcpy(rot, grot, sizeof(rot));\n int np = 20 + rng() % 80;\n for (int k = 0; k < np; k++) { int i = rng() % N, j = rng() % N; rot[i][j] = rng() % 4; }\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cur[i][j] = rt[orig[i][j]][rot[i][j]];\n greedy_match();\n } else {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { rot[i][j] = rng() % 4; cur[i][j] = rt[orig[i][j]][rot[i][j]]; }\n greedy_match();\n }\n\n init_cycle_counts();\n long long current_score = get_score();\n long long best_score = current_score;\n int brot[N][N]; memcpy(brot, rot, sizeof(rot));\n\n for (int iter = 0; ; iter++) {\n if (iter % 10000 == 0) {\n if (chrono::duration(chrono::steady_clock::now() - t0).count() > 1.7) break;\n }\n double frac = min(iter / 1000000.0, 1.0);\n double temp = 5000.0 * pow(0.001, frac);\n int idx = rng() % 900, i = idx / N, j = idx % N;\n int old_r = rot[i][j];\n int new_r = rng() % 4;\n if (old_r == new_r) continue;\n int new_t = rt[orig[i][j]][new_r];\n if (new_t == cur[i][j]) continue;\n\n update_tile(i, j, new_t);\n long long new_score = get_score();\n long long diff = new_score - current_score;\n\n if (diff >= 0) {\n current_score = new_score;\n rot[i][j] = new_r;\n if (current_score > best_score) {\n best_score = current_score;\n memcpy(brot, rot, sizeof(rot));\n }\n } else if ((double)(rng() & 0xFFFF) / 65536.0 < exp((double)diff / temp)) {\n current_score = new_score;\n rot[i][j] = new_r;\n } else {\n update_tile(i, j, rt[orig[i][j]][old_r]);\n rot[i][j] = old_r;\n }\n }\n\n if (best_score > gbest) {\n gbest = best_score;\n memcpy(grot, brot, sizeof(grot));\n have_best = true;\n }\n }\n\n // Final local search on global best\n memcpy(rot, grot, sizeof(rot));\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cur[i][j] = rt[orig[i][j]][rot[i][j]];\n init_cycle_counts();\n long long current_score = get_score();\n\n for (int pass = 0; pass < 10; pass++) {\n bool imp = false;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n int old_t = cur[i][j];\n int best_new_t = old_t;\n long long best_local_score = current_score;\n int best_new_r = rot[i][j];\n\n for (int r = 0; r < 4; r++) {\n int new_t = rt[orig[i][j]][r];\n if (new_t == old_t) continue;\n update_tile(i, j, new_t);\n long long new_score = get_score();\n if (new_score > best_local_score) {\n best_local_score = new_score;\n best_new_t = new_t;\n best_new_r = r;\n }\n update_tile(i, j, old_t); // revert\n }\n\n if (best_new_t != old_t) {\n update_tile(i, j, best_new_t);\n rot[i][j] = best_new_r;\n current_score = best_local_score;\n imp = true;\n }\n }\n if (!imp) break;\n }\n\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cout << rot[i][j];\n cout << endl;\n\n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N, T;\nint board[10][10];\nint er, ec;\n\nint par[100], gsz[100];\nint find_root(int x) { while (par[x] != x) x = par[x] = par[par[x]]; return x; }\nvoid unite(int x, int y) {\n x = find_root(x); y = find_root(y);\n if (x == y) return;\n if (gsz[x] < gsz[y]) swap(x, y);\n par[y] = x; gsz[x] += gsz[y];\n}\n\npair compute() {\n for (int i = 0; i < N*N; i++) { par[i] = i; gsz[i] = (board[i/N][i%N] ? 1 : 0); }\n int conn = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N-1; j++)\n if (board[i][j] && board[i][j+1] && (board[i][j] & 4) && (board[i][j+1] & 1))\n { unite(i*N+j, i*N+j+1); conn++; }\n for (int i = 0; i < N-1; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j] && board[i+1][j] && (board[i][j] & 8) && (board[i+1][j] & 2))\n { unite(i*N+j, (i+1)*N+j); conn++; }\n // Count edges per component for acyclicity check\n int cedge[100] = {};\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N-1; j++)\n if (board[i][j] && board[i][j+1] && (board[i][j] & 4) && (board[i][j+1] & 1))\n cedge[find_root(i*N+j)]++;\n for (int i = 0; i < N-1; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j] && board[i+1][j] && (board[i][j] & 8) && (board[i+1][j] & 2))\n cedge[find_root(i*N+j)]++;\n int mx = 0;\n for (int i = 0; i < N*N; i++)\n if (board[i/N][i%N] && find_root(i) == i) {\n // Tree = connected component without cycles (edges = vertices - 1)\n if (cedge[i] == gsz[i] - 1)\n mx = max(mx, gsz[i]);\n }\n return {mx, conn};\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> T;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n char c = s[j];\n board[i][j] = (c >= '0' && c <= '9') ? c - '0' : c - 'a' + 10;\n if (!board[i][j]) { er = i; ec = j; }\n }\n }\n \n constexpr int dr[] = {-1,1,0,0}, dc[] = {0,0,-1,1};\n constexpr char dc_c[] = {'U','D','L','R'};\n constexpr int rev_dir[] = {1,0,3,2};\n \n string moves; moves.reserve(T);\n auto [init_mx, init_conn] = compute();\n int best_mx = init_mx; size_t best_idx = 0;\n mt19937 rng(42);\n int last_d = -1;\n double temp = 3.0;\n int stale = 0;\n auto start = chrono::high_resolution_clock::now();\n \n while ((int)moves.size() < T) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now-start).count() > 2900) break;\n \n int ns_mx[4], ns_conn[4];\n for (int d = 0; d < 4; d++) {\n int nr = er+dr[d], nc = ec+dc[d];\n if (nr<0||nr>=N||nc<0||nc>=N) { ns_mx[d] = -1; ns_conn[d] = -1; continue; }\n swap(board[er][ec], board[nr][nc]);\n int oer=er, oec=ec; er=nr; ec=nc;\n auto [mx, conn] = compute();\n ns_mx[d] = mx; ns_conn[d] = conn;\n swap(board[er][ec], board[oer][oec]); er=oer; ec=oec;\n }\n \n long long ns_val[4];\n for (int d = 0; d < 4; d++)\n ns_val[d] = (ns_mx[d] < 0) ? -1e18 : (long long)ns_mx[d] * 100000LL + ns_conn[d] * 100LL;\n \n int bd = -1; long long bv = -1e18;\n for (int d = 0; d < 4; d++)\n if (ns_val[d] > bv) { bv = ns_val[d]; bd = d; }\n if (bd == -1) break;\n \n long long cur_val = (long long)init_mx * 100000LL + init_conn * 100LL;\n // Recompute current from actual state\n auto [cur_mx, cur_conn] = compute();\n cur_val = (long long)cur_mx * 100000LL + cur_conn * 100LL;\n \n int chosen;\n if (bv > cur_val) {\n chosen = bd;\n stale = 0;\n } else {\n stale++;\n double delta = (double)(bv - cur_val);\n double prob = exp(delta / max(temp, 0.01));\n if ((double)rng() / (double)UINT32_MAX < prob) {\n chosen = bd;\n } else {\n // Random walk - longer when stuck\n int walk_len = (stale > 30) ? 15 : 5;\n for (int w = 0; w < walk_len && (int)moves.size() < T; w++) {\n int valid[4], nv = 0;\n for (int d = 0; d < 4; d++) {\n int nr = er+dr[d], nc = ec+dc[d];\n if (nr<0||nr>=N||nc<0||nc>=N) continue;\n if (last_d >= 0 && d == rev_dir[last_d]) continue;\n valid[nv++] = d;\n }\n if (!nv)\n for (int d = 0; d < 4; d++) {\n int nr = er+dr[d], nc = ec+dc[d];\n if (nr>=0&&nr=0&&nc best_mx) { best_mx = mx2; best_idx = moves.size(); }\n init_mx = mx2; init_conn = conn2;\n continue;\n }\n }\n \n int nr = er+dr[chosen], nc = ec+dc[chosen];\n swap(board[er][ec], board[nr][nc]); er=nr; ec=nc;\n moves += dc_c[chosen]; last_d = chosen;\n init_mx = ns_mx[chosen]; init_conn = ns_conn[chosen];\n \n if (init_mx > best_mx) { best_mx = init_mx; best_idx = moves.size(); stale = 0; }\n \n temp *= 0.9997;\n if (stale > 50) { temp = min(temp * 2.0, 10.0); stale = 25; }\n if (best_mx == N*N-1) break;\n }\n done:\n cout << moves.substr(0, best_idx) << endl;\n}","ahc012":"#include \nusing namespace std;\ntypedef long long ll;\n\nint N, K;\nint a[11];\nvector px, py;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> K;\n for (int d = 1; d <= 10; d++) cin >> a[d];\n px.resize(N); py.resize(N);\n for (int i = 0; i < N; i++) cin >> px[i] >> py[i];\n \n vector> lines;\n auto start = chrono::steady_clock::now();\n \n for (int iter = 0; iter < K; iter++) {\n if (chrono::duration(chrono::steady_clock::now() - start).count() > 2.0) break;\n \n map, vector> groups;\n for (int i = 0; i < N; i++) {\n vector sig; bool dead = false;\n for (auto& L : lines) {\n ll la = L[3]-L[1], lb = L[0]-L[2], lc = L[2]*L[1]-L[0]*L[3];\n ll val = la*px[i] + lb*py[i] + lc;\n if (val == 0) { dead = true; break; }\n sig.push_back(val > 0 ? 1 : -1);\n }\n if (!dead) groups[sig].push_back(i);\n }\n \n int pc[11] = {};\n for (auto& [s, m] : groups) { int sz = m.size(); if (sz >= 1 && sz <= 10) pc[sz]++; }\n int cur_score = 0;\n for (int d = 1; d <= 10; d++) cur_score += min(a[d], pc[d]);\n int max_score = 0;\n for (int d = 1; d <= 10; d++) max_score += a[d];\n if (cur_score == max_score) break;\n \n vector>> cands;\n auto try_line = [&](ll x1, ll y1, ll x2, ll y2) {\n if (x1 == x2 && y1 == y2) return;\n ll la = y2-y1, lb = x1-x2, lc = x2*y1-x1*y2;\n int new_pc[11] = {};\n for (auto& [sig, members] : groups) {\n int pos = 0, neg = 0;\n for (int i : members) {\n ll val = la*px[i] + lb*py[i] + lc;\n if (val > 0) pos++; else if (val < 0) neg++;\n }\n if (pos >= 1 && pos <= 10) new_pc[pos]++;\n if (neg >= 1 && neg <= 10) new_pc[neg]++;\n }\n int score = 0;\n for (int d = 1; d <= 10; d++) score += min(a[d], new_pc[d]);\n cands.push_back({score, {x1, y1, x2, y2}});\n };\n \n for (auto& [sig, members] : groups) {\n int sz = members.size();\n if (sz <= 1) continue;\n if (sz <= 10 && pc[sz] <= a[sz]) continue;\n int lim = min((int)members.size(), 20);\n for (int ii = 0; ii < lim; ii++)\n for (int jj = ii+1; jj < lim; jj++) {\n int i = members[ii], j = members[jj];\n ll sx = px[i]+px[j], sy = py[i]+py[j];\n ll dx = 2*(py[i]-py[j]), dy = 2*(px[j]-px[i]);\n try_line(sx, sy, sx+dx, sy+dy);\n }\n ll cx = 0, cy = 0;\n for (int i : members) { cx += px[i]; cy += py[i]; }\n for (int angle = 0; angle < 18; angle++) {\n double a_rad = angle * M_PI / 9;\n ll dx = (ll)round(10000*cos(a_rad)), dy = (ll)round(10000*sin(a_rad));\n if (dx == 0 && dy == 0) continue;\n try_line(cx, cy, cx + dx*sz, cy + dy*sz);\n }\n }\n \n mt19937 rng(iter*12345+67890);\n for (int r = 0; r < 50; r++) {\n ll x1 = rng()%20001-10000, y1 = rng()%20001-10000;\n ll x2 = rng()%20001-10000, y2 = rng()%20001-10000;\n try_line(x1, y1, x2, y2);\n }\n \n if (cands.empty()) break;\n int best = 0;\n for (int i = 1; i < (int)cands.size(); i++)\n if (cands[i].first > cands[best].first) best = i;\n lines.push_back(cands[best].second);\n }\n \n cout << lines.size() << \"\\n\";\n for (auto& L : lines)\n cout << L[0] << \" \" << L[1] << \" \" << L[2] << \" \" << L[3] << \"\\n\";\n return 0;\n}","ahc014":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, M;\nvector> has_dot;\nvector> ops;\nmap>> segs[4];\n\nvector dots_y[65];\nvector dots_x[65];\nvector pt_idx[65];\nvector> existing_dots;\n\nset candidates;\nvector>> empty_pts_vec;\n\nint seg_type(int x1,int y1,int x2,int y2){\n if(y1==y2)return 0;\n if(x1==x2)return 1;\n if(x2-x1==y2-y1)return 2;\n return 3;\n}\nint line_id(int t,int x,int y){\n if(t==0)return y;\n if(t==1)return x;\n if(t==2)return x-y;\n return x+y;\n}\nint line_coord(int t,int x,int y){\n if(t==0||t==2||t==3)return x;\n return y;\n}\n\nbool check_overlap(int t,int lid,int s,int e){\n if(s>e)swap(s,e);\n auto it=segs[t].find(lid);\n if(it==segs[t].end())return false;\n for(auto& seg : it->second){\n int lo=min(seg.first,seg.second);\n int hi=max(seg.first,seg.second);\n if(max(s,lo)> corners={{x1,y1},{x2,y2},{x3,y3},{x4,y4}};\n auto chk=[&](int ax,int ay,int bx,int by){\n int dx=bx-ax, dy=by-ay;\n int g=gcd(abs(dx),abs(dy));\n if(g==0)return false;\n int sx=dx/g, sy=dy/g;\n for(int i=1;i find_rect(int ex, int ey) {\n // Axis-aligned\n for (int y1 : dots_y[ex]) {\n for (int x1 : dots_x[ey]) {\n if (has_dot[x1][y1]) {\n if (valid_rect(ex, ey, ex, y1, x1, y1, x1, ey)) {\n return {ex, ey, ex, y1, x1, y1, x1, ey};\n }\n }\n }\n }\n \n // Tilted 1 (same row for V1, V3)\n for (int x3 : dots_x[ey]) {\n int diff = x3 - ex;\n if (diff % 2 != 0) continue;\n int cx = (ex + x3) / 2;\n int dy = diff / 2;\n int y2 = ey + dy;\n int y4 = ey - dy;\n if (y2 >= 0 && y2 < N && y4 >= 0 && y4 < N && has_dot[cx][y2] && has_dot[cx][y4]) {\n if (valid_rect(ex, ey, cx, y2, x3, ey, cx, y4)) {\n return {ex, ey, cx, y2, x3, ey, cx, y4};\n }\n }\n }\n \n // Tilted 2 (same col for V1, V3)\n for (int y3 : dots_y[ex]) {\n int diff = y3 - ey;\n if (diff % 2 != 0) continue;\n int cy = (ey + y3) / 2;\n int dx = diff / 2;\n int x2 = ex + dx;\n int x4 = ex - dx;\n if (x2 >= 0 && x2 < N && x4 >= 0 && x4 < N && has_dot[x2][cy] && has_dot[x4][cy]) {\n if (valid_rect(ex, ey, x2, cy, ex, y3, x4, cy)) {\n return {ex, ey, x2, cy, ex, y3, x4, cy};\n }\n }\n }\n \n return {-1};\n}\n\nvoid add_cand(int x, int y) {\n if (x >= 0 && x < N && y >= 0 && y < N && !has_dot[x][y]) {\n int idx = pt_idx[x][y];\n if (idx != -1) {\n candidates.insert(idx);\n }\n }\n}\n\nvoid add_candidates(int x, int y) {\n for (auto [x2, y2] : existing_dots) {\n if ((x % 2) != (x2 % 2)) continue;\n if ((y % 2) != (y2 % 2)) continue;\n \n int cx = (x + x2) / 2;\n int cy = (y + y2) / 2;\n \n int dx = (y2 - y) / 2;\n int dy = (x2 - x) / 2;\n \n int va_x = cx - dx;\n int va_y = cy - dy;\n int vb_x = cx + dx;\n int vb_y = cy + dy;\n \n bool valid_a = (va_x >= 0 && va_x < N && va_y >= 0 && va_y < N);\n bool valid_b = (vb_x >= 0 && vb_x < N && vb_y >= 0 && vb_y < N);\n \n if (valid_a && valid_b) {\n if ((va_x == x && va_y == y) || (va_x == x2 && va_y == y2)) continue;\n \n bool dot_a = has_dot[va_x][va_y];\n bool dot_b = has_dot[vb_x][vb_y];\n \n if (dot_a && !dot_b) {\n add_cand(vb_x, vb_y);\n } else if (!dot_a && dot_b) {\n add_cand(va_x, va_y);\n }\n }\n }\n}\n\nint main(){\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n cin >> N >> M;\n has_dot.assign(N, vector(N, false));\n \n double c = (N - 1) / 2.0;\n \n for(int i=0;i> initial_dots(M);\n for(int i=0;i> x >> y;\n has_dot[x][y] = true;\n dots_y[x].push_back(y);\n dots_x[y].push_back(x);\n initial_dots[i] = {x, y};\n }\n \n for(int x=0;x{r[0], r[1], r[2], r[3], r[4], r[5], r[6], r[7]});\n candidates.erase(best_idx);\n pt_idx[x][y] = -1;\n add_candidates(x, y);\n } else {\n candidates.erase(best_idx);\n }\n }\n \n cout << ops.size() << \"\\n\";\n for(auto& op : ops){\n for(int i=0;i<8;i++){\n cout << op[i] << (i<7?\" \":\"\\n\");\n }\n }\n \n return 0;\n}","ahc015":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 10;\nint grid[N][N];\nint f[101];\nmt19937 rng(42);\n\nvoid tiltGrid(int g[N][N], int d) {\n if (d == 0) {\n for (int c = 0; c < N; c++) {\n int w = 0;\n for (int r = 0; r < N; r++) {\n if (g[r][c]) { if (w != r) { g[w][c] = g[r][c]; g[r][c] = 0; } w++; }\n }\n }\n } else if (d == 1) {\n for (int c = 0; c < N; c++) {\n int w = N - 1;\n for (int r = N - 1; r >= 0; r--) {\n if (g[r][c]) { if (w != r) { g[w][c] = g[r][c]; g[r][c] = 0; } w--; }\n }\n }\n } else if (d == 2) {\n for (int r = 0; r < N; r++) {\n int w = 0;\n for (int c = 0; c < N; c++) {\n if (g[r][c]) { if (w != c) { g[r][w] = g[r][c]; g[r][c] = 0; } w++; }\n }\n }\n } else {\n for (int r = 0; r < N; r++) {\n int w = N - 1;\n for (int c = N - 1; c >= 0; c--) {\n if (g[r][c]) { if (w != c) { g[r][w] = g[r][c]; g[r][c] = 0; } w--; }\n }\n }\n }\n}\n\nlong long calcScore(int g[N][N]) {\n bool visited[N][N] = {};\n long long score = 0;\n int dr[] = {-1, 1, 0, 0}, dc[] = {0, 0, -1, 1};\n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (!visited[r][c] && g[r][c]) {\n int flavor = g[r][c], size = 0;\n queue> q;\n q.push({r, c}); visited[r][c] = true;\n while (!q.empty()) {\n auto [cr, cc] = q.front(); q.pop(); size++;\n for (int d = 0; d < 4; d++) {\n int nr = cr + dr[d], nc = cc + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !visited[nr][nc] && g[nr][nc] == flavor) {\n visited[nr][nc] = true; q.push({nr, nc});\n }\n }\n }\n score += (long long)size * size;\n }\n }\n }\n return score;\n}\n\nlong long calcPotential(int g[N][N], int turn) {\n if (turn >= 100) return 0;\n int nextFlavor = f[turn + 1];\n long long potential = 0;\n int dr[] = {-1, 1, 0, 0}, dc[] = {0, 0, -1, 1};\n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (g[r][c] == 0) {\n for (int d = 0; d < 4; d++) {\n int nr = r + dr[d], nc = c + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && g[nr][nc] == nextFlavor) {\n potential++; break;\n }\n }\n }\n }\n }\n // Also count adjacency within same flavor groups\n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (g[r][c]) {\n if (r + 1 < N && g[r+1][c] == g[r][c]) potential++;\n if (c + 1 < N && g[r][c+1] == g[r][c]) potential++;\n }\n }\n }\n return potential;\n}\n\nlong long simulate(int start_t, int orig_g[N][N]) {\n int g[N][N];\n memcpy(g, orig_g, sizeof(g));\n for (int t = start_t; t <= 100; t++) {\n pair empty_cells[100];\n int cnt = 0;\n for (int r = 0; r < N; r++)\n for (int c = 0; c < N; c++)\n if (g[r][c] == 0) empty_cells[cnt++] = {r, c};\n if (cnt == 0) break;\n int idx = rng() % cnt;\n g[empty_cells[idx].first][empty_cells[idx].second] = f[t];\n // Greedy tilt in simulation\n long long best = -1; int best_d = 1;\n int saved[N][N];\n for (int d = 0; d < 4; d++) {\n memcpy(saved, g, sizeof(g));\n tiltGrid(g, d);\n long long sc = calcScore(g);\n if (sc > best) { best = sc; best_d = d; }\n memcpy(g, saved, sizeof(g));\n }\n tiltGrid(g, best_d);\n }\n return calcScore(g);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int i = 1; i <= 100; i++) cin >> f[i];\n memset(grid, 0, sizeof(grid));\n \n string dirs = \"FBLR\";\n int priority[] = {4, 1, 2, 3}; // B > L > R > F\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n int pos = 1, pr = -1, pc = -1;\n for (int r = 0; r < N && pr == -1; r++)\n for (int c = 0; c < N && pr == -1; c++)\n if (grid[r][c] == 0) { if (pos == p) { pr = r; pc = c; } pos++; }\n grid[pr][pc] = f[t];\n \n long long scores[4], pot[4];\n int saved[N][N];\n for (int d = 0; d < 4; d++) {\n memcpy(saved, grid, sizeof(grid));\n tiltGrid(grid, d);\n scores[d] = calcScore(grid);\n pot[d] = calcPotential(grid, t);\n memcpy(grid, saved, sizeof(grid));\n }\n \n long long maxScore = *max_element(scores, scores + 4);\n vector cands;\n for (int d = 0; d < 4; d++) if (scores[d] == maxScore) cands.push_back(d);\n \n int best_dir;\n if (cands.size() == 1) {\n best_dir = cands[0];\n } else {\n // Use potential to narrow down\n long long maxPot = -1;\n for (int d : cands) maxPot = max(maxPot, pot[d]);\n vector cands2;\n for (int d : cands) if (pot[d] == maxPot) cands2.push_back(d);\n \n if (cands2.size() == 1) {\n best_dir = cands2[0];\n } else if (t < 85) {\n // Monte Carlo tiebreak\n int num_sims = max(10, 50 - t / 3);\n long long mc[4] = {};\n for (int d : cands2) {\n int temp[N][N];\n memcpy(temp, grid, sizeof(grid));\n tiltGrid(temp, d);\n for (int s = 0; s < num_sims; s++) mc[d] += simulate(t + 1, temp);\n }\n best_dir = cands2[0];\n for (int d : cands2) if (mc[d] > mc[best_dir]) best_dir = d;\n } else {\n best_dir = *min_element(cands2.begin(), cands2.end(), [&](int a, int b) { return priority[a] < priority[b]; });\n }\n }\n \n tiltGrid(grid, best_dir);\n cout << dirs[best_dir] << '\\n';\n cout.flush();\n }\n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int M; double eps;\n cin >> M >> eps;\n \n int N;\n {\n double f = sqrt(max(eps * (1.0 - eps), 0.001));\n N = (int)round(2.5 * M * f + sqrt(2.0 * M) + 3);\n N = max(4, min(100, N));\n }\n \n int maxE = N * (N - 1) / 2;\n mt19937 rng(42);\n \n auto eidx = [&](int i, int j) -> int {\n if (i > j) swap(i, j);\n return i * (2 * N - i - 1) / 2 + (j - i - 1);\n };\n \n auto sortedDeg = [&](const string& g) -> vector {\n vector d(N, 0);\n for (int i = 0; i < N; i++)\n for (int j = i + 1; j < N; j++) {\n if (g[i * (2*N-i-1)/2 + (j-i-1)] == '1') { d[i]++; d[j]++; }\n }\n sort(d.begin(), d.end());\n return d;\n };\n \n int NC = min(2000, max(M * 10, 500));\n vector cands(NC, string(maxE, '0'));\n vector> cdeg(NC);\n \n for (int c = 0; c < NC; c++) {\n string g(maxE, '0');\n if (c < NC / 3) {\n double dens = (c + 1.0) / (NC / 3 + 1);\n int te = max(0, min(maxE, (int)round(dens * maxE)));\n vector p(maxE); iota(p.begin(), p.end(), 0);\n shuffle(p.begin(), p.end(), rng);\n for (int i = 0; i < te; i++) g[p[i]] = '1';\n } else if (c < 2 * NC / 3) {\n int code = c - NC / 3;\n vector b(N, 0);\n int numOnes = code / max(1, (NC / 3 / N)) + 1;\n int offset = code % max(1, (NC / 3 / N));\n for (int i = 0; i < min(numOnes, N); i++) {\n int pos = (offset + i * (N / max(numOnes, 1))) % N;\n b[pos] = 1;\n }\n for (int j = 0; j < N; j++)\n if (b[j])\n for (int i = 0; i < j; i++)\n g[eidx(i, j)] = '1';\n } else {\n int code = c - 2 * NC / 3;\n int cliqueSz = (code / max(1, NC / 3 / N)) + 1;\n cliqueSz = min(cliqueSz, N);\n int crossE = code % max(1, NC / 3 / N);\n for (int i = 0; i < cliqueSz; i++)\n for (int j = i + 1; j < cliqueSz; j++)\n g[eidx(i, j)] = '1';\n int added = 0;\n for (int i = 0; i < cliqueSz && added < crossE; i++)\n for (int j = cliqueSz; j < N && added < crossE; j++) {\n g[eidx(i, j)] = '1'; added++;\n }\n }\n cands[c] = g;\n cdeg[c] = sortedDeg(g);\n }\n \n vector> fp(NC, vector(N));\n for (int c = 0; c < NC; c++)\n for (int i = 0; i < N; i++)\n fp[c][i] = cdeg[c][i] * (1.0 - 2.0 * eps) + (N - 1) * eps;\n \n vector sel;\n vector minD(NC, 1e18);\n vector used(NC, false);\n \n sel.push_back(0); used[0] = true;\n for (int c = 0; c < NC; c++) {\n double d = 0;\n for (int i = 0; i < N; i++) { double df = fp[c][i] - fp[0][i]; d += df * df; }\n minD[c] = d;\n }\n \n for (int k = 1; k < M; k++) {\n int best = -1; double bestD = -1;\n for (int c = 0; c < NC; c++) {\n if (used[c]) continue;\n if (minD[c] > bestD) { bestD = minD[c]; best = c; }\n }\n sel.push_back(best); used[best] = true;\n for (int c = 0; c < NC; c++) {\n if (used[c]) continue;\n double d = 0;\n for (int i = 0; i < N; i++) { double df = fp[c][i] - fp[best][i]; d += df * df; }\n minD[c] = min(minD[c], d);\n }\n }\n \n // Precompute adjacency matrices for Hamming distance decoding\n vector> adjM(M, vector(maxE));\n vector> gfp(M, vector(N));\n for (int k = 0; k < M; k++) {\n gfp[k] = fp[sel[k]];\n for (int e = 0; e < maxE; e++) adjM[k][e] = (cands[sel[k]][e] == '1') ? 1 : 0;\n }\n \n cout << N << \"\\n\";\n for (int k = 0; k < M; k++) cout << cands[sel[k]] << \"\\n\";\n cout.flush();\n \n double dVar = max(1.0, (N - 1.0) * eps * (1.0 - eps));\n \n for (int q = 0; q < 100; q++) {\n string H; cin >> H;\n vector hd = sortedDeg(H);\n \n // Primary: fingerprint distance\n int bestK = 0; double bestS = -1e18;\n for (int k = 0; k < M; k++) {\n double s = 0;\n for (int i = 0; i < N; i++) {\n double diff = hd[i] - gfp[k][i];\n s -= diff * diff / (2.0 * dVar);\n }\n if (s > bestS) { bestS = s; bestK = k; }\n }\n \n cout << bestK << \"\\n\";\n cout.flush();\n }\n return 0;\n}","ahc017":"#include \nusing namespace std;\ntypedef long long ll;\ntypedef pair pli;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N,M,D,K; cin>>N>>M>>D>>K;\n vector u(M),v(M),w(M);\n vector>> adj(N);\n for(int i=0;i>u[i]>>v[i]>>w[i];u[i]--;v[i]--;adj[u[i]].push_back({i,v[i]});adj[v[i]].push_back({i,u[i]});}\n vector x(N),y(N);\n for(int i=0;i>x[i]>>y[i];\n\n int S=min(N,100);\n vector betw(M,0);\n for(int si=0;si dist(N,LLONG_MAX);vector pe(N,-1);\n dist[s]=0;priority_queue,greater> pq;pq.push({0,s});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>dist[nd])continue;for(auto[ei,nx]:adj[nd]){ll nd2=d+w[ei];if(nd2 ss(N,1);vector> ch(N);\n for(int t=0;t ord={s};for(int i=0;i<(int)ord.size();i++)for(int c:ch[ord[i]])ord.push_back(c);\n for(int i=(int)ord.size()-1;i>0;i--){int nd=ord[i];int o=(u[pe[nd]]==nd)?v[pe[nd]]:u[pe[nd]];ss[o]+=ss[nd];}\n for(int t=0;t> apsp(N,vector(N,LLONG_MAX));\n for(int s=0;s,greater> pq;pq.push({0,s});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>apsp[s][nd])continue;for(auto[ei,nx]:adj[nd]){ll nd2=d+w[ei];if(nd2 det(M,0);\n for(int ei=0;ei impact(M);\n for(int i=0;i> conflicts(M);\n vector dist(N);vector pe(N);\n for(int ei=0;ei,greater> pq;pq.push({0,u[ei]});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>dist[nd])continue;for(auto[ej,nx]:adj[nd]){if(ej==ei)continue;ll nd2=d+w[ej];if(nd2 order(M);iota(order.begin(),order.end(),0);\n sort(order.begin(),order.end(),[&](int a,int b){return impact[a]>impact[b];});\n\n vector r(M,-1),dc(D,0);vector day_imp(D,0);\n for(int ei:order){\n double bs=1e18;int bd=-1;\n for(int d=0;d=K)continue;double sc=0;for(int ej:conflicts[ei])if(r[ej]==d)sc+=impact[ei]*impact[ej];sc+=day_imp[d]*1e-4;if(sc(now-t0).count()>5.0)break;\n int ei=rng()%M;int od=r[ei];double cs=0;for(int ej:conflicts[ei])if(r[ej]==od)cs+=impact[ei]*impact[ej];\n int bd=-1;double bi=0;for(int d=0;d=K)continue;double ns=0;for(int ej:conflicts[ei])if(r[ej]==d)ns+=impact[ei]*impact[ej];double imp=cs-ns+((day_imp[od]-impact[ei])-(day_imp[d]+impact[ei]))*1e-4;if(imp>bi){bi=imp;bd=d;}}\n if(bd!=-1){r[ei]=bd;dc[od]--;dc[bd]++;day_imp[od]-=impact[ei];day_imp[bd]+=impact[ei];}}\n\n for(int i=0;i\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\nint D;\nusing Point=tuple;\nusing Array3D=vector>>;\n\nchrono::high_resolution_clock::time_point start_time;\n\nvector readSil(){vectors(D);for(int i=0;i>s[i];return s;}\nArray3D buildMF(const vector&f,const vector&r){Array3D b(D,vector>(D,vector(D,0)));for(int x=0;x> findComp(const Array3D&b){\n Array3D vis(D,vector>(D,vector(D,0)));vector>cs;\n const int dx[]={1,-1,0,0,0,0},dy[]={0,0,1,-1,0,0},dz[]={0,0,0,0,1,-1};\n for(int x=0;xc;queueq;q.push({x,y,z});vis[x][y][z]=1;\n while(!q.empty()){auto[cx,cy,cz]=q.front();q.pop();c.push_back({cx,cy,cz});\n for(int d=0;d<6;d++){int nx=cx+dx[d],ny=cy+dy[d],nz=cz+dz[d];\n if(0<=nx&&nx>> genRots(){\n vector>>rots;int B[6][3]={{1,0,0},{-1,0,0},{0,1,0},{0,-1,0},{0,0,1},{0,0,-1}};\n for(int i=0;i<6;i++)for(int j=0;j<6;j++){if(i/2==j/2)continue;int cr[3];\n cr[0]=B[i][1]*B[j][2]-B[i][2]*B[j][1];cr[1]=B[i][2]*B[j][0]-B[i][0]*B[j][2];cr[2]=B[i][0]*B[j][1]-B[i][1]*B[j][0];\n int dt=B[i][0]*(B[j][1]*cr[2]-B[j][2]*cr[1])-B[i][1]*(B[j][0]*cr[2]-B[j][2]*cr[0])+B[i][2]*(B[j][0]*cr[1]-B[j][1]*cr[0]);\n if(dt!=1)continue;rots.push_back({{B[i][0],B[i][1],B[i][2]},{B[j][0],B[j][1],B[j][2]},{cr[0],cr[1],cr[2]}});}\n return rots;\n}\n\nPoint appR(const vector>&M,const Point&p){auto[x,y,z]=p;return{M[0][0]*x+M[0][1]*y+M[0][2]*z,M[1][0]*x+M[1][1]*y+M[1][2]*z,M[2][0]*x+M[2][1]*y+M[2][2]*z};}\n\nvectorcanon(const vector&comp,const vector>>&rots){vectorbest;for(auto&M:rots){vectorr;for(auto&p:comp)r.push_back(appR(M,p));int mX=INT_MAX,mY=INT_MAX,mZ=INT_MAX;for(auto&[x,y,z]:r){mX=min(mX,x);mY=min(mY,y);mZ=min(mZ,z);}for(auto&[x,y,z]:r){x-=mX;y-=mY;z-=mZ;}sort(r.begin(),r.end());if(best.empty()||r> findSubComp(const vector&vox){setvs(vox.begin(),vox.end());mapvis;vector>cs;const int dx[]={1,-1,0,0,0,0},dy[]={0,0,1,-1,0,0},dz[]={0,0,0,0,1,-1};for(auto&p:vox){if(vis.count(p))continue;vectorc;queueq;q.push(p);vis[p]=1;while(!q.empty()){auto[cx,cy,cz]=q.front();q.pop();c.push_back({cx,cy,cz});for(int d=0;d<6;d++){Point np={cx+dx[d],cy+dy[d],cz+dz[d]};if(vs.count(np)&&!vis.count(np)){vis[np]=1;q.push(np);}}}cs.push_back(move(c));}return cs;}\n\nvoid doPartial(Array3D& asrc, Array3D& atgt, const Array3D& bsrc, const Array3D& btgt, const vector>>& rots, int& nextId) {\n while (true) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now - start_time).count() > 5000) break;\n \n Array3D us(D, vector>(D, vector(D, 0)));\n for(int x=0;x b.size();});\n \n bool found_match = false;\n for (auto& comp : srcC) {\n if (comp.size() < 2) continue;\n \n vector tuv;\n for(int x=0;x rot;\n for (auto& p : comp) rot.push_back(appR(rots[ri], p));\n int mX=INT_MAX, mY=INT_MAX, mZ=INT_MAX;\n for (auto& [x,y,z] : rot) { mX=min(mX,x); mY=min(mY,y); mZ=min(mZ,z); }\n for (auto& [x,y,z] : rot) { x-=mX; y-=mY; z-=mZ; }\n \n vector tc(S*S*S, 0);\n for (auto& [sx,sy,sz] : rot) \n for (auto& [px,py,pz] : tuv) {\n int kx = px-sx + OFF, ky = py-sy + OFF, kz = pz-sz + OFF;\n tc[kx + ky*S + kz*S*S]++;\n }\n for (int kz=0; kz bestO) { bestO = cnt; bestRi = ri; bestTx = kx-OFF; bestTy = ky-OFF; bestTz = kz-OFF; }\n }\n }\n \n if (bestRi != -1) {\n vector rot;\n for (auto& p : comp) rot.push_back(appR(rots[bestRi], p));\n int mX=INT_MAX, mY=INT_MAX, mZ=INT_MAX;\n for (auto& [x,y,z] : rot) { mX=min(mX,x); mY=min(mY,y); mZ=min(mZ,z); }\n for (auto& [x,y,z] : rot) { x-=mX; y-=mY; z-=mZ; }\n \n vector so, to;\n for (int i=0; i<(int)comp.size(); i++) {\n auto [rx,ry,rz] = rot[i];\n int tx=rx+bestTx, ty=ry+bestTy, tz=rz+bestTz;\n if (0<=tx&&tx s2i; for (int i=0; i<(int)so.size(); i++) s2i[so[i]] = i;\n \n for (auto& sc : scs) {\n if (sc.size() < 2) continue;\n found_match = true;\n int id = nextId++;\n for (auto& p : sc) {\n int i = s2i[p];\n auto [sx,sy,sz] = so[i]; auto [tx,ty,tz] = to[i];\n asrc[sx][sy][sz] = id; atgt[tx][ty][tz] = id;\n }\n }\n }\n if (found_match) break;\n }\n if (!found_match) break;\n }\n}\n\nint main(){\n ios::sync_with_stdio(false); cin.tie(nullptr);\n start_time = chrono::high_resolution_clock::now();\n cin >> D;\n vector> f(2), r(2);\n for (int i = 0; i < 2; i++) { f[i] = readSil(); r[i] = readSil(); }\n \n auto rots = genRots();\n auto b0 = buildMF(f[0], r[0]), b1 = buildMF(f[1], r[1]);\n Array3D a0(D, vector>(D, vector(D, 0)));\n Array3D a1(D, vector>(D, vector(D, 0)));\n int nid = 1;\n \n auto c0 = findComp(b0), c1 = findComp(b1);\n int n0 = c0.size(), n1 = c1.size();\n map, vector> cm1;\n for (int j=0; j o0(n0); for (int i=0; i c0[b].size();});\n \n vector u1(n1, false);\n for (int i : o0) {\n auto cn = canon(c0[i], rots);\n auto it = cm1.find(cn);\n if (it != cm1.end()) for (int j : it->second) if (!u1[j]) {\n int id = nid++;\n for (auto [x,y,z] : c0[i]) a0[x][y][z] = id;\n for (auto [x,y,z] : c1[j]) a1[x][y][z] = id;\n u1[j] = true; break;\n }\n }\n \n doPartial(a0, a1, b0, b1, rots, nid);\n doPartial(a1, a0, b1, b0, rots, nid);\n \n Array3D u0(D, vector>(D, vector(D, 0)));\n Array3D un1(D, vector>(D, vector(D, 0)));\n for(int x=0;x>(D, vector(D, 0)));\n for(int x=0;x\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n \n vector>> adj(N);\n vector eu(M), ev(M), ew(M);\n for (int j = 0; j < M; j++) {\n cin >> eu[j] >> ev[j] >> ew[j];\n eu[j]--; ev[j]--;\n adj[eu[j]].push_back({ev[j], j});\n adj[ev[j]].push_back({eu[j], j});\n }\n \n vector a(K), b(K);\n for (int k = 0; k < K; k++) cin >> a[k] >> b[k];\n \n const int PMAX = 5000;\n const long long PMAXSQ = (long long)PMAX * PMAX;\n \n vector> rsq(K, vector(N));\n for (int k = 0; k < K; k++)\n for (int i = 0; i < N; i++) {\n long long dx = a[k] - x[i], dy = b[k] - y[i];\n rsq[k][i] = dx * dx + dy * dy;\n }\n \n // Only include vertices within P_MAX range\n vector> clo(K);\n for (int k = 0; k < K; k++) {\n vector> v;\n for (int i = 0; i < N; i++)\n if (rsq[k][i] <= PMAXSQ) v.push_back({rsq[k][i], i});\n sort(v.begin(), v.end());\n for (int j = 0; j < min(15, (int)v.size()); j++)\n clo[k].push_back(v[j].second);\n }\n \n // Dijkstra from vertex 0\n vector sp(N, LLONG_MAX);\n vector par(N, -1), pe(N, -1);\n sp[0] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, 0});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > sp[u]) continue;\n for (auto [v, e] : adj[u])\n if (sp[u] + ew[e] < sp[v]) {\n sp[v] = sp[u] + ew[e];\n par[v] = u; pe[v] = e;\n pq.push({sp[v], v});\n }\n }\n \n vector> pth(N);\n for (int i = 1; i < N; i++) {\n int c = i;\n while (c) { pth[i].push_back(pe[c]); c = par[c]; }\n }\n \n auto calcP = [PMAX](long long sq) -> int {\n if (sq <= 0) return 0;\n int p = max(1, (int)ceil(sqrt((double)sq) - 1e-9));\n while ((long long)p * p < sq) p++;\n return min(p, PMAX);\n };\n \n // Initial assignment: closest vertex\n vector asgn(K);\n vector> vr(N);\n vector vmx(N, 0);\n for (int k = 0; k < K; k++) {\n asgn[k] = clo[k][0];\n vr[asgn[k]].push_back(k);\n vmx[asgn[k]] = max(vmx[asgn[k]], rsq[k][asgn[k]]);\n }\n \n vector P(N);\n long long pcost = 0;\n for (int i = 0; i < N; i++) { P[i] = calcP(vmx[i]); pcost += (long long)P[i] * P[i]; }\n \n vector eref(M, 0);\n long long ecost = 0;\n for (int i = 1; i < N; i++)\n if (P[i] > 0)\n for (int e : pth[i]) { if (!eref[e]) ecost += ew[e]; eref[e]++; }\n \n long long cost = pcost + ecost;\n vector best_P = P, best_asgn = asgn, best_eref = eref;\n long long best_cost = cost;\n \n mt19937 rng(42);\n uniform_real_distribution<> unif(0.0, 1.0);\n auto t0 = chrono::high_resolution_clock::now();\n \n for (int it = 0; ; it++) {\n double el = chrono::duration(chrono::high_resolution_clock::now() - t0).count();\n if (el > 1.5) break;\n double temp = 3e6 * pow(0.001, el / 1.5);\n \n int k = rng() % K;\n int ov = asgn[k];\n int nv = clo[k][rng() % clo[k].size()];\n if (nv == ov) continue;\n \n long long nmx_ov = 0;\n for (int r : vr[ov]) if (r != k) nmx_ov = max(nmx_ov, rsq[r][ov]);\n int nPov = calcP(nmx_ov);\n long long nmx_nv = max(vmx[nv], rsq[k][nv]);\n int nPnv = calcP(nmx_nv);\n \n long long dpc = (long long)nPov * nPov - (long long)P[ov] * P[ov]\n + (long long)nPnv * nPnv - (long long)P[nv] * P[nv];\n \n long long old_ecost = ecost;\n if (P[ov] > 0 && nPov == 0)\n for (int e : pth[ov]) { eref[e]--; if (!eref[e]) ecost -= ew[e]; }\n if (P[nv] == 0 && nPnv > 0)\n for (int e : pth[nv]) { if (!eref[e]) ecost += ew[e]; eref[e]++; }\n \n long long nc = pcost + dpc + ecost;\n if (nc < cost || unif(rng) < exp(-(double)(nc - cost) / temp)) {\n vr[ov].erase(find(vr[ov].begin(), vr[ov].end(), k));\n vr[nv].push_back(k);\n vmx[ov] = nmx_ov; vmx[nv] = nmx_nv;\n P[ov] = nPov; P[nv] = nPnv;\n pcost += dpc; asgn[k] = nv; cost = nc;\n if (cost < best_cost) {\n best_cost = cost; best_P = P; best_asgn = asgn; best_eref = eref;\n }\n } else {\n // Revert edge changes\n if (P[nv] == 0 && nPnv > 0)\n for (int e : pth[nv]) { eref[e]--; if (!eref[e]) ecost -= ew[e]; }\n if (P[ov] > 0 && nPov == 0)\n for (int e : pth[ov]) { if (!eref[e]) ecost += ew[e]; eref[e]++; }\n }\n }\n \n // Restore best state\n P = best_P; asgn = best_asgn; eref = best_eref;\n pcost = 0; for (int i = 0; i < N; i++) pcost += (long long)P[i] * P[i];\n ecost = 0; for (int j = 0; j < M; j++) if (eref[j] > 0) ecost += ew[j];\n \n // Steiner tree via SPH (Shortest Path Heuristic)\n vector terms = {0};\n for (int i = 1; i < N; i++) if (P[i] > 0) terms.push_back(i);\n int T = terms.size();\n \n if (T > 1) {\n vector in_tree(N, false);\n in_tree[0] = true;\n \n set rem;\n for (int t = 1; t < T; t++) rem.insert(terms[t]);\n \n vector neref(M, 0);\n long long necost = 0;\n \n while (!rem.empty()) {\n vector dist(N, LLONG_MAX);\n vector prev(N, -1), preve(N, -1);\n priority_queue, vector>, greater<>> pq2;\n for (int v = 0; v < N; v++) if (in_tree[v]) { dist[v] = 0; pq2.push({0, v}); }\n while (!pq2.empty()) {\n auto [d, u] = pq2.top(); pq2.pop();\n if (d > dist[u]) continue;\n for (auto [v, e] : adj[u])\n if (dist[u] + ew[e] < dist[v]) {\n dist[v] = dist[u] + ew[e];\n prev[v] = u; preve[v] = e;\n pq2.push({dist[v], v});\n }\n }\n \n long long bd = LLONG_MAX; int bt = -1;\n for (int t : rem) if (dist[t] < bd) { bd = dist[t]; bt = t; }\n \n int v = bt;\n while (v != -1 && !in_tree[v]) {\n int e = preve[v];\n if (!neref[e]) necost += ew[e];\n neref[e]++;\n in_tree[v] = true;\n v = prev[v];\n }\n rem.erase(bt);\n }\n \n if (necost < ecost) { eref = neref; ecost = necost; }\n }\n \n for (int i = 0; i < N; i++) cout << P[i] << \" \\n\"[i == N - 1];\n for (int j = 0; j < M; j++) cout << (eref[j] > 0 ? 1 : 0) << \" \\n\"[j == M - 1];\n \n return 0;\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint grid[N][N];\nvector> swaps;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++)\n for (int y = 0; y <= x; y++)\n cin >> grid[x][y];\n \n auto siftDown = [&](int x, int y) {\n while (x < N - 1) {\n int lv = grid[x+1][y], rv = grid[x+1][y+1], cv = grid[x][y];\n if (cv <= lv && cv <= rv) break;\n if (lv <= rv) {\n swap(grid[x][y], grid[x+1][y]);\n swaps.push_back({x, y, x+1, y});\n x++;\n } else {\n swap(grid[x][y], grid[x+1][y+1]);\n swaps.push_back({x, y, x+1, y+1});\n x++; y++;\n }\n if (swaps.size() >= 9999) return;\n }\n };\n \n // Heapify: bottom to top, full sift-down\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n siftDown(x, y);\n if (swaps.size() >= 9999) goto done;\n }\n }\n \n // Iteratively fix remaining violations\n // (caused by triangular grid's dual-parent structure)\n for (int iter = 0; iter < 500; iter++) {\n bool any = false;\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n if (grid[x][y] > grid[x+1][y] || grid[x][y] > grid[x+1][y+1]) {\n any = true;\n // One-step fix: swap parent with smaller child\n if (grid[x+1][y] <= grid[x+1][y+1]) {\n swap(grid[x][y], grid[x+1][y]);\n swaps.push_back({x, y, x+1, y});\n } else {\n swap(grid[x][y], grid[x+1][y+1]);\n swaps.push_back({x, y, x+1, y+1});\n }\n if (swaps.size() >= 9999) goto done;\n }\n }\n }\n if (!any) break;\n }\n \ndone:\n cout << swaps.size() << \"\\n\";\n for (auto& s : swaps)\n cout << s[0] << \" \" << s[1] << \" \" << s[2] << \" \" << s[3] << \"\\n\";\n \n return 0;\n}","toyota2023summer-final":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int D, N;\n cin >> D >> N;\n \n vector> is_obstacle(D, vector(D, false));\n for (int i = 0; i < N; i++) {\n int ri, rj;\n cin >> ri >> rj;\n is_obstacle[ri][rj] = true;\n }\n \n int entrance_i = 0, entrance_j = (D - 1) / 2;\n \n // Precompute distances from entrance\n vector> dist(D, vector(D, -1));\n queue> q;\n q.push({entrance_i, entrance_j});\n dist[entrance_i][entrance_j] = 0;\n \n const int di[] = {-1, 1, 0, 0};\n const int dj[] = {0, 0, -1, 1};\n \n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && dist[ni][nj] == -1 && !is_obstacle[ni][nj]) {\n dist[ni][nj] = dist[i][j] + 1;\n q.push({ni, nj});\n }\n }\n }\n \n int M = 0;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (!(i == entrance_i && j == entrance_j) && !is_obstacle[i][j])\n M++;\n \n struct Cell {\n int i, j;\n int dist;\n int current_degree;\n bool removed;\n int rank;\n };\n \n vector C(M);\n vector> cell_index(D, vector(D, -1));\n \n int idx = 0;\n for (int i = 0; i < D; i++) {\n for (int j = 0; j < D; j++) {\n if (!(i == entrance_i && j == entrance_j) && !is_obstacle[i][j]) {\n C[idx].i = i;\n C[idx].j = j;\n C[idx].dist = dist[i][j];\n C[idx].removed = false;\n cell_index[i][j] = idx;\n idx++;\n }\n }\n }\n \n // Calculate internal degrees (only counting valid container neighbors)\n for (int k = 0; k < M; k++) {\n C[k].current_degree = 0;\n for (int d = 0; d < 4; d++) {\n int ni = C[k].i + di[d], nj = C[k].j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && cell_index[ni][nj] != -1) {\n C[k].current_degree++;\n }\n }\n }\n \n // Peeling algorithm to assign topological removal ranks\n priority_queue, vector>, greater>> pq;\n \n for (int k = 0; k < M; k++) {\n if (C[k].current_degree <= 1) {\n pq.push({C[k].dist, C[k].i, C[k].j, k});\n }\n }\n \n int current_rank = 0;\n int removed_count = 0;\n \n while (removed_count < M) {\n if (pq.empty()) {\n // Break cycle by picking the remaining cell closest to the entrance\n int best_k = -1;\n for (int k = 0; k < M; k++) {\n if (!C[k].removed) {\n if (best_k == -1 || tie(C[k].dist, C[k].i, C[k].j) < tie(C[best_k].dist, C[best_k].i, C[best_k].j)) {\n best_k = k;\n }\n }\n }\n pq.push({C[best_k].dist, C[best_k].i, C[best_k].j, best_k});\n }\n \n auto [d, i, j, k] = pq.top();\n pq.pop();\n \n if (C[k].removed) continue;\n \n C[k].rank = current_rank++;\n C[k].removed = true;\n removed_count++;\n \n for (int dd = 0; dd < 4; dd++) {\n int ni = C[k].i + di[dd], nj = C[k].j + dj[dd];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && cell_index[ni][nj] != -1) {\n int nk = cell_index[ni][nj];\n if (!C[nk].removed) {\n C[nk].current_degree--;\n if (C[nk].current_degree <= 1) {\n pq.push({C[nk].dist, C[nk].i, C[nk].j, nk});\n }\n }\n }\n }\n }\n \n // Placement phase\n set> available_cells; // (Rank, index in C)\n for (int k = 0; k < M; k++) {\n available_cells.insert({C[k].rank, k});\n }\n \n vector> container_at(D, vector(D, -1));\n vector> is_empty(D, vector(D, true));\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (is_obstacle[i][j]) is_empty[i][j] = false;\n \n auto is_safe = [&](int exclude_i, int exclude_j) {\n vector> reachable(D, vector(D, false));\n queue> bfs_q;\n bfs_q.push({entrance_i, entrance_j});\n reachable[entrance_i][entrance_j] = true;\n int visited_count = 1; // includes entrance\n \n while (!bfs_q.empty()) {\n auto [i, j] = bfs_q.front(); bfs_q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && !reachable[ni][nj] && is_empty[ni][nj] && !(ni == exclude_i && nj == exclude_j)) {\n reachable[ni][nj] = true;\n bfs_q.push({ni, nj});\n visited_count++;\n }\n }\n }\n return visited_count == (int)available_cells.size();\n };\n \n for (int d = 0; d < M; d++) {\n int t; cin >> t;\n \n vector safe_indices;\n for (auto& p : available_cells) {\n int k = p.second;\n if (is_safe(C[k].i, C[k].j)) {\n safe_indices.push_back(k);\n }\n }\n \n int best_k = -1;\n int best_diff = M + 1;\n \n auto it = lower_bound(safe_indices.begin(), safe_indices.end(), t, [&](int k, int val) {\n return C[k].rank < val;\n });\n \n if (it != safe_indices.end()) {\n int diff = abs(C[*it].rank - t);\n if (diff < best_diff) {\n best_diff = diff;\n best_k = *it;\n } else if (diff == best_diff && C[*it].rank > C[best_k].rank) {\n best_k = *it;\n }\n }\n if (it != safe_indices.begin()) {\n --it;\n int diff = abs(C[*it].rank - t);\n if (diff < best_diff) {\n best_diff = diff;\n best_k = *it;\n } else if (diff == best_diff && C[*it].rank > C[best_k].rank) {\n best_k = *it;\n }\n }\n \n available_cells.erase({C[best_k].rank, best_k});\n cout << C[best_k].i << \" \" << C[best_k].j << endl;\n container_at[C[best_k].i][C[best_k].j] = t;\n is_empty[C[best_k].i][C[best_k].j] = false;\n }\n \n // Transport phase: Greedily remove the smallest numbered accessible container\n for (int iter = 0; iter < M; iter++) {\n vector> reachable(D, vector(D, false));\n queue> bfs_q;\n bfs_q.push({entrance_i, entrance_j});\n reachable[entrance_i][entrance_j] = true;\n \n while (!bfs_q.empty()) {\n auto [i, j] = bfs_q.front(); bfs_q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && !reachable[ni][nj] && is_empty[ni][nj]) {\n reachable[ni][nj] = true;\n bfs_q.push({ni, nj});\n }\n }\n }\n \n int min_t = M + 1, min_i = -1, min_j = -1;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (container_at[i][j] >= 0) {\n bool acc = false;\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && is_empty[ni][nj] && reachable[ni][nj]) {\n acc = true;\n break;\n }\n }\n if (acc && container_at[i][j] < min_t) {\n min_t = container_at[i][j];\n min_i = i; min_j = j;\n }\n }\n \n cout << min_i << \" \" << min_j << endl;\n is_empty[min_i][min_j] = true;\n container_at[min_i][min_j] = -1;\n }\n \n return 0;\n}","ahc024":"#include \nusing namespace std;\n\nconst int N = 50;\nconst int M = 100;\nconst int dx[] = {0, 0, 1, -1};\nconst int dy[] = {1, -1, 0, 0};\n\nint n, m;\nint grid[N][N], best_grid[N][N];\nint best_score;\nset> required_adj;\nint adj_cnt[M+1][M+1];\n\nbool valid(int x, int y) { return 0 <= x && x < n && 0 <= y && y < n; }\n\nvoid compute_init_adj() {\n memset(adj_cnt, 0, sizeof(adj_cnt));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) {\n if (j+1 < n && grid[i][j] != grid[i][j+1])\n adj_cnt[min(grid[i][j],grid[i][j+1])][max(grid[i][j],grid[i][j+1])]++;\n if (i+1 < n && grid[i][j] != grid[i+1][j])\n adj_cnt[min(grid[i][j],grid[i+1][j])][max(grid[i][j],grid[i+1][j])]++;\n if (i==0||i==n-1||j==0||j==n-1)\n adj_cnt[0][grid[i][j]]++;\n }\n for (int a = 0; a <= m; a++)\n for (int b = a; b <= m; b++)\n if (adj_cnt[a][b] > 0) required_adj.insert({a,b});\n}\n\nbool check_c0_conn() {\n bool has0 = false;\n for (int i = 0; i < n && !has0; i++)\n for (int j = 0; j < n && !has0; j++)\n if (grid[i][j] == 0) has0 = true;\n if (!has0) return true;\n \n vector> vis(n, vector(n));\n queue> q;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0 && (i==0||i==n-1||j==0||j==n-1))\n { q.push({i,j}); vis[i][j] = true; }\n \n while (!q.empty()) {\n auto [x,y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx=x+dx[d], ny=y+dy[d];\n if (valid(nx,ny) && !vis[nx][ny] && grid[nx][ny]==0)\n { vis[nx][ny] = true; q.push({nx,ny}); }\n }\n }\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0 && !vis[i][j]) return false;\n return true;\n}\n\nbool can_change(int i, int j, int nc) {\n int oc = grid[i][j];\n if (oc == nc) return true;\n if (nc != 0) {\n bool found = false;\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj) && grid[ni][nj] == nc) { found = true; break; }\n }\n if (!found) return false;\n }\n map,int> delta;\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj)) {\n int c = grid[ni][nj];\n if (oc != c) delta[{min(oc,c),max(oc,c)}]--;\n if (nc != c) delta[{min(nc,c),max(nc,c)}]++;\n }\n }\n if (i==0||i==n-1||j==0||j==n-1) {\n if (oc != 0) delta[{0,oc}]--;\n if (nc != 0) delta[{0,nc}]++;\n }\n for (auto& [p,d] : delta) {\n int ncnt = adj_cnt[p.first][p.second] + d;\n if (ncnt > 0 && required_adj.find(p) == required_adj.end()) return false;\n if (ncnt <= 0 && required_adj.find(p) != required_adj.end()) return false;\n }\n grid[i][j] = nc;\n bool ok = check_c0_conn();\n grid[i][j] = oc;\n return ok;\n}\n\nvoid apply_change(int i, int j, int nc) {\n int oc = grid[i][j];\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj)) {\n int c = grid[ni][nj];\n if (oc != c) adj_cnt[min(oc,c)][max(oc,c)]--;\n if (nc != c) adj_cnt[min(nc,c)][max(nc,c)]++;\n }\n }\n if (i==0||i==n-1||j==0||j==n-1) {\n if (oc != 0) adj_cnt[0][oc]--;\n if (nc != 0) adj_cnt[0][nc]++;\n }\n grid[i][j] = nc;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> n >> m;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) cin >> grid[i][j];\n \n compute_init_adj();\n memcpy(best_grid, grid, sizeof(grid));\n best_score = 2501;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) best_score++;\n \n bool improved = true;\n while (improved) {\n improved = false;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) {\n for (int d = 0; d < 4; d++) {\n int ni=i+dx[d], nj=j+dy[d];\n if (valid(ni,nj) && grid[ni][nj] != 0)\n if (can_change(i, j, grid[ni][nj])) {\n apply_change(i, j, grid[ni][nj]);\n improved = true;\n break;\n }\n }\n }\n }\n \n int cnt0 = 0;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (grid[i][j] == 0) cnt0++;\n if (cnt0+1 < best_score) {\n best_score = cnt0+1;\n memcpy(best_grid, grid, sizeof(grid));\n }\n \n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << best_grid[i][j];\n if (j < n-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n return 0;\n}","ahc025":"#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, D, Q;\nint qc = 0;\nint cmp[105][105];\n\nchar do_query(int a, int b) {\n if (cmp[a][b] == -1) return '<';\n if (cmp[a][b] == 1) return '>';\n if (cmp[a][b] == 2) return '=';\n if (qc >= Q) return '=';\n qc++;\n cout << \"1 1 \" << a << \" \" << b << endl;\n char res; cin >> res;\n if (res == '<') { cmp[a][b] = -1; cmp[b][a] = 1; }\n else if (res == '>') { cmp[a][b] = 1; cmp[b][a] = -1; }\n else if (res == '=') { cmp[a][b] = 2; cmp[b][a] = 2; }\n return res;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n vector items(N);\n for (int i = 0; i < N; i++) items[i] = i;\n \n // Heap Sort to prioritize finding heavy items\n // Build max-heap\n for (int i = 1; i < N; i++) {\n int cur = i;\n while (cur > 0) {\n int par = (cur - 1) / 2;\n char res = do_query(items[cur], items[par]);\n if (res == '>') {\n swap(items[cur], items[par]);\n cur = par;\n } else {\n break;\n }\n }\n }\n \n // Extract max\n for (int i = N - 1; i > 0; i--) {\n swap(items[0], items[i]);\n int cur = 0;\n while (true) {\n int left = 2 * cur + 1;\n int right = 2 * cur + 2;\n int largest = cur;\n if (left < i) {\n char res = do_query(items[left], items[largest]);\n if (res == '>') largest = left;\n }\n if (right < i) {\n char res = do_query(items[right], items[largest]);\n if (res == '>') largest = right;\n }\n if (largest != cur) {\n swap(items[cur], items[largest]);\n cur = largest;\n } else {\n break;\n }\n }\n }\n \n // Transitive closure\n for (int k = 0; k < N; k++)\n for (int i = 0; i < N; i++) { if (!cmp[i][k]) continue;\n for (int j = 0; j < N; j++) { if (!cmp[k][j]) continue;\n if (cmp[i][k]==1 && cmp[k][j]==1 && !cmp[i][j]) { cmp[i][j]=1; cmp[j][i]=-1; }\n else if (cmp[i][k]==1 && cmp[k][j]==2 && !cmp[i][j]) { cmp[i][j]=1; cmp[j][i]=-1; }\n else if (cmp[i][k]==2 && cmp[k][j]==1 && !cmp[i][j]) { cmp[i][j]=1; cmp[j][i]=-1; }\n else if (cmp[i][k]==2 && cmp[k][j]==2 && !cmp[i][j]) { cmp[i][j]=2; cmp[j][i]=2; }\n }\n }\n \n // Sort by wins\n vector wins(N, 0);\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (cmp[i][j]==1) wins[i]++;\n sort(items.begin(), items.end(), [&](int a, int b){ return wins[a]!=wins[b] ? wins[a]> res;\n qc++;\n }\n \n // Transitive closure again\n for (int k = 0; k < N; k++)\n for (int i = 0; i < N; i++) { if (!cmp[i][k]) continue;\n for (int j = 0; j < N; j++) { if (!cmp[k][j]) continue;\n if (cmp[i][k]==1 && cmp[k][j]==1 && !cmp[i][j]) { cmp[i][j]=1; cmp[j][i]=-1; }\n else if (cmp[i][k]==1 && cmp[k][j]==2 && !cmp[i][j]) { cmp[i][j]=1; cmp[j][i]=-1; }\n else if (cmp[i][k]==2 && cmp[k][j]==1 && !cmp[i][j]) { cmp[i][j]=1; cmp[j][i]=-1; }\n else if (cmp[i][k]==2 && cmp[k][j]==2 && !cmp[i][j]) { cmp[i][j]=2; cmp[j][i]=2; }\n }\n }\n \n // Sort by wins again\n for (int i = 0; i < N; i++) { wins[i]=0; for (int j = 0; j < N; j++) if (cmp[i][j]==1) wins[i]++; }\n sort(items.begin(), items.end(), [&](int a, int b){ return wins[a]!=wins[b] ? wins[a] ew(N);\n for (int i = 0; i < N; i++) { double p = (double)(i+1)/(N+1); ew[items[i]] = -log(1.0-p); }\n \n // LPT partitioning\n vector gw(D, 0); vector asgn(N);\n for (int i = N-1; i >= 0; i--) {\n int item = items[i], mg = 0;\n for (int g = 1; g < D; g++) if (gw[g] < gw[mg]) mg = g;\n asgn[item] = mg; gw[mg] += ew[item];\n }\n \n // SA + Hill climbing\n mt19937 rng(42); uniform_real_distribution ud(0,1);\n double temp = 5000.0;\n for (int it = 0; it < 1000000; it++) {\n temp *= 0.999995;\n if (rng() % 2 == 0) {\n int i = rng()%N, j = rng()%N;\n if (asgn[i]==asgn[j]) continue;\n int gi=asgn[i], gj=asgn[j];\n double osq = gw[gi]*gw[gi]+gw[gj]*gw[gj];\n double ngi = gw[gi]-ew[i]+ew[j], ngj = gw[gj]-ew[j]+ew[i];\n double nsq = ngi*ngi+ngj*ngj, delta = nsq-osq;\n if (delta < 0 || (temp > 1e-8 && exp(-delta/temp) > ud(rng))) { gw[gi]=ngi; gw[gj]=ngj; asgn[i]=gj; asgn[j]=gi; }\n } else {\n int i = rng()%N;\n int gi = asgn[i];\n int gj = rng()%D;\n if (gi == gj) continue;\n if (gw[gi] - ew[i] < 1e-9) continue;\n double osq = gw[gi]*gw[gi]+gw[gj]*gw[gj];\n double ngi = gw[gi]-ew[i], ngj = gw[gj]+ew[i];\n double nsq = ngi*ngi+ngj*ngj, delta = nsq-osq;\n if (delta < 0 || (temp > 1e-8 && exp(-delta/temp) > ud(rng))) { gw[gi]=ngi; gw[gj]=ngj; asgn[i]=gj; }\n }\n }\n for (int it = 0; it < 1000000; it++) {\n if (rng() % 2 == 0) {\n int i = rng()%N, j = rng()%N;\n if (asgn[i]==asgn[j]) continue;\n int gi=asgn[i], gj=asgn[j];\n double osq = gw[gi]*gw[gi]+gw[gj]*gw[gj];\n double ngi = gw[gi]-ew[i]+ew[j], ngj = gw[gj]-ew[j]+ew[i];\n double nsq = ngi*ngi+ngj*ngj;\n if (nsq < osq - 1e-10) { gw[gi]=ngi; gw[gj]=ngj; asgn[i]=gj; asgn[j]=gi; }\n } else {\n int i = rng()%N;\n int gi = asgn[i];\n int gj = rng()%D;\n if (gi == gj) continue;\n if (gw[gi] - ew[i] < 1e-9) continue;\n double osq = gw[gi]*gw[gi]+gw[gj]*gw[gj];\n double ngi = gw[gi]-ew[i], ngj = gw[gj]+ew[i];\n double nsq = ngi*ngi+ngj*ngj;\n if (nsq < osq - 1e-10) { gw[gi]=ngi; gw[gj]=ngj; asgn[i]=gj; }\n }\n }\n \n for (int i = 0; i < N; i++) cout << asgn[i] << \" \\n\"[i==N-1];\n return 0;\n}","ahc026":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n for (int i = 0; i < m; i++) {\n stacks[i].resize(n / m);\n for (int j = 0; j < n / m; j++)\n cin >> stacks[i][j];\n }\n \n vector box_stack(n + 1), box_pos(n + 1);\n for (int i = 0; i < m; i++)\n for (int j = 0; j < (int)stacks[i].size(); j++) {\n box_stack[stacks[i][j]] = i;\n box_pos[stacks[i][j]] = j;\n }\n \n vector> operations;\n const int INV_COST = 4;\n const int EMPTY_COST = 5;\n \n for (int v = 1; v <= n; v++) {\n int sid = box_stack[v], pos = box_pos[v];\n int k = (int)stacks[sid].size() - 1 - pos;\n \n if (k == 0) {\n operations.push_back({v, 0});\n stacks[sid].pop_back();\n continue;\n }\n \n vector A(stacks[sid].begin() + pos + 1, stacks[sid].end());\n \n vector dp(k + 1, INT_MAX);\n vector par(k + 1);\n dp[0] = 0;\n \n for (int i = 1; i <= k; i++) {\n for (int j = 1; j <= i; j++) {\n int int_inv = 0;\n for (int s = i - j; s < i; s++)\n for (int t = s + 1; t < i; t++)\n if (A[s] < A[t]) int_inv++;\n \n int best_dest_cost = INT_MAX;\n for (int d = 0; d < m; d++) {\n if (d == sid) continue;\n int ext_inv = 0, empty_pen = 0;\n if (stacks[d].empty()) empty_pen = EMPTY_COST;\n else {\n int top_val = stacks[d].back();\n for (int s = i - j; s < i; s++)\n if (A[s] > top_val) ext_inv++;\n }\n best_dest_cost = min(best_dest_cost, INV_COST * (int_inv + ext_inv) + empty_pen);\n }\n \n int cost = dp[i - j] + (j + 1) + best_dest_cost;\n if (cost < dp[i]) { dp[i] = cost; par[i] = j; }\n }\n }\n \n vector chunks;\n for (int cur = k; cur > 0; cur -= par[cur])\n chunks.push_back(par[cur]);\n \n for (int cs : chunks) {\n int off = stacks[sid].size() - cs;\n int best_dest = -1, best_priority = 4, best_subscore = INT_MAX;\n \n for (int d = 0; d < m; d++) {\n if (d == sid) continue;\n int ext_inv = 0;\n bool is_empty = stacks[d].empty();\n int top_val = is_empty ? 0 : stacks[d].back();\n \n if (!is_empty)\n for (int s = off; s < (int)stacks[sid].size(); s++)\n if (stacks[sid][s] > top_val) ext_inv++;\n \n int priority, subscore;\n if (ext_inv == 0 && !is_empty) { priority = 1; subscore = top_val; }\n else if (ext_inv == 0) { priority = 2; subscore = 0; }\n else { priority = 3; subscore = ext_inv * 1000 - top_val; }\n \n if (priority < best_priority || (priority == best_priority && subscore < best_subscore)) {\n best_priority = priority; best_subscore = subscore; best_dest = d;\n }\n }\n \n if (best_dest == -1) best_dest = (sid + 1) % m;\n \n int u = stacks[sid][off];\n operations.push_back({u, best_dest + 1});\n \n vector moved(stacks[sid].begin() + off, stacks[sid].end());\n stacks[sid].resize(off);\n stacks[best_dest].insert(stacks[best_dest].end(), moved.begin(), moved.end());\n \n for (int j = 0; j < (int)moved.size(); j++) {\n box_stack[moved[j]] = best_dest;\n box_pos[moved[j]] = stacks[best_dest].size() - moved.size() + j;\n }\n }\n \n operations.push_back({v, 0});\n stacks[sid].pop_back();\n }\n \n for (auto& op : operations)\n cout << op.first << \" \" << op.second << endl;\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\nchar dir_char[] = {'R', 'D', 'L', 'U'};\n\nbool can_move(int i, int j, int dir) {\n int ni = i + dx[dir], nj = j + dy[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0 && v[i][j] == '1') return false;\n if (dir == 1 && h[i][j] == '1') return false;\n if (dir == 2 && v[i][nj] == '1') return false;\n if (dir == 3 && h[ni][j] == '1') return false;\n return true;\n}\n\nint get_dir(char c) {\n if (c == 'R') return 0;\n if (c == 'D') return 1;\n if (c == 'L') return 2;\n return 3; // 'U'\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1); v.resize(N); d.resize(N, vector(N));\n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> d[i][j];\n \n int total_cells = N * N;\n vector all_dist(total_cells * total_cells, -1);\n vector all_prev_dir(total_cells * total_cells, -1);\n\n auto get_dist = [&](int si, int sj, int ei, int ej) -> int& {\n return all_dist[(si * N + sj) * total_cells + (ei * N + ej)];\n };\n auto get_prev = [&](int si, int sj, int ei, int ej) -> int& {\n return all_prev_dir[(si * N + sj) * total_cells + (ei * N + ej)];\n };\n\n // Precompute BFS from all cells\n for (int si = 0; si < N; ++si) {\n for (int sj = 0; sj < N; ++sj) {\n queue> q;\n get_dist(si, sj, si, sj) = 0;\n q.push({si, sj});\n while (!q.empty()) {\n auto [ci, cj] = q.front(); q.pop();\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(ci, cj, dir)) continue;\n int ni = ci + dx[dir], nj = cj + dy[dir];\n if (get_dist(si, sj, ni, nj) == -1) { \n get_dist(si, sj, ni, nj) = get_dist(si, sj, ci, cj) + 1; \n get_prev(si, sj, ni, nj) = (dir + 2) % 4; // Direction to go BACK\n q.push({ni, nj}); \n }\n }\n }\n }\n }\n\n auto get_path = [&](int si, int sj, int ei, int ej) -> string {\n string path_back;\n int ci = ei, cj = ej;\n while (ci != si || cj != sj) {\n int dir = get_prev(si, sj, ci, cj);\n path_back += dir_char[dir];\n ci += dx[dir];\n cj += dy[dir];\n }\n string path_to;\n for (int k = (int)path_back.size() - 1; k >= 0; --k) {\n char c = path_back[k];\n if (c == 'R') path_to += 'L';\n else if (c == 'D') path_to += 'U';\n else if (c == 'L') path_to += 'R';\n else path_to += 'D';\n }\n return path_to;\n };\n \n // Build DFS tour\n string base_tour;\n base_tour.reserve(N * N * 2);\n vector> visited(N, vector(N, false));\n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(i, j, dir)) continue;\n int ni = i + dx[dir], nj = j + dy[dir];\n if (!visited[ni][nj]) {\n base_tour += dir_char[dir];\n dfs(ni, nj);\n base_tour += dir_char[(dir + 2) % 4];\n }\n }\n };\n dfs(0, 0);\n \n int L = base_tour.size();\n vector> positions(L + 1);\n positions[0] = {0, 0};\n for (int t = 0; t < L; t++) {\n int dir = get_dir(base_tour[t]);\n positions[t+1] = {positions[t].first + dx[dir], positions[t].second + dy[dir]};\n }\n \n // Find closest insertion point on base tour for detours\n vector best_step(N * N, 0), best_cost(N * N, INT_MAX);\n for (int t = 0; t < L; t++) {\n auto [pi, pj] = positions[t];\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (pi == i && pj == j) continue;\n int cost = 2 * get_dist(pi, pj, i, j);\n if (cost < best_cost[i * N + j]) { best_cost[i * N + j] = cost; best_step[i * N + j] = t; }\n }\n }\n \n // Correctly calculate visits per cycle (t=0 to L-1)\n vector visit_count(N * N, 0);\n for (int t = 0; t < L; t++) { auto [i, j] = positions[t]; visit_count[i * N + j]++; }\n \n double S_factor = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) S_factor += (double)d[i][j] / visit_count[i * N + j];\n \n using Cell = tuple;\n priority_queue pq;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (i == 0 && j == 0) continue;\n int k = visit_count[i * N + j], cost = best_cost[i * N + j];\n if (cost == 0 || cost >= INT_MAX) continue;\n pq.push({(double)d[i][j] / ((long long)k * (k + 1)) / cost, i, j});\n }\n \n struct Detour { int step; int i; int j; };\n vector detours;\n int current_L = L;\n \n while (!pq.empty() && current_L < 100000) {\n auto [p, i, j] = pq.top(); pq.pop();\n int k = visit_count[i * N + j], cost = best_cost[i * N + j];\n if (cost >= INT_MAX) continue;\n double new_p = (double)d[i][j] / ((long long)k * (k + 1)) / cost;\n if (abs(new_p - p) > 1e-9) { pq.push({new_p, i, j}); continue; }\n \n if (current_L + cost > 100000) continue;\n \n // Benefit-cost check\n double benefit = (double)d[i][j] * (current_L + cost) / ((long long)k * (k + 1));\n double detour_cost_val = (double)cost * S_factor;\n if (benefit <= detour_cost_val) break; // No more beneficial detours possible\n \n int step = best_step[i * N + j];\n \n detours.push_back({step, i, j});\n current_L += cost;\n S_factor -= (double)d[i][j] / k;\n visit_count[i * N + j]++;\n S_factor += (double)d[i][j] / visit_count[i * N + j];\n int nk = visit_count[i * N + j];\n pq.push({(double)d[i][j] / ((long long)nk * (nk + 1)) / cost, i, j});\n }\n \n sort(detours.begin(), detours.end(), [](const auto& a, const auto& b) { return a.step < b.step; });\n \n string result;\n result.reserve(100000);\n int detour_idx = 0;\n for (int t = 0; t <= L; t++) {\n while (detour_idx < (int)detours.size() && detours[detour_idx].step == t) {\n auto [step, i, j] = detours[detour_idx];\n auto [pi, pj] = positions[step];\n string path_to = get_path(pi, pj, i, j);\n string path_back;\n for (int k2 = (int)path_to.size() - 1; k2 >= 0; k2--) {\n char c = path_to[k2];\n path_back += (c == 'R') ? 'L' : (c == 'D') ? 'U' : (c == 'L') ? 'R' : 'D';\n }\n result += path_to;\n result += path_back;\n detour_idx++;\n }\n if (t < L) result += base_tour[t];\n }\n \n cout << result << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n int N,M;cin>>N>>M;int si,sj;cin>>si>>sj;\n vector A(N);for(int i=0;i>A[i];\n vector t(M);for(int i=0;i>t[i];\n vector>> cp(26);\n for(int i=0;i> cd(26,vector(26,0));\n for(int c1=0;c1<26;c1++)for(int c2=0;c2<26;c2++){int md=INT_MAX;\n for(auto&[i1,j1]:cp[c1])for(auto&[i2,j2]:cp[c2])md=min(md,abs(i1-i2)+abs(j1-j2));cd[c1][c2]=md;}\n vector> ov(M,vector(M,0));\n for(int i=0;i=1;l--){bool ok=true;for(int k=0;k&o)->string{string s=t[o[0]];\n for(int i=1;i<(int)o.size();i++){int mx=min(5,(int)s.size()),a=0;\n for(int l=mx;l>=1;l--){bool ok=true;for(int k=0;k&o)->int{int tv=0;for(int i=1;i<(int)o.size();i++)tv+=ov[o[i-1]][o[i]];return tv;};\n mt19937 rng(42);\n auto greedyR=[&](int st,unsigned seed)->vector{mt19937 lr(seed);vectoro;o.push_back(st);\n vectoru(M,false);u[st]=true;for(int s=1;sc;\n for(int j=0;jbo){bo=ov[l][j];c.clear();c.push_back(j);}\n else if(ov[l][j]==bo)c.push_back(j);}o.push_back(c[lr()%c.size()]);u[o.back()]=true;}return o;};\n auto twoOpt=[&](vectoro)->vector{bool imp=true;while(imp){imp=false;\n for(int i=0;i0){os+=ov[o[i-1]][o[i]];ns+=ov[o[i-1]][o[i+1]];}\n os+=ov[o[i]][o[i+1]];ns+=ov[o[i+1]][o[i]];if(i+2os){swap(o[i],o[i+1]);imp=true;}}}return o;};\n auto orOpt=[&](vectoro)->vector{for(int it=0;it<10;it++){bool imp=false;\n for(int i=0;i0)rd-=ov[o[i-1]][w];if(i0&&iint{return(k0)?gr(j-1):-1,D=(jbd){bd=rd+id;bk=j;}}\n if(bk!=i){vectorrm;for(int k=0;ko,unsigned seed)->vector{int curOv=totalOv(o);int bestOv=curOv;auto bestO=o;\n mt19937 saRng(seed);uniform_int_distributiondistI(0,M-1);uniform_real_distributiondistD(0.0,1.0);\n double temp=3.0;for(int it=0;it<500000;it++){temp*=0.99999;int i=distI(saRng);int w=o[i];\n int rd=0;if(i>0)rd-=ov[o[i-1]][w];if(i0&&iint{return(k0)?gr(j-1):-1,D=(j0||distD(saRng)bestOv){bestOv=curOv;bestO=o;}}}return bestO;};\n auto hc=[&](const string&s)->int{int cost=s.size();for(int i=0;i<(int)s.size()-1;i++)cost+=cd[s[i]-'A'][s[i+1]-'A'];return cost;};\n vector>>cs;\n for(int s=0;s>eval;\n int topN=min((int)cs.size(),30);\n for(int i=0;iint{int L=s.size();vectorcur(225,INF);cur[si*15+sj]=0;\n for(int i=0;inx(225,INF);int ci=s[i]-'A';for(int q=0;q<225;q++){if(cur[q]>=INF)continue;\n int qi=q/15,qj=q%15;for(auto&[pi,pj]:cp[ci]){int p=pi*15+pj;int nc=cur[q]+abs(pi-qi)+abs(pj-qj)+1;\n if(nc>>dp(L+1,vector>(225,{INF,-1}));dp[0][si*15+sj]={0,-1};\n for(int i=0;i=INF)continue;\n int qi=q/15,qj=q%15;for(auto&[pi,pj]:cp[ci]){int p=pi*15+pj;int nc=dp[i][q].first+abs(pi-qi)+abs(pj-qj)+1;\n if(ncpp(L);int cr=be;for(int i=L-1;i>=0;i--){pp[i]=cr;cr=dp[i+1][cr].second;}\n for(int i=0;i\nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nvector max_di, max_dj;\nvector>> positions;\nvector>>> pos_cells;\nvector>> cell_pos;\nint known[25][25];\nint query_count = 0;\nvector> lw;\ndouble cov_val[25][25];\ndouble prob_oil_val[25][25];\n\nint drill_cell(int i, int j) {\n cout << \"q 1 \" << i << \" \" << j << endl;\n cout.flush();\n int v; cin >> v;\n known[i][j] = v;\n query_count++;\n return v;\n}\n\nint divine_cells(vector>& cells) {\n int k = cells.size();\n cout << \"q \" << k;\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << endl;\n cout.flush();\n int v; cin >> v;\n query_count++;\n return v;\n}\n\nbool submit_answer(vector>& cells) {\n sort(cells.begin(), cells.end());\n cells.erase(unique(cells.begin(), cells.end()), cells.end());\n cout << \"a \" << cells.size();\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << endl;\n cout.flush();\n int r; cin >> r;\n if (r == 0) query_count++; // Wrong answer costs 1 operation\n return r == 1;\n}\n\nvoid compute_prob_and_cov() {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n cov_val[i][j] = 0;\n prob_oil_val[i][j] = 1.0;\n }\n for (int k = 0; k < M; k++) {\n double mx = *max_element(lw[k].begin(), lw[k].end());\n double total = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) total += exp(lw[k][p] - mx);\n if (total < 1e-30) continue;\n vector cc(N * N, 0);\n for (int p = 0; p < (int)positions[k].size(); p++) {\n double wt = exp(lw[k][p] - mx) / total;\n for (auto& [ci, cj] : pos_cells[k][p]) cc[ci * N + cj] += wt;\n }\n for (int idx = 0; idx < N * N; idx++) {\n cov_val[idx / N][idx % N] += cc[idx];\n prob_oil_val[idx / N][idx % N] *= (1.0 - cc[idx]);\n }\n }\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)\n prob_oil_val[i][j] = 1.0 - prob_oil_val[i][j];\n}\n\nvoid update_divine(const vector>& qcells, int obs) {\n int ksz = qcells.size();\n double sigma2 = ksz * eps * (1 - eps);\n int Q = qcells.size();\n \n vector mx_arr(M), total_arr(M);\n for (int k = 0; k < M; k++) {\n mx_arr[k] = *max_element(lw[k].begin(), lw[k].end());\n total_arr[k] = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) total_arr[k] += exp(lw[k][p] - mx_arr[k]);\n }\n \n vector> fc(M, vector(Q, 0.0));\n for (int k = 0; k < M; k++) {\n if (total_arr[k] < 1e-30) continue;\n for (int q = 0; q < Q; q++) {\n auto& [i, j] = qcells[q];\n double covers = 0;\n for (int p : cell_pos[k][i * N + j]) covers += exp(lw[k][p] - mx_arr[k]);\n fc[k][q] = covers / total_arr[k];\n }\n }\n \n for (int k = 0; k < M; k++) {\n double S_others = 0;\n for (int q = 0; q < Q; q++) {\n for (int k2 = 0; k2 < M; k2++) {\n if (k2 != k) S_others += fc[k2][q];\n }\n }\n \n double var_others = 0;\n for (int k2 = 0; k2 < M; k2++) {\n if (k2 == k || total_arr[k2] < 1e-30) continue;\n \n vector joint_q(Q * Q, 0.0);\n vector idx(Q, 0);\n for (int p = 0; p < (int)positions[k2].size(); p++) {\n double wt = exp(lw[k2][p] - mx_arr[k2]) / total_arr[k2];\n vector covered_q;\n for (int q = 0; q < Q; q++) {\n auto& [i, j] = qcells[q];\n const auto& cp = cell_pos[k2][i * N + j];\n while (idx[q] < (int)cp.size() && cp[idx[q]] < p) idx[q]++;\n if (idx[q] < (int)cp.size() && cp[idx[q]] == p) {\n covered_q.push_back(q);\n }\n }\n for (int q1_idx = 0; q1_idx < (int)covered_q.size(); q1_idx++) {\n for (int q2_idx = q1_idx; q2_idx < (int)covered_q.size(); q2_idx++) {\n joint_q[covered_q[q1_idx] * Q + covered_q[q2_idx]] += wt;\n }\n }\n }\n for (int q1 = 0; q1 < Q; q1++) {\n var_others += fc[k2][q1] * (1.0 - fc[k2][q1]);\n for (int q2 = q1 + 1; q2 < Q; q2++) {\n double cov = joint_q[q1 * Q + q2] - fc[k2][q1] * fc[k2][q2];\n var_others += 2 * cov;\n }\n }\n }\n \n double total_var = sigma2 + var_others * (1 - 2 * eps) * (1 - 2 * eps);\n if (total_var < sigma2) total_var = sigma2; // Safety clamp\n \n vector pos_cnt(positions[k].size(), 0);\n for (int q = 0; q < Q; q++) {\n auto& [i, j] = qcells[q];\n for (int p : cell_pos[k][i * N + j]) pos_cnt[p]++;\n }\n \n for (int p = 0; p < (int)positions[k].size(); p++) {\n double ev = S_others + pos_cnt[p];\n double mean = ksz * eps + ev * (1 - 2 * eps);\n double diff = obs - mean;\n lw[k][p] += -diff * diff / (2 * total_var);\n }\n double mx = *max_element(lw[k].begin(), lw[k].end());\n for (auto& l : lw[k]) l -= mx;\n }\n compute_prob_and_cov();\n}\n\nvoid update_drill(int i, int j, int obs) {\n if (obs == 0) {\n for (int k = 0; k < M; k++) {\n for (int p : cell_pos[k][i * N + j]) {\n lw[k][p] = -1e9; // Completely eliminate positions covering a known 0-cell\n }\n double mx = *max_element(lw[k].begin(), lw[k].end());\n for (auto& l : lw[k]) l -= mx;\n }\n } else if (obs == M) {\n for (int k = 0; k < M; k++) {\n const auto& cp = cell_pos[k][i * N + j];\n for (int p = 0; p < (int)positions[k].size(); p++) {\n if (!binary_search(cp.begin(), cp.end(), p)) lw[k][p] = -1e9;\n }\n double mx = *max_element(lw[k].begin(), lw[k].end());\n for (auto& l : lw[k]) l -= mx;\n }\n } else {\n vector fc(M, 0.0);\n vector mx_arr(M), total_arr(M);\n for (int k = 0; k < M; k++) {\n mx_arr[k] = *max_element(lw[k].begin(), lw[k].end());\n total_arr[k] = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) total_arr[k] += exp(lw[k][p] - mx_arr[k]);\n if (total_arr[k] < 1e-30) { fc[k] = 0; continue; }\n double covers = 0;\n for (int p : cell_pos[k][i * N + j]) covers += exp(lw[k][p] - mx_arr[k]);\n fc[k] = covers / total_arr[k];\n }\n \n for (int k = 0; k < M; k++) {\n double others = 0;\n double var_others = 0;\n for (int k2 = 0; k2 < M; k2++) {\n if (k2 == k) continue;\n others += fc[k2];\n var_others += fc[k2] * (1.0 - fc[k2]);\n }\n \n double var_o = max(0.1, var_others);\n const auto& cp = cell_pos[k][i * N + j];\n \n for (int p = 0; p < (int)positions[k].size(); p++) {\n double covers = binary_search(cp.begin(), cp.end(), p) ? 1.0 : 0.0;\n double diff;\n if (covers > 0.5) {\n diff = obs - 1.0 - others;\n } else {\n diff = obs - others;\n }\n lw[k][p] += -diff * diff / (2 * var_o);\n }\n double mx = *max_element(lw[k].begin(), lw[k].end());\n for (auto& l : lw[k]) l -= mx;\n }\n }\n compute_prob_and_cov();\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> M >> eps;\n shapes.resize(M);\n for (int k = 0; k < M; k++) {\n int d; cin >> d;\n shapes[k].resize(d);\n for (int l = 0; l < d; l++) cin >> shapes[k][l].first >> shapes[k][l].second;\n }\n max_di.resize(M); max_dj.resize(M);\n for (int k = 0; k < M; k++) {\n max_di[k] = max_dj[k] = 0;\n for (auto& [i, j] : shapes[k]) { max_di[k] = max(max_di[k], i); max_dj[k] = max(max_dj[k], j); }\n }\n cell_pos.resize(M, vector>(N * N));\n for (int k = 0; k < M; k++) {\n vector> pos;\n vector>> cells;\n int pidx = 0;\n for (int di = 0; di <= N - 1 - max_di[k]; di++)\n for (int dj = 0; dj <= N - 1 - max_dj[k]; dj++) {\n pos.push_back({di, dj});\n vector> c;\n for (auto& [i, j] : shapes[k]) {\n int ci = di + i, cj = dj + j;\n c.push_back({ci, cj});\n cell_pos[k][ci * N + cj].push_back(pidx);\n }\n cells.push_back(c);\n pidx++;\n }\n positions.push_back(pos);\n pos_cells.push_back(cells);\n }\n memset(known, -1, sizeof(known));\n for (int k = 0; k < M; k++) lw.push_back(vector(positions[k].size(), 0.0));\n compute_prob_and_cov();\n \n for (int i = 0; i < N && query_count < 2*N*N - 1; i++) {\n vector> cells;\n for (int j = 0; j < N; j++) cells.push_back({i, j});\n update_divine(cells, divine_cells(cells));\n }\n for (int j = 0; j < N && query_count < 2*N*N - 1; j++) {\n vector> cells;\n for (int i = 0; i < N; i++) cells.push_back({i, j});\n update_divine(cells, divine_cells(cells));\n }\n if (eps <= 0.1) {\n int B = max(4, N / 3);\n int S = max(2, B / 2);\n for (int r1 = 0; r1 < N && query_count < 2*N*N - 1; r1 += S)\n for (int c1 = 0; c1 < N && query_count < 2*N*N - 1; c1 += S) {\n vector> cells;\n for (int i = r1; i < min(N, r1 + B); i++)\n for (int j = c1; j < min(N, c1 + B); j++)\n cells.push_back({i, j});\n if (cells.size() >= 2) update_divine(cells, divine_cells(cells));\n }\n }\n \n bool last_answer_wrong = false;\n while (query_count < 2*N*N) {\n double exp_err = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) continue;\n double p = prob_oil_val[i][j];\n exp_err += min(p, 1 - p);\n }\n if ((exp_err < 0.7 || query_count >= 2*N*N - 1) && !last_answer_wrong) {\n vector> ans;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] > 0) ans.push_back({i, j});\n else if (known[i][j] < 0 && prob_oil_val[i][j] > 0.5) ans.push_back({i, j});\n }\n if (submit_answer(ans)) return 0;\n last_answer_wrong = true;\n } else {\n if (query_count >= 2*N*N - 1) break;\n int bi = -1, bj = -1; double bent = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) continue;\n double p = max(0.001, min(0.999, prob_oil_val[i][j]));\n double ent = -p*log(p) - (1-p)*log(1-p);\n if (ent > bent) { bent = ent; bi = i; bj = j; }\n }\n if (bi < 0) break;\n update_drill(bi, bj, drill_cell(bi, bj));\n last_answer_wrong = false;\n }\n }\n \n if (query_count < 2*N*N) {\n vector> ans;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] > 0) ans.push_back({i, j});\n else if (known[i][j] < 0 && prob_oil_val[i][j] > 0.5) ans.push_back({i, j});\n }\n submit_answer(ans);\n }\n return 0;\n}","ahc031":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint W, D, N;\nvector> a;\n\nlong long day_def(int d, const vector& h) {\n long long c = 0;\n for (int k = 0; k < N; k++) {\n int area = h[k] * W;\n if (a[d][k] > area) c += 100LL * (a[d][k] - area);\n }\n return c;\n}\n\nvoid get_bounds(const vector& h, vector& b) {\n b.resize(N - 1);\n int y = 0;\n for (int k = 0; k < N - 1; k++) { y += h[k]; b[k] = y; }\n}\n\nlong long bound_diff(const vector& b1, const vector& b2) {\n int i = 0, j = 0; long long c = 0;\n while (i < (int)b1.size() && j < (int)b2.size()) {\n if (b1[i] == b2[j]) { i++; j++; }\n else if (b1[i] < b2[j]) { c++; i++; }\n else { c++; j++; }\n }\n c += (int)b1.size() - i + (int)b2.size() - j;\n return c;\n}\n\nvector greedy_day(int d) {\n vector h(N, 1);\n int rem = W - N;\n while (rem > 0) {\n int bk = -1; long long br = -1;\n for (int k = 0; k < N; k++) {\n int df = max(0, a[d][k] - h[k] * W);\n int nd = max(0, a[d][k] - (h[k] + 1) * W);\n long long r = df - nd;\n if (r > br || (r == br && bk >= 0 && a[d][k] > a[d][bk])) { br = r; bk = k; }\n }\n if (bk == -1 || br == 0) {\n int mx = -1; for (int k = 0; k < N; k++) if (a[d][k] > mx) { mx = a[d][k]; bk = k; }\n }\n if (bk == -1) break;\n h[bk]++; rem--;\n }\n return h;\n}\n\nint main(){\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> W >> D >> N;\n a.resize(D, vector(N));\n for (int d = 0; d < D; d++) for (int k = 0; k < N; k++) cin >> a[d][k];\n \n mt19937 rng(42);\n uniform_real_distribution uni(0, 1);\n \n vector fixed_h(N, 1);\n { int rem = W - N;\n while (rem > 0) {\n int bk = -1; long long bs = -1;\n for (int k = 0; k < N; k++) {\n long long td = 0, ntd = 0;\n for (int d = 0; d < D; d++) { td += max(0, a[d][k] - fixed_h[k] * W); ntd += max(0, a[d][k] - (fixed_h[k] + 1) * W); }\n long long s = td - ntd;\n if (s > bs) { bs = s; bk = k; }\n }\n if (bk == -1) break; fixed_h[bk]++; rem--;\n }\n }\n \n { vector ch = fixed_h;\n long long cc = 0; for (int d = 0; d < D; d++) cc += day_def(d, ch);\n long long bc = cc; vector bh = ch;\n auto st = chrono::high_resolution_clock::now();\n while (true) {\n auto nw = chrono::high_resolution_clock::now();\n double el = chrono::duration(nw - st).count();\n if (el > 0.25) break;\n int k1 = rng() % N, k2 = rng() % N;\n if (k1 == k2 || ch[k1] <= 1) continue;\n long long delta = 0;\n for (int d = 0; d < D; d++) {\n delta += 100LL * (max(0, a[d][k1] - (ch[k1] - 1) * W) - max(0, a[d][k1] - ch[k1] * W));\n delta += 100LL * (max(0, a[d][k2] - (ch[k2] + 1) * W) - max(0, a[d][k2] - ch[k2] * W));\n }\n double temp = 5e6 * max(1e-4, 1.0 - el / 0.25);\n if (delta <= 0 || exp(-(double)delta / temp) > uni(rng)) {\n ch[k1]--; ch[k2]++; cc += delta;\n if (cc < bc) { bc = cc; bh = ch; }\n }\n }\n fixed_h = bh;\n }\n \n vector>> cands(D);\n vector> cdef(D);\n vector>> cbnd(D);\n \n for (int d = 0; d < D; d++) {\n vector min_h(N);\n int sum_min = 0;\n for (int k = 0; k < N; k++) {\n min_h[k] = (a[d][k] + W - 1) / W;\n sum_min += min_h[k];\n }\n int extra = W - sum_min;\n \n if (extra >= 0) {\n cands[d].push_back(min_h);\n for (int k = 0; k < N; k++) {\n if (extra > 0) {\n vector h = min_h; h[k] += extra;\n cands[d].push_back(h);\n }\n }\n int num_random = max(15, extra / 5);\n for (int i = 0; i < num_random; i++) {\n vector h = min_h; int rem = extra;\n while (rem > 0) { h[rng() % N]++; rem--; }\n cands[d].push_back(h);\n }\n } else {\n vector ch = min_h; int rem = -extra;\n while (rem > 0) {\n int bk = -1; long long min_inc = LLONG_MAX;\n for (int k = 0; k < N; k++) {\n if (ch[k] > 1) {\n int od = max(0, a[d][k] - ch[k] * W); int nd = max(0, a[d][k] - (ch[k] - 1) * W);\n if (nd - od < min_inc) { min_inc = nd - od; bk = k; }\n }\n }\n if (bk == -1) break; ch[bk]--; rem--;\n }\n cands[d].push_back(ch);\n for (int k = 0; k < N; k++) {\n if (min_h[k] > 1) {\n vector h = min_h; h[k]--; int r2 = -extra - 1;\n while (r2 > 0) {\n int bk2 = -1; long long min_inc2 = LLONG_MAX;\n for (int j = 0; j < N; j++) {\n if (h[j] > 1) {\n int od = max(0, a[d][j] - h[j] * W); int nd = max(0, a[d][j] - (h[j] - 1) * W);\n if (nd - od < min_inc2) { min_inc2 = nd - od; bk2 = j; }\n }\n }\n if (bk2 == -1) break; h[bk2]--; r2--;\n }\n cands[d].push_back(h);\n }\n }\n for (int i = 0; i < 15; i++) {\n vector h = min_h; int rem = -extra;\n while (rem > 0) { int k = rng() % N; if (h[k] > 1) { h[k]--; rem--; } }\n cands[d].push_back(h);\n }\n }\n \n cands[d].push_back(fixed_h);\n cands[d].push_back(greedy_day(d));\n \n sort(cands[d].begin(), cands[d].end());\n cands[d].erase(unique(cands[d].begin(), cands[d].end()), cands[d].end());\n }\n \n vector ksz(D); int maxK = 0;\n for (int d = 0; d < D; d++) { ksz[d] = cands[d].size(); maxK = max(maxK, ksz[d]); }\n vector> dp(D, vector(maxK, LLONG_MAX));\n vector> par(D, vector(maxK, -1));\n \n for (int d = 0; d < D; d++) {\n cdef[d].resize(ksz[d]); cbnd[d].resize(ksz[d]);\n for (int i = 0; i < ksz[d]; i++) { cdef[d][i] = day_def(d, cands[d][i]); get_bounds(cands[d][i], cbnd[d][i]); }\n }\n \n for (int k = 0; k < ksz[0]; k++) dp[0][k] = cdef[0][k];\n for (int d = 1; d < D; d++)\n for (int k = 0; k < ksz[d]; k++)\n for (int j = 0; j < ksz[d-1]; j++) {\n if (dp[d-1][j] == LLONG_MAX) continue;\n long long cost = dp[d-1][j] + bound_diff(cbnd[d-1][j], cbnd[d][k]) * W + cdef[d][k];\n if (cost < dp[d][k]) { dp[d][k] = cost; par[d][k] = j; }\n }\n \n long long best_dp = LLONG_MAX; int best_k = -1;\n for (int k = 0; k < ksz[D-1]; k++) if (dp[D-1][k] < best_dp) { best_dp = dp[D-1][k]; best_k = k; }\n vector> dp_res(D);\n { int ck = best_k; for (int d = D-1; d >= 0; d--) { dp_res[d] = cands[d][ck]; ck = par[d][ck]; } }\n \n vector> cur_h = dp_res;\n vector> cur_bnd(D);\n vector pc_cache(D, 0);\n for (int d = 0; d < D; d++) get_bounds(cur_h[d], cur_bnd[d]);\n for (int d = 1; d < D; d++) pc_cache[d] = bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n \n long long cur_cost = 0;\n for (int d = 0; d < D; d++) cur_cost += day_def(d, cur_h[d]);\n for (int d = 1; d < D; d++) cur_cost += pc_cache[d];\n \n { long long fc = 0; for (int d = 0; d < D; d++) fc += day_def(d, fixed_h);\n if (fc < cur_cost) {\n cur_h.assign(D, fixed_h);\n for (int d = 0; d < D; d++) get_bounds(cur_h[d], cur_bnd[d]);\n for (int d = 1; d < D; d++) pc_cache[d] = bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n cur_cost = fc;\n }\n }\n long long best_cost = cur_cost; vector> best_h = cur_h;\n \n auto st = chrono::high_resolution_clock::now();\n while (true) {\n auto nw = chrono::high_resolution_clock::now();\n double el = chrono::duration(nw - st).count();\n if (el > 2.5) break;\n int d = rng() % D, k1 = rng() % N, k2 = rng() % N;\n if (k1 == k2 || cur_h[d][k1] <= 1) continue;\n long long dd = 100LL * (max(0, a[d][k1] - (cur_h[d][k1] - 1) * W) - max(0, a[d][k1] - cur_h[d][k1] * W))\n + 100LL * (max(0, a[d][k2] - (cur_h[d][k2] + 1) * W) - max(0, a[d][k2] - cur_h[d][k2] * W));\n cur_h[d][k1]--; cur_h[d][k2]++;\n int lo = min(k1, k2), hi = max(k1, k2);\n int dsign = (k1 < k2) ? -1 : 1;\n for (int i = lo; i < hi; i++) cur_bnd[d][i] += dsign;\n long long npd = (d > 0 ? bound_diff(cur_bnd[d-1], cur_bnd[d]) * W : 0)\n + (d < D-1 ? bound_diff(cur_bnd[d], cur_bnd[d+1]) * W : 0);\n long long opd = (d > 0 ? pc_cache[d] : 0) + (d < D-1 ? pc_cache[d+1] : 0);\n long long delta = dd + npd - opd;\n double temp = 5e6 * max(1e-4, 1.0 - el / 2.5);\n if (delta <= 0 || exp(-(double)delta / temp) > uni(rng)) {\n cur_cost += delta;\n if (d > 0) pc_cache[d] = bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n if (d < D-1) pc_cache[d+1] = bound_diff(cur_bnd[d], cur_bnd[d+1]) * W;\n if (cur_cost < best_cost) { best_cost = cur_cost; best_h = cur_h; }\n } else {\n cur_h[d][k1]++; cur_h[d][k2]--;\n for (int i = lo; i < hi; i++) cur_bnd[d][i] -= dsign;\n }\n }\n \n for (int d = 0; d < D; d++) {\n int y = 0;\n for (int k = 0; k < N; k++) { cout << y << \" 0 \" << y + best_h[d][k] << \" \" << W << \"\\n\"; y += best_h[d][k]; }\n }\n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long MOD = 998244353;\n\nlong long bmod[81];\nlong long s_val[180];\nint ops[81];\nint op_p[81];\nint op_q[81];\nint L = 0;\n\nstruct FastRNG {\n unsigned long long x = 123456789, y = 362436069, z = 521288629;\n unsigned long long operator()() {\n unsigned long long t;\n x ^= x << 16;\n x ^= x >> 5;\n x ^= x << 1;\n t = x;\n x = y;\n y = z;\n z = t ^ x ^ y;\n return z;\n }\n};\n\nFastRNG rng;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n for (int i = 0; i < 81; i++) cin >> bmod[i];\n \n for (int m = 0; m < M; m++)\n for (int i = 0; i < 9; i++)\n cin >> s_val[m * 9 + i];\n \n // Greedy Initialization\n for (int k = 0; k < K; k++) {\n int best_m = -1, best_p = -1, best_q = -1;\n long long best_delta = 0;\n for (int m = 0; m < M; m++) {\n for (int p = 0; p < 7; p++) {\n for (int q = 0; q < 7; q++) {\n long long delta = 0;\n for (int i = 0; i < 3; i++) {\n for (int j = 0; j < 3; j++) {\n int u = (p + i) * 9 + (q + j);\n long long nv = bmod[u] + s_val[m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n delta += nv - bmod[u];\n }\n }\n if (delta > best_delta) {\n best_delta = delta;\n best_m = m; best_p = p; best_q = q;\n }\n }\n }\n }\n if (best_delta <= 0) break;\n ops[L] = best_m; op_p[L] = best_p; op_q[L] = best_q;\n L++;\n for (int i = 0; i < 3; i++) {\n for (int j = 0; j < 3; j++) {\n int u = (best_p + i) * 9 + (best_q + j);\n long long nv = bmod[u] + s_val[best_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n }\n \n long long score = 0;\n for (int i = 0; i < 81; i++) score += bmod[i];\n \n long long best_score = score;\n int best_L = L;\n int best_ops[81], best_op_p[81], best_op_q[81];\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n \n double start_temp = 2e9, end_temp = 1e5;\n auto start_time = chrono::high_resolution_clock::now();\n \n int iter = 0;\n while (true) {\n iter++;\n if (iter % 10000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n if (elapsed > 1.8) break;\n }\n \n double temp = start_temp * pow(end_temp / start_temp, min(1.0, chrono::duration(chrono::high_resolution_clock::now() - start_time).count() / 1.8));\n \n int move_type = rng() % 100;\n long long delta = 0;\n \n if (move_type < 8 && L < K) {\n int new_m = rng() % M;\n int new_p = rng() % 7;\n int new_q = rng() % 7;\n \n long long old_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) old_score += bmod[(new_p + i) * 9 + (new_q + j)];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] + s_val[new_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) new_score += bmod[(new_p + i) * 9 + (new_q + j)];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[L] = new_m; op_p[L] = new_p; op_q[L] = new_q;\n L++;\n score += delta;\n if (score > best_score) {\n best_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] - s_val[new_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n }\n } else if (move_type < 12 && L > 0) {\n int idx = rng() % L;\n int old_m = ops[idx], old_p = op_p[idx], old_q = op_q[idx];\n \n long long old_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) old_score += bmod[(old_p + i) * 9 + (old_q + j)];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] - s_val[old_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) new_score += bmod[(old_p + i) * 9 + (old_q + j)];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[idx] = ops[L - 1]; op_p[idx] = op_p[L - 1]; op_q[idx] = op_q[L - 1];\n L--;\n score += delta;\n if (score > best_score) {\n best_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] + s_val[old_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n } else if (L > 0) {\n int idx = rng() % L;\n int old_m = ops[idx], old_p = op_p[idx], old_q = op_q[idx];\n \n int r = rng() % 5;\n int new_m = old_m, new_p = old_p, new_q = old_q;\n if (r == 0) new_m = rng() % M;\n else if (r == 1) new_p = rng() % 7;\n else if (r == 2) new_q = rng() % 7;\n else if (r == 3) { new_p = rng() % 7; new_q = rng() % 7; }\n else { new_m = rng() % M; new_p = rng() % 7; new_q = rng() % 7; }\n \n if (new_m == old_m && new_p == old_p && new_q == old_q) continue;\n \n bool affected[81] = {false};\n int affected_list[18];\n int affected_count = 0;\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n if (!affected[u]) {\n affected[u] = true;\n affected_list[affected_count++] = u;\n }\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n if (!affected[u]) {\n affected[u] = true;\n affected_list[affected_count++] = u;\n }\n }\n \n long long old_score = 0;\n for (int k = 0; k < affected_count; k++) old_score += bmod[affected_list[k]];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] - s_val[old_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] + s_val[new_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int k = 0; k < affected_count; k++) new_score += bmod[affected_list[k]];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[idx] = new_m; op_p[idx] = new_p; op_q[idx] = new_q;\n score += delta;\n if (score > best_score) {\n best_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] - s_val[new_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] + s_val[old_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n for (int k = 0; k < affected_count; k++) affected[affected_list[k]] = false;\n }\n }\n \n cout << best_L << \"\\n\";\n for (int i = 0; i < best_L; i++)\n cout << best_ops[i] << \" \" << best_op_p[i] << \" \" << best_op_q[i] << \"\\n\";\n \n return 0;\n}","ahc033":"#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N], grid[N][N];\nbool dispatched[N*N];\nint nxt_recv[N];\nint cr, cc, ch;\nint total_disp;\nvector acts(N);\n\nint next_exp(int g) {\n for (int j = 0; j < N; j++)\n if (!dispatched[N*g+j]) return N*g+j;\n return -1;\n}\n\nchar move_toward(int& r, int& c, int tr, int tc) {\n if (r < tr) { r++; return 'D'; }\n if (r > tr) { r--; return 'U'; }\n if (c < tc) { c++; return 'R'; }\n if (c > tc) { c--; return 'L'; }\n return '.';\n}\n\nint main() {\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> A[i][j];\n \n memset(grid, -1, sizeof(grid));\n fill(dispatched, dispatched+N*N, false);\n fill(nxt_recv, nxt_recv+N, 0);\n cr = cc = 0; ch = -1; total_disp = 0;\n \n // Turn 0: bomb small cranes\n for (int i = 0; i < N; i++) acts[i] += (i ? 'B' : '.');\n for (int i = 0; i < N; i++)\n if (nxt_recv[i] < N) grid[i][0] = A[i][nxt_recv[i]++];\n \n for (int t = 1; total_disp < N*N && (int)acts[0].size() < 9999; t++) {\n for (int i = 0; i < N; i++)\n if (nxt_recv[i] < N && grid[i][0] == -1 && !(cr==i && cc==0 && ch!=-1))\n grid[i][0] = A[i][nxt_recv[i]++];\n \n char a = '.';\n if (ch >= 0) {\n int g = ch/N, e = next_exp(g);\n int tr, tc;\n if (e >= 0 && e == ch) {\n tr = g; tc = N-1;\n } else {\n tr = tc = -1;\n int bd = INT_MAX;\n for (int c = 1; c < N-1; c++)\n for (int r = 0; r < N; r++)\n if (grid[r][c] == -1) {\n int d = abs(cr-r)+abs(cc-c)+abs(r-g)*3;\n if (d < bd) { bd=d; tr=r; tc=c; }\n }\n if (tr == -1) { tr = g; tc = N-1; }\n }\n if (cr==tr && cc==tc) { a='Q'; grid[tr][tc]=ch; ch=-1; }\n else a = move_toward(cr, cc, tr, tc);\n } else {\n int bc=-1, bs=INT_MAX, br=-1, bcc=-1;\n for (int r = 0; r < N; r++)\n for (int c = 0; c < N; c++) {\n if (grid[r][c] < 0) continue;\n int co=grid[r][c], g=co/N, e=next_exp(g);\n int d = abs(cr-r)+abs(cc-c), s;\n if (e >= 0 && e == co) s = -5000+d;\n else if (c==0 && nxt_recv[r]=0 && ne==nc) ? -3000+d : -1000+d;\n } else if (c==0) s = -500+d;\n else s = d+500;\n if (s=0) {\n if (cr==br && cc==bcc) { a='P'; ch=bc; grid[br][bcc]=-1; }\n else a = move_toward(cr, cc, br, bcc);\n }\n }\n \n acts[0] += a;\n for (int i = 1; i < N; i++) acts[i] += '.';\n \n for (int i = 0; i < N; i++)\n if (grid[i][N-1]>=0) { dispatched[grid[i][N-1]]=true; grid[i][N-1]=-1; total_disp++; }\n }\n \n int ml = 0;\n for (int i = 0; i < N; i++) ml = max(ml, (int)acts[i].size());\n for (int i = 0; i < N; i++) {\n while ((int)acts[i].size() < ml) acts[i] += '.';\n cout << acts[i] << endl;\n }\n return 0;\n}","ahc034":"#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\ntypedef long long ll;\nconst ll INF = 1e18;\nstruct Edge { int to, rev; ll cap, cost; };\nstruct MinCostFlow {\n int n; vector> graph; vector h; vector pv, pe;\n MinCostFlow(int n):n(n),graph(n),h(n,0),pv(n),pe(n){}\n void add_edge(int f,int t,ll cap,ll cost){\n graph[f].push_back({t,(int)graph[t].size(),cap,cost});\n graph[t].push_back({f,(int)graph[f].size()-1,0,-cost});\n }\n ll min_cost_flow(int s,int t,ll mf){\n ll res=0,flow=0;\n while(flow,vector>,greater<>>pq;\n vectordist(n,INF);dist[s]=0;pq.push({0,s});\n while(!pq.empty()){\n auto[d,v]=pq.top();pq.pop();\n if(dist[v]0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){\n dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];\n pv[e.to]=v;pe[e.to]=i;pq.push({dist[e.to],e.to});\n }\n }\n }\n if(dist[t]==INF)break;\n for(int v=0;v>n;\n vector>h(n,vector(n));\n for(int i=0;i>h[i][j];\n vector>sources,sinks;\n vector>sid(n,vector(n,-1)),kid(n,vector(n,-1));\n int tsup=0;\n for(int i=0;i0){sid[i][j]=sources.size();sources.push_back({i,j});tsup+=h[i][j];}\n else if(h[i][j]<0){kid[i][j]=sinks.size();sinks.push_back({i,j});}\n }\n int P=sources.size(),M=sinks.size();\n int S=0,T=P+M+1;\n MinCostFlow mcf(P+M+2);\n for(int i=0;i>fa(P,vector(M,0));\n for(int i=0;i=1+P&&e.to<1+P+M)fa[i][e.to-1-P]=(int)mcf.graph[e.to][e.rev].cap;\n vectorsnnd(P,0);\n for(int i=0;i0){auto[ti,tj]=sinks[j];best=min(best,abs(si-ti)+abs(sj-tj));}\n snnd[i]=(bestops;int r=0,c=0,load=0,rem=tsup;\n auto cur=h;\n while(ops.size()<100000&&(rem>0||load>0)){\n if(cur[r][c]>0){ops.push_back(\"+\"+to_string(cur[r][c]));load+=cur[r][c];rem-=cur[r][c];cur[r][c]=0;}\n while(cur[r][c]<0&&load>0){int d=min(load,-cur[r][c]);ops.push_back(\"-\"+to_string(d));load-=d;cur[r][c]+=d;}\n if(rem==0&&load==0)break;\n int br=-1,bc=-1;ll bcost=LLONG_MAX;\n if(load>0){\n for(int i=0;i0){\n int dt=abs(r-i)+abs(c-j);int s=sid[i][j];\n int dd=(s>=0)?snnd[s]:20;\n ll cost=(ll)dt*100+(ll)dd*(100+cur[i][j]);\n if(costr){r++;ops.push_back(\"D\");}\n else if(bc\n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 6, M = 15;\n const int SEED_COUNT = 2 * N * (N - 1);\n const int GRID_SIZE = N * N;\n \n int n, m, t;\n cin >> n >> m >> t;\n \n vector> X(SEED_COUNT, vector(M));\n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n cin >> X[i][j];\n \n vector> edges;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N-1; j++)\n edges.push_back({i*N+j, i*N+j+1});\n for (int i = 0; i < N-1; i++)\n for (int j = 0; j < N; j++)\n edges.push_back({i*N+j, (i+1)*N+j});\n \n const int NUM_EDGES = (int)edges.size();\n \n vector> posEdges(GRID_SIZE);\n vector> posNeighbors(GRID_SIZE);\n for (int e = 0; e < NUM_EDGES; e++) {\n posEdges[edges[e].first].push_back(e);\n posEdges[edges[e].second].push_back(e);\n posNeighbors[edges[e].first].push_back(edges[e].second);\n posNeighbors[edges[e].second].push_back(edges[e].first);\n }\n \n vector posOrder(GRID_SIZE);\n iota(posOrder.begin(), posOrder.end(), 0);\n sort(posOrder.begin(), posOrder.end(), [](int a, int b) {\n int ra = a / N, ca = a % N;\n int rb = b / N, cb = b % N;\n int da = abs(2*ra - (2*N-2)) + abs(2*ca - (2*N-2));\n int db = abs(2*rb - (2*N-2)) + abs(2*cb - (2*N-2));\n if (da != db) return da < db;\n return a < b;\n });\n \n mt19937 rng(42);\n uniform_real_distribution unif(0.0, 1.0);\n \n for (int turn = 0; turn < t; turn++) {\n vector values(SEED_COUNT, 0);\n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n values[i] += X[i][j];\n \n vector> pot(SEED_COUNT, vector(SEED_COUNT, 0));\n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = i+1; j < SEED_COUNT; j++) {\n for (int l = 0; l < M; l++)\n pot[i][j] += max(X[i][l], X[j][l]);\n pot[j][i] = pot[i][j];\n }\n \n // Greedy initial placement\n vector grid(GRID_SIZE, -1);\n vector used(SEED_COUNT, false);\n \n for (int pos : posOrder) {\n int bestSeed = -1;\n int bestScore = -1;\n \n for (int s = 0; s < SEED_COUNT; s++) {\n if (used[s]) continue;\n int score = 0;\n for (int npos : posNeighbors[pos]) {\n if (grid[npos] != -1) {\n score += pot[s][grid[npos]];\n }\n }\n if (score == 0) score = values[s];\n if (score > bestScore) {\n bestScore = score;\n bestSeed = s;\n }\n }\n \n grid[pos] = bestSeed;\n used[bestSeed] = true;\n }\n \n vector unplaced;\n for (int i = 0; i < SEED_COUNT; i++)\n if (!used[i]) unplaced.push_back(i);\n \n int currentScore = 0;\n for (int e = 0; e < NUM_EDGES; e++)\n currentScore += pot[grid[edges[e].first]][grid[edges[e].second]];\n \n int bestScore = currentScore;\n vector bestGrid = grid;\n \n auto startTime = chrono::high_resolution_clock::now();\n const double startTemp = 500.0, endTemp = 0.1;\n double temp = startTemp;\n \n for (int iter = 0; iter < 10000000; iter++) {\n if (iter % 10000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n auto elapsed = chrono::duration_cast(now - startTime).count();\n if (elapsed > 180000) break;\n double progress = (double)elapsed / 180000.0;\n temp = startTemp * pow(endTemp / startTemp, progress);\n }\n \n if (rng() % 5 != 0) {\n int i = rng() % GRID_SIZE, j = rng() % GRID_SIZE;\n if (i == j) continue;\n \n int delta = 0;\n for (int e : posEdges[i]) delta -= pot[grid[edges[e].first]][grid[edges[e].second]];\n for (int e : posEdges[j]) delta -= pot[grid[edges[e].first]][grid[edges[e].second]];\n \n swap(grid[i], grid[j]);\n \n for (int e : posEdges[i]) delta += pot[grid[edges[e].first]][grid[edges[e].second]];\n for (int e : posEdges[j]) delta += pot[grid[edges[e].first]][grid[edges[e].second]];\n \n if (delta >= 0 || (temp > 0.5 && unif(rng) < exp((double)delta / temp))) {\n currentScore += delta;\n if (currentScore > bestScore) { bestScore = currentScore; bestGrid = grid; }\n } else {\n swap(grid[i], grid[j]);\n }\n } else {\n int pos = rng() % GRID_SIZE;\n int old_seed = grid[pos];\n int up_idx = rng() % (int)unplaced.size();\n int new_seed = unplaced[up_idx];\n \n int delta = 0;\n for (int e : posEdges[pos]) delta -= pot[grid[edges[e].first]][grid[edges[e].second]];\n \n grid[pos] = new_seed;\n \n for (int e : posEdges[pos]) delta += pot[grid[edges[e].first]][grid[edges[e].second]];\n \n if (delta >= 0 || (temp > 0.5 && unif(rng) < exp((double)delta / temp))) {\n currentScore += delta;\n used[old_seed] = false;\n used[new_seed] = true;\n unplaced[up_idx] = old_seed;\n if (currentScore > bestScore) { bestScore = currentScore; bestGrid = grid; }\n } else {\n grid[pos] = old_seed;\n }\n }\n }\n \n grid = bestGrid;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cout << grid[i*N+j];\n if (j < N-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n cout.flush();\n \n for (int i = 0; i < SEED_COUNT; i++)\n for (int j = 0; j < M; j++)\n cin >> X[i][j];\n }\n \n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n \n vector s(N), t(N);\n for (int i = 0; i < N; i++) cin >> s[i];\n for (int i = 0; i < N; i++) cin >> t[i];\n \n int Vp = V;\n vector len(Vp, 1);\n for (int i = 1; i < Vp; i++) {\n len[i] = ((i - 1) % (N / 2)) + 1;\n }\n \n cout << Vp << \"\\n\";\n for (int i = 1; i < Vp; i++) cout << 0 << \" \" << len[i] << \"\\n\";\n \n vector> grid(N, vector(N)), target(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n grid[i][j] = s[i][j] - '0';\n target[i][j] = t[i][j] - '0';\n }\n \n vector> sources, targets;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n if (grid[i][j] && !target[i][j]) sources.push_back({i, j});\n if (!grid[i][j] && target[i][j]) targets.push_back({i, j});\n }\n \n int Mm = sources.size();\n \n vector match(Mm, -1);\n vector> pairs;\n for (int i = 0; i < Mm; i++)\n for (int j = 0; j < Mm; j++)\n pairs.push_back({abs(sources[i].first - targets[j].first) + \n abs(sources[i].second - targets[j].second), i, j});\n sort(pairs.begin(), pairs.end());\n \n vector sused(Mm, false), tused(Mm, false);\n for (auto& [d, i, j] : pairs) {\n if (!sused[i] && !tused[j]) {\n match[i] = j; sused[i] = true; tused[j] = true;\n }\n }\n \n int rx, ry;\n if (Mm > 0) {\n long long sum_x = 0, sum_y = 0;\n for (int i = 0; i < Mm; i++) {\n sum_x += sources[i].first;\n sum_y += sources[i].second;\n }\n rx = sum_x / Mm;\n ry = sum_y / Mm;\n } else {\n rx = N / 2; ry = N / 2;\n }\n cout << rx << \" \" << ry << \"\\n\";\n \n vector dir(Vp, 0);\n vector available_s(Mm, true);\n vector finger_state(Vp, 0); // 0: IDLE, 1: TO_SOURCE, 2: TO_TARGET\n vector finger_task(Vp, -1);\n vector f_target_x(Vp), f_target_y(Vp), f_target_dir(Vp);\n vector ops;\n \n auto dist_to_source = [&](int rx, int ry, int f, int s_idx) {\n int sx = sources[s_idx].first, sy = sources[s_idx].second;\n int best_dist = INT_MAX;\n for (int d = 0; d < 4; d++) {\n int nx = sx - dx[d] * len[f], ny = sy - dy[d] * len[f];\n if (0 <= nx && nx < N && 0 <= ny && ny < N) {\n int dist = abs(rx - nx) + abs(ry - ny);\n int rot = min((dir[f] - d + 4) % 4, (d - dir[f] + 4) % 4);\n int cost = max(dist, rot);\n if (cost < best_dist) best_dist = cost;\n }\n }\n return best_dist;\n };\n \n auto get_best_source_station = [&](int rx, int ry, int f, int s_idx) {\n int sx = sources[s_idx].first, sy = sources[s_idx].second;\n int best_dist = INT_MAX, best_nx = -1, best_ny = -1, best_dir = -1;\n for (int d = 0; d < 4; d++) {\n int nx = sx - dx[d] * len[f], ny = sy - dy[d] * len[f];\n if (0 <= nx && nx < N && 0 <= ny && ny < N) {\n int dist = abs(rx - nx) + abs(ry - ny);\n int rot = min((dir[f] - d + 4) % 4, (d - dir[f] + 4) % 4);\n int cost = max(dist, rot);\n if (cost < best_dist) {\n best_dist = cost; best_nx = nx; best_ny = ny; best_dir = d;\n }\n }\n }\n return make_tuple(best_nx, best_ny, best_dir);\n };\n \n auto get_best_target_station = [&](int rx, int ry, int f, int t_idx) {\n int tx = targets[t_idx].first, ty = targets[t_idx].second;\n int best_dist = INT_MAX, best_nx = -1, best_ny = -1, best_dir = -1;\n for (int d = 0; d < 4; d++) {\n int nx = tx - dx[d] * len[f], ny = ty - dy[d] * len[f];\n if (0 <= nx && nx < N && 0 <= ny && ny < N) {\n int dist = abs(rx - nx) + abs(ry - ny);\n int rot = min((dir[f] - d + 4) % 4, (d - dir[f] + 4) % 4);\n int cost = max(dist, rot);\n if (cost < best_dist) {\n best_dist = cost; best_nx = nx; best_ny = ny; best_dir = d;\n }\n }\n }\n return make_tuple(best_nx, best_ny, best_dir);\n };\n \n // Initial assignments\n for (int f = 1; f < Vp; f++) {\n int min_d = INT_MAX, best_s = -1;\n for (int i = 0; i < Mm; i++) {\n if (!available_s[i]) continue;\n int d = dist_to_source(rx, ry, f, i);\n if (d < min_d) { min_d = d; best_s = i; }\n }\n if (best_s != -1) {\n finger_state[f] = 1;\n finger_task[f] = best_s;\n available_s[best_s] = false;\n tie(f_target_x[f], f_target_y[f], f_target_dir[f]) = get_best_source_station(rx, ry, f, best_s);\n }\n }\n \n while (true) {\n int best_dist = INT_MAX;\n int best_f = -1;\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n int dist = abs(rx - f_target_x[f]) + abs(ry - f_target_y[f]);\n if (dist < best_dist) {\n best_dist = dist;\n best_f = f;\n }\n }\n \n if (best_f == -1) {\n bool any_available = false;\n for (int i = 0; i < Mm; i++) if (available_s[i]) any_available = true;\n if (!any_available) break;\n \n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) {\n int min_d = INT_MAX, best_s = -1;\n for (int i = 0; i < Mm; i++) {\n if (!available_s[i]) continue;\n int d = dist_to_source(rx, ry, f, i);\n if (d < min_d) { min_d = d; best_s = i; }\n }\n if (best_s != -1) {\n finger_state[f] = 1;\n finger_task[f] = best_s;\n available_s[best_s] = false;\n tie(f_target_x[f], f_target_y[f], f_target_dir[f]) = get_best_source_station(rx, ry, f, best_s);\n }\n }\n }\n continue;\n }\n \n string op(2 * Vp, '.');\n if (rx < f_target_x[best_f]) { op[0] = 'D'; rx++; }\n else if (rx > f_target_x[best_f]) { op[0] = 'U'; rx--; }\n else if (ry < f_target_y[best_f]) { op[0] = 'R'; ry++; }\n else if (ry > f_target_y[best_f]) { op[0] = 'L'; ry--; }\n \n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n if (dir[f] != f_target_dir[f]) {\n int diff = (f_target_dir[f] - dir[f] + 4) % 4;\n if (diff <= 2) { op[f] = 'R'; dir[f] = (dir[f] + 1) % 4; }\n else { op[f] = 'L'; dir[f] = (dir[f] + 3) % 4; }\n }\n }\n \n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n if (rx == f_target_x[f] && ry == f_target_y[f] && dir[f] == f_target_dir[f]) {\n op[Vp + f] = 'P';\n if (finger_state[f] == 1) {\n int s_idx = finger_task[f];\n grid[sources[s_idx].first][sources[s_idx].second] = 0;\n finger_state[f] = 2;\n int t_idx = match[s_idx];\n tie(f_target_x[f], f_target_y[f], f_target_dir[f]) = get_best_target_station(rx, ry, f, t_idx);\n } else {\n int s_idx = finger_task[f];\n int t_idx = match[s_idx];\n grid[targets[t_idx].first][targets[t_idx].second] = 1;\n finger_state[f] = 0;\n \n int min_d = INT_MAX, best_s = -1;\n for (int i = 0; i < Mm; i++) {\n if (!available_s[i]) continue;\n int d = dist_to_source(rx, ry, f, i);\n if (d < min_d) { min_d = d; best_s = i; }\n }\n if (best_s != -1) {\n finger_state[f] = 1;\n finger_task[f] = best_s;\n available_s[best_s] = false;\n tie(f_target_x[f], f_target_y[f], f_target_dir[f]) = get_best_source_station(rx, ry, f, best_s);\n }\n }\n }\n }\n \n ops.push_back(op);\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc039":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N; cin >> N;\n vector fx(2*N), fy(2*N);\n for (int i = 0; i < 2*N; i++) cin >> fx[i] >> fy[i];\n \n auto scoreRect = [&](int x1, int y1, int x2, int y2) {\n int s = 0;\n for (int i = 0; i < 2*N; i++) {\n if (x1 <= fx[i] && fx[i] <= x2 && y1 <= fy[i] && fy[i] <= y2)\n s += (i < N) ? 1 : -1;\n }\n return s;\n };\n \n int GS = 100, CS = 1001;\n vector> grid(GS, vector(GS, 0));\n for (int i = 0; i < 2*N; i++) {\n grid[min(fx[i]/CS,GS-1)][min(fy[i]/CS,GS-1)] += (i < N) ? 1 : -1;\n }\n vector> pf(GS+1, vector(GS+1, 0));\n for (int i = 0; i < GS; i++)\n for (int j = 0; j < GS; j++)\n pf[i+1][j+1] = grid[i][j] + pf[i][j+1] + pf[i+1][j] - pf[i][j];\n auto gs = [&](int x1, int y1, int x2, int y2) {\n return pf[x2+1][y2+1] - pf[x1][y2+1] - pf[x2+1][y1] + pf[x1][y1];\n };\n \n int bestGS = 0, bgx1=0, bgy1=0, bgx2=0, bgy2=0;\n for (int gx1 = 0; gx1 < GS; gx1++) {\n for (int gx2 = gx1; gx2 < GS; gx2++) {\n int cur=0, best=0, cy1=0, by1=0, by2=-1;\n for (int gy2 = 0; gy2 < GS; gy2++) {\n cur += gs(gx1, gy2, gx2, gy2);\n if (cur > best) { best = cur; by1 = cy1; by2 = gy2; }\n if (cur < 0) { cur = 0; cy1 = gy2+1; }\n }\n if (best > bestGS) { bestGS=best; bgx1=gx1; bgy1=by1; bgx2=gx2; bgy2=by2; }\n }\n }\n \n int rx1=bgx1*CS, ry1=bgy1*CS, rx2=min((bgx2+1)*CS-1,100000), ry2=min((bgy2+1)*CS-1,100000);\n \n for (int iter = 0; iter < 20; iter++) {\n bool improved = false;\n for (int dim = 0; dim < 2; dim++) {\n vector> ev;\n for (int i = 0; i < 2*N; i++) {\n bool inside = (dim==0) ? (rx1<=fx[i]&&fx[i]<=rx2) : (ry1<=fy[i]&&fy[i]<=ry2);\n if (inside) ev.push_back({(dim==0)?fy[i]:fx[i], (i bs) {\n bs = s;\n int v1 = (mpi==-1) ? 0 : ev[mpi].first;\n int v2 = (j==(int)ev.size()) ? 100000 : ev[j-1].first;\n b1 = v1; b2 = v2;\n }\n if (pfx < mp) { mp = pfx; mpi = j; }\n if (j < (int)ev.size()) pfx += ev[j].second;\n }\n if (dim==0) { ry1=b1; ry2=b2; } else { rx1=b1; rx2=b2; }\n }\n }\n \n int sc = scoreRect(rx1, ry1, rx2, ry2);\n if (sc <= 0) {\n cout << 4 << \"\\n50000 50000\\n50001 50000\\n50001 50001\\n50000 50001\\n\";\n } else {\n cout << 4 << \"\\n\" << rx1 << \" \" << ry1 << \"\\n\"\n << rx2 << \" \" << ry1 << \"\\n\"\n << rx2 << \" \" << ry2 << \"\\n\"\n << rx1 << \" \" << ry2 << \"\\n\";\n }\n return 0;\n}","ahc040":"#include \nusing namespace std;\nint N,T,sigma;\nvectorw_obs,h_obs;\nvectorw_est,h_est;\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n cin>>N>>T>>sigma;\n w_obs.resize(N);h_obs.resize(N);w_est.resize(N);h_est.resize(N);\n for(int i=0;i>w_obs[i]>>h_obs[i];w_est[i]=w_obs[i];h_est[i]=h_obs[i];}\n mt19937 rng(42);\n auto start=chrono::steady_clock::now();\n for(int t=0;t(now-start).count()>2700)break;\n vectorwc(N),hc(N);\n for(int i=0;ipx,py,pw,ph;vectorplc;vector>out;\n long long cW=0,cH=0;\n bool doRow=(t==0&&T>=20),doCol=(t==1&&T>=20);\n if(doRow){\n for(int i=0;i=5);\n if(addN)for(int i=0;irx)ry=max(ry,py[j]+ph[j]);\n long long nW=max(cW,rx+rw),nH=max(cH,ry+rh),s=nW+nH;\n if(strat==1)s+=abs(nW-nH)/2;else if(strat==2)s+=abs(nW-nH);else if(strat==3){long long w=nW*nH-cW*cH-rw*rh;s+=w/500;}else if(strat==4)s=max(nW,nH)*2;\n if(sry)rx=max(rx,px[j]+pw[j]);\n long long nW=max(cW,rx+rw),nH=max(cH,ry+rh),s=nW+nH;\n if(strat==1)s+=abs(nW-nH)/2;else if(strat==2)s+=abs(nW-nH);else if(strat==3){long long w=nW*nH-cW*cH-rw*rh;s+=w/500;}else if(strat==4)s=max(nW,nH)*2;\n if(s>Wp>>Hp;\n if(doRow){double ws=0;for(int i=0;i=cW-margin)rc++;if(py[j]+ph[j]>=cH-margin)bc++;}\n double lr=0.12;\n for(int j=0;j<(int)px.size();j++){\n int o=plc[j];bool rot=get<1>(out[j]);\n if(px[j]+pw[j]>=cW-margin&&rc>0){double es=We/rc*lr;if(rot)h_est[o]=max(1.0,h_est[o]+es);else w_est[o]=max(1.0,w_est[o]+es);}\n if(py[j]+ph[j]>=cH-margin&&bc>0){double es=He/bc*lr;if(rot)w_est[o]=max(1.0,w_est[o]+es);else h_est[o]=max(1.0,h_est[o]+es);}\n }\n }\n }\n return 0;\n}","ahc041":"#include \nusing namespace std;\nint N,M,H;\nvectorA;\nvector>adj;\nmt19937 rng(42);\nchrono::steady_clock::time_point T0;\ndouble el(){return chrono::duration(chrono::steady_clock::now()-T0).count();}\nstruct State{\nvectorparent,height;vectorsub_sum;vectorsub_max_h;long long score;\nvoid recompute(){\nvectordeg(N);for(int v=0;vq;for(int v=0;vord;\nwhile(!q.empty()){int v=q.front();q.pop();ord.push_back(v);if(parent[v]!=-1&&--deg[parent[v]]==0)q.push(parent[v]);}\nfor(int v:ord)height[v]=(parent[v]==-1)?0:height[parent[v]]+1;\nfill(sub_sum.begin(),sub_sum.end(),0);fill(sub_max_h.begin(),sub_max_h.end(),0);\nfor(int v:ord){sub_sum[v]+=A[v];sub_max_h[v]=max(sub_max_h[v],height[v]);\nif(parent[v]!=-1){sub_sum[parent[v]]+=sub_sum[v];sub_max_h[parent[v]]=max(sub_max_h[parent[v]],sub_max_h[v]);}}\nscore=0;for(int v=0;v&p){parent=p;height.resize(N);sub_sum.resize(N);sub_max_h.resize(N);recompute();}\n};\nvoid greedy(State&st){\nwhile(true){long long bg=0;int bv=-1,bu=-1;\nfor(int v=0;vH||st.cyc(v,u))continue;\nlong long g=(long long)d*st.sub_sum[v];if(g>bg){bg=g;bv=v;bu=u;}}\nif(bv==-1)break;st.parent[bv]=bu;st.recompute();}}\nvectormbfs(const vector&ro,bool bb){\nvectorp(N,-1),h(N,0);vectorvis(N);\nfor(int r:ro){if(vis[r])continue;queueq;q.push(r);vis[r]=true;\nwhile(!q.empty()){int u=q.front();q.pop();if(h[u]>=H)continue;\nvectornb=adj[u];if(bb)sort(nb.begin(),nb.end(),[](int a,int b){return A[a]>A[b];});\nelse shuffle(nb.begin(),nb.end(),rng);\nfor(int v:nb){if(vis[v])continue;vis[v]=true;p[v]=u;h[v]=h[u]+1;q.push(v);}}}return p;}\nvectormdfs(const vector&ro){\nvectorp(N,-1),h(N,0);vectorvis(N);\nfor(int r:ro){if(vis[r])continue;vis[r]=true;\nfunctiondfs=[&](int u){if(h[u]>=H)return;\nvectornb=adj[u];sort(nb.begin(),nb.end(),[](int a,int b){return A[a]>A[b];});\nfor(int v:nb){if(vis[v])continue;vis[v]=true;p[v]=u;h[v]=h[u]+1;dfs(v);}};dfs(r);}return p;}\nvectormchain(){\nvectorp(N,-1);vectorused(N);vectorord(N);iota(ord.begin(),ord.end(),0);\nsort(ord.begin(),ord.end(),[](int a,int b){return A[a]>A[b];});\nfor(int v:ord){if(used[v])continue;vectordist(N,-1),par(N,-1);queueq;\nq.push(v);dist[v]=0;int t=v;while(!q.empty()){int u=q.front();q.pop();\nif(dist[u]>dist[t])t=u;if(dist[u]==H)continue;\nfor(int w:adj[u])if(!used[w]&&dist[w]==-1){dist[w]=dist[u]+1;par[w]=u;q.push(w);}}\nvectorpath;for(int c=t;;c=par[c]){path.push_back(c);if(c==v)break;}\nfor(int i=0;i<(int)path.size();i++){used[path[i]]=true;p[path[i]]=(i==0)?-1:path[i-1];}}return p;}\nvoid sa(vector&par,long long&bs,double et){\nvectorht(N);\nauto rh=[&](){vectordeg(N);for(int v=0;vq;for(int v=0;vo;\nwhile(!q.empty()){int v=q.front();q.pop();o.push_back(v);if(par[v]!=-1&&--deg[par[v]]==0)q.push(par[v]);}\nfor(int v:o)ht[v]=(par[v]==-1)?0:ht[par[v]]+1;};rh();\nauto cc=[&](int v,int np)->bool{if(np==-1)return false;for(int c=np;c!=-1;c=par[c])if(c==v)return true;return false;};\nlong long cs=0;for(int v=0;vbp=par;double ss=el();double dur=max(.001,et-ss);\nuniform_real_distributionuf(0,1);\nfor(int it=0;;it++){double t=el();if(t>et)break;double T=2000.0*pow(0.001,(t-ss)/dur);\nint v=rng()%N;if(adj[v].empty())continue;int np;\nif(rng()%50==0)np=-1;else np=adj[v][rng()%adj[v].size()];\nif(np==par[v]||cc(v,np))continue;int nh=(np==-1)?0:ht[np]+1,d=nh-ht[v];\nif(d==0)continue;long long sm=0;int mh=0;\nstackstk;stk.push(v);while(!stk.empty()){int u=stk.top();stk.pop();sm+=A[u];mh=max(mh,ht[u]);\nfor(int w:adj[u])if(par[w]==u)stk.push(w);}\nif(mh+d>H)continue;long long g=(long long)d*sm;\nif(g>0||uf(rng)lb){lb=cs;bp=par;}}}\npar=bp;rh();bs=0;for(int v=0;v>N>>M>>H;A.resize(N);for(int i=0;i>A[i];adj.resize(N);\nfor(int i=0;i>u>>v;adj[u].push_back(v);adj[v].push_back(u);}\nvectorX(N),Y(N);for(int i=0;i>X[i]>>Y[i];\nlong long bs=0;vectorbp(N,-1);auto ts=[&](const vector&p){State st;st.init(p);greedy(st);\nif(st.score>bs){bs=st.score;bp=st.parent;}};\nts(vector(N,-1));\n{vectoro(N);iota(o.begin(),o.end(),0);sort(o.begin(),o.end(),[](int a,int b){return A[a]o(N);iota(o.begin(),o.end(),0);sort(o.begin(),o.end(),[&](int a,int b){\nreturn(X[a]-500)*(X[a]-500)+(Y[a]-500)*(Y[a]-500)<(X[b]-500)*(X[b]-500)+(Y[b]-500)*(Y[b]-500);});\nts(mbfs(o,true));ts(mdfs(o));}\n{vectoro(N);iota(o.begin(),o.end(),0);sort(o.begin(),o.end(),[](int a,int b){return A[a]roots(o.begin(),o.begin()+min(nr,N));\nts(mbfs(roots,true));ts(mdfs(roots));}\nint tr=0;while(el()<0.6){vectoro(N);iota(o.begin(),o.end(),0);shuffle(o.begin(),o.end(),rng);\nif(tr%3==0)ts(mbfs(o,true));else if(tr%3==1)ts(mbfs(o,false));else ts(mdfs(o));tr++;}\nlong long ss;sa(bp,ss,1.7);ts(bp);\nfor(int i=0;i\n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint main() {\n int N; cin >> N;\n vector board(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n vector initial_board = board;\n \n vector> moves;\n \n auto shift = [&](char dir, int idx) {\n if (dir == 'L') {\n for (int j = 0; j < N-1; j++) board[idx][j] = board[idx][j+1];\n board[idx][N-1] = '.';\n } else if (dir == 'R') {\n for (int j = N-1; j > 0; j--) board[idx][j] = board[idx][j-1];\n board[idx][0] = '.';\n } else if (dir == 'U') {\n for (int i = 0; i < N-1; i++) board[i][idx] = board[i+1][idx];\n board[N-1][idx] = '.';\n } else {\n for (int i = N-1; i > 0; i--) board[i][idx] = board[i-1][idx];\n board[0][idx] = '.';\n }\n moves.push_back({dir, idx});\n };\n \n // Phase 1: Greedy without shift-backs\n bool greedy_ok = true;\n while (true) {\n int best_cost = N + 2;\n int best_idx = -1;\n char best_dir = 0;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (board[i][j] != 'x') continue;\n {bool s=true; for(int k=0;k onis;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (board[i][j] == 'x') onis.push_back({i, j, (int)onis.size()});\n \n map, vector> batches;\n for (auto& o : onis) {\n bool us=true,ds=true,ls=true,rs=true;\n for(int k=0;k removed;\n for (char dir : {'U','D','L','R'}) {\n for (int idx = 0; idx < N; idx++) {\n auto key = make_pair(dir, idx);\n if (batches.find(key) == batches.end()) continue;\n int md = 0;\n for (int oid : batches[key]) { if(removed.count(oid)) continue; auto& o=onis[oid]; int d=(dir=='U')?o.i+1:(dir=='D')?N-o.i:(dir=='L')?o.j+1:N-o.j; md=max(md,d); }\n if (md == 0) continue;\n for (int k = 0; k < md; k++) shift(dir, idx);\n char opp = (dir=='U')?'D':(dir=='D')?'U':(dir=='L')?'R':'L';\n for (int k = 0; k < md; k++) shift(opp, idx);\n for (auto& o : onis) { if(removed.count(o.id)) continue; bool ip=false;\n if(dir=='U'&&o.j==idx&&o.i=N-md) ip=true;\n else if(dir=='L'&&o.i==idx&&o.j=N-md) ip=true;\n if(ip) removed.insert(o.id); }\n }\n }\n }\n \n for (auto& [d, p] : moves) cout << d << \" \" << p << \"\\n\";\n return 0;\n}","ahc044":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, L;\nint T[100];\nint a[100], b[100];\nint best_a[100], best_b[100];\nint best_error = INT_MAX;\n\nuint64_t rng_state = 1234567890123456789ULL;\nuint64_t rng64() {\n rng_state ^= rng_state >> 12;\n rng_state ^= rng_state << 25;\n rng_state ^= rng_state >> 27;\n return rng_state * 2685821657736338717ULL;\n}\n\nint simulate(int ai[], int bi[]) {\n int count[100] = {}, ti[100] = {};\n int cur = 0;\n for (int w = 0; w < L; w++) {\n ti[cur]++;\n count[cur]++;\n cur = (count[cur] & 1) ? ai[cur] : bi[cur];\n }\n int err = 0;\n for (int i = 0; i < N; i++) err += abs(ti[i] - T[i]);\n return err;\n}\n\nvoid try_init(int ai[], int bi[]) {\n int err = simulate(ai, bi);\n if (err < best_error) {\n best_error = err;\n memcpy(best_a, ai, sizeof(int) * N);\n memcpy(best_b, bi, sizeof(int) * N);\n }\n}\n\nvoid greedy_init(int ai[], int bi[], bool avoid_self) {\n int rem[100]; memcpy(rem, T, sizeof(T));\n int cnt[100] = {};\n bool as[100] = {}, bs[100] = {};\n memset(ai, 0, sizeof(int) * N);\n memset(bi, 0, sizeof(int) * N);\n int cur = 0;\n for (int w = 0; w < L; w++) {\n rem[cur]--;\n cnt[cur]++;\n if (cnt[cur] & 1) {\n if (!as[cur]) {\n int best = -1;\n for (int j = 0; j < N; j++) {\n if (avoid_self && j == cur) continue;\n if (best == -1 || rem[j] > rem[best]) best = j;\n }\n if (best == -1) best = (cur + 1) % N;\n ai[cur] = best; as[cur] = true;\n }\n cur = ai[cur];\n } else {\n if (!bs[cur]) {\n int best = -1;\n for (int j = 0; j < N; j++) {\n if (avoid_self && j == cur) continue;\n if (best == -1 || rem[j] > rem[best]) best = j;\n }\n if (best == -1) best = (cur + 1) % N;\n bi[cur] = best; bs[cur] = true;\n }\n cur = bi[cur];\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> L;\n for (int i = 0; i < N; i++) cin >> T[i];\n \n int ai[100], bi[100];\n \n // Init 1: Simple cycle\n for (int i = 0; i < N; i++) { ai[i] = (i+1)%N; bi[i] = (i+1)%N; }\n try_init(ai, bi);\n \n // Init 2: Greedy (allow self-loops)\n greedy_init(ai, bi, false);\n try_init(ai, bi);\n \n // Init 3: Greedy (avoid self-loops)\n greedy_init(ai, bi, true);\n try_init(ai, bi);\n \n // Init 4: Flow-based\n {\n struct Src { int emp; int flow; bool odd; };\n Src srcs[200];\n for (int i = 0; i < N; i++) {\n srcs[2*i] = {i, (T[i]+1)/2, true};\n srcs[2*i+1] = {i, T[i]/2, false};\n }\n sort(srcs, srcs+2*N, [](const Src& a, const Src& b) { return a.flow > b.flow; });\n int dem[100]; memcpy(dem, T, sizeof(T));\n for (int s = 0; s < 2*N; s++) {\n int best = 0;\n for (int j = 1; j < N; j++) if (dem[j] > dem[best]) best = j;\n if (srcs[s].odd) ai[srcs[s].emp] = best;\n else bi[srcs[s].emp] = best;\n dem[best] -= srcs[s].flow;\n }\n try_init(ai, bi);\n }\n \n // Use best init for SA\n memcpy(a, best_a, sizeof(a));\n memcpy(b, best_b, sizeof(b));\n int error = best_error;\n \n auto start = chrono::high_resolution_clock::now();\n double temp = max(50.0, error / 80.0);\n double cool = 0.993;\n \n while (true) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start).count() > 1.85) break;\n \n int i = rng64() % N;\n bool is_a = rng64() & 1;\n int old = is_a ? a[i] : b[i];\n int nv = rng64() % N;\n if (is_a) a[i] = nv; else b[i] = nv;\n \n int ne = simulate(a, b);\n double delta = ne - error;\n if (delta <= 0 || (double)(rng64() & 0xFFFFF) / 1048576.0 < exp(-delta / temp)) {\n error = ne;\n if (error < best_error) {\n best_error = error;\n memcpy(best_a, a, sizeof(a));\n memcpy(best_b, b, sizeof(b));\n }\n } else {\n if (is_a) a[i] = old; else b[i] = old;\n }\n temp *= cool;\n }\n \n for (int i = 0; i < N; i++)\n cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nuint64_t xy2d(int n, int x, int y) {\n uint64_t d = 0;\n for (int s = n/2; s > 0; s /= 2) {\n int rx = (x & s) > 0;\n int ry = (y & s) > 0;\n d += (uint64_t)s * s * ((3 * rx) ^ ry);\n if (ry == 0) {\n if (rx == 1) { x = s-1 - x; y = s-1 - y; }\n swap(x, y);\n }\n }\n return d;\n}\n\nint N, M, Q, L, W;\ndouble cx[800], cy[800], ddist[800][800];\nint qcnt = 0;\n\nvector> query(vector& v) {\n if (qcnt >= Q || (int)v.size() < 2) return {};\n qcnt++;\n cout << \"? \" << v.size();\n for (int x : v) cout << \" \" << x;\n cout << endl;\n vector> res(v.size() - 1);\n for (auto& [a, b] : res) cin >> a >> b;\n return res;\n}\n\nint par[800], rnk[800];\nvoid init_dsu() { iota(par, par + N, 0); fill(rnk, rnk + N, 0); }\nint find(int x) { return par[x] == x ? x : par[x] = find(par[x]); }\nbool unite(int x, int y) {\n x = find(x); y = find(y);\n if (x == y) return false;\n if (rnk[x] < rnk[y]) swap(x, y);\n par[y] = x;\n if (rnk[x] == rnk[y]) rnk[x]++;\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n mt19937 rng(1337);\n \n cin >> N >> M >> Q >> L >> W;\n vector G(M);\n for (int& g : G) cin >> g;\n \n for (int i = 0; i < N; i++) {\n int a, b, c, d;\n cin >> a >> b >> c >> d;\n cx[i] = (a + b) / 2.0;\n cy[i] = (c + d) / 2.0;\n }\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n double dx = cx[i] - cx[j], dy = cy[i] - cy[j];\n ddist[i][j] = sqrt(dx*dx + dy*dy);\n }\n \n vector hilbert_idx(N);\n for(int i=0; i ord(N);\n iota(ord.begin(), ord.end(), 0);\n sort(ord.begin(), ord.end(), [&](int a, int b) {\n return hilbert_idx[a] < hilbert_idx[b];\n });\n \n vector cut_cost(N, 0.0);\n for (int j = 1; j < N; j++) {\n cut_cost[j] = ddist[ord[j-1]][ord[j]];\n }\n \n vector p(M);\n iota(p.begin(), p.end(), 0);\n \n if (M <= 20) {\n vector dp(1 << M, -1.0);\n dp[0] = 0.0;\n for (int mask = 0; mask < (1 << M); mask++) {\n if (dp[mask] < -0.5) continue;\n int s = 0;\n for (int i = 0; i < M; i++) if (mask & (1 << i)) s += G[i];\n for (int i = 0; i < M; i++) {\n if (!(mask & (1 << i))) {\n int next_mask = mask | (1 << i);\n int next_s = s + G[i];\n double cost = dp[mask] + (next_s < N ? cut_cost[next_s] : 0.0);\n if (cost > dp[next_mask]) dp[next_mask] = cost;\n }\n }\n }\n int mask = (1 << M) - 1;\n for (int k = M - 1; k >= 0; k--) {\n int s = 0;\n for (int i = 0; i < M; i++) if (mask & (1 << i)) s += G[i];\n for (int i = 0; i < M; i++) {\n if (mask & (1 << i)) {\n int prev_mask = mask ^ (1 << i);\n double cost = dp[prev_mask] + (s < N ? cut_cost[s] : 0.0);\n if (abs(cost - dp[mask]) < 1e-9) {\n p[k] = i;\n mask = prev_mask;\n break;\n }\n }\n }\n }\n } else {\n sort(p.begin(), p.end(), [&](int a, int b) { return G[a] > G[b]; });\n vector prefix(M);\n int s = 0;\n for (int i = 0; i < M; i++) { s += G[p[i]]; prefix[i] = s; }\n \n double current_cost = 0.0;\n for (int i = 0; i < M - 1; i++) current_cost += cut_cost[prefix[i]];\n \n for (int iter = 0; iter < 1000000; iter++) {\n int i = rng() % M;\n int j = rng() % M;\n if (i == j) continue;\n if (i > j) swap(i, j);\n \n double old_cost = 0.0;\n for (int k = i; k < j; k++) old_cost += cut_cost[prefix[k]];\n \n swap(p[i], p[j]);\n int s_prev = (i == 0 ? 0 : prefix[i-1]);\n double new_cost = 0.0;\n for (int k = i; k < j; k++) {\n s_prev += G[p[k]];\n new_cost += cut_cost[s_prev];\n }\n \n if (new_cost > old_cost) {\n s_prev = (i == 0 ? 0 : prefix[i-1]);\n for (int k = i; k < j; k++) {\n s_prev += G[p[k]];\n prefix[k] = s_prev;\n }\n current_cost += (new_cost - old_cost);\n } else {\n swap(p[i], p[j]);\n }\n }\n }\n \n vector> grp(M);\n int curr = 0;\n for (int k = 0; k < M; k++) {\n int group_idx = p[k];\n int sz = G[group_idx];\n for (int j = 0; j < sz; j++) {\n grp[group_idx].push_back(ord[curr++]);\n }\n }\n \n vector proc_order(M);\n iota(proc_order.begin(), proc_order.end(), 0);\n sort(proc_order.begin(), proc_order.end(), [&](int a, int b) {\n return G[a] < G[b];\n });\n \n vector>> ans(M);\n \n for (int k : proc_order) {\n int G_size = grp[k].size();\n if (G_size <= 1) continue;\n \n init_dsu();\n vector> mst;\n \n if (G_size <= L) {\n if (qcnt < Q) mst = query(grp[k]);\n } else {\n int start = 0;\n while (start < G_size) {\n int end = min(start + L, G_size);\n if (end - start < 2) break;\n vector qv(grp[k].begin() + start, grp[k].begin() + end);\n if (qcnt < Q) {\n auto edges = query(qv);\n for (auto& [a, b] : edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n }\n }\n } else {\n break;\n }\n start += L - 1;\n }\n }\n \n if (mst.size() < (size_t)G_size - 1) {\n vector> edges;\n for (int i = 0; i < G_size; i++)\n for (int j = i + 1; j < G_size; j++)\n edges.emplace_back(ddist[grp[k][i]][grp[k][j]], grp[k][i], grp[k][j]);\n sort(edges.begin(), edges.end());\n for (auto& [d, a, b] : edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n }\n if (mst.size() == (size_t)G_size - 1) break;\n }\n }\n ans[k] = mst;\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int i = 0; i < (int)grp[k].size(); i++) cout << grp[k][i] << \" \\n\"[i==(int)grp[k].size()-1];\n for (auto& [a, b] : ans[k]) cout << a << \" \" << b << \"\\n\";\n }\n return 0;\n}","ahc046":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N, M;\n cin >> N >> M;\n vector> targets(M);\n for (int i = 0; i < M; i++) cin >> targets[i].first >> targets[i].second;\n \n bool block_grid[20][20] = {};\n int cur_r = targets[0].first, cur_c = targets[0].second;\n vector> actions;\n \n const int DR[] = {-1, 1, 0, 0};\n const int DC[] = {0, 0, -1, 1};\n const char DIR_CHAR[] = {'U', 'D', 'L', 'R'};\n const char ALTER_TOWARD[] = {'D', 'U', 'R', 'L'};\n \n bool is_target[20][20] = {};\n for (auto& [r, c] : targets) is_target[r][c] = true;\n \n auto slide_fn = [&](int r, int c, int d) -> pair {\n int nr = r + DR[d], nc = c + DC[d];\n while (nr >= 0 && nr < N && nc >= 0 && nc < N && !block_grid[nr][nc]) {\n nr += DR[d]; nc += DC[d];\n }\n return {nr - DR[d], nc - DC[d]};\n };\n \n auto bfs = [&](int sr, int sc, int tr, int tc) -> vector> {\n if (sr == tr && sc == tc) return {};\n int dist[20][20]; memset(dist, -1, sizeof(dist));\n int pr[20][20], pc[20][20], pa[20][20], pd[20][20];\n memset(pr, -1, sizeof(pr)); memset(pc, -1, sizeof(pc));\n \n queue> q;\n q.push({sr, sc}); dist[sr][sc] = 0;\n while (!q.empty()) {\n auto [r, c] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nr = r + DR[d], nc = c + DC[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !block_grid[nr][nc] && dist[nr][nc] < 0) {\n dist[nr][nc] = dist[r][c] + 1;\n pr[nr][nc] = r; pc[nr][nc] = c; pa[nr][nc] = 0; pd[nr][nc] = d;\n if (nr == tr && nc == tc) goto found;\n q.push({nr, nc});\n }\n auto [snr, snc] = slide_fn(r, c, d);\n if ((snr != r || snc != c) && dist[snr][snc] < 0) {\n dist[snr][snc] = dist[r][c] + 1;\n pr[snr][snc] = r; pc[snr][snc] = c; pa[snr][snc] = 1; pd[snr][snc] = d;\n if (snr == tr && snc == tc) goto found;\n q.push({snr, snc});\n }\n }\n }\n return {};\n found:\n vector> path;\n int cr = tr, cc = tc;\n while (cr != sr || cc != sc) {\n path.push_back({pa[cr][cc] ? 'S' : 'M', DIR_CHAR[pd[cr][cc]], cr, cc});\n int rr = pr[cr][cc], rc = pc[cr][cc]; cr = rr; cc = rc;\n }\n reverse(path.begin(), path.end());\n return path;\n };\n \n auto is_connected = [&]() -> bool {\n int sr = -1, sc = -1, fc = 0;\n for (int r = 0; r < N; r++)\n for (int c = 0; c < N; c++)\n if (!block_grid[r][c]) { fc++; if (sr < 0) { sr = r; sc = c; } }\n if (fc == 0) return true;\n bool vis[20][20] = {};\n queue> q;\n q.push({sr, sc}); vis[sr][sc] = true; int cnt = 1;\n while (!q.empty()) {\n auto [r, c] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nr = r + DR[d], nc = c + DC[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !block_grid[nr][nc] && !vis[nr][nc]) {\n vis[nr][nc] = true; cnt++; q.push({nr, nc});\n }\n }\n }\n return cnt == fc;\n };\n \n auto can_place = [&](int br, int bc, int t) -> bool {\n if (br < 0 || br >= N || bc < 0 || bc >= N) return false;\n if (block_grid[br][bc]) return false;\n if (is_target[br][bc]) return false;\n block_grid[br][bc] = true;\n bool ok = is_connected();\n if (ok) {\n for (int f = t + 1; f < M && ok; f++) {\n int ftr = targets[f].first, ftc = targets[f].second;\n if (block_grid[ftr][ftc]) { ok = false; break; }\n int bn = 0, vn = 0;\n for (int d = 0; d < 4; d++) {\n int nr = ftr + DR[d], nc = ftc + DC[d];\n if (nr < 0 || nr >= N || nc < 0 || nc >= N) continue;\n vn++; if (block_grid[nr][nc]) bn++;\n }\n if (vn > 0 && bn >= vn) ok = false;\n }\n }\n block_grid[br][bc] = false;\n return ok;\n };\n \n for (int t = 1; t < M; t++) {\n int tr = targets[t].first, tc = targets[t].second;\n \n if (block_grid[tr][tc]) {\n int best_d = -1, best_len = INT_MAX;\n vector> best_p;\n for (int d = 0; d < 4; d++) {\n int ar = tr + DR[d], ac = tc + DC[d];\n if (ar < 0 || ar >= N || ac < 0 || ac >= N) continue;\n if (block_grid[ar][ac]) continue;\n auto p = bfs(cur_r, cur_c, ar, ac);\n if (!p.empty() && (int)p.size() < best_len) {\n best_len = p.size(); best_d = d; best_p = move(p);\n }\n }\n if (best_d >= 0) {\n for (auto& [a, dir, nr, nc] : best_p) {\n actions.push_back({a, dir}); cur_r = nr; cur_c = nc;\n }\n block_grid[tr][tc] = false;\n actions.push_back({'A', ALTER_TOWARD[best_d]});\n }\n }\n \n auto path = bfs(cur_r, cur_c, tr, tc);\n for (auto& [a, dir, nr, nc] : path) {\n actions.push_back({a, dir}); cur_r = nr; cur_c = nc;\n }\n \n int placed = 0;\n for (int d : {1, 3, 0, 2}) {\n if (placed >= 2) break;\n int br = cur_r + DR[d], bc = cur_c + DC[d];\n if (can_place(br, bc, t)) {\n block_grid[br][bc] = true;\n actions.push_back({'A', DIR_CHAR[d]});\n placed++;\n }\n }\n }\n \n for (auto& [a, d] : actions) cout << a << \" \" << d << \"\\n\";\n return 0;\n}"},"8":{"ahc001":"#include \nusing namespace std;\n\nint n;\nvector x, y, r;\nvector ra, rb, rc, rd;\n\ninline double satisfaction(long long s, long long rv) {\n if (s <= 0 || rv <= 0) return 0;\n double ratio = (double)min(s, rv) / max(s, rv);\n return 1.0 - (1.0 - ratio) * (1.0 - ratio);\n}\n\ndouble compute_score() {\n double s = 0;\n for (int i = 0; i < n; i++)\n s += satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]), r[i]);\n return s;\n}\n\nstruct TNode {\n bool is_leaf; int company; bool vertical; int split_k;\n vector items; int lc, rc_node;\n long long total_r, left_r; int maxL, minR;\n int bL, bB, bR, bT;\n};\nvector tree;\nvector split_offset;\n\nint build_tree(vector items, mt19937& rng, int strategy) {\n int idx = tree.size();\n tree.push_back({});\n if (items.size() == 1) {\n tree[idx] = {true, items[0], false, 0, items, -1, -1, (long long)r[items[0]], 0LL, 0, 0, 0,0,0,0};\n return idx;\n }\n long long total_r = 0;\n for (int i : items) total_r += r[i];\n struct Cand { bool vert; int k; double score; };\n vector cands;\n for (int dir = 0; dir < 2; dir++) {\n bool vert = (dir == 0);\n auto sorted = items;\n sort(sorted.begin(), sorted.end(), [&](int i, int j) { return vert ? x[i] < x[j] : y[i] < y[j]; });\n auto& coord = vert ? x : y;\n long long sum = 0;\n for (int k = 1; k < (int)sorted.size(); k++) {\n sum += r[sorted[k-1]];\n if (coord[sorted[k-1]] >= coord[sorted[k]]) continue;\n double r_ratio = (double)sum / total_r;\n double score;\n switch(strategy % 9) {\n case 0: score = -abs(r_ratio-0.5)*2; break;\n case 1: score = (vert?0.5:-0.5)-abs(r_ratio-0.5); break;\n case 2: score = (!vert?0.5:-0.5)-abs(r_ratio-0.5); break;\n case 3: { int gap = coord[sorted[k]]-coord[sorted[k-1]]; score = gap*0.002-abs(r_ratio-0.5); break; }\n case 4: score = uniform_real_distribution(0,1)(rng); break;\n case 5: score = -abs(r_ratio-0.5); break;\n case 6: score = -abs(r_ratio-0.5)*0.5+uniform_real_distribution(0,0.3)(rng); break;\n case 7: score = -abs(r_ratio-0.5)*0.1+uniform_real_distribution(0,0.5)(rng); break;\n case 8: score = (vert?-0.2:0.2)-abs(r_ratio-0.5)*0.5+uniform_real_distribution(0,0.2)(rng); break;\n }\n score += uniform_real_distribution(0,0.05)(rng);\n cands.push_back({vert, k, score});\n }\n }\n if (cands.empty()) {\n tree[idx] = {true, items[0], false, 0, items, -1, -1, (long long)r[items[0]], 0LL, 0, 0, 0,0,0,0};\n return idx;\n }\n sort(cands.begin(), cands.end(), [](const Cand& a, const Cand& b) { return a.score > b.score; });\n int top = min((int)cands.size(), 5);\n uniform_int_distribution dist(0, top-1);\n const Cand& ch = cands[dist(rng)];\n sort(items.begin(), items.end(), [&](int i, int j) { return ch.vert ? x[i] li(items.begin(), items.begin()+ch.k), ri(items.begin()+ch.k, items.end());\n int lc = build_tree(li, rng, strategy), rc2 = build_tree(ri, rng, strategy);\n tree[idx] = {false, -1, ch.vert, ch.k, items, lc, rc2, total_r, left_r, mxL, mnR, 0,0,0,0};\n return idx;\n}\n\nvoid compute_rects(int idx, int L, int B, int R, int T) {\n if (tree[idx].is_leaf) { int i = tree[idx].company; ra[i]=L; rb[i]=B; rc[i]=R; rd[i]=T; return; }\n int lo = tree[idx].vertical ? L : B, hi = tree[idx].vertical ? R : T;\n long long ideal = lo + (long long)(hi-lo)*tree[idx].left_r/tree[idx].total_r;\n int sp = (int)ideal + split_offset[idx];\n sp = max(sp, tree[idx].maxL+1); sp = min(sp, tree[idx].minR);\n sp = max(sp, lo+1); sp = min(sp, hi-1);\n if (tree[idx].vertical) { compute_rects(tree[idx].lc,L,B,sp,T); compute_rects(tree[idx].rc_node,sp,B,R,T); }\n else { compute_rects(tree[idx].lc,L,B,R,sp); compute_rects(tree[idx].rc_node,L,sp,R,T); }\n}\n\nvoid update_subtree(int idx) {\n if (tree[idx].is_leaf) { int i = tree[idx].company; ra[i]=tree[idx].bL; rb[i]=tree[idx].bB; rc[i]=tree[idx].bR; rd[i]=tree[idx].bT; return; }\n int L=tree[idx].bL, B=tree[idx].bB, R=tree[idx].bR, T=tree[idx].bT;\n int lo = tree[idx].vertical ? L : B, hi = tree[idx].vertical ? R : T;\n long long ideal = lo + (long long)(hi-lo)*tree[idx].left_r/tree[idx].total_r;\n int sp = (int)ideal + split_offset[idx];\n sp = max(sp, tree[idx].maxL+1); sp = min(sp, tree[idx].minR);\n sp = max(sp, lo+1); sp = min(sp, hi-1);\n int lc = tree[idx].lc, rc2 = tree[idx].rc_node;\n if (tree[idx].vertical) {\n tree[lc].bL=L; tree[lc].bB=B; tree[lc].bR=sp; tree[lc].bT=T;\n tree[rc2].bL=sp; tree[rc2].bB=B; tree[rc2].bR=R; tree[rc2].bT=T;\n } else {\n tree[lc].bL=L; tree[lc].bB=B; tree[lc].bR=R; tree[lc].bT=sp;\n tree[rc2].bL=L; tree[rc2].bB=sp; tree[rc2].bR=R; tree[rc2].bT=T;\n }\n update_subtree(lc); update_subtree(rc2);\n}\n\nvoid full_update(int root) { tree[root].bL=0; tree[root].bB=0; tree[root].bR=10000; tree[root].bT=10000; update_subtree(root); }\n\ndouble subtree_score(int idx) {\n double s = 0;\n for (int i : tree[idx].items) s += satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]), r[i]);\n return s;\n}\n\nvoid optimize_offsets(int root) {\n split_offset.assign(tree.size(), 0);\n compute_rects(root, 0, 0, 10000, 10000);\n double best = compute_score();\n vector internal;\n for (int i = 0; i < (int)tree.size(); i++) if (!tree[i].is_leaf) internal.push_back(i);\n for (int round = 0; round < 15; round++) {\n bool improved = false;\n for (int idx : internal) {\n for (int d : {-1000,-500,-200,-100,-50,-20,-10,-5,-2,-1,1,2,5,10,20,50,100,200,500,1000}) {\n split_offset[idx] += d;\n compute_rects(root, 0, 0, 10000, 10000);\n bool valid = true;\n for (int i = 0; i < n && valid; i++) if (ra[i]>x[i]||rc[i]<=x[i]||rb[i]>y[i]||rd[i]<=y[i]) valid = false;\n if (valid) { double ns = compute_score(); if (ns > best+1e-12) { best=ns; improved=true; continue; } }\n split_offset[idx] -= d;\n }\n }\n if (!improved) break;\n }\n compute_rects(root, 0, 0, 10000, 10000);\n}\n\nvoid sa_offsets(int root, unsigned sa_seed, int max_iter) {\n full_update(root);\n vector internal;\n for (int i = 0; i < (int)tree.size(); i++) if (!tree[i].is_leaf) internal.push_back(i);\n if (internal.empty()) return;\n double cur = compute_score(), best = cur;\n vector best_off = split_offset;\n mt19937 rng(sa_seed);\n uniform_int_distribution idist(0, (int)internal.size()-1);\n uniform_real_distribution adist(0, 1);\n double temp = 0.03;\n for (int iter = 0; iter < max_iter; iter++) {\n int idx = internal[idist(rng)];\n int d;\n if (iter < max_iter/5) d = uniform_int_distribution(-500,500)(rng);\n else if (iter < max_iter*2/5) d = uniform_int_distribution(-100,100)(rng);\n else if (iter < max_iter*4/5) d = uniform_int_distribution(-10,10)(rng);\n else d = uniform_int_distribution(-3,3)(rng);\n if (!d) continue;\n double old_s = subtree_score(idx);\n split_offset[idx] += d;\n update_subtree(idx);\n bool valid = true;\n for (int i : tree[idx].items) if (ra[i]>x[i]||rc[i]<=x[i]||rb[i]>y[i]||rd[i]<=y[i]) { valid = false; break; }\n if (!valid) { split_offset[idx] -= d; update_subtree(idx); continue; }\n double new_s = subtree_score(idx);\n double diff = new_s - old_s;\n if (diff > 0 || adist(rng) < exp(diff/temp)) { cur += diff; if (cur > best) { best = cur; best_off = split_offset; } }\n else { split_offset[idx] -= d; update_subtree(idx); }\n temp *= 0.99997;\n }\n split_offset = best_off; full_update(root);\n}\n\nvoid post_process() {\n for (int i = 0; i < n; i++) {\n while (true) {\n long long area = (long long)(rc[i]-ra[i])*(rd[i]-rb[i]);\n if (area <= r[i]) break;\n double cs = satisfaction(area, r[i]);\n int bd=-1,bdr=0; double bs=cs;\n auto try_s = [&](int dim, int dir) {\n int na=ra[i],nb=rb[i],nc=rc[i],nd=rd[i];\n if(dim==0&&dir==1)nc--;else if(dim==0&&dir==-1)na++;\n else if(dim==1&&dir==1)nd--;else nb++;\n if(na>x[i]||nc<=x[i]||nb>y[i]||nd<=y[i])return;\n if(nc-na<1||nd-nb<1)return;\n double ns=satisfaction((long long)(nc-na)*(nd-nb),r[i]);\n if(ns>bs+1e-12){bs=ns;bd=dim;bdr=dir;}\n };\n try_s(0,1);try_s(0,-1);try_s(1,1);try_s(1,-1);\n if(bd<0)break;\n if(bd==0&&bdr==1)rc[i]--;else if(bd==0&&bdr==-1)ra[i]++;\n else if(bd==1&&bdr==1)rd[i]--;else rb[i]++;\n }\n }\n for (int step : {500,200,100,50,20,10,5,2,1}) {\n bool any = true;\n while (any) {\n any = false;\n vector> order;\n for (int i = 0; i < n; i++) {\n long long area = (long long)(rc[i]-ra[i])*(rd[i]-rb[i]);\n if (area < r[i]) order.push_back({-(1.0-satisfaction(area,r[i])), i});\n }\n sort(order.begin(), order.end());\n for (auto& [_, i] : order) {\n long long area = (long long)(rc[i]-ra[i])*(rd[i]-rb[i]);\n if (area >= r[i]) continue;\n double cs = satisfaction(area, r[i]);\n auto try_e = [&](int dim, int dir) -> bool {\n int na=ra[i],nb=rb[i],nc=rc[i],nd=rd[i];\n if(dim==0&&dir==1)nc+=step;else if(dim==0&&dir==-1)na-=step;\n else if(dim==1&&dir==1)nd+=step;else nb-=step;\n if(na<0||nc>10000||nb<0||nd>10000)return false;\n if(na>x[i]||nc<=x[i]||nb>y[i]||nd<=y[i])return false;\n for(int j=0;jra[j]&&nbrb[j])return false;}\n double ns=satisfaction((long long)(nc-na)*(nd-nb),r[i]);\n if(ns>cs+1e-12){ra[i]=na;rb[i]=nb;rc[i]=nc;rd[i]=nd;return true;}\n return false;\n };\n if(try_e(0,1)||try_e(0,-1)||try_e(1,1)||try_e(1,-1))any=true;\n }\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> n; x.resize(n); y.resize(n); r.resize(n); ra.resize(n); rb.resize(n); rc.resize(n); rd.resize(n);\n for (int i = 0; i < n; i++) cin >> x[i] >> y[i] >> r[i];\n auto start = chrono::steady_clock::now();\n vector indices(n); iota(indices.begin(), indices.end(), 0);\n vector ba(n),bb(n),bc(n),bd(n); double bs=-1;\n\n // Phase 1: Try many seeds with greedy + post-process\n vector> candidates;\n for (unsigned seed = 0; ; seed++) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now-start).count()>2200) break;\n tree.clear(); mt19937 rng(seed);\n int root = build_tree(indices, rng, seed % 9);\n optimize_offsets(root);\n post_process();\n double s = compute_score();\n candidates.push_back({s, seed});\n if (s > bs) { bs=s; ba=ra; bb=rb; bc=rc; bd=rd; }\n }\n\n // Phase 2: SA on top candidates\n sort(candidates.rbegin(), candidates.rend());\n int top_k = min((int)candidates.size(), 8);\n for (int ci = 0; ci < top_k; ci++) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now-start).count()>4600) break;\n unsigned seed = candidates[ci].second;\n tree.clear(); mt19937 rng(seed);\n int root = build_tree(indices, rng, seed % 9);\n optimize_offsets(root);\n sa_offsets(root, seed * 7919 + 42, 200000);\n post_process();\n double s = compute_score();\n if (s > bs) { bs=s; ba=ra; bb=rb; bc=rc; bd=rd; }\n }\n\n ra=ba; rb=bb; rc=bc; rd=bd;\n for (int i = 0; i < n; i++) cout << ra[i]<<\" \"<\n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 50;\nint si, sj;\nint t[N][N], p[N][N];\nint di[] = {-1, 1, 0, 0};\nint dj[] = {0, 0, -1, 1};\nchar dir[] = {'U', 'D', 'L', 'R'};\nmt19937 rng(42);\n\nint tile_value[2500], max_tile_id = 0;\nstring best_path;\nlong long best_score;\n\nstring find_path(double temperature) {\n bool square_visited[N][N] = {};\n bool tile_visited[2500] = {};\n string path;\n int ci = si, cj = sj;\n square_visited[ci][cj] = true;\n tile_visited[t[ci][cj]] = true;\n long long score = p[ci][cj];\n \n while (true) {\n vector> candidates;\n for (int d = 0; d < 4; d++) {\n int ni = ci + di[d], nj = cj + dj[d];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) continue;\n if (square_visited[ni][nj]) continue;\n bool same_tile = (t[ni][nj] == t[ci][cj]);\n if (same_tile || !tile_visited[t[ni][nj]]) {\n double w = same_tile ? p[ni][nj] : tile_value[t[ni][nj]];\n candidates.push_back({w, d});\n }\n }\n if (candidates.empty()) break;\n \n double max_w = -1e18;\n for (auto& [w, d] : candidates) max_w = max(max_w, w);\n double total = 0;\n for (auto& [w, d] : candidates) total += exp((w - max_w) / max(temperature, 0.01));\n \n double r = uniform_real_distribution(0, total)(rng);\n double cum = 0;\n int chosen = candidates[0].second;\n for (auto& [w, d] : candidates) {\n cum += exp((w - max_w) / max(temperature, 0.01));\n if (cum >= r) { chosen = d; break; }\n }\n \n int ni = ci + di[chosen], nj = cj + dj[chosen];\n square_visited[ni][nj] = true;\n tile_visited[t[ni][nj]] = true;\n score += p[ni][nj];\n path += dir[chosen];\n ci = ni; cj = nj;\n }\n \n if (score > best_score) { best_score = score; best_path = path; }\n return path;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) { cin >> t[i][j]; max_tile_id = max(max_tile_id, t[i][j]); }\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> p[i][j];\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) tile_value[t[i][j]] += p[i][j];\n \n best_score = 0;\n auto start = chrono::high_resolution_clock::now();\n int iter = 0;\n while (true) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now - start).count() > 1800) break;\n double temperature = 10.0 * (1.0 - min(iter / 100000.0, 1.0)) + 0.1;\n find_path(temperature);\n iter++;\n }\n \n cout << best_path << endl;\n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble row_h[N], col_v[N], row_h_var[N], col_v_var[N];\ndouble h_dev[N][N-1], v_dev[N-1][N], h_dev_var[N][N-1], v_dev_var[N-1][N];\nmt19937 rng(42);\nnormal_distribution norm_dist(0, 1);\n\ndouble get_h_est(int i, int j) { return row_h[i] + h_dev[i][j]; }\ndouble get_v_est(int i, int j) { return col_v[j] + v_dev[i][j]; }\ndouble get_h_var(int i, int j) { return row_h_var[i] + h_dev_var[i][j]; }\ndouble get_v_var(int i, int j) { return col_v_var[j] + v_dev_var[i][j]; }\n\ntuple dijkstra_with_cost(int si, int sj, int ti, int tj, double temperature) {\n double hw[N][N-1], vw[N-1][N];\n for(int i=0; i prev_node[N][N]; bool vis[N][N] = {};\n for(int i=0;i,vector>,greater<>> pq;\n pq.push({0,si,sj});\n while(!pq.empty()){\n auto[d,i,j]=pq.top(); pq.pop();\n if(vis[i][j]) continue; vis[i][j]=true;\n if(i==ti&&j==tj) break;\n if(i>0&&!vis[i-1][j]){double w=vw[i-1][j];if(d+w0&&!vis[i][j-1]){double w=hw[i][j-1];if(d+w edges;\n map hr, vc; int ci=si,cj=sj;\n for(char c:path){\n if(c=='U'){edges.push_back({'v',ci-1,cj});vc[cj]++;ci--;}\n else if(c=='D'){edges.push_back({'v',ci,cj});vc[cj]++;ci++;}\n else if(c=='L'){edges.push_back({'h',ci,cj-1});hr[ci]++;cj--;}\n else{edges.push_back({'h',ci,cj});hr[ci]++;cj++;}\n }\n double pred=0;\n for(auto&e:edges) pred+=(e.t=='h')?get_h_est(e.i,e.j):get_v_est(e.i,e.j);\n double residual=observed-pred, obs_var=pred*pred/300.0, S=obs_var;\n for(auto&[i,n]:hr) S+=n*n*row_h_var[i];\n for(auto&[j,n]:vc) S+=n*n*col_v_var[j];\n for(auto&e:edges) S+=(e.t=='h')?h_dev_var[e.i][e.j]:v_dev_var[e.i][e.j];\n for(auto&[i,n]:hr){\n double K=row_h_var[i]*n/S;row_h[i]+=K*residual;row_h_var[i]*=(1-K*n);\n row_h[i]=max(500.0,min(15000.0,row_h[i]));row_h_var[i]=max(100.0,row_h_var[i]);\n }\n for(auto&[j,n]:vc){\n double K=col_v_var[j]*n/S;col_v[j]+=K*residual;col_v_var[j]*=(1-K*n);\n col_v[j]=max(500.0,min(15000.0,col_v[j]));col_v_var[j]=max(100.0,col_v_var[j]);\n }\n for(auto&e:edges){\n double&dev=(e.t=='h')?h_dev[e.i][e.j]:v_dev[e.i][e.j];\n double&dv=(e.t=='h')?h_dev_var[e.i][e.j]:v_dev_var[e.i][e.j];\n double K=dv/S;dev+=K*residual;dv*=(1-K);\n dev=max(-5000.0,min(5000.0,dev));dv=max(100.0,dv);\n }\n}\n\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>si>>sj>>ti>>tj;\n double temperature=max(0.0,1.0-k/300.0);\n double decay=max(0.0,1.0-k/400.0);\n string best_path;double best_eval=1e18;\n for(int t=0;t<5;t++){\n auto[path,cost,pvar]=dijkstra_with_cost(si,sj,ti,tj,temperature);\n double eval=cost-0.15*sqrt(pvar)*decay;\n if(eval>obs;update(si,sj,best_path,obs);\n }\n return 0;\n}","ahc004":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct Entry {\n uint16_t m, pi;\n};\n\nint main() {\n int N, M;\n cin >> N >> M;\n vector s(M);\n for (int m = 0; m < M; m++) cin >> s[m];\n \n const int NUM_CHARS = 8;\n mt19937 rng(42);\n auto start_time = chrono::high_resolution_clock::now();\n \n vector slen(M);\n for (int m = 0; m < M; m++) slen[m] = s[m].length();\n \n // Fast Frequency Voting Initialization\n vector> votes(N * N, {0});\n for (int m = 0; m < M; m++) {\n int k = slen[m];\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n for (int p = 0; p < k; p++) {\n votes[i * N + (j + p) % N][s[m][p] - 'A']++;\n votes[((i + p) % N) * N + j][s[m][p] - 'A']++;\n }\n }\n }\n }\n \n vector mat(N, string(N, 'A'));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int maxVote = 0; char best = 'A';\n for (int c = 0; c < NUM_CHARS; c++) {\n if (votes[i * N + j][c] > maxVote) { maxVote = votes[i * N + j][c]; best = 'A' + c; }\n }\n mat[i][j] = best;\n }\n }\n \n // Build Character-Based Adjacency Lists\n vector adj[400][8];\n for (int m = 0; m < M; m++) {\n int k = slen[m];\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int piH = 2 * (i * N + j);\n for (int p = 0; p < k; p++) adj[i * N + (j + p) % N][s[m][p] - 'A'].push_back({(uint16_t)m, (uint16_t)piH});\n int piV = 2 * (i * N + j) + 1;\n for (int p = 0; p < k; p++) adj[((i + p) % N) * N + j][s[m][p] - 'A'].push_back({(uint16_t)m, (uint16_t)piV});\n }\n }\n }\n \n // Match Counts\n vector matchCount(M * 800, 0);\n vector fullMatchCount(M, 0);\n int totalMatched = 0, numDots = 0;\n \n auto recompute = [&]() {\n numDots = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (mat[i][j] == '.') numDots++;\n for (int m = 0; m < M; m++) {\n int k = slen[m]; fullMatchCount[m] = 0;\n int base = m * 800;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n int cH = 0, cV = 0;\n for (int p = 0; p < k; p++) { if (mat[i][(j+p)%N] == s[m][p]) cH++; if (mat[(i+p)%N][j] == s[m][p]) cV++; }\n matchCount[base + 2*(i*N+j)] = cH; matchCount[base + 2*(i*N+j)+1] = cV;\n if (cH == k) fullMatchCount[m]++; if (cV == k) fullMatchCount[m]++;\n }\n }\n totalMatched = 0;\n for (int m = 0; m < M; m++) if (fullMatchCount[m] > 0) totalMatched++;\n };\n \n recompute();\n int bestMatched = totalMatched, bestDots = -1;\n vector bestMat = mat;\n if (totalMatched == M) bestDots = numDots;\n \n // SA Phase\n int stepCount = 0;\n while (true) {\n stepCount++;\n if ((stepCount & 0xFFF) == 0) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start_time).count() > 2.8) break;\n }\n double temp = 3.0 * max(0.0, 1.0 - chrono::duration(chrono::high_resolution_clock::now() - start_time).count() / 3.0) + 0.05;\n \n // 5% String-level move to force unmatched strings\n if (rng() % 100 < 5 && totalMatched < M) {\n int m = rng() % M;\n int tries = 0;\n while (fullMatchCount[m] > 0 && tries < 10) { m = rng() % M; tries++; }\n if (fullMatchCount[m] > 0) goto cell_move;\n \n {\n int k = slen[m], bestMC = -1, bestPi = -1;\n int base = m * 800;\n for (int pi = 0; pi < 2 * N * N; pi++) if (matchCount[base + pi] > bestMC) { bestMC = matchCount[base + pi]; bestPi = pi; }\n if (bestPi < 0) goto cell_move;\n \n int dir = bestPi % 2, ij = bestPi / 2, si = ij / N, sj = ij % N;\n int deltaMatched = 0, deltaDots = 0;\n char oldChars[13];\n \n for (int p = 0; p < k; p++) {\n int ci2 = dir == 0 ? si : (si + p) % N, cj2 = dir == 0 ? (sj + p) % N : sj;\n int idx2 = ci2 * N + cj2;\n oldChars[p] = mat[ci2][cj2];\n char newC2 = s[m][p];\n if (oldChars[p] == newC2) continue;\n \n if (oldChars[p] != '.') {\n for (auto& e : adj[idx2][oldChars[p] - 'A']) {\n int m2 = e.m, pi2 = e.pi, k2 = slen[m2], base2 = m2 * 800;\n int8_t oldMC = matchCount[base2 + pi2];\n int8_t newMC = oldMC - 1;\n matchCount[base2 + pi2] = newMC;\n if (oldMC == k2) { if (fullMatchCount[m2] == 1) deltaMatched--; fullMatchCount[m2]--; }\n }\n } else { deltaDots--; }\n \n for (auto& e : adj[idx2][newC2 - 'A']) {\n int m2 = e.m, pi2 = e.pi, k2 = slen[m2], base2 = m2 * 800;\n int8_t oldMC = matchCount[base2 + pi2];\n int8_t newMC = oldMC + 1;\n matchCount[base2 + pi2] = newMC;\n if (newMC == k2) { if (fullMatchCount[m2] == 0) deltaMatched++; fullMatchCount[m2]++; }\n }\n mat[ci2][cj2] = newC2;\n }\n \n bool accept;\n if (deltaMatched > 0) accept = true;\n else if (deltaMatched == 0) accept = true;\n else if (totalMatched == M && totalMatched + deltaMatched < M) accept = false;\n else accept = (rng() % 10000 < (int)(exp((double)deltaMatched / temp) * 10000));\n \n if (accept) {\n totalMatched += deltaMatched; numDots += deltaDots;\n if (totalMatched > bestMatched || (totalMatched == M && numDots > bestDots)) {\n bestMatched = totalMatched; bestMat = mat; if (totalMatched == M) bestDots = numDots;\n }\n } else {\n for (int p = k - 1; p >= 0; p--) {\n int ci2 = dir == 0 ? si : (si + p) % N, cj2 = dir == 0 ? (sj + p) % N : sj;\n int idx2 = ci2 * N + cj2;\n char newC2 = s[m][p], oldC2 = oldChars[p];\n if (oldC2 == newC2) continue;\n for (auto& e : adj[idx2][newC2 - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t curMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = curMC - 1; if (curMC == k2) fullMatchCount[m2]--; }\n if (oldC2 != '.') { for (auto& e : adj[idx2][oldC2 - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t curMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = curMC + 1; if (curMC + 1 == k2) fullMatchCount[m2]++; } }\n mat[ci2][cj2] = oldC2;\n }\n }\n }\n continue;\n }\n \n cell_move:\n int ci = rng() % N, cj = rng() % N;\n int idx = ci * N + cj;\n char oldC = mat[ci][cj];\n char newC;\n if (totalMatched == M && (rng() % 2 == 0)) newC = '.';\n else newC = 'A' + rng() % NUM_CHARS;\n if (newC == oldC) continue;\n \n int deltaMatched = 0;\n int deltaDots = (newC == '.' && oldC != '.') ? 1 : ((newC != '.' && oldC == '.') ? -1 : 0);\n \n if (oldC != '.') {\n for (auto& e : adj[idx][oldC - 'A']) {\n int m = e.m, pi = e.pi, k = slen[m], base = m * 800;\n int8_t oldMC = matchCount[base + pi];\n int8_t newMC = oldMC - 1;\n matchCount[base + pi] = newMC;\n if (oldMC == k) { if (fullMatchCount[m] == 1) deltaMatched--; fullMatchCount[m]--; }\n }\n }\n if (newC != '.') {\n for (auto& e : adj[idx][newC - 'A']) {\n int m = e.m, pi = e.pi, k = slen[m], base = m * 800;\n int8_t oldMC = matchCount[base + pi];\n int8_t newMC = oldMC + 1;\n matchCount[base + pi] = newMC;\n if (newMC == k) { if (fullMatchCount[m] == 0) deltaMatched++; fullMatchCount[m]++; }\n }\n }\n \n bool accept;\n if (deltaMatched > 0) accept = true;\n else if (deltaMatched == 0) accept = (deltaDots > 0) || (rng() % 2 == 0);\n else if (totalMatched == M && totalMatched + deltaMatched < M) accept = false;\n else accept = (rng() % 10000 < (int)(exp((double)deltaMatched / temp) * 10000));\n \n if (accept) {\n mat[ci][cj] = newC; totalMatched += deltaMatched; numDots += deltaDots;\n if (totalMatched > bestMatched || (totalMatched == M && numDots > bestDots)) {\n bestMatched = totalMatched; bestMat = mat; if (totalMatched == M) bestDots = numDots;\n }\n } else {\n if (newC != '.') { for (auto& e : adj[idx][newC - 'A']) { int m = e.m, pi = e.pi, k = slen[m]; int8_t curMC = matchCount[m*800+pi]; matchCount[m*800+pi] = curMC - 1; if (curMC == k) fullMatchCount[m]--; } }\n if (oldC != '.') { for (auto& e : adj[idx][oldC - 'A']) { int m = e.m, pi = e.pi, k = slen[m]; int8_t curMC = matchCount[m*800+pi]; matchCount[m*800+pi] = curMC + 1; if (curMC + 1 == k) fullMatchCount[m]++; } }\n }\n }\n \n mat = bestMat; recompute();\n \n // Greedy Repair\n for (int rep = 0; rep < 3; rep++) {\n bool anyImproved = false;\n for (int m = 0; m < M; m++) {\n if (fullMatchCount[m] > 0) continue;\n int k = slen[m], bestMC = -1, bestPi = -1, base = m * 800;\n for (int pi = 0; pi < 2 * N * N; pi++) if (matchCount[base + pi] > bestMC) { bestMC = matchCount[base + pi]; bestPi = pi; }\n if (bestPi < 0) continue;\n int dir = bestPi % 2, ij = bestPi / 2, si = ij / N, sj = ij % N;\n int deltaMatched = 0, deltaDots = 0;\n for (int p = 0; p < k; p++) {\n int ci2 = dir == 0 ? si : (si + p) % N, cj2 = dir == 0 ? (sj + p) % N : sj;\n int idx2 = ci2 * N + cj2; char oldC2 = mat[ci2][cj2], newC2 = s[m][p];\n if (oldC2 == newC2) continue;\n if (oldC2 == '.') deltaDots--;\n if (oldC2 != '.') { for (auto& e : adj[idx2][oldC2 - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t oMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = oMC - 1; if (oMC == k2) { if (fullMatchCount[m2] == 1) deltaMatched--; fullMatchCount[m2]--; } } }\n for (auto& e : adj[idx2][newC2 - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t oMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = oMC + 1; if (oMC + 1 == k2) { if (fullMatchCount[m2] == 0) deltaMatched++; fullMatchCount[m2]++; } }\n mat[ci2][cj2] = newC2;\n }\n totalMatched += deltaMatched; numDots += deltaDots;\n if (deltaMatched > 0) anyImproved = true;\n }\n if (totalMatched > bestMatched || (totalMatched == M && numDots > bestDots)) { bestMatched = totalMatched; bestMat = mat; if (totalMatched == M) bestDots = numDots; }\n if (!anyImproved) break;\n }\n \n mat = bestMat; recompute();\n \n // Dot Maximization\n if (totalMatched == M) {\n for (int ci = 0; ci < N; ci++) {\n for (int cj = 0; cj < N; cj++) {\n if (mat[ci][cj] == '.') continue;\n char oldC2 = mat[ci][cj]; int deltaMatched = 0, idx2 = ci * N + cj;\n for (auto& e : adj[idx2][oldC2 - 'A']) { int m = e.m, pi = e.pi, k = slen[m]; if (matchCount[m*800+pi] == k) { if (fullMatchCount[m] == 1) deltaMatched--; } }\n if (deltaMatched == 0) {\n for (auto& e : adj[idx2][oldC2 - 'A']) { int m = e.m, pi = e.pi, k = slen[m]; matchCount[m*800+pi]--; if (matchCount[m*800+pi] + 1 == k) fullMatchCount[m]--; }\n mat[ci][cj] = '.'; numDots++;\n }\n }\n }\n if (numDots > bestDots) { bestDots = numDots; bestMat = mat; }\n }\n \n for (int i = 0; i < N; i++) cout << bestMat[i] << '\\n';\n return 0;\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\nvector>>> vis_from;\nint total_roads;\nbitset<4800> road_mask;\n\nbool is_road(int i, int j) { return i>=0&&i=0&&j>>(N));\n for(int i=0;i=0&&is_road(i,jj);jj--) vis_from[i][j].push_back({i,jj});\n for(int jj=j+1;jj=0&&is_road(ii,j);ii--) vis_from[i][j].push_back({ii,j});\n for(int ii=i+1;ii>, vector>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX)), prev(N, vector(N, -1));\n priority_queue>, vector>>, greater<>> pq;\n dist[si][sj] = 0; pq.push({0, {si, sj}});\n while(!pq.empty()) {\n auto [d, p] = pq.top(); pq.pop();\n auto [i, j] = p;\n if(d > dist[i][j]) continue;\n for(int k=0;k<4;k++) {\n int ni = i+di[k], nj = j+dj[k];\n if(is_road(ni, nj)) {\n int nd = d + cell_cost(ni, nj);\n if(nd < dist[ni][nj]) { dist[ni][nj] = nd; prev[ni][nj] = k; pq.push({nd, {ni, nj}}); }\n }\n }\n }\n return {dist, prev};\n}\n\nstring reconstruct(int si, int sj, int ti, int tj, const vector>& prev) {\n if(si==ti && sj==tj) return \"\";\n string path; int ci=ti, cj=tj;\n while(ci!=si || cj!=sj) { int k=prev[ci][cj]; if(k==-1) return \"\"; path+=dc[k]; ci-=di[k]; cj-=dj[k]; }\n reverse(path.begin(), path.end()); return path;\n}\n\nvector> build_greedy(double alpha) {\n vector> covered(N, vector(N, false));\n auto mark = [&](int i, int j)->int {\n int c=0; for(auto& [vi, vj] : vis_from[i][j]) if(!covered[vi][vj]){covered[vi][vj]=true;c++;} return c;\n };\n vector> targets;\n int ci = si, cj = sj, cc = mark(ci, cj);\n \n while(cc < total_roads) {\n auto [dist, prev] = dijkstra(ci, cj);\n vector>>> children(N, vector>>(N));\n for(int i=0; i scores(N*N, -1.0);\n int current_nv = 0;\n vector> changes;\n vector> tmp = covered;\n \n function dfs = [&](int ui, int uj) {\n int sz = changes.size();\n for(auto& [vi, vj] : vis_from[ui][uj]) {\n if(!tmp[vi][vj]) { tmp[vi][vj] = true; changes.push_back({vi, vj}); current_nv++; }\n }\n if(current_nv > 0 && dist[ui][uj] > 0) scores[ui*N+uj] = pow((double)current_nv, alpha) / (double)dist[ui][uj];\n for(auto& [vi, vj] : children[ui][uj]) dfs(vi, vj);\n while(changes.size() > sz) { auto [vi, vj] = changes.back(); tmp[vi][vj] = false; changes.pop_back(); current_nv--; }\n };\n dfs(ci, cj);\n \n int best_idx = -1; double best_score = -1e18;\n for(int i=0; i best_score) { best_score = scores[i]; best_idx = i; }\n if(best_idx == -1) break;\n \n int bi = best_idx / N, bj = best_idx % N;\n targets.push_back({bi, bj});\n string path = reconstruct(ci, cj, bi, bj, prev);\n for(char c : path) { int k = char_to_idx(c); ci += di[k]; cj += dj[k]; cc += mark(ci, cj); }\n }\n return targets;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> si >> sj; grid.resize(N); for(int i=0;i> grid[i];\n precompute_visibility();\n total_roads = road_mask.count();\n auto st = chrono::high_resolution_clock::now();\n \n set> pool_set;\n pool_set.insert({si, sj});\n vector alphas = {0.5, 1.0, 1.5, 2.5};\n for(double alpha : alphas) { auto targets = build_greedy(alpha); for(auto& t : targets) pool_set.insert(t); }\n \n mt19937 rng(1337);\n vector> roads;\n for(int i=0;i> T(pool_set.begin(), pool_set.end());\n int M = T.size(), S = -1;\n for(int i=0; i> d(M, vector(M, INT_MAX));\n vector>> path_vis(M, vector>(M));\n vector>> all_prev(M, vector>(N, vector(N, -1)));\n \n for(int u=0; u bs;\n for(auto& [vi, vj] : vis_from[T[u].first][T[u].second]) bs[vi*N+vj] = 1;\n int ci = T[v].first, cj = T[v].second;\n while(ci != T[u].first || cj != T[u].second) {\n for(auto& [vi, vj] : vis_from[ci][cj]) bs[vi*N+vj] = 1;\n int k = prev[ci][cj]; ci -= di[k]; cj -= dj[k];\n }\n path_vis[u][v] = bs;\n }\n }\n \n auto evaluate_seq = [&](const vector& seq) -> pair {\n if(seq.empty()) { bitset<4800> vis = path_vis[S][S]; return {(vis & road_mask).count() == total_roads, 0}; }\n int cost = d[S][seq[0]] + d[seq.back()][S];\n bitset<4800> vis = path_vis[S][seq[0]] | path_vis[seq.back()][S];\n for(int i=0; i+1<(int)seq.size(); ++i) { cost += d[seq[i]][seq[i+1]]; vis |= path_vis[seq[i]][seq[i+1]]; }\n return {(vis & road_mask).count() == total_roads, cost};\n };\n \n vector best_greedy_seq; int best_greedy_cost = INT_MAX;\n for(double alpha : alphas) {\n auto targets = build_greedy(alpha);\n vector seq; for(auto& t : targets) for(int i=0; i cur_seq = best_greedy_seq, best_seq = best_greedy_seq;\n int cur_cost = best_greedy_cost, best_cost = best_greedy_cost;\n if(cur_seq.empty() || !evaluate_seq(cur_seq).first) { cur_seq.clear(); for(int i=0; i<20; ++i) cur_seq.push_back(rng() % M); auto [v, c] = evaluate_seq(cur_seq); cur_cost = v ? c : INT_MAX; }\n \n double T_sa = 1000.0;\n mt19937 rng_sa(12345);\n uniform_real_distribution dist01(0.0, 1.0);\n \n while(true) {\n auto now = chrono::high_resolution_clock::now();\n if(chrono::duration_cast(now - st).count() > 2800) break;\n vector new_seq = cur_seq;\n int op = rng_sa() % 5;\n if(op == 0 && new_seq.size() >= 2) { int l = rng_sa() % new_seq.size(), r = rng_sa() % new_seq.size(); if(l > r) swap(l, r); reverse(new_seq.begin() + l, new_seq.begin() + r + 1); }\n else if(op == 1 && new_seq.size() >= 2) { int i = rng_sa() % new_seq.size(), j = rng_sa() % new_seq.size(); swap(new_seq[i], new_seq[j]); }\n else if(op == 2 && new_seq.size() > 1) { int i = rng_sa() % new_seq.size(); new_seq.erase(new_seq.begin() + i); }\n else if(op == 3) { int x = rng_sa() % M, i = rng_sa() % (new_seq.size() + 1); new_seq.insert(new_seq.begin() + i, x); }\n else if(op == 4 && new_seq.size() > 0) { int i = rng_sa() % new_seq.size(), x = rng_sa() % M; new_seq[i] = x; }\n \n auto [valid, new_cost] = evaluate_seq(new_seq);\n if(valid) {\n double delta = new_cost - cur_cost;\n if(delta < 0 || dist01(rng_sa) < exp(-delta / T_sa)) { cur_seq = new_seq; cur_cost = new_cost; if(new_cost < best_cost) { best_cost = new_cost; best_seq = new_seq; } }\n }\n T_sa *= 0.9999;\n }\n \n string final_route;\n if(!best_seq.empty()) {\n int ci = si, cj = sj;\n for(int idx=0; idx<(int)best_seq.size(); ++idx) {\n int u = (idx == 0) ? S : best_seq[idx-1], v = best_seq[idx];\n final_route += reconstruct(T[u].first, T[u].second, T[v].first, T[v].second, all_prev[u]);\n }\n final_route += reconstruct(T[best_seq.back()].first, T[best_seq.back()].second, si, sj, all_prev[best_seq.back()]);\n }\n cout << final_route << endl;\n return 0;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint N, M, K, R;\nvector> d, deps, rev_deps;\nvector> skill_est;\nvector crit_path;\nvector task_start, task_done;\nvector>> member_obs;\n\nvector hungarian(const vector>& cost) {\n int n = cost.size(), m = cost[0].size();\n const double INF = 1e18;\n vector u(n+1,0), v(m+1,0);\n vector p(m+1,0), way(m+1,0);\n for (int i = 1; i <= n; i++) {\n p[0] = i; int j0 = 0;\n vector minv(m+1, INF);\n vector used(m+1, false);\n do {\n used[j0] = true;\n int i0 = p[j0], j1 = 0;\n double delta = INF;\n for (int j = 1; j <= m; j++) if (!used[j]) {\n double cur = cost[i0-1][j-1] - u[i0] - v[j];\n if (cur < minv[j]) { minv[j] = cur; way[j] = j0; }\n if (minv[j] < delta) { delta = minv[j]; j1 = j; }\n }\n for (int j = 0; j <= m; j++) {\n if (used[j]) { u[p[j]] += delta; v[j] -= delta; }\n else minv[j] -= delta;\n }\n j0 = j1;\n } while (p[j0] != 0);\n do { int j1 = way[j0]; p[j0] = p[j1]; j0 = j1; } while (j0);\n }\n vector asgn(n, -1);\n for (int j = 1; j <= m; j++) if (p[j] > 0 && p[j] <= n) asgn[p[j]-1] = j-1;\n return asgn;\n}\n\nvoid recompute_crit_path() {\n vector et(N);\n for (int i = 0; i < N; ++i) {\n if (task_done[i] != -1) { et[i] = 0; continue; }\n if (task_start[i] != -1) { et[i] = 0.1; continue; } // Already started, will finish soon\n double min_w = 1e9;\n for (int j = 0; j < M; ++j) {\n double w = 0;\n for (int k = 0; k < K; ++k) w += max(0.0, (double)d[i][k] - skill_est[j][k]);\n min_w = min(min_w, w);\n }\n et[i] = max(1.0, min_w);\n }\n for (int i = N - 1; i >= 0; i--) {\n crit_path[i] = et[i];\n for (int v : rev_deps[i]) crit_path[i] = max(crit_path[i], et[i] + crit_path[v]);\n }\n}\n\nvoid reestimate(int j) {\n auto& ob = member_obs[j];\n if (ob.empty()) return;\n for (int iter = 0; iter < 30; ++iter) {\n for (auto& [task, t] : ob) {\n double w_pred = 0;\n for (int k = 0; k < K; ++k) w_pred += max(0.0, (double)d[task][k] - skill_est[j][k]);\n \n if (t == 1) {\n if (w_pred > 0) {\n for (int k = 0; k < K; ++k) {\n if (d[task][k] > skill_est[j][k]) {\n skill_est[j][k] += 0.3 * (d[task][k] - skill_est[j][k]);\n }\n }\n }\n } else {\n double target_w = t;\n double diff = w_pred - target_w;\n if (abs(diff) < 0.5) continue;\n \n if (w_pred > 0) {\n for (int k = 0; k < K; ++k) {\n if (d[task][k] > skill_est[j][k]) {\n skill_est[j][k] += 0.3 * diff * (d[task][k] - skill_est[j][k]) / w_pred;\n }\n }\n } else { \n double sum_d = 0;\n for (int k = 0; k < K; ++k) sum_d += d[task][k];\n if (sum_d > 0) {\n for (int k = 0; k < K; ++k) {\n skill_est[j][k] += 0.3 * diff * d[task][k] / sum_d;\n }\n }\n }\n }\n }\n for (auto& [task, t] : ob) {\n if (t == 1) {\n for (int k = 0; k < K; ++k) {\n skill_est[j][k] = max(skill_est[j][k], (double)d[task][k]);\n }\n }\n }\n for (int k = 0; k < K; ++k) skill_est[j][k] = max(0.0, skill_est[j][k]);\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> M >> K >> R;\n d.resize(N, vector(K)); deps.resize(N); rev_deps.resize(N);\n for (int i = 0; i < N; i++) for (int k = 0; k < K; k++) cin >> d[i][k];\n for (int r = 0; r < R; r++) { int u, v; cin >> u >> v; u--; v--; deps[v].push_back(u); rev_deps[u].push_back(v); }\n \n crit_path.resize(N, 0); task_start.resize(N, -1); task_done.resize(N, -1);\n skill_est.resize(M, vector(K)); member_obs.resize(M);\n \n for (int k = 0; k < K; k++) {\n vector dk(N); for (int i = 0; i < N; i++) dk[i] = d[i][k];\n sort(dk.begin(), dk.end());\n double init = dk[N/2] * 1.5;\n for (int j = 0; j < M; j++) skill_est[j][k] = init;\n }\n \n vector member_task(M, -1), member_start_day(M, -1);\n set available_tasks; vector deps_rem(N);\n for (int i = 0; i < N; i++) { deps_rem[i] = deps[i].size(); if (!deps_rem[i]) available_tasks.insert(i); }\n \n int current_day = 0;\n while (true) {\n current_day++;\n recompute_crit_path();\n \n vector free_members;\n for (int j = 0; j < M; j++) if (member_task[j] == -1) free_members.push_back(j);\n int fm = free_members.size();\n \n if (fm > 0 && !available_tasks.empty()) {\n vector av(available_tasks.begin(), available_tasks.end());\n sort(av.begin(), av.end(), [&](int a, int b){ return crit_path[a] > crit_path[b]; });\n \n int nr = min((int)av.size(), fm * 5);\n int na = max(nr, fm);\n vector> cost(fm, vector(na, 1e9));\n for (int mi = 0; mi < fm; mi++) { \n int j = free_members[mi];\n for (int ti = 0; ti < nr; ti++) { \n int i = av[ti];\n double w = 0; for (int k = 0; k < K; k++) w += max(0.0, (double)d[i][k]-skill_est[j][k]);\n cost[mi][ti] = max(1.0, w);\n }\n }\n auto asgn = hungarian(cost);\n vector> assigns;\n for (int mi = 0; mi < fm; mi++) { \n int ti = asgn[mi];\n if (ti >= 0 && ti < nr) assigns.push_back({free_members[mi], av[ti]});\n }\n \n cout << assigns.size();\n for (auto [j,i] : assigns) {\n cout << \" \" << (j+1) << \" \" << (i+1);\n member_task[j]=i; member_start_day[j]=current_day; task_start[i]=current_day;\n available_tasks.erase(i);\n }\n cout << endl;\n } else cout << 0 << endl;\n \n int n; cin >> n; if (n == -1) break;\n for (int idx = 0; idx < n; idx++) {\n int j; cin >> j; j--;\n int i = member_task[j], tt = current_day - member_start_day[j] + 1;\n task_done[i] = current_day;\n member_obs[j].push_back({i, tt});\n reestimate(j);\n member_task[j] = -1;\n for (int v : rev_deps[i]) { \n deps_rem[v]--; \n if (deps_rem[v] == 0 && task_start[v] == -1 && task_done[v] == -1) available_tasks.insert(v); \n }\n }\n }\n return 0;\n}","ahc006":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint a[N], b[N], c[N], d[N];\n\ninline int dist(int x1, int y1, int x2, int y2) { return abs(x1-x2) + abs(y1-y2); }\n\nstruct Xor128 {\n unsigned x = 123456789, y = 362436069, z = 521288629, w = 88675123;\n unsigned next() {\n unsigned t = x ^ (x << 11);\n x = y; y = z; z = w;\n return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));\n }\n double nextDouble() {\n return next() / 4294967295.0;\n }\n int nextInt(int n) {\n return next() % n;\n }\n};\n\nXor128 rng;\n\nint route[100];\nint bestRouteArr[100];\nint orders[M];\nint bestOrders[M];\nbool isSelected[N];\n\nint calcCost() {\n int cost = 0, x = CX, y = CY;\n for (int i = 0; i < 2 * M; i++) {\n int ord = orders[route[i] / 2]; \n bool isD = route[i] % 2;\n int nx = isD ? c[ord] : a[ord], ny = isD ? d[ord] : b[ord];\n cost += dist(x, y, nx, ny); \n x = nx; y = ny;\n }\n return cost + dist(x, y, CX, CY);\n}\n\nbool isValidForInsert(int ip) {\n int k = route[ip] / 2;\n bool isD = route[ip] % 2;\n if (!isD) { // It's a restaurant\n for (int i = ip + 1; i < 2 * M; i++) {\n if (route[i] == k * 2 + 1) return true;\n }\n return false;\n } else { // It's a delivery\n for (int i = 0; i < ip; i++) {\n if (route[i] == k * 2) return true;\n }\n return false;\n }\n}\n\nvoid constructRoute() {\n bool vR[M], vD[M];\n memset(vR, 0, sizeof vR);\n memset(vD, 0, sizeof vD);\n int cx = CX, cy = CY;\n for (int step = 0; step < 2 * M; step++) {\n int best = -1, bestD = INT_MAX;\n for (int i = 0; i < M; i++) {\n if (!vR[i]) { \n int d2 = dist(cx, cy, a[orders[i]], b[orders[i]]); \n if (d2 < bestD) { bestD = d2; best = i * 2; } \n }\n if (vR[i] && !vD[i]) { \n int d2 = dist(cx, cy, c[orders[i]], d[orders[i]]); \n if (d2 < bestD) { bestD = d2; best = i * 2 + 1; } \n }\n }\n route[step] = best;\n if (best % 2 == 0) { vR[best / 2] = true; cx = a[orders[best / 2]]; cy = b[orders[best / 2]]; }\n else { vD[best / 2] = true; cx = c[orders[best / 2]]; cy = d[orders[best / 2]]; }\n }\n}\n\npair getCoord(int idx) {\n if (idx < 0 || idx >= 2 * M) return {CX, CY};\n int ord = orders[route[idx] / 2];\n bool isD = route[idx] % 2;\n if (isD) return {c[ord], d[ord]};\n else return {a[ord], b[ord]};\n}\n\nint distByIdx(int i, int j) {\n auto [x1, y1] = getCoord(i);\n auto [x2, y2] = getCoord(j);\n return abs(x1 - x2) + abs(y1 - y2);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n for (int i = 0; i < N; i++) cin >> a[i] >> b[i] >> c[i] >> d[i];\n \n auto startTime = chrono::high_resolution_clock::now();\n \n vector> scores;\n for (int i = 0; i < N; i++) {\n int cost = dist(CX, CY, a[i], b[i]) + dist(a[i], b[i], c[i], d[i]) + dist(c[i], d[i], CX, CY);\n scores.push_back({cost, i});\n }\n sort(scores.begin(), scores.end());\n \n for (int i = 0; i < M; i++) { orders[i] = scores[i].second; isSelected[orders[i]] = true; }\n \n constructRoute();\n int curCost = calcCost(), bestCost = curCost;\n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n \n double temp = 100.0, cooling = 0.99999;\n int iter = 0;\n \n while (true) {\n if (iter % 1000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - startTime).count() > 1.8) break;\n }\n iter++;\n \n int mt = rng.nextInt(10);\n if (mt < 5) {\n int from = rng.nextInt(2 * M), to = rng.nextInt(2 * M);\n if (from == to) continue;\n \n int savedRoute[100];\n memcpy(savedRoute, route, sizeof(route));\n \n int val = route[from];\n for (int i = from; i < 2 * M - 1; i++) route[i] = route[i + 1];\n int ip = to > from ? to - 1 : to;\n for (int i = 2 * M - 1; i > ip; i--) route[i] = route[i - 1];\n route[ip] = val;\n \n if (isValidForInsert(ip)) {\n int nc = calcCost(); double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n } else {\n memcpy(route, savedRoute, sizeof(route));\n }\n } else {\n memcpy(route, savedRoute, sizeof(route));\n }\n } else if (mt < 8) {\n int ii = rng.nextInt(M), oi = rng.nextInt(N);\n if (isSelected[oi]) continue;\n \n int savedOrders[50];\n memcpy(savedOrders, orders, sizeof(orders));\n int savedRoute[100];\n memcpy(savedRoute, route, sizeof(route));\n \n int oo = orders[ii]; \n orders[ii] = oi; \n isSelected[oo] = false; \n isSelected[oi] = true;\n \n constructRoute(); \n int nc = calcCost(); \n double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n } else { \n memcpy(orders, savedOrders, sizeof(orders));\n isSelected[oi] = false; \n isSelected[oo] = true; \n memcpy(route, savedRoute, sizeof(route));\n }\n } else {\n int l = rng.nextInt(2 * M - 1), r = l + 1 + rng.nextInt(2 * M - 1 - l);\n bool valid = true;\n bool inSegment[50] = {false};\n for (int i = l; i <= r; i++) {\n int k = route[i] / 2;\n if (inSegment[k]) { valid = false; break; }\n inSegment[k] = true;\n }\n if (valid) {\n int delta = distByIdx(l - 1, r) + distByIdx(l, r + 1) - distByIdx(l - 1, l) - distByIdx(r, r + 1);\n int nc = curCost + delta;\n double d = nc - curCost;\n if (d < 0 || rng.nextDouble() < exp(-d / temp)) { \n reverse(route + l, route + r + 1);\n curCost = nc; \n if (nc < bestCost) { \n bestCost = nc; \n memcpy(bestRouteArr, route, sizeof(route));\n memcpy(bestOrders, orders, sizeof(orders));\n } \n }\n }\n }\n temp *= cooling;\n }\n \n cout << M;\n for(int i = 0; i < M; i++) cout << \" \" << bestOrders[i] + 1;\n cout << endl;\n cout << 2 * M + 2 << \" \" << CX << \" \" << CY;\n for(int i = 0; i < 2 * M; i++) {\n int ord = bestOrders[bestRouteArr[i] / 2]; bool isD = bestRouteArr[i] % 2;\n cout << \" \" << (isD ? c[ord] : a[ord]) << \" \" << (isD ? d[ord] : b[ord]);\n }\n cout << \" \" << CX << \" \" << CY << endl;\n}","ahc007":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct UnionFind {\n vector parent, rank_;\n int components;\n \n UnionFind(int n) : parent(n), rank_(n, 0), components(n) {\n for (int i = 0; i < n; i++) parent[i] = i;\n }\n \n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n \n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n components--;\n return true;\n }\n \n bool connected(int x, int y) {\n return find(x) == find(y);\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n vector x(N), y(N);\n vector u(M), v(M);\n vector d(M);\n \n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dist = sqrt((double)(x[u[i]] - x[v[i]]) * (x[u[i]] - x[v[i]]) + \n (double)(y[u[i]] - y[v[i]]) * (y[u[i]] - y[v[i]]));\n d[i] = max(1, (int)round(dist));\n }\n \n // Compute reference MST using d_i\n vector order(M);\n for (int i = 0; i < M; i++) order[i] = i;\n sort(order.begin(), order.end(), [&](int a, int b) { return d[a] < d[b]; });\n \n UnionFind refUF(N);\n vector inRefMST(M, false);\n for (int idx : order) {\n if (refUF.unite(u[idx], v[idx])) {\n inRefMST[idx] = true;\n }\n }\n \n // Process edges online\n UnionFind uf(N);\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int adopt = 0;\n \n if (!uf.connected(u[i], v[i])) {\n if (inRefMST[i]) {\n // Always accept reference MST edges - guarantees connectivity\n adopt = 1;\n uf.unite(u[i], v[i]);\n } else {\n // Accept non-MST edges only if they're cheap enough\n // to potentially replace expensive MST edges\n double percentile = (double)(l - d[i]) / (2.0 * d[i]);\n percentile = max(0.0, min(1.0, percentile));\n \n int remaining = M - i - 1;\n int needed = uf.components - 1;\n double safety = (needed > 0) ? (double)remaining / needed : 999.0;\n \n double threshold;\n if (safety >= 5) threshold = 0.3;\n else if (safety >= 3) threshold = 0.4;\n else if (safety >= 2) threshold = 0.5;\n else threshold = 0.65;\n \n if (percentile <= threshold) {\n adopt = 1;\n uf.unite(u[i], v[i]);\n }\n }\n }\n \n cout << adopt << endl;\n }\n \n return 0;\n}","ahc008":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int SIZE = 30;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\n\nint N, M;\nvector px, py, pt;\nvector hx, hy;\nbool wall[SIZE][SIZE];\n\nbool inBounds(int x, int y) { return x >= 0 && x < SIZE && y >= 0 && y < SIZE; }\n\nvoid bfs(int sx, int sy, int dist[SIZE][SIZE]) {\n memset(dist, -1, sizeof(int) * SIZE * SIZE);\n if (!inBounds(sx, sy) || wall[sx][sy]) return;\n queue> q;\n dist[sx][sy] = 0;\n q.push({sx, sy});\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && dist[nx][ny] == -1) {\n dist[nx][ny] = dist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n}\n\ndouble petThreatWeight(int t) {\n switch(t) { case 1: return 1.0; case 2: return 1.5; case 3: return 2.0; case 4: return 2.5; case 5: return 2.0; default: return 1.0; }\n}\n\ndouble computeScoreWithDist(int dist[SIZE][SIZE]) {\n int area = 0;\n double effectivePets = 0;\n for (int i = 0; i < SIZE; i++)\n for (int j = 0; j < SIZE; j++)\n if (dist[i][j] >= 0) area++;\n for (int i = 0; i < N; i++)\n if (dist[px[i]][py[i]] >= 0) effectivePets += 1.0;\n\n int boundaryDist[SIZE][SIZE];\n memset(boundaryDist, -1, sizeof(int) * SIZE * SIZE);\n queue> q;\n for (int x = 0; x < SIZE; x++)\n for (int y = 0; y < SIZE; y++)\n if (dist[x][y] < 0 && !wall[x][y]) {\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && dist[nx][ny] >= 0) {\n if (boundaryDist[x][y] == -1) { boundaryDist[x][y] = 1; q.push({x, y}); }\n break;\n }\n }\n }\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && boundaryDist[nx][ny] == -1 && dist[nx][ny] < 0) {\n boundaryDist[nx][ny] = boundaryDist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n for (int i = 0; i < N; i++) {\n if (dist[px[i]][py[i]] >= 0) continue;\n int d = boundaryDist[px[i]][py[i]];\n if (d >= 1 && d <= 10) effectivePets += petThreatWeight(pt[i]) * 0.2 * exp(-0.2 * d);\n }\n return (double)area / 900.0 * pow(2.0, -effectivePets);\n}\n\nbool petAdjacentTo(int x, int y, const vector& ppx, const vector& ppy) {\n for (int i = 0; i < N; i++) {\n if (ppx[i] == x && ppy[i] == y) return true;\n for (int d = 0; d < 4; d++)\n if (ppx[i] == x + dx[d] && ppy[i] == y + dy[d]) return true;\n }\n return false;\n}\n\nbool humanAt(int x, int y, const vector& hhx, const vector& hhy) {\n for (int i = 0; i < M; i++) if (hhx[i] == x && hhy[i] == y) return true;\n return false;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N;\n px.resize(N); py.resize(N); pt.resize(N);\n for (int i = 0; i < N; i++) { cin >> px[i] >> py[i] >> pt[i]; px[i]--; py[i]--; }\n cin >> M;\n hx.resize(M); hy.resize(M);\n for (int i = 0; i < M; i++) { cin >> hx[i] >> hy[i]; hx[i]--; hy[i]--; }\n memset(wall, false, sizeof(wall));\n\n for (int turn = 0; turn < 300; turn++) {\n vector startPx = px, startPy = py, startHx = hx, startHy = hy;\n string actions(M, '.');\n bool newWall[SIZE][SIZE] = {};\n\n for (int i = 0; i < M; i++) {\n int myHx = startHx[i], myHy = startHy[i];\n int distBefore[SIZE][SIZE];\n bfs(myHx, myHy, distBefore);\n double bestScore = computeScoreWithDist(distBefore);\n char bestAction = '.';\n\n for (int d = 0; d < 4; d++) {\n int wx = myHx + dx[d], wy = myHy + dy[d];\n if (inBounds(wx, wy) && !wall[wx][wy] && !newWall[wx][wy] &&\n !petAdjacentTo(wx, wy, startPx, startPy) && !humanAt(wx, wy, startHx, startHy)) {\n wall[wx][wy] = true;\n int distAfter[SIZE][SIZE];\n bfs(myHx, myHy, distAfter);\n double newScore = computeScoreWithDist(distAfter);\n for (int j = 0; j < N; j++)\n if (distBefore[startPx[j]][startPy[j]] >= 0 && distAfter[startPx[j]][startPy[j]] < 0)\n newScore += 0.05;\n for (int dd = 0; dd < 4; dd++) {\n int nx = wx + dx[dd], ny = wy + dy[dd];\n if (!inBounds(nx, ny) || wall[nx][ny]) newScore += 0.003;\n }\n newScore += 0.001;\n wall[wx][wy] = false;\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"udlr\"[d]; }\n }\n }\n for (int d = 0; d < 4; d++) {\n int nx = myHx + dx[d], ny = myHy + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && !newWall[nx][ny]) {\n int distAfter[SIZE][SIZE];\n bfs(nx, ny, distAfter);\n double newScore = computeScoreWithDist(distAfter);\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"UDLR\"[d]; }\n }\n }\n actions[i] = bestAction;\n switch (actions[i]) {\n case 'u': newWall[myHx-1][myHy]=true; wall[myHx-1][myHy]=true; break;\n case 'd': newWall[myHx+1][myHy]=true; wall[myHx+1][myHy]=true; break;\n case 'l': newWall[myHx][myHy-1]=true; wall[myHx][myHy-1]=true; break;\n case 'r': newWall[myHx][myHy+1]=true; wall[myHx][myHy+1]=true; break;\n case 'U': hx[i]=myHx-1; hy[i]=myHy; break;\n case 'D': hx[i]=myHx+1; hy[i]=myHy; break;\n case 'L': hx[i]=myHx; hy[i]=myHy-1; break;\n case 'R': hx[i]=myHx; hy[i]=myHy+1; break;\n }\n }\n cout << actions << endl;\n for (int i = 0; i < N; i++) {\n string move; cin >> move;\n for (char c : move) {\n if (c=='U') px[i]--; else if (c=='D') px[i]++;\n else if (c=='L') py[i]--; else if (c=='R') py[i]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\nint si,sj,ti,tj;double p;int ti_idx;\nint md[400][4];double fv[400][202];int c2d[256];\nmt19937 rng(42);\n\nvoid init(){\n vectorh(20),v(19);for(int i=0;i<20;i++)cin>>h[i];for(int i=0;i<19;i++)cin>>v[i];\n ti_idx=ti*20+tj;int di[]={-1,1,0,0},dj[]={0,0,-1,1};\n for(int i=0;i<20;i++)for(int j=0;j<20;j++){int idx=i*20+j;\n for(int d=0;d<4;d++){int ni=i+di[d],nj=j+dj[d];bool bl=(ni<0||ni>=20||nj<0||nj>=20);\n if(!bl){if(d==0&&v[i-1][j]=='1')bl=true;else if(d==1&&v[i][j]=='1')bl=true;\n else if(d==2&&h[i][j-1]=='1')bl=true;else if(d==3&&h[i][j]=='1')bl=true;}\n if(bl){ni=i;nj=j;}md[idx][d]=ni*20+nj;}}\n memset(fv,0,sizeof(fv));\n for(int t=200;t>=1;t--)for(int idx=0;idx<400;idx++){\n if(idx==ti_idx){fv[idx][t]=0;continue;}\n double b=0;for(int d=0;d<4;d++){int ni=md[idx][d];\n double sc=p*fv[idx][t+1];if(ni==ti_idx)sc+=(1-p)*(401-t);else sc+=(1-p)*fv[ni][t+1];\n b=max(b,sc);}fv[idx][t]=b;}}\n\ndouble compute_score(const string&s){\n double pr[400]={},np[400];pr[si*20+sj]=1;double es=0;\n for(int t=0;t<(int)s.size();t++){int d=c2d[(unsigned char)s[t]];memset(np,0,sizeof(np));\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;\n if(i==ti_idx)continue;\n np[i]+=p*pr[i];int ni=md[i][d];\n if(ni==ti_idx)es+=(1-p)*pr[i]*(400-t);else np[ni]+=(1-p)*pr[i];}\n memcpy(pr,np,sizeof(pr));}return es;}\n\nstring bfs_path(){int dist[400],pdir[400];memset(dist,-1,sizeof(dist));\n queueq;int start=si*20+sj;q.push(start);dist[start]=0;\n while(!q.empty()){int idx=q.front();q.pop();if(idx==ti_idx)break;\n for(int d=0;d<4;d++){int ni=md[idx][d];if(ni!=idx&&dist[ni]==-1){dist[ni]=dist[idx]+1;pdir[ni]=d;q.push(ni);}}}\n string path;int idx=ti_idx;int di[]={-1,1,0,0},dj[]={0,0,-1,1};\n while(idx!=start){int d=pdir[idx];path=string(1,\"UDLR\"[d])+path;idx=(idx/20-di[d])*20+(idx%20-dj[d]);}return path;}\n\nstring greedy(){double pr[400]={};pr[si*20+sj]=1;string res;\n for(int t=1;t<=200;t++){double bsc=-1;int ba=0;\n for(int d=0;d<4;d++){double rp=0;double np[400]={};\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;\n if(i==ti_idx)continue;np[i]+=p*pr[i];int ni=md[i][d];\n if(ni==ti_idx)rp+=(1-p)*pr[i];else np[ni]+=(1-p)*pr[i];}\n double sc=rp*(401-t);for(int i=0;i<400;i++)sc+=np[i]*fv[i][t+1];\n if(sc>bsc){bsc=sc;ba=d;}}\n res+=\"UDLR\"[ba];double np[400]={};\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;\n if(i==ti_idx)continue;np[i]+=p*pr[i];int ni=md[i][ba];\n if(ni!=ti_idx)np[ni]+=(1-p)*pr[i];}memcpy(pr,np,sizeof(pr));}return res;}\n\nstring beam_search(int B, double noise=0.0){\n vector pr_flat(B * 400, 0.0);\n vector acc(B, 0.0);\n vector> act(B);\n int cur_B = 1;\n pr_flat[si*20+sj] = 1.0;\n\n for(int t=0; t<200; ++t){\n vector>> scores;\n scores.reserve(cur_B * 4);\n for(int i=0; i 0) h += uniform_real_distribution(-noise, noise)(rng);\n scores.push_back({h, {i, d}});\n }\n }\n int next_B = min(B, (int)scores.size());\n if(next_B == 0) break;\n if(next_B < (int)scores.size()) {\n nth_element(scores.begin(), scores.begin() + next_B - 1, scores.end(), [](const auto& a, const auto& b){\n return a.first > b.first;\n });\n }\n\n vector npr_flat(next_B * 400, 0.0);\n vector nacc(next_B, 0.0);\n vector> nact(next_B);\n\n for(int k=0; k bsc) {\n bsc = acc[i];\n br = \"\";\n for(int t=0;t<200;++t) br += \"UDLR\"[act[i][t]];\n }\n }\n return br;\n}\n\nstring suffix_opt(string s) {\n for(int k=5; k<200; k+=5) {\n if(k >= (int)s.size()) continue;\n double pr[400] = {}; pr[si*20+sj] = 1;\n for(int t=0; t bsc2) { bsc2 = sc; ba = d; }\n }\n ns += \"UDLR\"[ba];\n double np[400] = {};\n for(int i=0; i<400; ++i) {\n if(pr[i] < 1e-18) continue;\n if(i == ti_idx) continue;\n np[i] += p * pr[i];\n int ni = md[i][ba];\n if(ni != ti_idx) np[ni] += (1-p) * pr[i];\n }\n memcpy(pr, np, sizeof(pr));\n }\n s = ns;\n }\n return s;\n}\n\nvoid coordinate_descent(string& best) {\n int L = best.size();\n double pr_arr[201][400];\n double W[201][400];\n \n memset(pr_arr[0], 0, sizeof(pr_arr[0]));\n pr_arr[0][si*20+sj] = 1.0;\n for(int t=0; t=0; --t) {\n int d = c2d[(unsigned char)best[t]];\n for(int i=0; i<400; ++i) {\n if(i == ti_idx) { W[t][i] = 0; continue; }\n double val = p * W[t+1][i];\n int ni = md[i][d];\n if(ni == ti_idx) val += (1-p) * (400 - t);\n else val += (1-p) * W[t+1][ni];\n W[t][i] = val;\n }\n }\n \n for(int pass=0; pass<50; ++pass) {\n bool changed = false;\n for(int pos=0; pos best_new_score + 1e-9) {\n best_new_score = new_score;\n best_d = d;\n }\n }\n \n if(best_d != c2d[(unsigned char)best[pos]]) {\n changed = true;\n best[pos] = \"UDLR\"[best_d];\n \n for(int t=pos; t=0; --t) {\n int dd = c2d[(unsigned char)best[t]];\n for(int i=0; i<400; ++i) {\n if(i == ti_idx) { W[t][i] = 0; continue; }\n double val = p * W[t+1][i];\n int ni = md[i][dd];\n if(ni == ti_idx) val += (1-p) * (400 - t);\n else val += (1-p) * W[t+1][ni];\n W[t][i] = val;\n }\n }\n }\n}\n\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n c2d['U']=0;c2d['D']=1;c2d['L']=2;c2d['R']=3;\n cin>>si>>sj>>ti>>tj>>p;init();\n string best; double bs = -1;\n \n auto optimize = [&](string s) {\n s = suffix_opt(s);\n coordinate_descent(s);\n double sc = compute_score(s);\n if(sc > bs) { bs = sc; best = s; }\n };\n \n string sp = bfs_path();\n {string s; while((int)(s.size()+sp.size())<=200) s+=sp; optimize(s);}\n for(int r=2; r<=5; r++) {string s; for(char c:sp) for(int k=0; k(0, 199)(rng);\n s[pos] = \"UDLR\"[uniform_int_distribution(0, 3)(rng)];\n }\n optimize(s);\n }\n \n for(int i=0; i<3; ++i) {\n string s = best;\n s = suffix_opt(s);\n coordinate_descent(s);\n double sc = compute_score(s);\n if(sc > bs) { bs = sc; best = s; }\n }\n \n for(int len=50; len<=200; len+=10) {\n if(len < (int)best.size()) {\n string ns = best.substr(0, len);\n double sc = compute_score(ns);\n if(sc > bs) { bs = sc; best = ns; }\n }\n }\n \n cout<\nusing namespace std;\n\nconst int N = 30;\nint orig[N][N], cur[N][N], rot[N][N];\nconstexpr int di[]={0,-1,0,1}, dj[]={-1,0,1,0};\nconstexpr int to[8][4]={{1,0,-1,-1},{3,-1,-1,0},{-1,-1,3,2},{-1,2,1,-1},{1,0,3,2},{3,2,1,0},{2,-1,0,-1},{-1,3,-1,1}};\nconstexpr int rt[8][4]={{0,1,2,3},{1,2,3,0},{2,3,0,1},{3,0,1,2},{4,5,4,5},{5,4,5,4},{6,7,6,7},{7,6,7,6}};\n\nint cycle_counts[2002] = {};\nset active_lengths;\nlong long total_loop_edges = 0;\n\nint vm[N][N][4]; \nunsigned int vcnt=0;\n\nvoid update_cycle_counts(int len, int delta) {\n if (delta == 1) {\n if (cycle_counts[len] == 0) active_lengths.insert(len);\n cycle_counts[len]++;\n total_loop_edges += len;\n } else {\n cycle_counts[len]--;\n total_loop_edges -= len;\n if (cycle_counts[len] == 0) active_lengths.erase(len);\n }\n}\n\nvoid init_cycle_counts() {\n memset(cycle_counts, 0, sizeof(cycle_counts));\n active_lengths.clear();\n total_loop_edges = 0;\n \n ++vcnt;\n if (vcnt == 0) { memset(vm, 0, sizeof(vm)); vcnt = 1; }\n \n for (int i=0; i= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == si && nj == sj && nd == sd) { is_cycle = true; break; }\n if (vm[ni][nj][nd] == vcnt) break;\n if (len > 2000) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n update_cycle_counts(len, 1);\n }\n }\n }\n}\n\nvoid update_tile(int i, int j, int new_t) {\n int old_t = cur[i][j];\n if (old_t == new_t) return;\n\n bool visited_old[4] = {false, false, false, false};\n for (int d = 0; d < 4; d++) {\n if (visited_old[d] || to[old_t][d] == -1) continue;\n int len = 0;\n int ci = i, cj = j, cd = d;\n bool is_cycle = false;\n while (true) {\n int t2 = (ci == i && cj == j) ? old_t : cur[ci][cj];\n int d2 = to[t2][cd];\n if (d2 == -1) break;\n if (ci == i && cj == j) { visited_old[cd] = true; visited_old[d2] = true; }\n int ni = ci + di[d2], nj = cj + dj[d2];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == i && nj == j && nd == d) { is_cycle = true; break; }\n if (len > 2000) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n update_cycle_counts(len, -1);\n }\n }\n\n cur[i][j] = new_t;\n bool visited_new[4] = {false, false, false, false};\n for (int d = 0; d < 4; d++) {\n if (visited_new[d] || to[new_t][d] == -1) continue;\n int len = 0;\n int ci = i, cj = j, cd = d;\n bool is_cycle = false;\n while (true) {\n int t2 = (ci == i && cj == j) ? new_t : cur[ci][cj];\n int d2 = to[t2][cd];\n if (d2 == -1) break;\n if (ci == i && cj == j) { visited_new[cd] = true; visited_new[d2] = true; }\n int ni = ci + di[d2], nj = cj + dj[d2];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == i && nj == j && nd == d) { is_cycle = true; break; }\n if (len > 2000) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n update_cycle_counts(len, 1);\n }\n }\n}\n\nlong long get_score() {\n if (active_lengths.empty()) return 0;\n auto it = active_lengths.rbegin();\n int L1 = *it;\n if (cycle_counts[L1] >= 2) return (long long)L1 * L1;\n if (active_lengths.size() == 1) return 0;\n int L2 = *next(it);\n return (long long)L1 * L2;\n}\n\nlong long get_sa_energy() {\n if (active_lengths.empty()) return 0;\n auto it = active_lengths.rbegin();\n int L1 = *it;\n \n if (cycle_counts[L1] >= 2) {\n return (long long)L1 * L1 * 1000 + total_loop_edges;\n }\n if (active_lengths.size() == 1) {\n return total_loop_edges;\n }\n int L2 = *next(it);\n return (long long)L1 * L2 * 1000 + total_loop_edges;\n}\n\nint lmatch(int i, int j) {\n int t = cur[i][j], m = 0;\n for (int d = 0; d < 4; d++) {\n if (to[t][d] == -1) continue;\n int ni = i + di[d], nj = j + dj[d];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) continue;\n if (to[cur[ni][nj]][(d + 2) % 4] != -1) m++;\n }\n return m;\n}\n\nvoid greedy_match() {\n for (int pass = 0; pass < 10; pass++) {\n bool ch = false;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n int br = rot[i][j], bm = lmatch(i, j);\n for (int r = 0; r < 4; r++) {\n if (r == rot[i][j]) continue;\n cur[i][j] = rt[orig[i][j]][r];\n int m = lmatch(i, j);\n if (m > bm) { bm = m; br = r; ch = true; }\n }\n rot[i][j] = br; cur[i][j] = rt[orig[i][j]][br];\n }\n if (!ch) break;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(0);\n for (int i = 0; i < N; i++) { string s; cin >> s; for (int j = 0; j < N; j++) orig[i][j] = s[j] - '0'; }\n mt19937 rng(42);\n long long gbest = 0; int grot[N][N] = {};\n auto t0 = chrono::steady_clock::now();\n bool have_best = false;\n\n for (int trial = 0; ; trial++) {\n double elapsed = chrono::duration(chrono::steady_clock::now() - t0).count();\n if (elapsed > 1.5) break;\n\n if (have_best && trial % 2 == 1) {\n memcpy(rot, grot, sizeof(rot));\n int np = 20 + rng() % 80;\n for (int k = 0; k < np; k++) { int i = rng() % N, j = rng() % N; rot[i][j] = rng() % 4; }\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cur[i][j] = rt[orig[i][j]][rot[i][j]];\n greedy_match();\n } else {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { rot[i][j] = rng() % 4; cur[i][j] = rt[orig[i][j]][rot[i][j]]; }\n greedy_match();\n }\n\n init_cycle_counts();\n long long current_energy = get_sa_energy();\n long long best_score = get_score();\n int brot[N][N]; memcpy(brot, rot, sizeof(rot));\n\n for (int iter = 0; ; iter++) {\n if (iter % 10000 == 0) {\n if (chrono::duration(chrono::steady_clock::now() - t0).count() > 1.7) break;\n }\n double frac = min(iter / 2000000.0, 1.0);\n double temp = 50000.0 * pow(0.00002, frac);\n int idx = (rng() >> 2) % 900, i = idx / N, j = idx % N;\n int old_r = rot[i][j];\n int new_r = (rng() >> 12) & 3;\n if (old_r == new_r) continue;\n int new_t = rt[orig[i][j]][new_r];\n if (new_t == cur[i][j]) continue;\n\n update_tile(i, j, new_t);\n long long new_energy = get_sa_energy();\n long long diff = new_energy - current_energy;\n\n if (diff >= 0 || (double)(rng() & 0xFFFF) / 65536.0 < exp((double)diff / temp)) {\n current_energy = new_energy;\n rot[i][j] = new_r;\n long long true_score = get_score();\n if (true_score > best_score) {\n best_score = true_score;\n memcpy(brot, rot, sizeof(rot));\n }\n } else {\n update_tile(i, j, rt[orig[i][j]][old_r]);\n rot[i][j] = old_r;\n }\n }\n\n if (best_score > gbest) {\n gbest = best_score;\n memcpy(grot, brot, sizeof(grot));\n have_best = true;\n }\n }\n\n memcpy(rot, grot, sizeof(rot));\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cur[i][j] = rt[orig[i][j]][rot[i][j]];\n init_cycle_counts();\n long long current_score = get_score();\n\n for (int pass = 0; pass < 10; pass++) {\n bool imp = false;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n int old_t = cur[i][j];\n int best_new_t = old_t;\n long long best_local_score = current_score;\n int best_new_r = rot[i][j];\n\n for (int r = 0; r < 4; r++) {\n int new_t = rt[orig[i][j]][r];\n if (new_t == old_t) continue;\n update_tile(i, j, new_t);\n long long new_score = get_score();\n if (new_score > best_local_score) {\n best_local_score = new_score;\n best_new_t = new_t;\n best_new_r = r;\n }\n update_tile(i, j, old_t);\n }\n\n if (best_new_t != old_t) {\n update_tile(i, j, best_new_t);\n rot[i][j] = best_new_r;\n current_score = best_local_score;\n imp = true;\n }\n }\n if (!imp) break;\n }\n\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cout << rot[i][j];\n cout << endl;\n\n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N,T,board[10][10],init_board[10][10],er,ec,init_er,init_ec;\nint target[10][10],tile_count[16];\nconst int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\nconst int BS[]={2,8,1,4},BN[]={8,2,4,1};\nconst char DC_C[]={'U','D','L','R'};\nconst int REV[]={1,0,3,2};\n\nvoid gen_target(mt19937& rng,int skip_r,int skip_c){\n vector> el;\n for(int i=0;i par(N*N),rnk(N*N,0);iota(par.begin(),par.end(),0);\n function f=[&](int x)->int{return par[x]==x?x:par[x]=f(par[x]);};\n memset(target,0,sizeof(target));\n for(auto&[w,u,v]:el){\n int pu=f(u),pv=f(v);\n if(pu!=pv){\n int r1=u/N,c1=u%N,r2=v/N,c2=v%N;\n if(r2==r1+1){target[r1][c1]|=8;target[r2][c2]|=2;}\n else{target[r1][c1]|=4;target[r2][c2]|=1;}\n if(rnk[pu]>N>>T;\n memset(tile_count,0,sizeof(tile_count));\n for(int i=0;i>s;for(int j=0;j='0'&&c<='9')?c-'0':c-'a'+10;if(board[i][j])tile_count[board[i][j]]++;else{init_er=i;init_ec=j;}}}\n memcpy(init_board,board,sizeof(board));er=init_er;ec=init_ec;\n int gbm=max_tree();string gbm_moves;\n auto start=chrono::high_resolution_clock::now();\n for(int trial=0;;trial++){\n auto now=chrono::high_resolution_clock::now();\n if(chrono::duration_cast(now-start).count()>2800)break;\n mt19937 rng(42+trial*137);\n int skip_r=rng()%N,skip_c=rng()%N;\n gen_target(rng,skip_r,skip_c);\n int ub=match_ub();if(ub(now2-start).count()>2800)break;\n long long dv[4];\n for(int d=0;d<4;d++){\n int nr=er+DR[d],nc=ec+DC[d];\n if(nr<0||nr>=N||nc<0||nc>=N){dv[d]=-1e18;continue;}\n int X=board[nr][nc];\n int dm=0;\n if(target[nr][nc]&&(X&target[nr][nc])==target[nr][nc])dm--;\n if(target[er][ec]&&(X&target[er][ec])==target[er][ec])dm++;\n int dtc=0,dxc=0;\n for(int dd=0;dd<4;dd++){\n int r=er+DR[dd],c=ec+DC[dd];\n if(r>=0&&r=0&&c=0&&r=0&&cbv){bv=dv[d];bd=d;}\n if(bd==-1)break;\n int ch;\n if(bv>0){ch=bd;stale=0;}\n else{stale++;double delta=(double)bv/1000.0;if(exp(delta/max(temp,0.01))>(double)rng()/(double)UINT32_MAX)ch=bd;\n else{int v[4],nv=0;for(int d=0;d<4;d++){if(dv[d]<=-1e18)continue;if(ld>=0&&d==REV[ld])continue;v[nv++]=d;}\n if(!nv)for(int d=0;d<4;d++)if(dv[d]>-1e18)v[nv++]=d;if(!nv)break;ch=v[rng()%nv];}}\n int nr=er+DR[ch],nc=ec+DC[ch],X=board[nr][nc];\n if(target[nr][nc]&&(X&target[nr][nc])==target[nr][nc])cm--;\n if(target[er][ec]&&(X&target[er][ec])==target[er][ec])cm++;\n for(int dd=0;dd<4;dd++){\n int r=er+DR[dd],c=ec+DC[dd];\n if(r>=0&&r=0&&c=0&&r=0&&c=150){chk=0;int mx=max_tree();if(mx>bm){bm=mx;bi=mv.size();stale=0;}if(mx==N*N-1)break;}\n temp*=0.99998;if(stale>400){temp=min(temp*2.5,8.0);stale=200;}\n }\n int mx=max_tree();if(mx>bm){bm=mx;bi=mv.size();}\n if(bm>gbm){gbm=bm;gbm_moves=mv.substr(0,bi);}\n if(gbm==N*N-1)break;\n }\n cout<\nusing namespace std;\ntypedef long long ll;\n\nint N, K;\nint a_arr[11];\nvector px, py;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> K;\n for (int d = 1; d <= 10; d++) cin >> a_arr[d];\n px.resize(N); py.resize(N);\n for (int i = 0; i < N; i++) cin >> px[i] >> py[i];\n \n auto start = chrono::steady_clock::now();\n \n struct Line { ll la, lb, lc, p1x, p1y, p2x, p2y; };\n vector lines;\n \n auto compute_groups = [&]() {\n int nl = lines.size();\n vector, int>> entries;\n entries.reserve(N);\n for (int i = 0; i < N; i++) {\n vector sig; sig.reserve(nl);\n bool dead = false;\n for (int j = 0; j < nl; j++) {\n ll val = lines[j].la*px[i] + lines[j].lb*py[i] + lines[j].lc;\n if (val == 0) { dead = true; break; }\n sig.push_back(val > 0 ? 1 : -1);\n }\n if (!dead) entries.push_back({move(sig), i});\n }\n sort(entries.begin(), entries.end());\n vector, vector>> groups;\n for (int i = 0; i < (int)entries.size(); ) {\n int j = i; vector members;\n while (j < (int)entries.size() && entries[j].first == entries[i].first)\n members.push_back(entries[j++].second);\n groups.push_back({entries[i].first, move(members)});\n i = j;\n }\n return groups;\n };\n \n auto score_groups = [&](auto& groups) {\n int pc[11] = {};\n for (auto& [sig, mem] : groups) { int sz = mem.size(); if (sz >= 1 && sz <= 10) pc[sz]++; }\n int s = 0; for (int d = 1; d <= 10; d++) s += min(a_arr[d], pc[d]); return s;\n };\n \n auto eval_line = [&](ll la, ll lb, ll lc, auto& groups) {\n int pc[11] = {};\n for (auto& [sig, mem] : groups) {\n int pos = 0, neg = 0;\n for (int i : mem) {\n ll val = la*px[i] + lb*py[i] + lc;\n if (val > 0) pos++; else if (val < 0) neg++;\n }\n if (pos >= 1 && pos <= 10) pc[pos]++;\n if (neg >= 1 && neg <= 10) pc[neg]++;\n }\n int s = 0; for (int d = 1; d <= 10; d++) s += min(a_arr[d], pc[d]); return s;\n };\n \n auto make_sep = [&](int i, int j) -> Line {\n ll dx = py[i] - py[j], dy = px[j] - px[i];\n ll g = __gcd(abs(dx), abs(dy)); if (g > 0) { dx /= g; dy /= g; }\n ll mx = px[i] + px[j], my = py[i] + py[j];\n for (int r = 0; r < 4; r++) {\n ll cx = (mx + (r & 1)) / 2, cy = (my + ((r >> 1) & 1)) / 2;\n ll la = dy, lb = -dx, lc = -dy*cx + dx*cy;\n ll vi = la*px[i]+lb*py[i]+lc, vj = la*px[j]+lb*py[j]+lc;\n if (vi != 0 && vj != 0 && (vi > 0) != (vj > 0))\n return {la, lb, lc, cx, cy, cx+dx, cy+dy};\n }\n ll cx = mx/2, cy = my/2;\n ll la = dy, lb = -dx, lc = -dy*cx + dx*cy;\n return {la, lb, lc, cx, cy, cx+dx, cy+dy};\n };\n \n auto make_through = [&](ll cx, ll cy, ll dx, ll dy) -> Line {\n ll g = __gcd(abs(dx), abs(dy)); if (g > 0) { dx /= g; dy /= g; }\n if (dx == 0 && dy == 0) dx = 1;\n ll la = dy, lb = -dx, lc = -dy*cx + dx*cy;\n return {la, lb, lc, cx, cy, cx+dx, cy+dy};\n };\n \n auto gen_cands = [&](auto& groups, bool all = false) {\n int pc[11] = {};\n for (auto& [sig, mem] : groups) { int sz = mem.size(); if (sz >= 1 && sz <= 10) pc[sz]++; }\n vector cands;\n set> seen;\n auto add = [&](Line l) {\n ll a=l.la, b=l.lb, c=l.lc;\n ll g = __gcd(__gcd(abs(a),abs(b)),abs(c));\n if(g>0){a/=g;b/=g;c/=g;}\n if(a<0||(a==0&&b<0)||(a==0&&b==0&&c<0)){a=-a;b=-b;c=-c;}\n if(seen.insert({a,b,c}).second) cands.push_back(l);\n };\n for (auto& [sig, mem] : groups) {\n int sz = mem.size();\n if (sz <= 1) continue;\n if (!all && sz <= 10 && pc[sz] <= a_arr[sz]) continue;\n int lim = min((int)mem.size(), 12);\n for (int ii = 0; ii < lim; ii++)\n for (int jj = ii+1; jj < lim; jj++)\n add(make_sep(mem[ii], mem[jj]));\n ll cx = 0, cy = 0;\n for (int i : mem) { cx += px[i]; cy += py[i]; }\n cx /= sz; cy /= sz;\n for (int ag = 0; ag < 12; ag++) {\n double ar = ag*M_PI/6;\n ll ddx = (ll)round(10000*cos(ar)), ddy = (ll)round(10000*sin(ar));\n if (ddx || ddy) add(make_through(cx, cy, ddx, ddy));\n }\n for (int ii = 0; ii < min(lim,5); ii++)\n for (int jj = ii+1; jj < min(lim,5); jj++) {\n ll mx2 = (px[mem[ii]]+px[mem[jj]])/2, my2 = (py[mem[ii]]+py[mem[jj]])/2;\n for (int ag = 0; ag < 6; ag++) {\n double ar = ag*M_PI/3;\n ll ddx = (ll)round(10000*cos(ar)), ddy = (ll)round(10000*sin(ar));\n if (ddx || ddy) add(make_through(mx2, my2, ddx, ddy));\n }\n }\n }\n return cands;\n };\n \n for (int iter = 0; iter < K; iter++) {\n if (chrono::duration(chrono::steady_clock::now()-start).count() > 1.2) break;\n auto groups = compute_groups();\n int cs = score_groups(groups);\n int mx = 0; for(int d=1;d<=10;d++) mx += a_arr[d];\n if (cs == mx) break;\n auto cands = gen_cands(groups);\n if (cands.empty()) break;\n int bs = cs, bi = -1;\n for (int i = 0; i < (int)cands.size(); i++) {\n int s = eval_line(cands[i].la, cands[i].lb, cands[i].lc, groups);\n if (s > bs) { bs = s; bi = i; }\n }\n if (bi >= 0) lines.push_back(cands[bi]);\n else {\n int max_sz = 1, max_i = -1;\n for (int i = 0; i < (int)groups.size(); i++)\n if ((int)groups[i].second.size() > max_sz) { max_sz = groups[i].second.size(); max_i = i; }\n if (max_sz > 1 && (int)lines.size() < K)\n lines.push_back(make_sep(groups[max_i].second[0], groups[max_i].second[1]));\n else break;\n }\n }\n \n mt19937 rng(42);\n int ni = 0;\n while (chrono::duration(chrono::steady_clock::now()-start).count() < 2.8) {\n int nl = lines.size();\n if (nl == 0) break;\n int idx = rng() % nl;\n auto old = lines[idx];\n lines[idx] = lines.back(); lines.pop_back();\n auto groups = compute_groups();\n int cs = score_groups(groups);\n auto cands = gen_cands(groups);\n cands.push_back(old);\n int bs = cs, bi = -1;\n for (int i = 0; i < (int)cands.size(); i++) {\n int s = eval_line(cands[i].la, cands[i].lb, cands[i].lc, groups);\n if (s > bs) { bs = s; bi = i; }\n }\n if (bi >= 0) lines.push_back(cands[bi]); else lines.push_back(old);\n if (bs > cs) ni = 0; else ni++;\n if (ni > 300) break;\n if ((int)lines.size() < K) {\n groups = compute_groups(); cs = score_groups(groups);\n cands = gen_cands(groups, true);\n bs = cs; bi = -1;\n for (int i = 0; i < (int)cands.size(); i++) {\n int s = eval_line(cands[i].la, cands[i].lb, cands[i].lc, groups);\n if (s > bs) { bs = s; bi = i; }\n }\n if (bi >= 0) { lines.push_back(cands[bi]); ni = 0; }\n }\n }\n \n cout << lines.size() << \"\\n\";\n for (auto& l : lines)\n cout << l.p1x << \" \" << l.p1y << \" \" << l.p2x << \" \" << l.p2y << \"\\n\";\n return 0;\n}","ahc014":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, M;\nvector> has_dot;\nvector> ops;\nmap>> segs[4];\n\nvector dots_y[65];\nvector dots_x[65];\nvector dots_u[130];\nvector dots_v[130];\nvector pt_idx[65];\nvector> existing_dots;\n\nset candidates;\nvector>> empty_pts_vec;\n\nint seg_type(int x1,int y1,int x2,int y2){\n if(y1==y2)return 0;\n if(x1==x2)return 1;\n if(x2-x1==y2-y1)return 2;\n return 3;\n}\nint line_id(int t,int x,int y){\n if(t==0)return y;\n if(t==1)return x;\n if(t==2)return x-y;\n return x+y;\n}\nint line_coord(int t,int x,int y){\n if(t==0||t==2||t==3)return x;\n return y;\n}\n\nbool check_overlap(int t, int lid, int s, int e) {\n if (s > e) swap(s, e);\n auto it = segs[t].find(lid);\n if (it == segs[t].end()) return false;\n auto& st = it->second;\n auto jt = st.upper_bound({s, 1e9});\n if (jt != st.begin()) {\n auto kt = prev(jt);\n if (kt->second > s) return true;\n }\n if (jt != st.end()) {\n if (jt->first < e) return true;\n }\n return false;\n}\n\nvoid add_seg(int t, int lid, int s, int e) {\n if (s > e) swap(s, e);\n auto& st = segs[t][lid];\n auto it = st.upper_bound({s, 1e9});\n if (it != st.begin()) {\n auto kt = prev(it);\n if (kt->second >= s) {\n s = min(s, kt->first);\n e = max(e, kt->second);\n st.erase(kt);\n }\n }\n it = st.upper_bound({s, 1e9});\n while (it != st.end() && it->first <= e) {\n e = max(e, it->second);\n it = st.erase(it);\n }\n st.insert({s, e});\n}\n\nbool has_perim_overlap(int x1,int y1,int x2,int y2,int x3,int y3,int x4,int y4){\n int e[4][4]={{x1,y1,x2,y2},{x2,y2,x3,y3},{x3,y3,x4,y4},{x4,y4,x1,y1}};\n for(int i=0;i<4;i++){\n int t=seg_type(e[i][0],e[i][1],e[i][2],e[i][3]);\n int lid=line_id(t,e[i][0],e[i][1]);\n int s=line_coord(t,e[i][0],e[i][1]);\n int ee=line_coord(t,e[i][2],e[i][3]);\n if(check_overlap(t,lid,s,ee))return true;\n }\n return false;\n}\nvoid add_perim(int x1,int y1,int x2,int y2,int x3,int y3,int x4,int y4){\n int e[4][4]={{x1,y1,x2,y2},{x2,y2,x3,y3},{x3,y3,x4,y4},{x4,y4,x1,y1}};\n for(int i=0;i<4;i++){\n int t=seg_type(e[i][0],e[i][1],e[i][2],e[i][3]);\n int lid=line_id(t,e[i][0],e[i][1]);\n int s=line_coord(t,e[i][0],e[i][1]);\n int ee=line_coord(t,e[i][2],e[i][3]);\n add_seg(t,lid,s,ee);\n }\n}\n\nbool dot_on_perim(int x1,int y1,int x2,int y2,int x3,int y3,int x4,int y4){\n set> corners={{x1,y1},{x2,y2},{x3,y3},{x4,y4}};\n auto chk=[&](int ax,int ay,int bx,int by){\n int dx=bx-ax, dy=by-ay;\n int g=gcd(abs(dx),abs(dy));\n if(g==0)return false;\n int sx=dx/g, sy=dy/g;\n for(int i=1;i find_best_rect(int ex, int ey) {\n int best_cost = 1e9;\n array best_r = {-1};\n \n auto update = [&](array r, int cost) {\n if (cost < best_cost) {\n best_cost = cost;\n best_r = r;\n }\n };\n \n // Axis-aligned\n for (int y1 : dots_x[ex]) {\n for (int x1 : dots_y[ey]) {\n if (has_dot[x1][y1]) {\n if (valid_rect(ex, ey, ex, y1, x1, y1, x1, ey)) {\n int cost = abs(x1 - ex) + abs(y1 - ey);\n update({ex, ey, ex, y1, x1, y1, x1, ey}, cost);\n }\n }\n }\n }\n \n // 45 degree inclined (using u, v space)\n int eu = ex + ey;\n int ev = ex - ey;\n \n for (int v2 : dots_u[eu]) {\n if ((eu + v2) % 2 != 0) continue;\n int x3 = (eu + v2) / 2;\n int y3 = (eu - v2) / 2;\n if (x3 < 0 || x3 >= N || y3 < 0 || y3 >= N) continue;\n \n for (int u2 : dots_v[ev + N]) {\n if ((u2 + ev) % 2 != 0) continue;\n int x4 = (u2 + ev) / 2;\n int y4 = (u2 - ev) / 2;\n if (x4 < 0 || x4 >= N || y4 < 0 || y4 >= N) continue;\n \n int x2 = (u2 + v2) / 2;\n int y2 = (u2 - v2) / 2;\n if (x2 < 0 || x2 >= N || y2 < 0 || y2 >= N) continue;\n \n if (has_dot[x2][y2]) {\n if (valid_rect(ex, ey, x3, y3, x2, y2, x4, y4)) {\n int cost = abs(u2 - eu) + abs(v2 - ev);\n update({ex, ey, x3, y3, x2, y2, x4, y4}, cost);\n }\n }\n }\n }\n \n return best_r;\n}\n\nvoid add_cand(int x, int y) {\n if (x >= 0 && x < N && y >= 0 && y < N && !has_dot[x][y]) {\n int idx = pt_idx[x][y];\n if (idx != -1) {\n candidates.insert(idx);\n }\n }\n}\n\nvoid add_candidates(int x, int y) {\n int u = x + y;\n int v = x - y;\n \n for (auto [x2, y2] : existing_dots) {\n // Axis-aligned check\n if (x != x2 && y != y2) {\n bool c1 = (y2 >= 0 && y2 < N);\n bool c2 = (x2 >= 0 && x2 < N);\n if (c1 && c2 && has_dot[x][y2] && !has_dot[x2][y]) add_cand(x2, y);\n if (c1 && c2 && has_dot[x2][y] && !has_dot[x][y2]) add_cand(x, y2);\n }\n \n // 45 degree inclined check\n int u2 = x2 + y2;\n int v2 = x2 - y2;\n \n if (u != u2 && v != v2) {\n if ((u + v2) % 2 == 0 && (u2 + v) % 2 == 0) {\n int x3 = (u + v2) / 2;\n int y3 = (u - v2) / 2;\n int x4 = (u2 + v) / 2;\n int y4 = (u2 - v) / 2;\n \n if (x3 >= 0 && x3 < N && y3 >= 0 && y3 < N &&\n x4 >= 0 && x4 < N && y4 >= 0 && y4 < N) {\n if (has_dot[x3][y3] && !has_dot[x4][y4]) add_cand(x4, y4);\n if (has_dot[x4][y4] && !has_dot[x3][y3]) add_cand(x3, y3);\n }\n }\n }\n }\n}\n\nint main(){\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n cin >> N >> M;\n has_dot.assign(N, vector(N, false));\n \n double c = (N - 1) / 2.0;\n \n for(int i=0;i> initial_dots(M);\n for(int i=0;i> x >> y;\n has_dot[x][y] = true;\n dots_x[x].push_back(y);\n dots_y[y].push_back(x);\n int u = x + y;\n int v = x - y;\n dots_u[u].push_back(v);\n dots_v[v + N].push_back(u);\n initial_dots[i] = {x, y};\n }\n \n for(int x=0;x{r[0], r[1], r[2], r[3], r[4], r[5], r[6], r[7]});\n candidates.erase(best_idx);\n pt_idx[x][y] = -1;\n add_candidates(x, y);\n } else {\n candidates.erase(best_idx);\n }\n }\n \n cout << ops.size() << \"\\n\";\n for(auto& op : ops){\n for(int i=0;i<8;i++){\n cout << op[i] << (i<7?\" \":\"\\n\");\n }\n }\n \n return 0;\n}","ahc015":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 10;\nint grid[N][N];\nint flavors[101];\nmt19937 rng(42);\n\nvoid applyTilt(int g[N][N], int d) {\n if (d == 0) { for (int c = 0; c < N; c++) { int w = 0; for (int r = 0; r < N; r++) if (g[r][c]) { if (w != r) { g[w][c] = g[r][c]; g[r][c] = 0; } w++; } } }\n else if (d == 1) { for (int c = 0; c < N; c++) { int w = N-1; for (int r = N-1; r >= 0; r--) if (g[r][c]) { if (w != r) { g[w][c] = g[r][c]; g[r][c] = 0; } w--; } } }\n else if (d == 2) { for (int r = 0; r < N; r++) { int w = 0; for (int c = 0; c < N; c++) if (g[r][c]) { if (w != c) { g[r][w] = g[r][c]; g[r][c] = 0; } w++; } } }\n else { for (int r = 0; r < N; r++) { int w = N-1; for (int c = N-1; c >= 0; c--) if (g[r][c]) { if (w != c) { g[r][w] = g[r][c]; g[r][c] = 0; } w--; } } }\n}\n\nint getScore(int g[N][N]) {\n bool vis[N][N] = {}; int s = 0;\n constexpr int dr[] = {-1,1,0,0}, dc[] = {0,0,-1,1};\n int q[N*N], fr, bk;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) {\n if (!vis[r][c] && g[r][c]) {\n int fl = g[r][c], sz = 0; fr = 0; bk = 0;\n q[bk++] = r*N+c; vis[r][c] = true;\n while (fr < bk) { int id = q[fr++], cr = id/N, cc = id%N; sz++;\n for (int d = 0; d < 4; d++) { int nr = cr+dr[d], nc = cc+dc[d];\n if (nr>=0&&nr=0&&nc= 100) return getScore(orig);\n int nf = flavors[turn + 1];\n long long total = 0; int count = 0;\n int g[N][N]; memcpy(g, orig, sizeof(g));\n int saved[N][N];\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) {\n if (g[r][c] == 0) {\n g[r][c] = nf;\n int bestS = 0;\n for (int d = 0; d < 4; d++) {\n memcpy(saved, g, sizeof(saved));\n applyTilt(g, d);\n int s = getScore(g);\n bestS = max(bestS, s);\n memcpy(g, saved, sizeof(saved));\n }\n total += bestS;\n g[r][c] = 0;\n count++;\n }\n }\n return count > 0 ? total / count : getScore(orig);\n}\n\nlong long runMC(int startT, int base[N][N]) {\n int sim[N][N]; memcpy(sim, base, sizeof(sim));\n for (int t = startT; t <= 100; t++) {\n int er[100], ec[100], cnt = 0;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) if (!sim[r][c]) { er[cnt] = r; ec[cnt] = c; cnt++; }\n if (!cnt) break;\n int idx = rng() % cnt;\n sim[er[idx]][ec[idx]] = flavors[t];\n int bestS = -1, bestD = 0, sv[N][N];\n for (int d = 0; d < 4; d++) { memcpy(sv, sim, sizeof(sv)); applyTilt(sim, d); int s = getScore(sim); if (s > bestS) { bestS = s; bestD = d; } memcpy(sim, sv, sizeof(sv)); }\n applyTilt(sim, bestD);\n }\n return getScore(sim);\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n for (int i = 1; i <= 100; i++) cin >> flavors[i];\n memset(grid, 0, sizeof(grid));\n const char dirChars[] = \"FBLR\";\n const int dirPrio[] = {4, 1, 2, 3};\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n int pos = 1;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) if (!grid[r][c]) { if (pos == p) { grid[r][c] = flavors[t]; goto placed; } pos++; }\n placed:;\n \n int scores[4], adjs[4];\n int saved[N][N]; memcpy(saved, grid, sizeof(grid));\n for (int d = 0; d < 4; d++) {\n applyTilt(grid, d);\n scores[d] = getScore(grid);\n adjs[d] = getAdj(grid);\n memcpy(grid, saved, sizeof(grid));\n }\n \n int maxScore = *max_element(scores, scores + 4);\n vector tied; for (int d = 0; d < 4; d++) if (scores[d] == maxScore) tied.push_back(d);\n \n int bestDir;\n if (tied.size() == 1) {\n bestDir = tied[0];\n } else {\n long long ply1[4] = {};\n for (int d : tied) {\n applyTilt(grid, d);\n ply1[d] = compute1Ply(grid, t);\n memcpy(grid, saved, sizeof(grid));\n }\n long long maxPly = -1; for (int d : tied) maxPly = max(maxPly, ply1[d]);\n vector tied2; for (int d : tied) if (ply1[d] == maxPly) tied2.push_back(d);\n \n if (tied2.size() == 1) {\n bestDir = tied2[0];\n } else {\n int maxAdj = -1; for (int d : tied2) maxAdj = max(maxAdj, adjs[d]);\n vector tied3; for (int d : tied2) if (adjs[d] == maxAdj) tied3.push_back(d);\n \n if (tied3.size() == 1) {\n bestDir = tied3[0];\n } else if (t >= 40) {\n int numSims = max(3, min(10, (100 - t) / 5));\n long long mcBest = -1; bestDir = tied3[0];\n for (int d : tied3) {\n int tmp[N][N]; memcpy(tmp, grid, sizeof(grid)); applyTilt(tmp, d);\n long long total = 0;\n for (int s = 0; s < numSims; s++) total += runMC(t + 1, tmp);\n if (total > mcBest) { mcBest = total; bestDir = d; }\n }\n } else {\n bestDir = tied3[0];\n for (int d : tied3) if (dirPrio[d] < dirPrio[bestDir]) bestDir = d;\n }\n }\n }\n \n applyTilt(grid, bestDir);\n cout << dirChars[bestDir] << '\\n'; cout.flush();\n }\n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int M; double eps;\n cin >> M >> eps;\n \n // Phase 1: Find best N\n double bestScore = -1e18;\n int bestN = max(5, (int)ceil(log2(max(M,2))) + 2);\n \n vector tryN;\n for (int n = 4; n <= 15; n++) tryN.push_back(n);\n for (int n = 18; n <= 40; n += 3) tryN.push_back(n);\n for (int n = 45; n <= 80; n += 5) tryN.push_back(n);\n for (int n = 90; n <= 100; n += 10) tryN.push_back(n);\n \n for (int Nt : tryN) {\n double dVD = max(1.0, (Nt - 1.0) * eps * (1.0 - eps));\n double dVE = max(1.0, (double)(Nt * (Nt - 1) / 2) * eps * (1.0 - eps));\n \n int NCt = min(4000, (Nt - 1 <= 20) ? (1 << (Nt - 1)) : 4000);\n if (NCt < M) continue;\n \n vector> fps(NCt, vector(Nt + 1));\n for (int c = 0; c < NCt; ++c) {\n auto& fp = fps[c];\n vector exp_deg(Nt, (Nt - 1.0) * eps);\n int edges = 0;\n int maxEt = Nt * (Nt - 1) / 2;\n \n if (Nt - 1 <= 13) {\n for (int j = 1; j < Nt; ++j) {\n if ((c >> (j - 1)) & 1) {\n edges += j;\n for (int i = 0; i < j; ++i) exp_deg[i] += (1.0 - 2.0 * eps);\n exp_deg[j] += j * (1.0 - 2.0 * eps);\n }\n }\n } else {\n uint64_t state = (uint64_t)c * 0x9e3779b97f4a7c15ULL + 12345;\n for (int j = 1; j < Nt; ++j) {\n state = state * 6364136223846793005ULL + 1442695040888963407ULL;\n if ((state >> 33) & 1) {\n edges += j;\n for (int i = 0; i < j; ++i) exp_deg[i] += (1.0 - 2.0 * eps);\n exp_deg[j] += j * (1.0 - 2.0 * eps);\n }\n }\n }\n sort(exp_deg.begin(), exp_deg.end());\n fp[0] = edges * (1.0 - 2.0 * eps) + maxEt * eps;\n for (int i = 0; i < Nt; ++i) fp[i + 1] = exp_deg[i];\n }\n \n vector used(NCt, false);\n vector minD(NCt, 1e18);\n used[0] = true;\n for (int c = 1; c < NCt; ++c) {\n double d = (fps[c][0] - fps[0][0]); d = d * d / dVE;\n for (int i = 1; i <= Nt; ++i) { double df = fps[c][i] - fps[0][i]; d += df * df / dVD; }\n minD[c] = d;\n }\n \n double dMin = 1e18;\n bool ok = true;\n for (int k = 1; k < M; ++k) {\n int best = -1; double bestD = -1;\n for (int c = 0; c < NCt; ++c) if (!used[c] && minD[c] > bestD) { bestD = minD[c]; best = c; }\n if (best < 0) { ok = false; break; }\n used[best] = true; dMin = min(dMin, bestD);\n for (int c = 0; c < NCt; ++c) {\n if (used[c]) continue;\n double d = (fps[c][0] - fps[best][0]); d = d * d / dVE;\n for (int i = 1; i <= Nt; ++i) { double df = fps[c][i] - fps[best][i]; d += df * df / dVD; }\n minD[c] = min(minD[c], d);\n }\n }\n if (!ok || dMin <= 0) continue;\n \n double pErr = (eps < 0.005) ? 1e-15 : max(1e-15, min(0.5, (M - 1.0) * 0.5 * erfc(sqrt(dMin / 8.0))));\n double estScore = pow(0.9, 100.0 * pErr) / Nt;\n if (estScore > bestScore) { bestScore = estScore; bestN = Nt; }\n }\n \n // Phase 2: Generate M graphs for chosen N\n int N = bestN;\n int maxE = N * (N - 1) / 2;\n double dVD = max(1.0, (N - 1.0) * eps * (1.0 - eps));\n double dVE = max(1.0, (double)maxE * eps * (1.0 - eps));\n \n int NC = min(4000, (N - 1 <= 13) ? (1 << (N - 1)) : 4000);\n if (NC < M) NC = M;\n \n auto eidx = [&](int i, int j) -> int { if (i > j) swap(i, j); return i * (2 * N - i - 1) / 2 + (j - i - 1); };\n \n vector> fps(NC, vector(N + 1));\n for (int c = 0; c < NC; ++c) {\n auto& fp = fps[c];\n vector exp_deg(N, (N - 1.0) * eps);\n int edges = 0;\n \n if (N - 1 <= 13) {\n for (int j = 1; j < N; ++j) {\n if ((c >> (j - 1)) & 1) {\n edges += j;\n for (int i = 0; i < j; ++i) exp_deg[i] += (1.0 - 2.0 * eps);\n exp_deg[j] += j * (1.0 - 2.0 * eps);\n }\n }\n } else {\n uint64_t state = (uint64_t)c * 0x9e3779b97f4a7c15ULL + 12345;\n for (int j = 1; j < N; ++j) {\n state = state * 6364136223846793005ULL + 1442695040888963407ULL;\n if ((state >> 33) & 1) {\n edges += j;\n for (int i = 0; i < j; ++i) exp_deg[i] += (1.0 - 2.0 * eps);\n exp_deg[j] += j * (1.0 - 2.0 * eps);\n }\n }\n }\n sort(exp_deg.begin(), exp_deg.end());\n fp[0] = edges * (1.0 - 2.0 * eps) + maxE * eps;\n for (int i = 0; i < N; ++i) fp[i + 1] = exp_deg[i];\n }\n \n vector sel;\n vector minD(NC, 1e18);\n vector used(NC, false);\n \n sel.push_back(0); used[0] = true;\n for (int c = 1; c < NC; ++c) {\n double d = (fps[c][0] - fps[0][0]); d = d * d / dVE;\n for (int i = 1; i <= N; ++i) { double df = fps[c][i] - fps[0][i]; d += df * df / dVD; }\n minD[c] = d;\n }\n \n for (int k = 1; k < M; ++k) {\n int best = -1; double bestD = -1;\n for (int c = 0; c < NC; ++c) if (!used[c] && minD[c] > bestD) { bestD = minD[c]; best = c; }\n if (best < 0) break;\n sel.push_back(best); used[best] = true;\n for (int c = 0; c < NC; ++c) {\n if (used[c]) continue;\n double d = (fps[c][0] - fps[best][0]); d = d * d / dVE;\n for (int i = 1; i <= N; ++i) { double df = fps[c][i] - fps[best][i]; d += df * df / dVD; }\n minD[c] = min(minD[c], d);\n }\n }\n while ((int)sel.size() < M) sel.push_back(0);\n \n cout << N << \"\\n\";\n for (int k = 0; k < M; ++k) {\n int c = sel[k];\n string g(maxE, '0');\n if (N - 1 <= 13) {\n for (int j = 1; j < N; ++j) {\n if ((c >> (j - 1)) & 1) {\n for (int i = 0; i < j; ++i) g[eidx(i, j)] = '1';\n }\n }\n } else {\n uint64_t state = (uint64_t)c * 0x9e3779b97f4a7c15ULL + 12345;\n for (int j = 1; j < N; ++j) {\n state = state * 6364136223846793005ULL + 1442695040888963407ULL;\n if ((state >> 33) & 1) {\n for (int i = 0; i < j; ++i) g[eidx(i, j)] = '1';\n }\n }\n }\n cout << g << \"\\n\";\n }\n cout.flush();\n \n vector> gefp(M, vector(N + 1));\n for (int k = 0; k < M; ++k) gefp[k] = fps[sel[k]];\n \n for (int q = 0; q < 100; ++q) {\n string H; cin >> H;\n int hEdges = count(H.begin(), H.end(), '1');\n vector hd(N, 0);\n for (int i = 0; i < N; ++i) for (int j = i + 1; j < N; ++j)\n if (H[eidx(i, j)] == '1') { hd[i]++; hd[j]++; }\n sort(hd.begin(), hd.end());\n \n int bestK = 0; double bestDist = 1e18;\n for (int k = 0; k < M; ++k) {\n double dist = (hEdges - gefp[k][0]); dist = dist * dist / dVE;\n for (int i = 1; i <= N; ++i) { double diff = hd[i - 1] - gefp[k][i]; dist += diff * diff / dVD; }\n if (dist < bestDist) { bestDist = dist; bestK = k; }\n }\n cout << bestK << \"\\n\"; cout.flush();\n }\n return 0;\n}","ahc017":"#include \nusing namespace std;\ntypedef long long ll;\ntypedef pair pli;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N,M,D,K; cin>>N>>M>>D>>K;\n vector u(M),v(M),w(M);\n vector>> adj(N);\n for(int i=0;i>u[i]>>v[i]>>w[i];u[i]--;v[i]--;adj[u[i]].push_back({i,v[i]});adj[v[i]].push_back({i,u[i]});}\n vector x(N),y(N);\n for(int i=0;i>x[i]>>y[i];\n\n int S=min(N,100);\n vector betw(M,0);\n for(int si=0;si dist(N,LLONG_MAX);vector pe(N,-1);\n dist[s]=0;priority_queue,greater> pq;pq.push({0,s});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>dist[nd])continue;for(auto[ei,nx]:adj[nd]){ll nd2=d+w[ei];if(nd2 ss(N,1);vector> ch(N);\n for(int t=0;t ord={s};for(int i=0;i<(int)ord.size();i++)for(int c:ch[ord[i]])ord.push_back(c);\n for(int i=(int)ord.size()-1;i>0;i--){int nd=ord[i];int o=(u[pe[nd]]==nd)?v[pe[nd]]:u[pe[nd]];ss[o]+=ss[nd];}\n for(int t=0;t> apsp(N,vector(N,LLONG_MAX));\n for(int s=0;s,greater> pq;pq.push({0,s});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>apsp[s][nd])continue;for(auto[ei,nx]:adj[nd]){ll nd2=d+w[ei];if(nd2 det(M,0);\n for(int ei=0;ei impact(M);\n for(int i=0;i> conflicts(M);\n vector dist(N);vector pe(N);\n for(int ei=0;ei,greater> pq;pq.push({0,u[ei]});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>dist[nd])continue;for(auto[ej,nx]:adj[nd]){if(ej==ei)continue;ll nd2=d+w[ej];if(nd2 order(M);iota(order.begin(),order.end(),0);\n sort(order.begin(),order.end(),[&](int a,int b){return impact[a]>impact[b];});\n\n vector r(M,-1),dc(D,0);vector day_imp(D,0);\n for(int ei:order){\n double bs=1e18;int bd=-1;\n for(int d=0;d=K)continue;double sc=0;for(int ej:conflicts[ei])if(r[ej]==d)sc+=impact[ei]*impact[ej];sc+=day_imp[d]*1e-4;if(sc(now-t0).count()>5.0)break;\n int ei=rng()%M;int od=r[ei];double cs=0;for(int ej:conflicts[ei])if(r[ej]==od)cs+=impact[ei]*impact[ej];\n int bd=-1;double bi=0;for(int d=0;d=K)continue;double ns=0;for(int ej:conflicts[ei])if(r[ej]==d)ns+=impact[ei]*impact[ej];double imp=cs-ns+((day_imp[od]-impact[ei])-(day_imp[d]+impact[ei]))*1e-4;if(imp>bi){bi=imp;bd=d;}}\n if(bd!=-1){r[ei]=bd;dc[od]--;dc[bd]++;day_imp[od]-=impact[ei];day_imp[bd]+=impact[ei];}}\n\n for(int i=0;i\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\nint D;\nusing Point=tuple;\nusing Array3D=vector>>;\n\nchrono::high_resolution_clock::time_point start_time;\n\nvector readSil(){vectors(D);for(int i=0;i>s[i];return s;}\nArray3D buildMF(const vector&f,const vector&r){Array3D b(D,vector>(D,vector(D,0)));for(int x=0;x> findComp(const Array3D&b){\n Array3D vis(D,vector>(D,vector(D,0)));vector>cs;\n const int dx[]={1,-1,0,0,0,0},dy[]={0,0,1,-1,0,0},dz[]={0,0,0,0,1,-1};\n for(int x=0;xc;queueq;q.push({x,y,z});vis[x][y][z]=1;\n while(!q.empty()){auto[cx,cy,cz]=q.front();q.pop();c.push_back({cx,cy,cz});\n for(int d=0;d<6;d++){int nx=cx+dx[d],ny=cy+dy[d],nz=cz+dz[d];\n if(0<=nx&&nx>> genRots(){\n vector>>rots;int B[6][3]={{1,0,0},{-1,0,0},{0,1,0},{0,-1,0},{0,0,1},{0,0,-1}};\n for(int i=0;i<6;i++)for(int j=0;j<6;j++){if(i/2==j/2)continue;int cr[3];\n cr[0]=B[i][1]*B[j][2]-B[i][2]*B[j][1];cr[1]=B[i][2]*B[j][0]-B[i][0]*B[j][2];cr[2]=B[i][0]*B[j][1]-B[i][1]*B[j][0];\n int dt=B[i][0]*(B[j][1]*cr[2]-B[j][2]*cr[1])-B[i][1]*(B[j][0]*cr[2]-B[j][2]*cr[0])+B[i][2]*(B[j][0]*cr[1]-B[j][1]*cr[0]);\n if(dt!=1)continue;rots.push_back({{B[i][0],B[i][1],B[i][2]},{B[j][0],B[j][1],B[j][2]},{cr[0],cr[1],cr[2]}});}\n return rots;\n}\n\nPoint appR(const vector>&M,const Point&p){auto[x,y,z]=p;return{M[0][0]*x+M[0][1]*y+M[0][2]*z,M[1][0]*x+M[1][1]*y+M[1][2]*z,M[2][0]*x+M[2][1]*y+M[2][2]*z};}\n\nvectorcanon(const vector&comp,const vector>>&rots){vectorbest;for(auto&M:rots){vectorr;for(auto&p:comp)r.push_back(appR(M,p));int mX=INT_MAX,mY=INT_MAX,mZ=INT_MAX;for(auto&[x,y,z]:r){mX=min(mX,x);mY=min(mY,y);mZ=min(mZ,z);}for(auto&[x,y,z]:r){x-=mX;y-=mY;z-=mZ;}sort(r.begin(),r.end());if(best.empty()||r> findSubComp(const vector&vox){setvs(vox.begin(),vox.end());mapvis;vector>cs;const int dx[]={1,-1,0,0,0,0},dy[]={0,0,1,-1,0,0},dz[]={0,0,0,0,1,-1};for(auto&p:vox){if(vis.count(p))continue;vectorc;queueq;q.push(p);vis[p]=1;while(!q.empty()){auto[cx,cy,cz]=q.front();q.pop();c.push_back({cx,cy,cz});for(int d=0;d<6;d++){Point np={cx+dx[d],cy+dy[d],cz+dz[d]};if(vs.count(np)&&!vis.count(np)){vis[np]=1;q.push(np);}}}cs.push_back(move(c));}return cs;}\n\nvoid doPartial(Array3D& a0, Array3D& a1, const Array3D& b0, const Array3D& b1, const vector>>& rots, int& nextId) {\n while (true) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration_cast(now - start_time).count() > 5000) break;\n \n Array3D U0(D, vector>(D, vector(D, 0)));\n Array3D U1(D, vector>(D, vector(D, 0)));\n vector P1;\n for(int x=0;x b.size();});\n \n bool found_match = false;\n for (auto& comp : comps0) {\n if (comp.size() < 2) break;\n int bestO = 1, bestRi = -1, bestTx = 0, bestTy = 0, bestTz = 0;\n const int OFF = 15, S = 30;\n vector tc(S*S*S);\n \n for (int ri = 0; ri < 24; ri++) {\n vector rot;\n for (auto& p : comp) rot.push_back(appR(rots[ri], p));\n int mX=INT_MAX, mY=INT_MAX, mZ=INT_MAX;\n for (auto& [x,y,z] : rot) { mX=min(mX,x); mY=min(mY,y); mZ=min(mZ,z); }\n for (auto& [x,y,z] : rot) { x-=mX; y-=mY; z-=mZ; }\n \n fill(tc.begin(), tc.end(), 0);\n for (auto& [sx,sy,sz] : rot) \n for (auto& [px,py,pz] : P1) {\n int kx = px-sx + OFF, ky = py-sy + OFF, kz = pz-sz + OFF;\n tc[kx + ky*S + kz*S*S]++;\n }\n for (int kz=0; kz bestO) { bestO = cnt; bestRi = ri; bestTx = kx-OFF; bestTy = ky-OFF; bestTz = kz-OFF; }\n }\n if (bestO == comp.size()) break;\n }\n \n if (bestRi != -1) {\n vector rot;\n for (auto& p : comp) rot.push_back(appR(rots[bestRi], p));\n int mX=INT_MAX, mY=INT_MAX, mZ=INT_MAX;\n for (auto& [x,y,z] : rot) { mX=min(mX,x); mY=min(mY,y); mZ=min(mZ,z); }\n for (auto& [x,y,z] : rot) { x-=mX; y-=mY; z-=mZ; }\n \n vector so, to;\n for (int i=0; i<(int)comp.size(); i++) {\n auto [rx,ry,rz] = rot[i];\n int tx=rx+bestTx, ty=ry+bestTy, tz=rz+bestTz;\n if (0<=tx&&tx s2i; for (int i=0; i<(int)so.size(); i++) s2i[so[i]] = i;\n \n for (auto& sc : scs) {\n if (sc.size() < 2) continue;\n found_match = true;\n int id = nextId++;\n for (auto& p : sc) {\n int i = s2i[p];\n auto [sx,sy,sz] = so[i]; auto [tx,ty,tz] = to[i];\n a0[sx][sy][sz] = id; a1[tx][ty][tz] = id;\n }\n }\n if (found_match) break;\n }\n }\n if (!found_match) break;\n }\n}\n\nint main(){\n ios::sync_with_stdio(false); cin.tie(nullptr);\n start_time = chrono::high_resolution_clock::now();\n cin >> D;\n vector> f(2), r(2);\n for (int i = 0; i < 2; i++) { f[i] = readSil(); r[i] = readSil(); }\n \n auto rots = genRots();\n auto b0 = buildMF(f[0], r[0]), b1 = buildMF(f[1], r[1]);\n Array3D a0(D, vector>(D, vector(D, 0)));\n Array3D a1(D, vector>(D, vector(D, 0)));\n int nid = 1;\n \n auto c0 = findComp(b0), c1 = findComp(b1);\n int n0 = c0.size(), n1 = c1.size();\n map, vector> cm1;\n for (int j=0; j o0(n0); for (int i=0; i c0[b].size();});\n \n vector u1(n1, false);\n for (int i : o0) {\n auto cn = canon(c0[i], rots);\n auto it = cm1.find(cn);\n if (it != cm1.end()) for (int j : it->second) if (!u1[j]) {\n int id = nid++;\n for (auto [x,y,z] : c0[i]) a0[x][y][z] = id;\n for (auto [x,y,z] : c1[j]) a1[x][y][z] = id;\n u1[j] = true; break;\n }\n }\n \n doPartial(a0, a1, b0, b1, rots, nid);\n doPartial(a1, a0, b1, b0, rots, nid);\n \n Array3D U0(D, vector>(D, vector(D, 0)));\n Array3D U1(D, vector>(D, vector(D, 0)));\n for(int x=0;x>(D, vector(D, 0)));\n for(int x=0;x> blocks0, blocks1;\n for(int x=0;x ids_in_1;\n for(int x=0;x shared_ids;\n for(int x=0;x, vector> canon_unshared1;\n for (auto& [id, pts] : blocks1) {\n if (!shared_ids.count(id)) {\n auto cn = canon(pts, rots);\n canon_unshared1[cn].push_back(id);\n }\n }\n \n for (auto& [id0, pts0] : blocks0) {\n if (!shared_ids.count(id0)) {\n auto cn = canon(pts0, rots);\n auto it = canon_unshared1.find(cn);\n if (it != canon_unshared1.end()) {\n int id1 = it->second.back();\n it->second.pop_back();\n if (it->second.empty()) canon_unshared1.erase(it);\n for (auto [x,y,z] : blocks1[id1]) a1[x][y][z] = id0;\n }\n }\n }\n \n map id_remap;\n int next_remap_id = 1;\n for(int x=0;x\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n \n vector>> adj(N);\n vector eu(M), ev(M), ew(M);\n for (int j = 0; j < M; j++) {\n cin >> eu[j] >> ev[j] >> ew[j];\n eu[j]--; ev[j]--;\n adj[eu[j]].push_back({ev[j], j});\n adj[ev[j]].push_back({eu[j], j});\n }\n \n vector a(K), b(K);\n for (int k = 0; k < K; k++) cin >> a[k] >> b[k];\n \n const int PMAX = 5000;\n const long long PMAXSQ = (long long)PMAX * PMAX;\n \n vector> rsq(K, vector(N));\n for (int k = 0; k < K; k++)\n for (int i = 0; i < N; i++) {\n long long dx = a[k] - x[i], dy = b[k] - y[i];\n rsq[k][i] = dx * dx + dy * dy;\n }\n \n vector> clo(K);\n for (int k = 0; k < K; k++) {\n vector> v;\n for (int i = 0; i < N; i++)\n if (rsq[k][i] <= PMAXSQ) v.push_back({rsq[k][i], i});\n sort(v.begin(), v.end());\n for (int j = 0; j < min(25, (int)v.size()); j++)\n clo[k].push_back(v[j].second);\n }\n \n // Dijkstra from vertex 0\n vector sp(N, LLONG_MAX);\n vector par(N, -1), pe(N, -1);\n sp[0] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, 0});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > sp[u]) continue;\n for (auto [v, e] : adj[u])\n if (sp[u] + ew[e] < sp[v]) {\n sp[v] = sp[u] + ew[e];\n par[v] = u; pe[v] = e;\n pq.push({sp[v], v});\n }\n }\n \n vector> pth(N);\n for (int i = 1; i < N; i++) {\n int c = i;\n while (c) { pth[i].push_back(pe[c]); c = par[c]; }\n }\n \n auto calcP = [](long long sq) -> int {\n if (sq <= 0) return 0;\n int p = max(1, (int)ceil(sqrt((double)sq) - 1e-9));\n while ((long long)p * p < sq) p++;\n return min(p, 5000);\n };\n \n // State with swap-and-pop vectors\n vector asgn(K);\n vector> vr(N);\n vector vmx(N, 0);\n for (int k = 0; k < K; k++) {\n asgn[k] = clo[k][0];\n vr[asgn[k]].push_back(k);\n vmx[asgn[k]] = max(vmx[asgn[k]], rsq[k][asgn[k]]);\n }\n \n vector P(N);\n long long pcost = 0;\n for (int i = 0; i < N; i++) { P[i] = calcP(vmx[i]); pcost += (long long)P[i] * P[i]; }\n \n vector eref(M, 0);\n long long ecost = 0;\n for (int i = 1; i < N; i++)\n if (P[i] > 0)\n for (int e : pth[i]) { if (!eref[e]) ecost += ew[e]; eref[e]++; }\n \n long long cost = pcost + ecost;\n vector best_P = P, best_asgn = asgn;\n long long best_cost = cost;\n \n mt19937 rng(42);\n uniform_real_distribution<> unif(0.0, 1.0);\n auto t0 = chrono::high_resolution_clock::now();\n \n // SA Phase 1: resident reassignment with SPT cost\n while (true) {\n double el = chrono::duration(chrono::high_resolution_clock::now() - t0).count();\n if (el > 1.6) break;\n double temp = 8e6 * pow(1e-5, el / 1.6);\n \n int k = rng() % K;\n int ov = asgn[k];\n int nv = clo[k][rng() % clo[k].size()];\n if (nv == ov) continue;\n \n long long nmx_ov = vmx[ov];\n if (rsq[k][ov] == vmx[ov]) {\n nmx_ov = 0;\n for (int r : vr[ov]) if (r != k) nmx_ov = max(nmx_ov, rsq[r][ov]);\n }\n int nPov = calcP(nmx_ov);\n long long nmx_nv = max(vmx[nv], rsq[k][nv]);\n int nPnv = calcP(nmx_nv);\n \n long long dpc = (long long)nPov * nPov - (long long)P[ov] * P[ov]\n + (long long)nPnv * nPnv - (long long)P[nv] * P[nv];\n \n if (P[ov] > 0 && nPov == 0)\n for (int e : pth[ov]) { eref[e]--; if (!eref[e]) ecost -= ew[e]; }\n if (P[nv] == 0 && nPnv > 0)\n for (int e : pth[nv]) { if (!eref[e]) ecost += ew[e]; eref[e]++; }\n \n long long nc = pcost + dpc + ecost;\n if (nc < cost || unif(rng) < exp(-(double)(nc - cost) / temp)) {\n // Swap-and-pop removal from vr[ov]\n auto it = find(vr[ov].begin(), vr[ov].end(), k);\n *it = vr[ov].back(); vr[ov].pop_back();\n vr[nv].push_back(k);\n vmx[ov] = nmx_ov; vmx[nv] = nmx_nv;\n P[ov] = nPov; P[nv] = nPnv;\n pcost += dpc; asgn[k] = nv; cost = nc;\n if (cost < best_cost) {\n best_cost = cost; best_P = P; best_asgn = asgn;\n }\n } else {\n if (P[nv] == 0 && nPnv > 0)\n for (int e : pth[nv]) { eref[e]--; if (!eref[e]) ecost -= ew[e]; }\n if (P[ov] > 0 && nPov == 0)\n for (int e : pth[ov]) { if (!eref[e]) ecost += ew[e]; eref[e]++; }\n }\n }\n \n // Restore best state\n asgn = best_asgn;\n for (int i = 0; i < N; i++) vr[i].clear();\n fill(vmx.begin(), vmx.end(), 0);\n for (int k = 0; k < K; k++) {\n vr[asgn[k]].push_back(k);\n vmx[asgn[k]] = max(vmx[asgn[k]], rsq[k][asgn[k]]);\n }\n for (int i = 0; i < N; i++) P[i] = calcP(vmx[i]);\n pcost = 0; for (int i = 0; i < N; i++) pcost += (long long)P[i] * P[i];\n \n // Limited vertex deactivation with SPH cost\n auto compute_sph = [&](const vector& P_arr) -> pair> {\n vector act;\n for (int i = 0; i < N; i++) if (P_arr[i] > 0) act.push_back(i);\n if (act.empty()) return {0, vector(M, 0)};\n \n vector B(M, 0);\n vector in_tree(N, false);\n in_tree[0] = true;\n set rem(act.begin(), act.end());\n rem.erase(0);\n long long ec = 0;\n \n while (!rem.empty()) {\n vector d(N, LLONG_MAX);\n vector prev(N, -1), preve(N, -1);\n priority_queue, vector>, greater<>> pq2;\n for (int v = 0; v < N; v++) if (in_tree[v]) { d[v] = 0; pq2.push({0, v}); }\n while (!pq2.empty()) {\n auto [dd, u] = pq2.top(); pq2.pop();\n if (dd > d[u]) continue;\n for (auto [v, e] : adj[u])\n if (d[u] + ew[e] < d[v]) {\n d[v] = d[u] + ew[e];\n prev[v] = u; preve[v] = e;\n pq2.push({d[v], v});\n }\n }\n long long bd = LLONG_MAX; int bt = -1;\n for (int t : rem) if (d[t] < bd) { bd = d[t]; bt = t; }\n int v = bt;\n while (v != -1 && !in_tree[v]) {\n B[preve[v]] = 1;\n in_tree[v] = true;\n v = prev[v];\n }\n ec += bd;\n rem.erase(bt);\n }\n return {ec, B};\n };\n \n // Try deactivating each non-zero vertex once\n for (int pass = 0; pass < 2; pass++) {\n bool improved = false;\n for (int v = 1; v < N; v++) {\n if (P[v] == 0 || vr[v].empty()) continue;\n \n // Find reassignment for each resident of v\n vector> reassigns;\n bool feasible = true;\n for (int k : vr[v]) {\n int best_nv = -1;\n for (int nv : clo[k]) {\n if (nv != v && P[nv] > 0) { best_nv = nv; break; }\n }\n if (best_nv == -1) { feasible = false; break; }\n reassigns.push_back({k, best_nv});\n }\n if (!feasible) continue;\n \n // Compute new P\n vector nP = P;\n vector nvmx = vmx;\n nP[v] = 0; nvmx[v] = 0;\n for (auto [k, nv] : reassigns)\n nvmx[nv] = max(nvmx[nv], rsq[k][nv]);\n for (int i = 0; i < N; i++) nP[i] = calcP(nvmx[i]);\n \n long long npc = 0;\n for (int i = 0; i < N; i++) npc += (long long)nP[i] * nP[i];\n \n auto [nec, nB] = compute_sph(nP);\n \n long long old_total;\n { auto [oec, oB] = compute_sph(P); old_total = pcost + oec; }\n \n if (npc + nec < old_total) {\n for (auto [k, nv] : reassigns) {\n auto it = find(vr[asgn[k]].begin(), vr[asgn[k]].end(), k);\n *it = vr[asgn[k]].back(); vr[asgn[k]].pop_back();\n asgn[k] = nv;\n vr[nv].push_back(k);\n }\n vr[v].clear();\n P = nP; vmx = nvmx; pcost = npc;\n improved = true;\n }\n }\n if (!improved) break;\n }\n \n // Final SPH tree\n auto [final_ec, final_B] = compute_sph(P);\n \n for (int i = 0; i < N; i++) cout << P[i] << \" \\n\"[i == N - 1];\n for (int j = 0; j < M; j++) cout << final_B[j] << \" \\n\"[j == M - 1];\n \n return 0;\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint grid[N][N];\nvector> swaps;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++)\n for (int y = 0; y <= x; y++)\n cin >> grid[x][y];\n \n auto siftDown = [&](int x, int y) {\n while (x < N - 1) {\n int lv = grid[x+1][y], rv = grid[x+1][y+1], cv = grid[x][y];\n if (cv <= lv && cv <= rv) break;\n if (lv <= rv) {\n swap(grid[x][y], grid[x+1][y]);\n swaps.push_back({x, y, x+1, y});\n x++;\n } else {\n swap(grid[x][y], grid[x+1][y+1]);\n swaps.push_back({x, y, x+1, y+1});\n x++; y++;\n }\n if (swaps.size() >= 9999) return;\n }\n };\n \n // Heapify: bottom to top, full sift-down\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n siftDown(x, y);\n if (swaps.size() >= 9999) goto done;\n }\n }\n \n // Iteratively fix remaining violations\n // (caused by triangular grid's dual-parent structure)\n for (int iter = 0; iter < 500; iter++) {\n bool any = false;\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n if (grid[x][y] > grid[x+1][y] || grid[x][y] > grid[x+1][y+1]) {\n any = true;\n // One-step fix: swap parent with smaller child\n if (grid[x+1][y] <= grid[x+1][y+1]) {\n swap(grid[x][y], grid[x+1][y]);\n swaps.push_back({x, y, x+1, y});\n } else {\n swap(grid[x][y], grid[x+1][y+1]);\n swaps.push_back({x, y, x+1, y+1});\n }\n if (swaps.size() >= 9999) goto done;\n }\n }\n }\n if (!any) break;\n }\n \ndone:\n cout << swaps.size() << \"\\n\";\n for (auto& s : swaps)\n cout << s[0] << \" \" << s[1] << \" \" << s[2] << \" \" << s[3] << \"\\n\";\n \n return 0;\n}","toyota2023summer-final":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int D, N;\n cin >> D >> N;\n \n vector> is_obstacle(D, vector(D, false));\n for (int i = 0; i < N; i++) {\n int ri, rj;\n cin >> ri >> rj;\n is_obstacle[ri][rj] = true;\n }\n \n int entrance_i = 0, entrance_j = (D - 1) / 2;\n \n // Precompute distances from entrance\n vector> dist(D, vector(D, -1));\n queue> q;\n q.push({entrance_i, entrance_j});\n dist[entrance_i][entrance_j] = 0;\n \n const int di[] = {-1, 1, 0, 0};\n const int dj[] = {0, 0, -1, 1};\n \n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && dist[ni][nj] == -1 && !is_obstacle[ni][nj]) {\n dist[ni][nj] = dist[i][j] + 1;\n q.push({ni, nj});\n }\n }\n }\n \n int M = 0;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (!(i == entrance_i && j == entrance_j) && !is_obstacle[i][j])\n M++;\n \n struct Cell {\n int i, j;\n int dist;\n int current_degree;\n bool removed;\n int rank;\n };\n \n vector C(M);\n vector> cell_index(D, vector(D, -1));\n \n int idx = 0;\n for (int i = 0; i < D; i++) {\n for (int j = 0; j < D; j++) {\n if (!(i == entrance_i && j == entrance_j) && !is_obstacle[i][j]) {\n C[idx].i = i;\n C[idx].j = j;\n C[idx].dist = dist[i][j];\n C[idx].removed = false;\n cell_index[i][j] = idx;\n idx++;\n }\n }\n }\n \n // Calculate internal degrees (only counting valid container neighbors)\n for (int k = 0; k < M; k++) {\n C[k].current_degree = 0;\n for (int d = 0; d < 4; d++) {\n int ni = C[k].i + di[d], nj = C[k].j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && cell_index[ni][nj] != -1) {\n C[k].current_degree++;\n }\n }\n }\n \n // Peeling algorithm to assign topological removal ranks\n priority_queue, vector>, greater>> pq;\n \n for (int k = 0; k < M; k++) {\n if (C[k].current_degree <= 1) {\n pq.push({C[k].dist, C[k].i, C[k].j, k});\n }\n }\n \n int current_rank = 0;\n int removed_count = 0;\n \n while (removed_count < M) {\n if (pq.empty()) {\n // Break cycle by picking the remaining cell closest to the entrance\n int best_k = -1;\n for (int k = 0; k < M; k++) {\n if (!C[k].removed) {\n if (best_k == -1 || tie(C[k].dist, C[k].i, C[k].j) < tie(C[best_k].dist, C[best_k].i, C[best_k].j)) {\n best_k = k;\n }\n }\n }\n pq.push({C[best_k].dist, C[best_k].i, C[best_k].j, best_k});\n }\n \n auto [d, i, j, k] = pq.top();\n pq.pop();\n \n if (C[k].removed) continue;\n \n C[k].rank = current_rank++;\n C[k].removed = true;\n removed_count++;\n \n for (int dd = 0; dd < 4; dd++) {\n int ni = C[k].i + di[dd], nj = C[k].j + dj[dd];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && cell_index[ni][nj] != -1) {\n int nk = cell_index[ni][nj];\n if (!C[nk].removed) {\n C[nk].current_degree--;\n if (C[nk].current_degree <= 1) {\n pq.push({C[nk].dist, C[nk].i, C[nk].j, nk});\n }\n }\n }\n }\n }\n \n // Placement phase\n set> available_cells; // (Rank, index in C)\n for (int k = 0; k < M; k++) {\n available_cells.insert({C[k].rank, k});\n }\n \n vector> container_at(D, vector(D, -1));\n vector> is_empty(D, vector(D, true));\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (is_obstacle[i][j]) is_empty[i][j] = false;\n \n auto is_safe = [&](int exclude_i, int exclude_j) {\n vector> reachable(D, vector(D, false));\n queue> bfs_q;\n bfs_q.push({entrance_i, entrance_j});\n reachable[entrance_i][entrance_j] = true;\n int visited_count = 1; // includes entrance\n \n while (!bfs_q.empty()) {\n auto [i, j] = bfs_q.front(); bfs_q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && !reachable[ni][nj] && is_empty[ni][nj] && !(ni == exclude_i && nj == exclude_j)) {\n reachable[ni][nj] = true;\n bfs_q.push({ni, nj});\n visited_count++;\n }\n }\n }\n return visited_count == (int)available_cells.size();\n };\n \n for (int d = 0; d < M; d++) {\n int t; cin >> t;\n \n vector safe_indices;\n for (auto& p : available_cells) {\n int k = p.second;\n if (is_safe(C[k].i, C[k].j)) {\n safe_indices.push_back(k);\n }\n }\n \n int best_k = -1;\n int best_diff = M + 1;\n \n auto it = lower_bound(safe_indices.begin(), safe_indices.end(), t, [&](int k, int val) {\n return C[k].rank < val;\n });\n \n if (it != safe_indices.end()) {\n int diff = abs(C[*it].rank - t);\n if (diff < best_diff) {\n best_diff = diff;\n best_k = *it;\n } else if (diff == best_diff && C[*it].rank > C[best_k].rank) {\n best_k = *it;\n }\n }\n if (it != safe_indices.begin()) {\n --it;\n int diff = abs(C[*it].rank - t);\n if (diff < best_diff) {\n best_diff = diff;\n best_k = *it;\n } else if (diff == best_diff && C[*it].rank > C[best_k].rank) {\n best_k = *it;\n }\n }\n \n available_cells.erase({C[best_k].rank, best_k});\n cout << C[best_k].i << \" \" << C[best_k].j << endl;\n container_at[C[best_k].i][C[best_k].j] = t;\n is_empty[C[best_k].i][C[best_k].j] = false;\n }\n \n // Transport phase: Greedily remove the smallest numbered accessible container\n for (int iter = 0; iter < M; iter++) {\n vector> reachable(D, vector(D, false));\n queue> bfs_q;\n bfs_q.push({entrance_i, entrance_j});\n reachable[entrance_i][entrance_j] = true;\n \n while (!bfs_q.empty()) {\n auto [i, j] = bfs_q.front(); bfs_q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && !reachable[ni][nj] && is_empty[ni][nj]) {\n reachable[ni][nj] = true;\n bfs_q.push({ni, nj});\n }\n }\n }\n \n int min_t = M + 1, min_i = -1, min_j = -1;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (container_at[i][j] >= 0) {\n bool acc = false;\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && is_empty[ni][nj] && reachable[ni][nj]) {\n acc = true;\n break;\n }\n }\n if (acc && container_at[i][j] < min_t) {\n min_t = container_at[i][j];\n min_i = i; min_j = j;\n }\n }\n \n cout << min_i << \" \" << min_j << endl;\n is_empty[min_i][min_j] = true;\n container_at[min_i][min_j] = -1;\n }\n \n return 0;\n}","ahc024":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 50, M = 100;\nconst int dx[] = {0, 0, 1, -1};\nconst int dy[] = {1, -1, 0, 0};\n\nint n, m;\nint grid[N][N], best_grid[N][N];\nint bestE = -1;\nint ac[M+1][M+1];\nbool is_req[M+1][M+1];\nint color_cnt[M+1];\nmt19937 rng(42);\n\nint vis[N][N];\nint timer = 0;\n\nbool ok(int x, int y) { return 0 <= x && x < n && 0 <= y && y < n; }\n\nvoid cadj() {\n memset(ac, 0, sizeof(ac));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) {\n if (j + 1 < n && grid[i][j] != grid[i][j+1])\n ac[min(grid[i][j], grid[i][j+1])][max(grid[i][j], grid[i][j+1])]++;\n if (i + 1 < n && grid[i][j] != grid[i+1][j])\n ac[min(grid[i][j], grid[i+1][j])][max(grid[i][j], grid[i+1][j])]++;\n if ((i == 0 || i == n - 1 || j == 0 || j == n - 1) && grid[i][j] != 0)\n ac[0][grid[i][j]]++;\n }\n}\n\nvoid creq() {\n memset(is_req, 0, sizeof(is_req));\n cadj();\n for (int a = 0; a <= m; a++)\n for (int b = a; b <= m; b++)\n if (ac[a][b] > 0) is_req[a][b] = true;\n}\n\nbool check_c_connect(int i, int j, int c) {\n if (color_cnt[c] == 1) return false;\n if (color_cnt[c] == 2) return true;\n \n vector> oc_neighs;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == c) oc_neighs.push_back({ni, nj});\n }\n if (oc_neighs.size() <= 1) return true;\n \n timer++;\n queue> q;\n q.push(oc_neighs[0]);\n vis[oc_neighs[0].first][oc_neighs[0].second] = timer;\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (ok(nx, ny) && vis[nx][ny] != timer && grid[nx][ny] == c && !(nx == i && ny == j)) {\n vis[nx][ny] = timer;\n q.push({nx, ny});\n }\n }\n }\n for (size_t k = 1; k < oc_neighs.size(); k++)\n if (vis[oc_neighs[k].first][oc_neighs[k].second] != timer) return false;\n return true;\n}\n\nbool check_0_connect(int i, int j) {\n vector> zero_neighs;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == 0) zero_neighs.push_back({ni, nj});\n }\n if (zero_neighs.empty()) return true;\n \n timer++;\n queue> q;\n q.push(zero_neighs[0]);\n vis[zero_neighs[0].first][zero_neighs[0].second] = timer;\n bool reached_bnd = (zero_neighs[0].first == 0 || zero_neighs[0].first == n - 1 || zero_neighs[0].second == 0 || zero_neighs[0].second == n - 1);\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (ok(nx, ny) && vis[nx][ny] != timer && grid[nx][ny] == 0 && !(nx == i && ny == j)) {\n vis[nx][ny] = timer;\n q.push({nx, ny});\n if (nx == 0 || nx == n - 1 || ny == 0 || ny == n - 1) reached_bnd = true;\n }\n }\n }\n if (!reached_bnd) return false;\n for (size_t k = 1; k < zero_neighs.size(); k++)\n if (vis[zero_neighs[k].first][zero_neighs[k].second] != timer) return false;\n return true;\n}\n\nbool is_valid_move(int i, int j, int nc) {\n int oc = grid[i][j];\n if (oc == nc) return false;\n \n pair deltas[10];\n int d_vals[10] = {0};\n int d_cnt = 0;\n \n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj)) {\n int nb = grid[ni][nj];\n if (oc != nb) {\n pair p = {min(oc, nb), max(oc, nb)};\n bool found = false;\n for(int k=0; k p = {min(nc, nb), max(nc, nb)};\n bool found = false;\n for(int k=0; k p = {0, oc};\n bool found = false;\n for(int k=0; k p = {0, nc};\n bool found = false;\n for(int k=0; k 0 && !is_req[deltas[k].first][deltas[k].second]) return false;\n if (ncnt <= 0 && is_req[deltas[k].first][deltas[k].second]) return false;\n }\n \n if (oc != 0) { if (!check_c_connect(i, j, oc)) return false; }\n else { if (!check_0_connect(i, j)) return false; }\n \n if (nc != 0) {\n bool has_nc = false;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == nc) has_nc = true;\n }\n if (!has_nc) return false;\n } else {\n bool adj_to_0 = is_bnd;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == 0) adj_to_0 = true;\n }\n if (!adj_to_0) return false;\n }\n return true;\n}\n\nvoid apply_move(int i, int j, int nc) {\n int oc = grid[i][j];\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj)) {\n int nb = grid[ni][nj];\n if (oc != nb) ac[min(oc, nb)][max(oc, nb)]--;\n if (nc != nb) ac[min(nc, nb)][max(nc, nb)]++;\n }\n }\n if (i == 0 || i == n - 1 || j == 0 || j == n - 1) {\n if (oc != 0) ac[0][oc]--;\n if (nc != 0) ac[0][nc]++;\n }\n grid[i][j] = nc;\n color_cnt[oc]--;\n color_cnt[nc]++;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> n >> m;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) cin >> grid[i][j];\n \n memset(color_cnt, 0, sizeof(color_cnt));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) color_cnt[grid[i][j]]++;\n \n creq();\n \n int E = 0;\n bestE = E;\n memcpy(best_grid, grid, sizeof(grid));\n \n auto start = chrono::high_resolution_clock::now();\n \n uniform_int_distribution cell_dist(0, n * n - 1);\n uniform_real_distribution prob_dist(0.0, 1.0);\n double T = 3.0;\n double prob_accept_worse = exp(-1.0 / T);\n \n long long iterations = 0;\n while (true) {\n if (iterations % 1000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 1.8) break;\n T = max(0.01, 3.0 * (1.0 - elapsed / 1.8));\n prob_accept_worse = exp(-1.0 / T);\n }\n iterations++;\n \n int idx = cell_dist(rng);\n int i = idx / n;\n int j = idx % n;\n int oc = grid[i][j];\n \n int options[5];\n int opt_cnt = 0;\n if (oc != 0) options[opt_cnt++] = 0;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] != oc) {\n bool already = false;\n for(int k=0; k opt_dist(0, opt_cnt - 1);\n int nc = options[opt_dist(rng)];\n \n if (is_valid_move(i, j, nc)) {\n int delta_E = (nc == 0 ? 1 : (oc == 0 ? -1 : 0));\n if (delta_E >= 0 || prob_dist(rng) < prob_accept_worse) {\n apply_move(i, j, nc);\n E += delta_E;\n if (E > bestE) {\n bestE = E;\n memcpy(best_grid, grid, sizeof(grid));\n }\n }\n }\n }\n \n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << best_grid[i][j];\n if (j < n - 1) cout << \" \";\n }\n cout << \"\\n\";\n }\n return 0;\n}","ahc025":"#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, D, Q;\nint qc = 0;\nint cmp[105][105];\n\nchar do_query(int a, int b) {\n if (cmp[a][b] == -1) return '<';\n if (cmp[a][b] == 1) return '>';\n if (cmp[a][b] == 2) return '=';\n if (qc >= Q) return '=';\n qc++;\n cout << \"1 1 \" << a << \" \" << b << endl;\n char res; cin >> res;\n if (res == '<') { cmp[a][b] = -1; cmp[b][a] = 1; }\n else if (res == '>') { cmp[a][b] = 1; cmp[b][a] = -1; }\n else if (res == '=') { cmp[a][b] = 2; cmp[b][a] = 2; }\n return res;\n}\n\nchar do_query_sets(const vector& L, const vector& R) {\n if (L.empty() || R.empty()) return '=';\n cout << L.size() << \" \" << R.size();\n for (int x : L) cout << \" \" << x;\n for (int x : R) cout << \" \" << x;\n cout << endl;\n char res; cin >> res;\n qc++;\n return res;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n vector items(N);\n for (int i = 0; i < N; i++) items[i] = i;\n \n // Phase 1: Heap Sort to find heavy items efficiently\n for (int i = 1; i < N && qc < Q; i++) {\n int cur = i;\n while (cur > 0 && qc < Q) {\n int par = (cur - 1) / 2;\n char res = do_query(items[cur], items[par]);\n if (res == '>') { swap(items[cur], items[par]); cur = par; }\n else break;\n }\n }\n for (int i = N - 1; i > 0 && qc < Q; i--) {\n swap(items[0], items[i]);\n int cur = 0;\n while (qc < Q) {\n int l = 2 * cur + 1, r = 2 * cur + 2, largest = cur;\n if (l < i) { if (do_query(items[l], items[largest]) == '>') largest = l; }\n if (r < i) { if (do_query(items[r], items[largest]) == '>') largest = r; }\n if (largest != cur) { swap(items[cur], items[largest]); cur = largest; }\n else break;\n }\n }\n \n // Phase 2: Initial LPT Assignment\n vector ew(N);\n double cur_ew = 0;\n for (int i = 0; i < N; i++) { cur_ew += 1.0 / (N - i); ew[items[i]] = cur_ew; }\n \n vector sum_g(D, 0);\n vector> group_items(D);\n vector asgn(N);\n \n for (int i = N - 1; i >= 0; i--) {\n int item = items[i], mg = 0;\n for (int g = 1; g < D; g++) if (sum_g[g] < sum_g[mg]) mg = g;\n asgn[item] = mg; sum_g[mg] += ew[item]; group_items[mg].push_back(item);\n }\n \n // Phase 3: Exact Local Search with Real Queries\n while (qc < Q) {\n int A = 0; bool abort = false;\n for (int g = 1; g < D; g++) {\n if (qc >= Q) { abort = true; break; }\n if (do_query_sets(group_items[g], group_items[A]) == '>') A = g;\n }\n if (abort) break;\n \n int B = 0;\n for (int g = 1; g < D; g++) {\n if (qc >= Q) { abort = true; break; }\n if (do_query_sets(group_items[g], group_items[B]) == '<') B = g;\n }\n if (abort) break;\n if (A == B) break;\n \n vector& items_A = group_items[A];\n vector& items_B = group_items[B];\n bool improved = false;\n \n // Try single moves from A to B\n sort(items_A.begin(), items_A.end(), [&](int x, int y){ return ew[x] < ew[y]; });\n for (int idx = 0; idx < min(5, (int)items_A.size()); idx++) {\n if ((int)items_A.size() <= 1) break;\n int i = items_A[idx];\n vector L = items_B;\n vector R = items_A;\n R.erase(find(R.begin(), R.end(), i));\n \n if (qc >= Q) break;\n char res = do_query_sets(L, R);\n if (res == '<' || res == '=') {\n items_A.erase(find(items_A.begin(), items_A.end(), i));\n items_B.push_back(i); asgn[i] = B;\n sum_g[A] -= ew[i]; sum_g[B] += ew[i];\n improved = true; break;\n }\n }\n \n if (!improved) {\n // Try swaps between A and B\n if (items_A.size() > 1 && items_B.size() > 1) {\n sort(items_A.begin(), items_A.end(), [&](int x, int y){ return ew[x] > ew[y]; });\n sort(items_B.begin(), items_B.end(), [&](int x, int y){ return ew[x] < ew[y]; });\n for (int idx_i = 0; idx_i < min(5, (int)items_A.size()) && !improved; idx_i++) {\n for (int idx_j = 0; idx_j < min(5, (int)items_B.size()); idx_j++) {\n int i = items_A[idx_i], j = items_B[idx_j];\n if (cmp[i][j] != 1) { if (qc >= Q) { abort = true; break; } if (do_query(i, j) != '>') continue; }\n \n vector L = items_B; L.erase(find(L.begin(), L.end(), j));\n vector R = items_A; R.erase(find(R.begin(), R.end(), i));\n \n if (qc >= Q) { abort = true; break; }\n char res = do_query_sets(L, R);\n if (res == '<' || res == '=') {\n items_A.erase(find(items_A.begin(), items_A.end(), i));\n items_A.push_back(j);\n items_B.erase(find(items_B.begin(), items_B.end(), j));\n items_B.push_back(i);\n asgn[i] = B; asgn[j] = A;\n sum_g[A] += ew[j] - ew[i]; sum_g[B] += ew[i] - ew[j];\n improved = true; break;\n }\n }\n if (abort) break;\n }\n }\n }\n if (!improved || abort) break;\n }\n \n // Waste remaining queries safely\n while (qc < Q) { cout << \"1 1 0 1\" << endl; char res; cin >> res; qc++; }\n \n for (int i = 0; i < N; i++) cout << asgn[i] << \" \\n\"[i==N-1];\n return 0;\n}","ahc026":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n for (int i = 0; i < m; i++) {\n stacks[i].resize(n / m);\n for (int j = 0; j < n / m; j++)\n cin >> stacks[i][j];\n }\n \n vector box_stack(n + 1), box_pos(n + 1);\n for (int i = 0; i < m; i++)\n for (int j = 0; j < (int)stacks[i].size(); j++) {\n box_stack[stacks[i][j]] = i;\n box_pos[stacks[i][j]] = j;\n }\n \n vector> operations;\n const int INV_COST = 4;\n const int EMPTY_COST = 5;\n \n for (int v = 1; v <= n; v++) {\n int sid = box_stack[v], pos = box_pos[v];\n int k = (int)stacks[sid].size() - 1 - pos;\n \n if (k == 0) {\n operations.push_back({v, 0});\n stacks[sid].pop_back();\n continue;\n }\n \n vector A(stacks[sid].begin() + pos + 1, stacks[sid].end());\n \n vector dp(k + 1, INT_MAX);\n vector par(k + 1);\n dp[0] = 0;\n \n for (int i = 1; i <= k; i++) {\n for (int j = 1; j <= i; j++) {\n int int_inv = 0;\n for (int s = i - j; s < i; s++)\n for (int t = s + 1; t < i; t++)\n if (A[s] < A[t]) int_inv++;\n \n int best_dest_cost = INT_MAX;\n for (int d = 0; d < m; d++) {\n if (d == sid) continue;\n int ext_inv = 0, empty_pen = 0;\n if (stacks[d].empty()) empty_pen = EMPTY_COST;\n else {\n int top_val = stacks[d].back();\n for (int s = i - j; s < i; s++)\n if (A[s] > top_val) ext_inv++;\n }\n best_dest_cost = min(best_dest_cost, INV_COST * (int_inv + ext_inv) + empty_pen);\n }\n \n int cost = dp[i - j] + (j + 1) + best_dest_cost;\n if (cost < dp[i]) { dp[i] = cost; par[i] = j; }\n }\n }\n \n vector chunks;\n for (int cur = k; cur > 0; cur -= par[cur])\n chunks.push_back(par[cur]);\n \n for (int cs : chunks) {\n int off = stacks[sid].size() - cs;\n int best_dest = -1, best_priority = 4, best_subscore = INT_MAX;\n \n for (int d = 0; d < m; d++) {\n if (d == sid) continue;\n int ext_inv = 0;\n bool is_empty = stacks[d].empty();\n int top_val = is_empty ? 0 : stacks[d].back();\n \n if (!is_empty)\n for (int s = off; s < (int)stacks[sid].size(); s++)\n if (stacks[sid][s] > top_val) ext_inv++;\n \n int priority, subscore;\n if (ext_inv == 0 && !is_empty) { priority = 1; subscore = top_val; }\n else if (ext_inv == 0) { priority = 2; subscore = 0; }\n else { priority = 3; subscore = ext_inv * 1000 - top_val; }\n \n if (priority < best_priority || (priority == best_priority && subscore < best_subscore)) {\n best_priority = priority; best_subscore = subscore; best_dest = d;\n }\n }\n \n if (best_dest == -1) best_dest = (sid + 1) % m;\n \n int u = stacks[sid][off];\n operations.push_back({u, best_dest + 1});\n \n vector moved(stacks[sid].begin() + off, stacks[sid].end());\n stacks[sid].resize(off);\n stacks[best_dest].insert(stacks[best_dest].end(), moved.begin(), moved.end());\n \n for (int j = 0; j < (int)moved.size(); j++) {\n box_stack[moved[j]] = best_dest;\n box_pos[moved[j]] = stacks[best_dest].size() - moved.size() + j;\n }\n }\n \n operations.push_back({v, 0});\n stacks[sid].pop_back();\n }\n \n for (auto& op : operations)\n cout << op.first << \" \" << op.second << endl;\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\nchar dir_char[] = {'R', 'D', 'L', 'U'};\n\nbool can_move(int i, int j, int dir) {\n int ni = i + dx[dir], nj = j + dy[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0 && v[i][j] == '1') return false;\n if (dir == 1 && h[i][j] == '1') return false;\n if (dir == 2 && v[i][nj] == '1') return false;\n if (dir == 3 && h[ni][j] == '1') return false;\n return true;\n}\n\nint get_dir(char c) {\n if (c == 'R') return 0;\n if (c == 'D') return 1;\n if (c == 'L') return 2;\n return 3; // 'U'\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1); v.resize(N); d.resize(N, vector(N));\n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> d[i][j];\n \n int total_cells = N * N;\n vector all_dist(total_cells * total_cells, -1);\n vector all_prev_dir(total_cells * total_cells, -1);\n\n auto get_dist = [&](int si, int sj, int ei, int ej) -> int& {\n return all_dist[(si * N + sj) * total_cells + (ei * N + ej)];\n };\n auto get_prev = [&](int si, int sj, int ei, int ej) -> int& {\n return all_prev_dir[(si * N + sj) * total_cells + (ei * N + ej)];\n };\n\n // Precompute BFS from all cells\n for (int si = 0; si < N; ++si) {\n for (int sj = 0; sj < N; ++sj) {\n queue> q;\n get_dist(si, sj, si, sj) = 0;\n q.push({si, sj});\n while (!q.empty()) {\n auto [ci, cj] = q.front(); q.pop();\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(ci, cj, dir)) continue;\n int ni = ci + dx[dir], nj = cj + dy[dir];\n if (get_dist(si, sj, ni, nj) == -1) { \n get_dist(si, sj, ni, nj) = get_dist(si, sj, ci, cj) + 1; \n get_prev(si, sj, ni, nj) = (dir + 2) % 4; // Direction to go BACK\n q.push({ni, nj}); \n }\n }\n }\n }\n }\n\n auto get_path = [&](int si, int sj, int ei, int ej) -> string {\n string path_back;\n int ci = ei, cj = ej;\n while (ci != si || cj != sj) {\n int dir = get_prev(si, sj, ci, cj);\n path_back += dir_char[dir];\n ci += dx[dir];\n cj += dy[dir];\n }\n string path_to;\n for (int k = (int)path_back.size() - 1; k >= 0; --k) {\n char c = path_back[k];\n if (c == 'R') path_to += 'L';\n else if (c == 'D') path_to += 'U';\n else if (c == 'L') path_to += 'R';\n else path_to += 'D';\n }\n return path_to;\n };\n \n // Build DFS tour\n string base_tour;\n base_tour.reserve(N * N * 2);\n vector> visited(N, vector(N, false));\n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(i, j, dir)) continue;\n int ni = i + dx[dir], nj = j + dy[dir];\n if (!visited[ni][nj]) {\n base_tour += dir_char[dir];\n dfs(ni, nj);\n base_tour += dir_char[(dir + 2) % 4];\n }\n }\n };\n dfs(0, 0);\n \n int L = base_tour.size();\n vector> positions(L + 1);\n positions[0] = {0, 0};\n for (int t = 0; t < L; t++) {\n int dir = get_dir(base_tour[t]);\n positions[t+1] = {positions[t].first + dx[dir], positions[t].second + dy[dir]};\n }\n \n // Find closest insertion point on base tour for detours\n vector best_step(N * N, 0), best_cost(N * N, INT_MAX);\n for (int t = 0; t < L; t++) {\n auto [pi, pj] = positions[t];\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (pi == i && pj == j) continue;\n int cost = 2 * get_dist(pi, pj, i, j);\n if (cost < best_cost[i * N + j]) { best_cost[i * N + j] = cost; best_step[i * N + j] = t; }\n }\n }\n \n // Correctly calculate visits per cycle (t=0 to L-1)\n vector visit_count(N * N, 0);\n for (int t = 0; t < L; t++) { auto [i, j] = positions[t]; visit_count[i * N + j]++; }\n \n double S_factor = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) S_factor += (double)d[i][j] / visit_count[i * N + j];\n \n using Cell = tuple;\n priority_queue pq;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (i == 0 && j == 0) continue;\n int k = visit_count[i * N + j], cost = best_cost[i * N + j];\n if (cost == 0 || cost >= INT_MAX) continue;\n pq.push({(double)d[i][j] / ((long long)k * (k + 1)) / cost, i, j});\n }\n \n struct Detour { int step; int i; int j; };\n vector detours;\n int current_L = L;\n \n while (!pq.empty() && current_L < 100000) {\n auto [p, i, j] = pq.top(); pq.pop();\n int k = visit_count[i * N + j], cost = best_cost[i * N + j];\n if (cost >= INT_MAX) continue;\n double new_p = (double)d[i][j] / ((long long)k * (k + 1)) / cost;\n if (abs(new_p - p) > 1e-9) { pq.push({new_p, i, j}); continue; }\n \n if (current_L + cost > 100000) continue;\n \n // Benefit-cost check\n double benefit = (double)d[i][j] * (current_L + cost) / ((long long)k * (k + 1));\n double detour_cost_val = (double)cost * S_factor;\n if (benefit <= detour_cost_val) break; // No more beneficial detours possible\n \n int step = best_step[i * N + j];\n \n detours.push_back({step, i, j});\n current_L += cost;\n S_factor -= (double)d[i][j] / k;\n visit_count[i * N + j]++;\n S_factor += (double)d[i][j] / visit_count[i * N + j];\n int nk = visit_count[i * N + j];\n pq.push({(double)d[i][j] / ((long long)nk * (nk + 1)) / cost, i, j});\n }\n \n sort(detours.begin(), detours.end(), [](const auto& a, const auto& b) { return a.step < b.step; });\n \n string result;\n result.reserve(100000);\n int detour_idx = 0;\n for (int t = 0; t <= L; t++) {\n while (detour_idx < (int)detours.size() && detours[detour_idx].step == t) {\n auto [step, i, j] = detours[detour_idx];\n auto [pi, pj] = positions[step];\n string path_to = get_path(pi, pj, i, j);\n string path_back;\n for (int k2 = (int)path_to.size() - 1; k2 >= 0; k2--) {\n char c = path_to[k2];\n path_back += (c == 'R') ? 'L' : (c == 'D') ? 'U' : (c == 'L') ? 'R' : 'D';\n }\n result += path_to;\n result += path_back;\n detour_idx++;\n }\n if (t < L) result += base_tour[t];\n }\n \n cout << result << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint main(){\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N,M; cin>>N>>M;\n int si,sj; cin>>si>>sj;\n vector A(N);\n for(int i=0;i>A[i];\n vector t(M);\n for(int i=0;i>t[i];\n vector>> cp(26);\n for(int i=0;i> cd(26,vector(26,0));\n for(int c1=0;c1<26;c1++) for(int c2=0;c2<26;c2++){\n int md=INT_MAX;\n for(auto&[i1,j1]:cp[c1]) for(auto&[i2,j2]:cp[c2]) md=min(md,abs(i1-i2)+abs(j1-j2));\n cd[c1][c2]=md;\n }\n vector> ov(M,vector(M,0));\n for(int i=0;i=1;l--){ bool ok=true; for(int k=0;k> fail(M,vector(6,0));\n for(int k=0;k0&&t[k][f]!=t[k][i-1]) f=fail[k][f]; if(t[k][f]==t[k][i-1]) f++; fail[k][i]=f;}\n auto buildS=[&](const vector&o)->string{ string s=t[o[0]];\n for(int i=1;i<(int)o.size();i++){ int mx=min(5,(int)s.size()),a=0;\n for(int l=mx;l>=1;l--){ bool ok=true; for(int k=0;k&o)->int{ int tv=0; for(int i=1;i<(int)o.size();i++) tv+=ov[o[i-1]][o[i]]; return tv;};\n mt19937 rng(42);\n auto greedyR=[&](int st,unsigned seed)->vector{ mt19937 lr(seed); vectoro; o.push_back(st);\n vectoru(M,false); u[st]=true; for(int s=1;sc;\n for(int j=0;jbo){bo=ov[l][j];c.clear();c.push_back(j);}\n else if(ov[l][j]==bo) c.push_back(j);} o.push_back(c[lr()%c.size()]); u[o.back()]=true;} return o;};\n auto twoOpt=[&](vectoro)->vector{ bool imp=true; while(imp){ imp=false;\n for(int i=0;i0){os+=ov[o[i-1]][o[i]];ns+=ov[o[i-1]][o[i+1]];}\n os+=ov[o[i]][o[i+1]]; ns+=ov[o[i+1]][o[i]]; if(i+2os){swap(o[i],o[i+1]);imp=true;}}} return o;};\n auto orOpt=[&](vectoro)->vector{ for(int it=0;it<10;it++){ bool imp=false;\n for(int i=0;i0) rd-=ov[o[i-1]][w]; if(i0&&iint{return(k0)?gr(j-1):-1,D=(jbd){bd=rd+id;bk=j;}}\n if(bk!=i){ vectorrm; for(int k=0;ko,unsigned seed)->vector{ int curOv=totalOv(o); int bestOv=curOv; auto bestO=o;\n mt19937 saRng(seed); uniform_int_distributiondistI(0,M-1); uniform_real_distributiondistD(0.0,1.0);\n double temp=3.0; for(int it=0;it<300000;it++){ temp*=0.99998;\n if(saRng()%3==0){ int i=distI(saRng),j=distI(saRng); if(i==j) continue; int w=o[i],rd=0;\n if(i>0) rd-=ov[o[i-1]][w]; if(i0&&iint{return(k0)?gr(j-1):-1,D=(j0||distD(saRng)bestOv){bestOv=curOv;bestO=o;}}}\n else{ int i=distI(saRng),j=distI(saRng); if(i==j) continue; if(i>j) swap(i,j); int delta=0;\n if(j==i+1){ if(i>0){delta-=ov[o[i-1]][o[i]];delta+=ov[o[i-1]][o[j]];}\n delta-=ov[o[i]][o[j]]; delta+=ov[o[j]][o[i]]; if(j+10){delta-=ov[o[i-1]][o[i]];delta+=ov[o[i-1]][o[j]];}\n if(i+10){delta-=ov[o[j-1]][o[j]];delta+=ov[o[j-1]][o[i]];}\n if(j+10||distD(saRng)bestOv){bestOv=curOv;bestO=o;}}}} return bestO;};\n const int INF=1e9;\n auto dpStep=[&](const vector&cur, vector& nx, char c){ \n fill(nx.begin(), nx.end(), INF); int ci=c-'A';\n for(int q=0;q<225;q++){ if(cur[q]>=INF) continue; int qi=q/15,qj=q%15;\n for(auto&[pi,pj]:cp[ci]){ int p=pi*15+pj; int nc=cur[q]+abs(pi-qi)+abs(pj-qj)+1; if(ncstring{ \n vectorcur(225,INF), nx(225); cur[si*15+sj]=0; string S; vectorused(M,false);\n if(forceFirst>=0){ for(char c:t[forceFirst]) { dpStep(cur, nx, c); swap(cur, nx); } S+=t[forceFirst]; used[forceFirst]=true;}\n for(int step=(forceFirst>=0?1:0);step>cands;\n for(int j=0;j=1;l--){ bool ok=true; for(int k=0;kbestNx(225); string bestExt;\n for(int k=0;k=1;l--){ bool ok=true; for(int kk=0;kkstring{ vectorml(M,0); vectormatched(M,false); int nm=0;\n string S; int ci=si,cj=sj; while(nm0&&t[k][l]!=('A'+c)) l=fail[k][l]; if(t[k][l]==('A'+c)) l++;\n if(l==5) comp++; else if(l>ml[k]) adv+=(l-ml[k]);}\n double score=comp*w1+adv*w2-md*w3; if(score>bscore){bscore=score;bchar=c;bpi=pi;bpj=pj;}}\n S+=('A'+bchar); ci=bpi; cj=bpj;\n for(int k=0;k0&&t[k][l]!=('A'+bchar)) l=fail[k][l]; if(t[k][l]==('A'+bchar)) l++; ml[k]=l;\n if(l==5){matched[k]=true;nm++;}}} return S;};\n auto dpCharGreedy=[&]()->string{ \n vectorcur(225,INF), nx(225), bestNx(225); cur[si*15+sj]=0; string S;\n vectorml(M,0); vectormatched(M,false); int nm=0;\n while(nm0&&t[k][l]!=('A'+c)) l=fail[k][l]; if(t[k][l]==('A'+c)) l++;\n if(l==5) comp++; else if(l>ml[k]) adv+=(l-ml[k]);}\n bool better=false; if(comp>bestComp) better=true; else if(comp==bestComp){if(costbestAdv) better=true;}\n if(better){bestComp=comp;bestAdv=adv;bestCost=cost;bchar=c;swap(bestNx,nx);}}\n S+=('A'+bchar); swap(cur,bestNx);\n for(int k=0;k0&&t[k][l]!=('A'+bchar)) l=fail[k][l]; if(t[k][l]==('A'+bchar)) l++; ml[k]=l;\n if(l==5){matched[k]=true;nm++;}}} return S;};\n vectorcandidates; vector>>cs;\n for(int s=0;sint{ int L=s.size(); vectorcur(225,INF), nx(225); cur[si*15+sj]=0;\n for(int i=0;i>>dp(L+1,vector>(225,{INF,-1})); dp[0][si*15+sj]={0,-1};\n for(int i=0;i=INF) continue; int qi=q/15,qj=q%15;\n for(auto&[pi,pj]:cp[ci]){ int p=pi*15+pj; int nc=dp[i][q].first+abs(pi-qi)+abs(pj-qj)+1;\n if(ncpp(L); int cr=be; for(int i=L-1;i>=0;i--){pp[i]=cr;cr=dp[i+1][cr].second;}\n for(int i=0;i\nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nvector max_di, max_dj;\nvector>> positions;\nvector>>> pos_cells;\nvector>> cell_pos;\nint known[25][25];\nint query_count = 0;\nvector> lw;\ndouble cov_val[25][25];\ndouble prob_oil_val[25][25];\n\nint drill_cell(int i, int j) {\n cout << \"q 1 \" << i << \" \" << j << endl;\n cout.flush();\n int v; cin >> v;\n known[i][j] = v;\n query_count++;\n return v;\n}\n\nint divine_cells(vector>& cells) {\n int k = cells.size();\n cout << \"q \" << k;\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << endl;\n cout.flush();\n int v; cin >> v;\n query_count++;\n return v;\n}\n\nbool submit_answer(vector>& cells) {\n sort(cells.begin(), cells.end());\n cells.erase(unique(cells.begin(), cells.end()), cells.end());\n cout << \"a \" << cells.size();\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << endl;\n cout.flush();\n int r; cin >> r;\n if (r == 0) query_count++; // Wrong answer costs 1 operation\n return r == 1;\n}\n\nvoid compute_prob_and_cov() {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n cov_val[i][j] = 0;\n prob_oil_val[i][j] = 1.0;\n }\n for (int k = 0; k < M; k++) {\n double mx = -1e9;\n for (auto& l : lw[k]) { if (l > mx) mx = l; }\n double total = 0;\n double wt_arr[600];\n for (int p = 0; p < (int)positions[k].size(); p++) {\n wt_arr[p] = exp(lw[k][p] - mx);\n total += wt_arr[p];\n }\n if (total < 1e-30) continue;\n for (int p = 0; p < (int)positions[k].size(); p++) wt_arr[p] /= total;\n \n double cc_arr[450];\n memset(cc_arr, 0, sizeof(double) * N * N);\n for (int p = 0; p < (int)positions[k].size(); p++) {\n double wt = wt_arr[p];\n for (auto& [ci, cj] : pos_cells[k][p]) cc_arr[ci * N + cj] += wt;\n }\n for (int idx = 0; idx < N * N; idx++) {\n cov_val[idx / N][idx % N] += cc_arr[idx];\n prob_oil_val[idx / N][idx % N] *= (1.0 - cc_arr[idx]);\n }\n }\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)\n prob_oil_val[i][j] = 1.0 - prob_oil_val[i][j];\n}\n\nvoid update_divine(const vector>& qcells, int obs) {\n int ksz = qcells.size();\n double sigma2 = ksz * eps * (1 - eps);\n \n bool in_Q[25][25];\n memset(in_Q, 0, sizeof(in_Q));\n for (auto& [i, j] : qcells) in_Q[i][j] = true;\n \n double S_Q = 0;\n for (auto& [i, j] : qcells) S_Q += cov_val[i][j];\n \n for (int k = 0; k < M; k++) {\n double mx = -1e9;\n for (auto& l : lw[k]) { if (l > mx) mx = l; }\n double total = 0;\n double wt_arr[600];\n for (int p = 0; p < (int)positions[k].size(); p++) {\n wt_arr[p] = exp(lw[k][p] - mx);\n total += wt_arr[p];\n }\n if (total < 1e-30) continue;\n for (int p = 0; p < (int)positions[k].size(); p++) wt_arr[p] /= total;\n \n int pos_cnt[600];\n double S_k = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) {\n int cnt = 0;\n for (auto& [ci, cj] : pos_cells[k][p]) {\n if (in_Q[ci][cj]) cnt++;\n }\n pos_cnt[p] = cnt;\n S_k += wt_arr[p] * cnt;\n }\n \n double S_others = S_Q - S_k;\n double var_others = max(S_others * 1.5, 0.5); // Fast and reasonable approximation\n \n double total_var = sigma2 + var_others * (1 - 2 * eps) * (1 - 2 * eps);\n if (total_var < sigma2) total_var = sigma2;\n \n for (int p = 0; p < (int)positions[k].size(); p++) {\n double ev = S_others + pos_cnt[p];\n double mean = ksz * eps + ev * (1 - 2 * eps);\n double diff = obs - mean;\n double penalty = diff * diff / (2 * total_var);\n if (penalty > 15.0) penalty = 15.0; // Cap to prevent catastrophic drops\n lw[k][p] += -penalty;\n }\n mx = -1e9;\n for (auto& l : lw[k]) { if (l > mx) mx = l; }\n if (mx > -1e8) {\n for (auto& l : lw[k]) l -= mx;\n }\n }\n compute_prob_and_cov();\n}\n\nvoid update_drill(int i, int j, int obs) {\n if (obs == 0) {\n for (int k = 0; k < M; k++) {\n for (int p : cell_pos[k][i * N + j]) {\n lw[k][p] = -1e9; \n }\n double mx = -1e9;\n for (auto& l : lw[k]) { if (l > mx) mx = l; }\n if (mx > -1e8) {\n for (auto& l : lw[k]) l -= mx;\n }\n }\n } else if (obs == M) {\n for (int k = 0; k < M; k++) {\n bool covers_arr[600];\n memset(covers_arr, 0, sizeof(bool) * positions[k].size());\n for (int p : cell_pos[k][i * N + j]) covers_arr[p] = true;\n for (int p = 0; p < (int)positions[k].size(); p++) {\n if (!covers_arr[p]) lw[k][p] = -1e9;\n }\n double mx = -1e9;\n for (auto& l : lw[k]) { if (l > mx) mx = l; }\n if (mx > -1e8) {\n for (auto& l : lw[k]) l -= mx;\n }\n }\n } else {\n double fc_arr[25];\n double S_total = cov_val[i][j];\n for (int k = 0; k < M; k++) {\n double mx = -1e9;\n for (auto& l : lw[k]) { if (l > mx) mx = l; }\n double total = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) total += exp(lw[k][p] - mx);\n if (total < 1e-30) { fc_arr[k] = 0; continue; }\n double covers = 0;\n for (int p : cell_pos[k][i * N + j]) covers += exp(lw[k][p] - mx);\n fc_arr[k] = covers / total;\n }\n \n for (int k = 0; k < M; k++) {\n double others = S_total - fc_arr[k];\n double var_others = max(0.3, others * 1.5);\n bool covers_arr[600];\n memset(covers_arr, 0, sizeof(bool) * positions[k].size());\n for (int p : cell_pos[k][i * N + j]) covers_arr[p] = true;\n \n for (int p = 0; p < (int)positions[k].size(); p++) {\n double diff = covers_arr[p] ? obs - 1.0 - others : obs - others;\n double penalty = diff * diff / (2 * var_others);\n if (penalty > 15.0) penalty = 15.0;\n lw[k][p] += -penalty;\n }\n double mx = -1e9;\n for (auto& l : lw[k]) { if (l > mx) mx = l; }\n if (mx > -1e8) {\n for (auto& l : lw[k]) l -= mx;\n }\n }\n }\n compute_prob_and_cov();\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> M >> eps;\n shapes.resize(M);\n for (int k = 0; k < M; k++) {\n int d; cin >> d;\n shapes[k].resize(d);\n for (int l = 0; l < d; l++) cin >> shapes[k][l].first >> shapes[k][l].second;\n }\n max_di.resize(M); max_dj.resize(M);\n for (int k = 0; k < M; k++) {\n max_di[k] = max_dj[k] = 0;\n for (auto& [i, j] : shapes[k]) { max_di[k] = max(max_di[k], i); max_dj[k] = max(max_dj[k], j); }\n }\n cell_pos.resize(M, vector>(N * N));\n for (int k = 0; k < M; k++) {\n vector> pos;\n vector>> cells;\n int pidx = 0;\n for (int di = 0; di <= N - 1 - max_di[k]; di++)\n for (int dj = 0; dj <= N - 1 - max_dj[k]; dj++) {\n pos.push_back({di, dj});\n vector> c;\n for (auto& [i, j] : shapes[k]) {\n int ci = di + i, cj = dj + j;\n c.push_back({ci, cj});\n cell_pos[k][ci * N + cj].push_back(pidx);\n }\n cells.push_back(c);\n pidx++;\n }\n positions.push_back(pos);\n pos_cells.push_back(cells);\n }\n memset(known, -1, sizeof(known));\n for (int k = 0; k < M; k++) lw.push_back(vector(positions[k].size(), 0.0));\n compute_prob_and_cov();\n \n for (int i = 0; i < N && query_count < 2*N*N - 1; i++) {\n vector> cells;\n for (int j = 0; j < N; j++) cells.push_back({i, j});\n update_divine(cells, divine_cells(cells));\n }\n for (int j = 0; j < N && query_count < 2*N*N - 1; j++) {\n vector> cells;\n for (int i = 0; i < N; i++) cells.push_back({i, j});\n update_divine(cells, divine_cells(cells));\n }\n \n int targeted_queries = 0;\n while (query_count < N * N && targeted_queries < 50) {\n int best_k = -1;\n double max_ent = -1;\n for (int k = 0; k < M; k++) {\n double total = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) total += exp(lw[k][p]);\n if (total < 1e-30) continue;\n double ent = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) {\n double prob = exp(lw[k][p]) / total;\n if (prob > 1e-9 && prob < 1 - 1e-9) ent -= prob * log(prob);\n }\n if (ent > max_ent) { max_ent = ent; best_k = k; }\n }\n if (best_k == -1 || max_ent < 0.5) break;\n if (eps > 0.1 && max_ent < 2.0) break;\n \n int best_p = max_element(lw[best_k].begin(), lw[best_k].end()) - lw[best_k].begin();\n vector> qcells = pos_cells[best_k][best_p];\n if (qcells.size() >= 2) {\n update_divine(qcells, divine_cells(qcells));\n targeted_queries++;\n } else break;\n }\n \n bool last_answer_wrong = false;\n while (query_count < 2*N*N) {\n double exp_err = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) continue;\n double p = prob_oil_val[i][j];\n exp_err += min(p, 1 - p);\n }\n if ((exp_err < 0.7 || query_count >= 2*N*N - 1) && !last_answer_wrong) {\n vector> ans;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] > 0) ans.push_back({i, j});\n else if (known[i][j] < 0 && prob_oil_val[i][j] > 0.5) ans.push_back({i, j});\n }\n if (submit_answer(ans)) return 0;\n last_answer_wrong = true;\n } else {\n if (query_count >= 2*N*N - 1) break;\n int bi = -1, bj = -1; double bent = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) continue;\n double p = max(0.001, min(0.999, prob_oil_val[i][j]));\n double ent = -p*log(p) - (1-p)*log(1-p);\n if (ent > bent) { bent = ent; bi = i; bj = j; }\n }\n if (bi < 0) break;\n update_drill(bi, bj, drill_cell(bi, bj));\n last_answer_wrong = false;\n }\n }\n \n vector> ans;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] > 0) ans.push_back({i, j});\n else if (known[i][j] < 0 && prob_oil_val[i][j] > 0.5) ans.push_back({i, j});\n }\n submit_answer(ans);\n return 0;\n}","ahc031":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint W, D, N;\nvector> a;\n\nlong long day_def(int d, const vector& h) {\n long long c = 0;\n for (int k = 0; k < N; k++) {\n int area = h[k] * W;\n if (a[d][k] > area) c += 100LL * (a[d][k] - area);\n }\n return c;\n}\n\nvoid get_bounds(const vector& h, vector& b) {\n b.resize(N - 1);\n int y = 0;\n for (int k = 0; k < N - 1; k++) { y += h[k]; b[k] = y; }\n}\n\nlong long bound_diff(const vector& b1, const vector& b2) {\n int i = 0, j = 0; long long c = 0;\n while (i < (int)b1.size() && j < (int)b2.size()) {\n if (b1[i] == b2[j]) { i++; j++; }\n else if (b1[i] < b2[j]) { c++; i++; }\n else { c++; j++; }\n }\n c += (int)b1.size() - i + (int)b2.size() - j;\n return c;\n}\n\nvector greedy_day(int d) {\n vector h(N, 1);\n int rem = W - N;\n while (rem > 0) {\n int bk = -1; long long br = -1;\n for (int k = 0; k < N; k++) {\n int df = max(0, a[d][k] - h[k] * W);\n int nd = max(0, a[d][k] - (h[k] + 1) * W);\n long long r = df - nd;\n if (r > br || (r == br && bk >= 0 && a[d][k] > a[d][bk])) { br = r; bk = k; }\n }\n if (bk == -1 || br == 0) {\n int mx = -1; for (int k = 0; k < N; k++) if (a[d][k] > mx) { mx = a[d][k]; bk = k; }\n }\n if (bk == -1) break;\n h[bk]++; rem--;\n }\n return h;\n}\n\nvector adjust_toward(int d, vector h, int max_iter=300) {\n for (int iter = 0; iter < max_iter; iter++) {\n int bk = -1; long long br = -1;\n for (int k = 0; k < N; k++) {\n int df = max(0, a[d][k] - h[k] * W);\n int nd = max(0, a[d][k] - (h[k] + 1) * W);\n long long r = df - nd;\n if (r > br) { br = r; bk = k; }\n }\n if (bk == -1 || br == 0) break;\n int bk2 = -1; long long min_inc = LLONG_MAX;\n for (int k = 0; k < N; k++) {\n if (h[k] > 1 && k != bk) {\n int od = max(0, a[d][k] - h[k] * W); int nd = max(0, a[d][k] - (h[k] - 1) * W);\n if (nd - od < min_inc) { min_inc = nd - od; bk2 = k; }\n }\n }\n if (bk2 == -1) break;\n h[bk]++; h[bk2]--;\n }\n return h;\n}\n\n// Morph from source layout toward target layout, recording intermediate candidates\nvector> morph_candidates(int d, const vector& src, const vector& tgt, int max_steps=20) {\n vector> result;\n vector h = src;\n vector src_b, tgt_b;\n get_bounds(src, src_b);\n get_bounds(tgt, tgt_b);\n \n result.push_back(h);\n \n for (int step = 0; step < max_steps; step++) {\n // Find the boundary with the largest difference from target\n int best_b = -1, best_diff = 0;\n for (int b = 0; b < N-1; b++) {\n int diff = tgt_b[b] - src_b[b];\n if (abs(diff) > abs(best_diff)) { best_diff = diff; best_b = b; }\n }\n if (best_b == -1 || best_diff == 0) break;\n \n int dir = (best_diff > 0) ? 1 : -1;\n // Move boundary best_b by dir\n int k1 = (dir > 0) ? best_b + 1 : best_b;\n int k2 = (dir > 0) ? best_b : best_b + 1;\n \n if (h[k1] <= 1) break;\n h[k1]--; h[k2]++;\n src_b[best_b] += dir;\n \n // Adjust toward optimal for day d\n h = adjust_toward(d, h, 5);\n get_bounds(h, src_b);\n \n result.push_back(h);\n }\n \n return result;\n}\n\nlong long total_cost(const vector>& h) {\n long long c = 0;\n for (int d = 0; d < D; d++) c += day_def(d, h[d]);\n for (int d = 1; d < D; d++) {\n vector b1, b2;\n get_bounds(h[d-1], b1); get_bounds(h[d], b2);\n c += bound_diff(b1, b2) * W;\n }\n return c;\n}\n\nint main(){\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> W >> D >> N;\n a.resize(D, vector(N));\n for (int d = 0; d < D; d++) for (int k = 0; k < N; k++) cin >> a[d][k];\n \n mt19937 rng(42);\n uniform_real_distribution uni(0, 1);\n \n // Fixed layout\n vector fixed_h(N, 1);\n { int rem = W - N;\n while (rem > 0) {\n int bk = -1; long long bs = -1;\n for (int k = 0; k < N; k++) {\n long long td = 0, ntd = 0;\n for (int d = 0; d < D; d++) { td += max(0, a[d][k] - fixed_h[k] * W); ntd += max(0, a[d][k] - (fixed_h[k] + 1) * W); }\n long long s = td - ntd;\n if (s > bs) { bs = s; bk = k; }\n }\n if (bk == -1) break; fixed_h[bk]++; rem--;\n }\n }\n \n // Fixed layout SA\n { vector ch = fixed_h;\n long long cc = 0; for (int d = 0; d < D; d++) cc += day_def(d, ch);\n long long bc = cc; vector bh = ch;\n auto st = chrono::high_resolution_clock::now();\n while (true) {\n auto nw = chrono::high_resolution_clock::now();\n double el = chrono::duration(nw - st).count();\n if (el > 0.05) break;\n int k1 = rng() % N, k2 = rng() % N;\n if (k1 == k2 || ch[k1] <= 1) continue;\n long long delta = 0;\n for (int d = 0; d < D; d++) {\n delta += 100LL * (max(0, a[d][k1] - (ch[k1] - 1) * W) - max(0, a[d][k1] - ch[k1] * W));\n delta += 100LL * (max(0, a[d][k2] - (ch[k2] + 1) * W) - max(0, a[d][k2] - ch[k2] * W));\n }\n double temp = 5e6 * max(1e-4, 1.0 - el / 0.05);\n if (delta <= 0 || exp(-(double)delta / temp) > uni(rng)) {\n ch[k1]--; ch[k2]++; cc += delta;\n if (cc < bc) { bc = cc; bh = ch; }\n }\n }\n fixed_h = bh;\n }\n \n // Per-day greedy\n vector> greedy_seq(D);\n for (int d = 0; d < D; d++) greedy_seq[d] = greedy_day(d);\n \n // Generate candidates per day\n vector>> cands(D);\n \n for (int d = 0; d < D; d++) {\n // Core candidates\n cands[d].push_back(greedy_seq[d]);\n cands[d].push_back(fixed_h);\n cands[d].push_back(adjust_toward(d, fixed_h));\n \n // Min height candidates\n vector min_h(N);\n int sum_min = 0;\n for (int k = 0; k < N; k++) {\n min_h[k] = (a[d][k] + W - 1) / W;\n sum_min += min_h[k];\n }\n int extra = W - sum_min;\n \n if (extra >= 0) {\n vector h = min_h;\n for (int k = 0; k < N && extra > 0; k++) { h[k] += extra; cands[d].push_back(adjust_toward(d, h)); h[k] -= extra; }\n for (int i = 0; i < 20; i++) {\n vector hh = min_h; int rem = extra;\n while (rem > 0) { hh[rng() % N]++; rem--; }\n cands[d].push_back(adjust_toward(d, hh));\n }\n } else {\n vector ch = min_h; int rem = -extra;\n while (rem > 0) {\n int bk = -1; long long min_inc = LLONG_MAX;\n for (int k = 0; k < N; k++) {\n if (ch[k] > 1) {\n int od = max(0, a[d][k] - ch[k] * W); int nd = max(0, a[d][k] - (ch[k] - 1) * W);\n if (nd - od < min_inc) { min_inc = nd - od; bk = k; }\n }\n }\n if (bk == -1) break; ch[bk]--; rem--;\n }\n cands[d].push_back(adjust_toward(d, ch));\n for (int k = 0; k < N; k++) {\n if (min_h[k] > 1) {\n vector h = min_h; h[k]--;\n cands[d].push_back(adjust_toward(d, h, -extra));\n }\n }\n }\n \n // Morph candidates from/to adjacent days\n for (int dd = max(0, d-3); dd <= min(D-1, d+3); dd++) {\n if (dd == d) continue;\n auto morphed = morph_candidates(d, greedy_seq[d], greedy_seq[dd], 30);\n for (auto& h : morphed) cands[d].push_back(h);\n morphed = morph_candidates(d, greedy_seq[dd], greedy_seq[d], 30);\n for (auto& h : morphed) cands[d].push_back(h);\n \n // Random perturbations from adjacent day's greedy\n for (int i = 0; i < 5; i++) {\n vector h = greedy_seq[dd];\n int rem = 5 + rng() % 10;\n for (int j = 0; j < rem; j++) {\n int k1 = rng() % N, k2 = rng() % N;\n if (k1 != k2 && h[k1] > 1) { h[k1]--; h[k2]++; }\n }\n cands[d].push_back(adjust_toward(d, h, 50));\n }\n }\n \n // Morph from fixed layout\n auto morphed = morph_candidates(d, fixed_h, greedy_seq[d], 30);\n for (auto& h : morphed) cands[d].push_back(h);\n \n // Validate and deduplicate\n vector> valid_cands;\n for (auto& c : cands[d]) {\n if ((int)c.size() != N) continue;\n bool ok = true; int sum = 0;\n for (int k = 0; k < N; k++) { if (c[k] < 1) { ok = false; break; } sum += c[k]; }\n if (ok && sum == W) valid_cands.push_back(c);\n }\n cands[d] = valid_cands;\n \n sort(cands[d].begin(), cands[d].end());\n cands[d].erase(unique(cands[d].begin(), cands[d].end()), cands[d].end());\n \n if ((int)cands[d].size() > 150) {\n sort(cands[d].begin(), cands[d].end(), [&](const vector& x, const vector& y) {\n return day_def(d, x) < day_def(d, y);\n });\n cands[d].resize(150);\n }\n }\n \n // DP\n vector ksz(D); int maxK = 0;\n for (int d = 0; d < D; d++) { ksz[d] = cands[d].size(); maxK = max(maxK, ksz[d]); }\n vector> dp(D, vector(maxK, LLONG_MAX));\n vector> par(D, vector(maxK, -1));\n vector> cdef(D);\n vector>> cbnd(D);\n \n for (int d = 0; d < D; d++) {\n cdef[d].resize(ksz[d]); cbnd[d].resize(ksz[d]);\n for (int i = 0; i < ksz[d]; i++) { cdef[d][i] = day_def(d, cands[d][i]); get_bounds(cands[d][i], cbnd[d][i]); }\n }\n \n for (int k = 0; k < ksz[0]; k++) dp[0][k] = cdef[0][k];\n for (int d = 1; d < D; d++)\n for (int k = 0; k < ksz[d]; k++)\n for (int j = 0; j < ksz[d-1]; j++) {\n if (dp[d-1][j] == LLONG_MAX) continue;\n long long cost = dp[d-1][j] + bound_diff(cbnd[d-1][j], cbnd[d][k]) * W + cdef[d][k];\n if (cost < dp[d][k]) { dp[d][k] = cost; par[d][k] = j; }\n }\n \n long long best_dp = LLONG_MAX; int best_k = -1;\n for (int k = 0; k < ksz[D-1]; k++) if (dp[D-1][k] < best_dp) { best_dp = dp[D-1][k]; best_k = k; }\n vector> dp_res(D);\n { int ck = best_k; for (int d = D-1; d >= 0; d--) { dp_res[d] = cands[d][ck]; ck = par[d][ck]; } }\n \n // SA\n auto sa_run = [&](vector> cur_h, double time_limit, int seed) -> pair>> {\n mt19937 local_rng(seed);\n uniform_real_distribution local_uni(0, 1);\n \n vector> cur_bnd(D);\n vector pc_cache(D, 0);\n for (int d = 0; d < D; d++) get_bounds(cur_h[d], cur_bnd[d]);\n for (int d = 1; d < D; d++) pc_cache[d] = bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n \n long long cur_cost = 0;\n for (int d = 0; d < D; d++) cur_cost += day_def(d, cur_h[d]);\n for (int d = 1; d < D; d++) cur_cost += pc_cache[d];\n \n long long best_cost = cur_cost;\n vector> best_h = cur_h;\n \n auto st = chrono::high_resolution_clock::now();\n long long iters = 0; double el = 0;\n while (true) {\n if (++iters % 5000 == 0) {\n auto nw = chrono::high_resolution_clock::now();\n el = chrono::duration(nw - st).count();\n if (el > time_limit) break;\n }\n \n int move_type = local_rng() % 25;\n \n if (move_type < 18) {\n int d = local_rng() % D, k1 = local_rng() % N, k2 = local_rng() % N;\n if (k1 == k2 || cur_h[d][k1] <= 1) continue;\n \n long long dd = 100LL * (max(0, a[d][k1] - (cur_h[d][k1] - 1) * W) - max(0, a[d][k1] - cur_h[d][k1] * W))\n + 100LL * (max(0, a[d][k2] - (cur_h[d][k2] + 1) * W) - max(0, a[d][k2] - cur_h[d][k2] * W));\n \n cur_h[d][k1]--; cur_h[d][k2]++;\n int lo = min(k1, k2), hi = max(k1, k2);\n int dsign = (k1 < k2) ? -1 : 1;\n for (int i = lo; i < hi; i++) cur_bnd[d][i] += dsign;\n \n long long npd = (d > 0 ? bound_diff(cur_bnd[d-1], cur_bnd[d]) * W : 0)\n + (d < D-1 ? bound_diff(cur_bnd[d], cur_bnd[d+1]) * W : 0);\n long long opd = (d > 0 ? pc_cache[d] : 0) + (d < D-1 ? pc_cache[d+1] : 0);\n long long delta = dd + npd - opd;\n \n double temp = 5e6 * max(1e-4, 1.0 - el / time_limit);\n if (delta <= 0 || exp(-(double)delta / temp) > local_uni(local_rng)) {\n cur_cost += delta;\n if (d > 0) pc_cache[d] = bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n if (d < D-1) pc_cache[d+1] = bound_diff(cur_bnd[d], cur_bnd[d+1]) * W;\n if (cur_cost < best_cost) { best_cost = cur_cost; best_h = cur_h; }\n } else {\n cur_h[d][k1]++; cur_h[d][k2]--;\n for (int i = lo; i < hi; i++) cur_bnd[d][i] -= dsign;\n }\n } else if (move_type < 22) {\n if (D < 2) continue;\n int d = 1 + local_rng() % (D - 1);\n int b = local_rng() % (N - 1);\n int dir = (cur_bnd[d][b] < cur_bnd[d-1][b]) ? 1 : -1;\n if (cur_bnd[d][b] == cur_bnd[d-1][b]) continue;\n \n int k1, k2;\n if (dir > 0) { k1 = b + 1; k2 = b; } else { k1 = b; k2 = b + 1; }\n if (cur_h[d][k1] <= 1) continue;\n \n long long dd = 100LL * (max(0, a[d][k1] - (cur_h[d][k1] - 1) * W) - max(0, a[d][k1] - cur_h[d][k1] * W))\n + 100LL * (max(0, a[d][k2] - (cur_h[d][k2] + 1) * W) - max(0, a[d][k2] - cur_h[d][k2] * W));\n \n cur_h[d][k1]--; cur_h[d][k2]++;\n cur_bnd[d][b] += dir;\n \n long long npd = (d > 0 ? bound_diff(cur_bnd[d-1], cur_bnd[d]) * W : 0)\n + (d < D-1 ? bound_diff(cur_bnd[d], cur_bnd[d+1]) * W : 0);\n long long opd = (d > 0 ? pc_cache[d] : 0) + (d < D-1 ? pc_cache[d+1] : 0);\n long long delta = dd + npd - opd;\n \n double temp = 5e6 * max(1e-4, 1.0 - el / time_limit);\n if (delta <= 0 || exp(-(double)delta / temp) > local_uni(local_rng)) {\n cur_cost += delta;\n if (d > 0) pc_cache[d] = bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n if (d < D-1) pc_cache[d+1] = bound_diff(cur_bnd[d], cur_bnd[d+1]) * W;\n if (cur_cost < best_cost) { best_cost = cur_cost; best_h = cur_h; }\n } else {\n cur_h[d][k1]++; cur_h[d][k2]--;\n cur_bnd[d][b] -= dir;\n }\n } else if (move_type < 24) {\n int d = local_rng() % D, k1 = local_rng() % N, k2 = local_rng() % N;\n if (k1 == k2) continue;\n int units = 2 + local_rng() % 4;\n if (cur_h[d][k1] <= units) continue;\n \n long long dd = 100LL * (max(0, a[d][k1] - (cur_h[d][k1] - units) * W) - max(0, a[d][k1] - cur_h[d][k1] * W))\n + 100LL * (max(0, a[d][k2] - (cur_h[d][k2] + units) * W) - max(0, a[d][k2] - cur_h[d][k2] * W));\n \n cur_h[d][k1] -= units; cur_h[d][k2] += units;\n int lo = min(k1, k2), hi = max(k1, k2);\n int dsign = (k1 < k2) ? -1 : 1;\n for (int i = lo; i < hi; i++) cur_bnd[d][i] += dsign * units;\n \n long long npd = (d > 0 ? bound_diff(cur_bnd[d-1], cur_bnd[d]) * W : 0)\n + (d < D-1 ? bound_diff(cur_bnd[d], cur_bnd[d+1]) * W : 0);\n long long opd = (d > 0 ? pc_cache[d] : 0) + (d < D-1 ? pc_cache[d+1] : 0);\n long long delta = dd + npd - opd;\n \n double temp = 5e6 * max(1e-4, 1.0 - el / time_limit);\n if (delta <= 0 || exp(-(double)delta / temp) > local_uni(local_rng)) {\n cur_cost += delta;\n if (d > 0) pc_cache[d] = bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n if (d < D-1) pc_cache[d+1] = bound_diff(cur_bnd[d], cur_bnd[d+1]) * W;\n if (cur_cost < best_cost) { best_cost = cur_cost; best_h = cur_h; }\n } else {\n cur_h[d][k1] += units; cur_h[d][k2] -= units;\n for (int i = lo; i < hi; i++) cur_bnd[d][i] -= dsign * units;\n }\n } else {\n if (D < 2) continue;\n int d = local_rng() % (D - 1);\n int b = local_rng() % (N - 1);\n int dir = (local_rng() % 2) ? 1 : -1;\n \n int k1_d = (dir > 0) ? b : b + 1;\n int k2_d = (dir > 0) ? b + 1 : b;\n \n bool can_d = (dir > 0) ? (cur_h[d][b] > 1) : (cur_h[d][b+1] > 1);\n bool can_d1 = (dir > 0) ? (cur_h[d+1][b] > 1) : (cur_h[d+1][b+1] > 1);\n if (!can_d || !can_d1) continue;\n \n long long dd = 100LL * (max(0, a[d][k1_d] - (cur_h[d][k1_d] - 1) * W) - max(0, a[d][k1_d] - cur_h[d][k1_d] * W))\n + 100LL * (max(0, a[d][k2_d] - (cur_h[d][k2_d] + 1) * W) - max(0, a[d][k2_d] - cur_h[d][k2_d] * W))\n + 100LL * (max(0, a[d+1][k1_d] - (cur_h[d+1][k1_d] - 1) * W) - max(0, a[d+1][k1_d] - cur_h[d+1][k1_d] * W))\n + 100LL * (max(0, a[d+1][k2_d] - (cur_h[d+1][k2_d] + 1) * W) - max(0, a[d+1][k2_d] - cur_h[d+1][k2_d] * W));\n \n cur_h[d][k1_d]--; cur_h[d][k2_d]++;\n cur_h[d+1][k1_d]--; cur_h[d+1][k2_d]++;\n cur_bnd[d][b] -= dir;\n cur_bnd[d+1][b] -= dir;\n \n long long npd = 0;\n if (d > 0) npd += bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n npd += bound_diff(cur_bnd[d], cur_bnd[d+1]) * W;\n if (d+1 < D-1) npd += bound_diff(cur_bnd[d+1], cur_bnd[d+2]) * W;\n \n long long opd = 0;\n if (d > 0) opd += pc_cache[d];\n opd += pc_cache[d+1];\n if (d+1 < D-1) opd += pc_cache[d+2];\n \n long long delta = dd + npd - opd;\n double temp = 5e6 * max(1e-4, 1.0 - el / time_limit);\n if (delta <= 0 || exp(-(double)delta / temp) > local_uni(local_rng)) {\n cur_cost += delta;\n if (d > 0) pc_cache[d] = bound_diff(cur_bnd[d-1], cur_bnd[d]) * W;\n pc_cache[d+1] = bound_diff(cur_bnd[d], cur_bnd[d+1]) * W;\n if (d+1 < D-1) pc_cache[d+2] = bound_diff(cur_bnd[d+1], cur_bnd[d+2]) * W;\n if (cur_cost < best_cost) { best_cost = cur_cost; best_h = cur_h; }\n } else {\n cur_h[d][k1_d]++; cur_h[d][k2_d]--;\n cur_h[d+1][k1_d]++; cur_h[d+1][k2_d]++;\n cur_bnd[d][b] += dir;\n cur_bnd[d+1][b] += dir;\n }\n }\n }\n return {best_cost, best_h};\n };\n \n // Try multiple starting points\n vector>>> starts;\n starts.push_back({total_cost(dp_res), dp_res});\n starts.push_back({total_cost(vector>(D, fixed_h)), vector>(D, fixed_h)});\n starts.push_back({total_cost(greedy_seq), greedy_seq});\n sort(starts.begin(), starts.end());\n \n long long global_best_cost = starts[0].first;\n vector> global_best_h = starts[0].second;\n \n auto total_st = chrono::high_resolution_clock::now();\n double time_budget = 2.7;\n \n for (int s = 0; s < min(3, (int)starts.size()); s++) {\n auto nw = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(nw - total_st).count();\n if (elapsed > time_budget - 0.05) break;\n double remaining = time_budget - elapsed - 0.05;\n double alloc = remaining / max(1, min(3, (int)starts.size()) - s);\n \n auto [cost, h] = sa_run(starts[s].second, alloc, 42 + s * 1000);\n if (cost < global_best_cost) {\n global_best_cost = cost;\n global_best_h = h;\n }\n }\n \n for (int d = 0; d < D; d++) {\n int y = 0;\n for (int k = 0; k < N; k++) { cout << y << \" 0 \" << y + global_best_h[d][k] << \" \" << W << \"\\n\"; y += global_best_h[d][k]; }\n }\n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long MOD = 998244353;\n\nlong long bmod[81];\nlong long a[81];\nlong long s_val[180];\nint ops[81];\nint op_p[81];\nint op_q[81];\nint L = 0;\n\nint best_ops[81], best_op_p[81], best_op_q[81];\nint best_L = 0;\nlong long best_total_score = 0;\n\nlong long best_score[9][10];\nlong long best_counts[9][10][20];\nlong long current_counts[20];\n\nstruct FastRNG {\n unsigned long long x = 123456789, y = 362436069, z = 521288629;\n unsigned long long operator()() {\n unsigned long long t;\n x ^= x << 16; x ^= x >> 5; x ^= x << 1;\n t = x; x = y; y = z; z = t ^ x ^ y;\n return z;\n }\n};\n\nFastRNG rng;\n\nvoid dfs(int m, int remaining_ops, long long current_values[9], int used_ops, int subgrid_idx) {\n long long score = 0;\n for (int i = 0; i < 9; i++) score += current_values[i];\n if (score > best_score[subgrid_idx][used_ops]) {\n best_score[subgrid_idx][used_ops] = score;\n memcpy(best_counts[subgrid_idx][used_ops], current_counts, sizeof(current_counts));\n }\n \n if (remaining_ops == 0 || m == 20) return;\n\n dfs(m + 1, remaining_ops, current_values, used_ops, subgrid_idx);\n\n for (int i = 1; i <= remaining_ops; i++) {\n current_counts[m]++;\n for (int j = 0; j < 9; j++) {\n current_values[j] += s_val[m * 9 + j];\n if (current_values[j] >= MOD) current_values[j] -= MOD;\n }\n dfs(m + 1, remaining_ops - i, current_values, used_ops + i, subgrid_idx);\n }\n for (int i = 1; i <= remaining_ops; i++) {\n current_counts[m]--;\n for (int j = 0; j < 9; j++) {\n current_values[j] -= s_val[m * 9 + j];\n if (current_values[j] < 0) current_values[j] += MOD;\n }\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n for (int i = 0; i < 81; i++) cin >> a[i];\n for (int m = 0; m < 20; m++)\n for (int i = 0; i < 9; i++)\n cin >> s_val[m * 9 + i];\n \n auto start_time = chrono::high_resolution_clock::now();\n \n // Phase 1: Exhaustive search for optimal independent subgrid configurations\n for (int j = 0; j < 9; j++) {\n int pj = (j / 3) * 3;\n int qj = (j % 3) * 3;\n long long initial_values[9];\n for (int i = 0; i < 3; i++) {\n for (int jj = 0; jj < 3; jj++) {\n initial_values[i * 3 + jj] = a[(pj + i) * 9 + (qj + jj)];\n }\n }\n memset(current_counts, 0, sizeof(current_counts));\n memset(best_score[j], 0, sizeof(best_score[j]));\n dfs(0, 9, initial_values, 0, j);\n }\n \n // Phase 2: Knapsack DP to distribute operations optimally\n long long dp[10][82];\n int choice[10][82];\n memset(dp, -1, sizeof(dp));\n dp[0][0] = 0;\n for (int i = 0; i < 9; i++) {\n for (int k = 0; k <= 81; k++) {\n if (dp[i][k] < 0) continue;\n for (int kj = 0; kj <= 9; kj++) {\n if (k + kj <= 81) {\n if (dp[i][k] + best_score[i][kj] > dp[i+1][k+kj]) {\n dp[i+1][k+kj] = dp[i][k] + best_score[i][kj];\n choice[i+1][k+kj] = kj;\n }\n }\n }\n }\n }\n \n long long max_total_score = 0;\n int best_total_k = 0;\n for (int k = 0; k <= 81; k++) {\n if (dp[9][k] > max_total_score) {\n max_total_score = dp[9][k];\n best_total_k = k;\n }\n }\n \n int current_k = best_total_k;\n int optimal_k[9];\n for (int i = 8; i >= 0; i--) {\n int kj = choice[i+1][current_k];\n optimal_k[i] = kj;\n current_k -= kj;\n }\n \n // Build initial board and operations array from DP results\n for (int i = 0; i < 81; i++) bmod[i] = a[i];\n L = 0;\n for (int j = 0; j < 9; j++) {\n int pj = (j / 3) * 3;\n int qj = (j % 3) * 3;\n int kj = optimal_k[j];\n for (int m = 0; m < 20; m++) {\n for (int c = 0; c < best_counts[j][kj][m]; c++) {\n ops[L] = m;\n op_p[L] = pj;\n op_q[L] = qj;\n for (int i = 0; i < 3; i++) {\n for (int jj = 0; jj < 3; jj++) {\n int u = (pj + i) * 9 + (qj + jj);\n long long nv = bmod[u] + s_val[m * 9 + i * 3 + jj];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n L++;\n }\n }\n }\n \n long long score = 0;\n for (int i = 0; i < 81; i++) score += bmod[i];\n \n best_total_score = score;\n best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n \n // Phase 3: Simulated Annealing for overlapping synergies\n double start_temp = 1e10, end_temp = 1e4;\n auto sa_start_time = chrono::high_resolution_clock::now();\n double sa_time_limit = 1.9 - chrono::duration(sa_start_time - start_time).count();\n \n int iter = 0;\n while (true) {\n iter++;\n if (iter % 10000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - sa_start_time).count();\n if (elapsed > sa_time_limit) break;\n }\n \n double temp = start_temp * pow(end_temp / start_temp, min(1.0, chrono::duration(chrono::high_resolution_clock::now() - sa_start_time).count() / sa_time_limit));\n \n int move_type = rng() % 100;\n long long delta = 0;\n \n if (move_type < 20 && L < K) {\n int new_m = rng() % 20;\n int new_p = rng() % 7;\n int new_q = rng() % 7;\n \n long long old_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) old_score += bmod[(new_p + i) * 9 + (new_q + j)];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] + s_val[new_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) new_score += bmod[(new_p + i) * 9 + (new_q + j)];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[L] = new_m; op_p[L] = new_p; op_q[L] = new_q;\n L++;\n score += delta;\n if (score > best_total_score) {\n best_total_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] - s_val[new_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n }\n } else if (move_type < 30 && L > 0) {\n int idx = rng() % L;\n int old_m = ops[idx], old_p = op_p[idx], old_q = op_q[idx];\n \n long long old_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) old_score += bmod[(old_p + i) * 9 + (old_q + j)];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] - s_val[old_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) new_score += bmod[(old_p + i) * 9 + (old_q + j)];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[idx] = ops[L - 1]; op_p[idx] = op_p[L - 1]; op_q[idx] = op_q[L - 1];\n L--;\n score += delta;\n if (score > best_total_score) {\n best_total_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] + s_val[old_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n } else if (L > 0) {\n int idx = rng() % L;\n int old_m = ops[idx], old_p = op_p[idx], old_q = op_q[idx];\n \n int r = rng() % 5;\n int new_m = old_m, new_p = old_p, new_q = old_q;\n if (r == 0) new_m = rng() % 20;\n else if (r == 1) new_p = rng() % 7;\n else if (r == 2) new_q = rng() % 7;\n else if (r == 3) { new_p = rng() % 7; new_q = rng() % 7; }\n else { new_m = rng() % 20; new_p = rng() % 7; new_q = rng() % 7; }\n \n if (new_m == old_m && new_p == old_p && new_q == old_q) continue;\n \n bool affected[81] = {false};\n int affected_list[18];\n int affected_count = 0;\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n if (!affected[u]) { affected[u] = true; affected_list[affected_count++] = u; }\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n if (!affected[u]) { affected[u] = true; affected_list[affected_count++] = u; }\n }\n \n long long old_score = 0;\n for (int k = 0; k < affected_count; k++) old_score += bmod[affected_list[k]];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] - s_val[old_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] + s_val[new_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int k = 0; k < affected_count; k++) new_score += bmod[affected_list[k]];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[idx] = new_m; op_p[idx] = new_p; op_q[idx] = new_q;\n score += delta;\n if (score > best_total_score) {\n best_total_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] - s_val[new_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] + s_val[old_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n for (int k = 0; k < affected_count; k++) affected[affected_list[k]] = false;\n }\n }\n \n cout << best_L << \"\\n\";\n for (int i = 0; i < best_L; i++)\n cout << best_ops[i] << \" \" << best_op_p[i] << \" \" << best_op_q[i] << \"\\n\";\n \n return 0;\n}","ahc033":"#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N], grid[N][N];\nbool dispatched[N*N];\nint nxt_recv[N];\nint lr, lc, lh;\nint total_disp;\n\nint next_exp(int g) {\n for (int j = 0; j < N; j++)\n if (!dispatched[N*g+j]) return N*g+j;\n return -1;\n}\n\nint main() {\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> A[i][j];\n \n memset(grid, -1, sizeof(grid));\n fill(dispatched, dispatched+N*N, false);\n fill(nxt_recv, nxt_recv+N, 0);\n lr = 0; lc = 0; lh = -1; total_disp = 0;\n \n vector acts(N);\n // Turn 0: bomb small cranes to prevent deadlocks\n for (int i = 0; i < N; i++) acts[i] += (i ? 'B' : '.');\n \n // Receive turn 0\n for (int i = 0; i < N; i++)\n if (nxt_recv[i] < N) grid[i][0] = A[i][nxt_recv[i]++];\n \n for (int t = 1; total_disp < N*N && (int)acts[0].size() < 9999; t++) {\n // Step 1: Receive\n for (int i = 0; i < N; i++) {\n if (nxt_recv[i] < N && grid[i][0] == -1 && !(lr == i && lc == 0 && lh >= 0)) {\n grid[i][0] = A[i][nxt_recv[i]++];\n }\n }\n \n // Step 2: Large crane action\n char act = '.';\n if (lh >= 0) {\n // Holding: Deliver directly to the correct dispatch gate\n int g = lh / N;\n int tr = g, tc = N - 1;\n \n if (lr == tr && lc == tc) {\n act = 'Q'; \n grid[tr][tc] = lh; \n lh = -1;\n } else {\n if (lr < tr) { lr++; act = 'D'; }\n else if (lr > tr) { lr--; act = 'U'; }\n else if (lc < tc) { lc++; act = 'R'; }\n else { lc--; act = 'L'; }\n }\n } else {\n // Not holding: Pick up the best available container\n int bc = -1, bs = INT_MAX, br = -1, bcc = -1;\n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (grid[r][c] < 0) continue;\n int co = grid[r][c], g = co / N, e = next_exp(g);\n int d = abs(lr - r) + abs(lc - c);\n int s;\n \n if (e >= 0 && e == co) s = -10000 + d; // Expected container (minimizes M1)\n else if (c == 0 && nxt_recv[r] < N) {\n int nc = A[r][nxt_recv[r]], ng = nc / N, ne = next_exp(ng);\n s = (ne >= 0 && ne == nc) ? -5000 + d : -1000 + d; // Blocks expected container\n } else if (c == 0) {\n s = -500 + d; // Blocks receiving gate\n } else {\n s = d + 500; // Other (shouldn't exist in this strategy)\n }\n \n if (s < bs) { bs = s; bc = co; br = r; bcc = c; }\n }\n }\n \n if (bc >= 0) {\n if (lr == br && lc == bcc) {\n act = 'P'; \n lh = bc; \n grid[br][bcc] = -1;\n } else {\n if (lr < br) { lr++; act = 'D'; }\n else if (lr > br) { lr--; act = 'U'; }\n else if (lc < bcc) { lc++; act = 'R'; }\n else { lc--; act = 'L'; }\n }\n }\n }\n \n acts[0] += act;\n for (int i = 1; i < N; i++) acts[i] += '.';\n \n // Step 3: Dispatch\n for (int i = 0; i < N; i++) {\n if (grid[i][N-1] >= 0) {\n dispatched[grid[i][N-1]] = true;\n grid[i][N-1] = -1;\n total_disp++;\n }\n }\n }\n \n int ml = 0;\n for (int i = 0; i < N; i++) ml = max(ml, (int)acts[i].size());\n for (int i = 0; i < N; i++) {\n while ((int)acts[i].size() < ml) acts[i] += '.';\n cout << acts[i] << endl;\n }\n return 0;\n}","ahc034":"#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\ntypedef long long ll;\nconst ll INF = 1e18;\nstruct Edge { int to, rev; ll cap, cost; };\nstruct MinCostFlow {\n int n; vector> graph; vector h; vector pv, pe;\n MinCostFlow(int n):n(n),graph(n),h(n,0),pv(n),pe(n){}\n void add_edge(int f,int t,ll cap,ll cost){\n graph[f].push_back({t,(int)graph[t].size(),cap,cost});\n graph[t].push_back({f,(int)graph[f].size()-1,0,-cost});\n }\n ll min_cost_flow(int s,int t,ll mf){\n ll res=0,flow=0;\n while(flow,vector>,greater<>>pq;\n vectordist(n,INF);dist[s]=0;pq.push({0,s});\n while(!pq.empty()){\n auto[d,v]=pq.top();pq.pop();\n if(dist[v]0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){\n dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];\n pv[e.to]=v;pe[e.to]=i;pq.push({dist[e.to],e.to});\n }\n }\n }\n if(dist[t]==INF)break;\n for(int v=0;v>n;\n vector>h(n,vector(n));\n for(int i=0;i>h[i][j];\n vector>sources,sinks;\n vector>sid(n,vector(n,-1)),kid(n,vector(n,-1));\n int tsup=0;\n for(int i=0;i0){sid[i][j]=sources.size();sources.push_back({i,j});tsup+=h[i][j];}\n else if(h[i][j]<0){kid[i][j]=sinks.size();sinks.push_back({i,j});}\n }\n int P=sources.size(),M=sinks.size();\n int S=0,T=P+M+1;\n MinCostFlow mcf(P+M+2);\n for(int i=0;i>fa(P,vector(M,0));\n for(int i=0;i=1+P&&e.to<1+P+M)fa[i][e.to-1-P]=(int)mcf.graph[e.to][e.rev].cap;\n vectorsnnd(P,0);\n for(int i=0;i0){auto[ti,tj]=sinks[j];best=min(best,abs(si-ti)+abs(sj-tj));}\n snnd[i]=(bestops;int r=0,c=0,load=0,rem=tsup;\n auto cur=h;\n while(ops.size()<100000&&(rem>0||load>0)){\n if(cur[r][c]>0){ops.push_back(\"+\"+to_string(cur[r][c]));load+=cur[r][c];rem-=cur[r][c];cur[r][c]=0;}\n while(cur[r][c]<0&&load>0){int d=min(load,-cur[r][c]);ops.push_back(\"-\"+to_string(d));load-=d;cur[r][c]+=d;}\n if(rem==0&&load==0)break;\n int br=-1,bc=-1;ll bcost=LLONG_MAX;\n if(load>0){\n for(int i=0;i0){\n int dt=abs(r-i)+abs(c-j);int s=sid[i][j];\n int dd=(s>=0)?snnd[s]:20;\n ll cost=(ll)dt*100+(ll)dd*(100+cur[i][j]);\n if(costr){r++;ops.push_back(\"D\");}\n else if(bc\n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct RNG {\n unsigned long long s[2];\n RNG() : s{0x123456789ABCDEF0ULL, 0xFEDCBA9876543210ULL} {}\n unsigned long long next() {\n unsigned long long s1 = s[0]; unsigned long long s0 = s[1];\n unsigned long long result = s0 + s1;\n s[0] = s0; s1 ^= s1 << 23;\n s[1] = s1 ^ s0 ^ (s1 >> 18) ^ (s0 >> 5);\n return result;\n }\n int nextInt(int n) { return (int)(next() % (unsigned long long)n); }\n double nextDouble() { return (double)(next() >> 11) * 0x1.0p-53; }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n const int N=6,M=15,SC=60,GS=36,NE=60;\n int n,mm,t; cin>>n>>mm>>t;\n int X[SC][M];\n for(int i=0;i>X[i][j];\n int eu[NE],ev[NE]; int ei=0;\n for(int i=0;ibsc){bsc=sc;bs=s;}\n }\n grid[pos]=bs;used[bs]=true;pf[pos]=true;\n }\n } else {\n int ba=0,bb=1,bp=pot[0][1];\n for(int i=0;ibp){bp=pot[i][j];ba=i;bb=j;}\n grid[14]=ba;used[ba]=true;pf[14]=true; grid[15]=bb;used[bb]=true;pf[15]=true;\n for(int idx=0;idxbsc){bsc=sc;bs=s;}\n }\n grid[pos]=bs;used[bs]=true;pf[pos]=true;\n }\n }\n int sc=0; for(int e=0;ebestScore){bestScore=sc;memcpy(bestGrid,grid,sizeof(grid));\n memcpy(bestUsed,used,sizeof(used));bestUnc=0;\n for(int i=0;i(chrono::high_resolution_clock::now()-st).count();\n if(el>180000)break;\n double p=(double)el/180000.0; double tmp=500.0*pow(0.1/500.0,p); invT=1.0/tmp;\n }\n if(rng.next()&3){\n int i=rng.nextInt(GS),j=rng.nextInt(GS); if(i==j)continue;\n int delta=0;\n for(int k=0;k=0){cs+=delta;if(cs>bs){bs=cs;memcpy(bg,grid,sizeof(grid));}}\n else{int idx=(int)(-delta*invT*100.0);\n if(idxbs){bs=cs;memcpy(bg,grid,sizeof(grid));}}\n else swap(grid[i],grid[j]);}\n } else {\n int pos=rng.nextInt(GS); int os=grid[pos]; int ui=rng.nextInt(unc); int ns=un[ui];\n int delta=0;\n for(int k=0;k=0){cs+=delta;used[os]=false;used[ns]=true;un[ui]=os;\n if(cs>bs){bs=cs;memcpy(bg,grid,sizeof(grid));}}\n else{int idx=(int)(-delta*invT*100.0);\n if(idxbs){bs=cs;memcpy(bg,grid,sizeof(grid));}}\n else grid[pos]=os;}\n }\n }\n memcpy(grid,bg,sizeof(grid));\n for(int i=0;i>X[i][j];\n }\n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n \n vector s(N), t(N);\n for (int i = 0; i < N; i++) cin >> s[i];\n for (int i = 0; i < N; i++) cin >> t[i];\n \n int Vp = V;\n vector len(Vp, 1);\n int idx = 1;\n for (int l = 1; idx < Vp; l++) {\n int cnt = (l <= 3) ? 2 : 1;\n for (int k = 0; k < cnt && idx < Vp; k++) {\n len[idx++] = min(l, N / 2);\n }\n }\n \n cout << Vp << \"\\n\";\n for (int i = 1; i < Vp; i++) cout << 0 << \" \" << len[i] << \"\\n\";\n \n vector> grid(N, vector(N)), target(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n grid[i][j] = s[i][j] - '0';\n target[i][j] = t[i][j] - '0';\n }\n \n vector> sources, targets;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n if (grid[i][j] && !target[i][j]) sources.push_back({i, j});\n if (!grid[i][j] && target[i][j]) targets.push_back({i, j});\n }\n \n int Mm = sources.size();\n if (Mm == 0) {\n cout << N/2 << \" \" << N/2 << \"\\n\";\n return 0;\n }\n \n // Cluster sources\n vector s_cluster(Mm, -1);\n int num_s_clusters = 0;\n for (int i = 0; i < Mm; i++) {\n if (s_cluster[i] != -1) continue;\n queue q; q.push(i); s_cluster[i] = num_s_clusters;\n while (!q.empty()) {\n int u = q.front(); q.pop();\n for (int v = 0; v < Mm; v++) {\n if (s_cluster[v] != -1) continue;\n if (abs(sources[u].first - sources[v].first) + abs(sources[u].second - sources[v].second) <= 6) {\n s_cluster[v] = num_s_clusters; q.push(v);\n }\n }\n }\n num_s_clusters++;\n }\n\n // Cluster targets\n vector t_cluster(Mm, -1);\n int num_t_clusters = 0;\n for (int i = 0; i < Mm; i++) {\n if (t_cluster[i] != -1) continue;\n queue q; q.push(i); t_cluster[i] = num_t_clusters;\n while (!q.empty()) {\n int u = q.front(); q.pop();\n for (int v = 0; v < Mm; v++) {\n if (t_cluster[v] != -1) continue;\n if (abs(targets[u].first - targets[v].first) + abs(targets[u].second - targets[v].second) <= 6) {\n t_cluster[v] = num_t_clusters; q.push(v);\n }\n }\n }\n num_t_clusters++;\n }\n \n vector> s_center(num_s_clusters, {0, 0});\n vector s_count(num_s_clusters, 0);\n for (int i = 0; i < Mm; i++) {\n s_center[s_cluster[i]].first += sources[i].first;\n s_center[s_cluster[i]].second += sources[i].second;\n s_count[s_cluster[i]]++;\n }\n for (int i = 0; i < num_s_clusters; i++) { s_center[i].first /= s_count[i]; s_center[i].second /= s_count[i]; }\n \n vector> t_center(num_t_clusters, {0, 0});\n vector t_count(num_t_clusters, 0);\n for (int i = 0; i < Mm; i++) {\n t_center[t_cluster[i]].first += targets[i].first;\n t_center[t_cluster[i]].second += targets[i].second;\n t_count[t_cluster[i]]++;\n }\n for (int i = 0; i < num_t_clusters; i++) { t_center[i].first /= t_count[i]; t_center[i].second /= t_count[i]; }\n \n vector cluster_match(num_s_clusters, -1);\n vector t_cluster_used(num_t_clusters, false);\n vector s_cluster_order(num_s_clusters);\n iota(s_cluster_order.begin(), s_cluster_order.end(), 0);\n sort(s_cluster_order.begin(), s_cluster_order.end(), [&](int a, int b) { return s_count[a] > s_count[b]; });\n \n for (int i : s_cluster_order) {\n long long best_dist = 1e18; int best_t = -1;\n for (int j = 0; j < num_t_clusters; j++) {\n if (t_cluster_used[j]) continue;\n long long dist = abs(s_center[i].first - t_center[j].first) + abs(s_center[i].second - t_center[j].second);\n if (dist < best_dist) { best_dist = dist; best_t = j; }\n }\n if (best_t != -1) { cluster_match[i] = best_t; t_cluster_used[best_t] = true; }\n }\n \n vector match(Mm, -1);\n vector sused(Mm, false), tused(Mm, false);\n \n for (int i = 0; i < num_s_clusters; i++) {\n if (cluster_match[i] == -1) continue;\n int j = cluster_match[i];\n vector s_indices, t_indices;\n for (int k = 0; k < Mm; k++) {\n if (s_cluster[k] == i) s_indices.push_back(k);\n if (t_cluster[k] == j) t_indices.push_back(k);\n }\n vector> pairs;\n for (int si : s_indices) {\n for (int ti : t_indices) {\n if (tused[ti]) continue;\n pairs.push_back({abs(sources[si].first - targets[ti].first) + abs(sources[si].second - targets[ti].second), si, ti});\n }\n }\n sort(pairs.begin(), pairs.end());\n for (auto& [d, si, ti] : pairs) {\n if (!sused[si] && !tused[ti]) { match[si] = ti; sused[si] = true; tused[ti] = true; }\n }\n }\n \n vector> pairs;\n for (int i = 0; i < Mm; i++) {\n if (sused[i]) continue;\n for (int j = 0; j < Mm; j++) {\n if (tused[j]) continue;\n pairs.push_back({abs(sources[i].first - targets[j].first) + abs(sources[i].second - targets[j].second), i, j});\n }\n }\n sort(pairs.begin(), pairs.end());\n for (auto& [d, i, j] : pairs) {\n if (!sused[i] && !tused[j]) { match[i] = j; sused[i] = true; tused[j] = true; }\n }\n \n int best_cluster = max_element(s_count.begin(), s_count.end()) - s_count.begin();\n int rx = s_center[best_cluster].first;\n int ry = s_center[best_cluster].second;\n cout << rx << \" \" << ry << \"\\n\";\n \n vector dir(Vp, 0);\n vector available_s(Mm, true);\n vector finger_state(Vp, 0); // 0: IDLE, 1: TO_SOURCE, 2: TO_TARGET\n vector finger_task(Vp, -1);\n vector f_target_x(Vp), f_target_y(Vp), f_target_dir(Vp);\n vector ops;\n \n auto get_best_station = [&](int rx, int ry, int f, int cell_x, int cell_y) {\n int best_cost = INT_MAX, best_nx = -1, best_ny = -1, best_dir = -1;\n for (int d = 0; d < 4; d++) {\n int nx = cell_x - dx[d] * len[f], ny = cell_y - dy[d] * len[f];\n if (0 <= nx && nx < N && 0 <= ny && ny < N) {\n int dist = abs(rx - nx) + abs(ry - ny);\n int rot = min((dir[f] - d + 4) % 4, (d - dir[f] + 4) % 4);\n int cost = max(dist, rot) * 10 + rot;\n if (cost < best_cost) { best_cost = cost; best_nx = nx; best_ny = ny; best_dir = d; }\n }\n }\n return make_tuple(best_nx, best_ny, best_dir, best_cost);\n };\n \n while (true) {\n bool any_idle = false;\n for (int f = 1; f < Vp; f++) if (finger_state[f] == 0) { any_idle = true; break; }\n \n if (any_idle) {\n int min_dist_to_pending = INT_MAX;\n for (int f2 = 1; f2 < Vp; f2++) {\n if (finger_state[f2] != 0) {\n int d = abs(rx - f_target_x[f2]) + abs(ry - f_target_y[f2]);\n min_dist_to_pending = min(min_dist_to_pending, d);\n }\n }\n int max_accept_dist = (min_dist_to_pending == INT_MAX) ? INT_MAX : min_dist_to_pending + N / 2;\n\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) {\n int min_d = INT_MAX, best_s = -1, b_nx, b_ny, b_dir;\n for (int i = 0; i < Mm; i++) {\n if (!available_s[i]) continue;\n auto [nx, ny, d, cost] = get_best_station(rx, ry, f, sources[i].first, sources[i].second);\n if (cost < min_d && cost <= max_accept_dist) {\n min_d = cost; best_s = i; b_nx = nx; b_ny = ny; b_dir = d;\n }\n }\n if (best_s != -1) {\n finger_state[f] = 1; finger_task[f] = best_s; available_s[best_s] = false;\n f_target_x[f] = b_nx; f_target_y[f] = b_ny; f_target_dir[f] = b_dir;\n }\n }\n }\n }\n\n bool any_pending = false, any_available = false;\n for (int f = 1; f < Vp; f++) if (finger_state[f] != 0) any_pending = true;\n for (int i = 0; i < Mm; i++) if (available_s[i]) any_available = true;\n if (!any_pending && !any_available) break;\n\n int best_dist = INT_MAX, best_f = -1;\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n int dist = abs(rx - f_target_x[f]) + abs(ry - f_target_y[f]);\n if (dist < best_dist) { best_dist = dist; best_f = f; }\n }\n\n string op(2 * Vp, '.');\n if (best_f != -1) {\n if (rx < f_target_x[best_f]) { op[0] = 'D'; rx++; }\n else if (rx > f_target_x[best_f]) { op[0] = 'U'; rx--; }\n else if (ry < f_target_y[best_f]) { op[0] = 'R'; ry++; }\n else if (ry > f_target_y[best_f]) { op[0] = 'L'; ry--; }\n }\n\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n if (dir[f] != f_target_dir[f]) {\n int diff = (f_target_dir[f] - dir[f] + 4) % 4;\n if (diff <= 2) { op[f] = 'R'; dir[f] = (dir[f] + 1) % 4; }\n else { op[f] = 'L'; dir[f] = (dir[f] + 3) % 4; }\n }\n }\n\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n if (rx == f_target_x[f] && ry == f_target_y[f] && dir[f] == f_target_dir[f]) {\n op[Vp + f] = 'P';\n if (finger_state[f] == 1) {\n int s_idx = finger_task[f];\n grid[sources[s_idx].first][sources[s_idx].second] = 0;\n finger_state[f] = 2;\n auto [nx, ny, d, cost] = get_best_station(rx, ry, f, targets[match[s_idx]].first, targets[match[s_idx]].second);\n f_target_x[f] = nx; f_target_y[f] = ny; f_target_dir[f] = d;\n } else {\n int s_idx = finger_task[f]; int t_idx = match[s_idx];\n grid[targets[t_idx].first][targets[t_idx].second] = 1;\n finger_state[f] = 0;\n }\n }\n }\n ops.push_back(op);\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc039":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct GridRect { int score, x1, y1, x2, y2; };\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N; cin >> N;\n vector fx(2*N), fy(2*N), val(2*N);\n for (int i = 0; i < 2*N; i++) {\n cin >> fx[i] >> fy[i];\n val[i] = (i < N) ? 1 : -1;\n }\n \n int GS = 700, CS = 143;\n vector> grid(GS, vector(GS, 0));\n for (int i = 0; i < 2*N; i++) {\n int gx = min(fx[i] / CS, GS - 1);\n int gy = min(fy[i] / CS, GS - 1);\n grid[gx][gy] += val[i];\n }\n \n vector grid_rects;\n for (int gx1 = 0; gx1 < GS; gx1++) {\n vector col_sums(GS, 0);\n for (int gx2 = gx1; gx2 < GS; gx2++) {\n for (int gy = 0; gy < GS; gy++) {\n col_sums[gy] += grid[gx2][gy];\n }\n int cur = 0, best = 0, cy1 = 0, by1 = 0, by2 = -1;\n for (int gy2 = 0; gy2 < GS; gy2++) {\n cur += col_sums[gy2];\n if (cur > best) { best = cur; by1 = cy1; by2 = gy2; }\n if (cur < 0) { cur = 0; cy1 = gy2 + 1; }\n }\n if (best > 0) grid_rects.push_back({best, gx1, by1, gx2, by2});\n }\n }\n sort(grid_rects.begin(), grid_rects.end(), [](const GridRect& a, const GridRect& b) { return a.score > b.score; });\n \n int best_exact_score = 0;\n int final_x1 = 0, final_y1 = 0, final_x2 = 0, final_y2 = 0;\n for (int k = 0; k < min(20, (int)grid_rects.size()); k++) {\n int bestX1 = grid_rects[k].x1 * CS;\n int bestY1 = grid_rects[k].y1 * CS;\n int bestX2 = min((grid_rects[k].x2 + 1) * CS, 100000);\n int bestY2 = min((grid_rects[k].y2 + 1) * CS, 100000);\n \n for (int iter = 0; iter < 20; iter++) {\n for (int dim = 0; dim < 2; dim++) {\n vector> ev;\n for (int i = 0; i < 2 * N; i++) {\n bool inside = (dim == 0) ? (fx[i] >= bestX1 && fx[i] <= bestX2) : (fy[i] >= bestY1 && fy[i] <= bestY2);\n if (inside) ev.push_back({(dim == 0) ? fy[i] : fx[i], val[i]});\n }\n sort(ev.begin(), ev.end());\n \n // Group coordinates to fix the 1D overestimation bug\n vector> ev_unique;\n for (int i = 0; i < (int)ev.size(); i++) {\n if (i > 0 && ev[i].first == ev[i-1].first) {\n ev_unique.back().second += ev[i].second;\n } else {\n ev_unique.push_back(ev[i]);\n }\n }\n \n int bs = -1000000000, b1 = (dim == 0) ? bestY1 : bestX1, b2 = (dim == 0) ? bestY2 : bestX2;\n int mp = 0, mpi = -1, pfx = 0;\n for (int j = 0; j <= (int)ev_unique.size(); j++) {\n int s = pfx - mp;\n if (s > bs) {\n bs = s;\n b1 = (mpi == -1) ? 0 : ev_unique[mpi].first;\n b2 = (j == (int)ev_unique.size()) ? 100000 : ev_unique[j - 1].first;\n }\n if (pfx < mp) {\n mp = pfx;\n mpi = j;\n }\n if (j < (int)ev_unique.size()) pfx += ev_unique[j].second;\n }\n \n if (dim == 0) { bestY1 = b1; bestY2 = b2; } else { bestX1 = b1; bestX2 = b2; }\n }\n }\n \n int current_score = 0;\n for (int i = 0; i < 2 * N; i++) {\n if (fx[i] >= bestX1 && fx[i] <= bestX2 && fy[i] >= bestY1 && fy[i] <= bestY2) {\n current_score += val[i];\n }\n }\n \n if (current_score > best_exact_score) {\n best_exact_score = current_score;\n final_x1 = bestX1; final_y1 = bestY1;\n final_x2 = bestX2; final_y2 = bestY2;\n }\n }\n \n if (best_exact_score > 0) {\n cout << 4 << \"\\n\" << final_x1 << \" \" << final_y1 << \"\\n\"\n << final_x2 << \" \" << final_y1 << \"\\n\"\n << final_x2 << \" \" << final_y2 << \"\\n\"\n << final_x1 << \" \" << final_y2 << \"\\n\";\n } else {\n cout << 4 << \"\\n50000 50000\\n50001 50000\\n50001 50001\\n50000 50001\\n\";\n }\n \n return 0;\n}","ahc040":"#include \nusing namespace std;\nint N,T,sigma;\nvectorw_obs,h_obs;\nvectorw_est,h_est;\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n cin>>N>>T>>sigma;\n w_obs.resize(N);h_obs.resize(N);w_est.resize(N);h_est.resize(N);\n for(int i=0;i>w_obs[i]>>h_obs[i];w_est[i]=w_obs[i];h_est[i]=h_obs[i];}\n mt19937 rng(42);\n auto start=chrono::steady_clock::now();\n for(int t=0;t(now-start).count()>2700)break;\n vectorwc(N),hc(N);\n for(int i=0;ipx,py,pw,ph;vectorplc;vector>out;\n long long cW=0,cH=0;\n bool doRow=(t==0&&T>=20),doCol=(t==1&&T>=20);\n if(doRow){\n for(int i=0;i=5);\n if(addN)for(int i=0;irx)ry=max(ry,py[j]+ph[j]);\n long long nW=max(cW,rx+rw),nH=max(cH,ry+rh),s=nW+nH;\n if(strat==1)s+=abs(nW-nH)/2;else if(strat==2)s+=abs(nW-nH);else if(strat==3){long long w=nW*nH-cW*cH-rw*rh;s+=w/500;}else if(strat==4)s=max(nW,nH)*2;\n if(sry)rx=max(rx,px[j]+pw[j]);\n long long nW=max(cW,rx+rw),nH=max(cH,ry+rh),s=nW+nH;\n if(strat==1)s+=abs(nW-nH)/2;else if(strat==2)s+=abs(nW-nH);else if(strat==3){long long w=nW*nH-cW*cH-rw*rh;s+=w/500;}else if(strat==4)s=max(nW,nH)*2;\n if(s>Wp>>Hp;\n if(doRow){double ws=0;for(int i=0;i=cW-margin)rc++;if(py[j]+ph[j]>=cH-margin)bc++;}\n double lr=0.12;\n for(int j=0;j<(int)px.size();j++){\n int o=plc[j];bool rot=get<1>(out[j]);\n if(px[j]+pw[j]>=cW-margin&&rc>0){double es=We/rc*lr;if(rot)h_est[o]=max(1.0,h_est[o]+es);else w_est[o]=max(1.0,w_est[o]+es);}\n if(py[j]+ph[j]>=cH-margin&&bc>0){double es=He/bc*lr;if(rot)w_est[o]=max(1.0,w_est[o]+es);else h_est[o]=max(1.0,h_est[o]+es);}\n }\n }\n }\n return 0;\n}","ahc041":"#include \nusing namespace std;\nint N,M,H;\nvectorA;\nvector>adj;\nmt19937 rng(42);\nchrono::steady_clock::time_point T0;\ndouble el(){return chrono::duration(chrono::steady_clock::now()-T0).count();}\nstruct State{\nvectorparent,height;vectorsub_sum;vectorsub_max_h;long long score;\nvoid recompute(){\nvectordeg(N);for(int v=0;vq;for(int v=0;vord;\nwhile(!q.empty()){int v=q.front();q.pop();ord.push_back(v);if(parent[v]!=-1&&--deg[parent[v]]==0)q.push(parent[v]);}\nfor(int v:ord)height[v]=(parent[v]==-1)?0:height[parent[v]]+1;\nfill(sub_sum.begin(),sub_sum.end(),0);fill(sub_max_h.begin(),sub_max_h.end(),0);\nfor(int v:ord){sub_sum[v]+=A[v];sub_max_h[v]=max(sub_max_h[v],height[v]);\nif(parent[v]!=-1){sub_sum[parent[v]]+=sub_sum[v];sub_max_h[parent[v]]=max(sub_max_h[parent[v]],sub_max_h[v]);}}\nscore=0;for(int v=0;v&p){parent=p;height.resize(N);sub_sum.resize(N);sub_max_h.resize(N);recompute();}\n};\nvoid greedy(State&st){\nwhile(true){long long bg=0;int bv=-1,bu=-1;\nfor(int v=0;vH||st.cyc(v,u))continue;\nlong long g=(long long)d*st.sub_sum[v];if(g>bg){bg=g;bv=v;bu=u;}}\nif(bv==-1)break;st.parent[bv]=bu;st.recompute();}}\nvectormbfs(const vector&ro,bool bb){\nvectorp(N,-1),h(N,0);vectorvis(N);\nfor(int r:ro){if(vis[r])continue;queueq;q.push(r);vis[r]=true;\nwhile(!q.empty()){int u=q.front();q.pop();if(h[u]>=H)continue;\nvectornb=adj[u];if(bb)sort(nb.begin(),nb.end(),[](int a,int b){return A[a]>A[b];});\nelse shuffle(nb.begin(),nb.end(),rng);\nfor(int v:nb){if(vis[v])continue;vis[v]=true;p[v]=u;h[v]=h[u]+1;q.push(v);}}}return p;}\nvectormdfs(const vector&ro){\nvectorp(N,-1),h(N,0);vectorvis(N);\nfor(int r:ro){if(vis[r])continue;vis[r]=true;\nfunctiondfs=[&](int u){if(h[u]>=H)return;\nvectornb=adj[u];sort(nb.begin(),nb.end(),[](int a,int b){return A[a]>A[b];});\nfor(int v:nb){if(vis[v])continue;vis[v]=true;p[v]=u;h[v]=h[u]+1;dfs(v);}};dfs(r);}return p;}\nvectormchain(){\nvectorp(N,-1);vectorused(N);vectorord(N);iota(ord.begin(),ord.end(),0);\nsort(ord.begin(),ord.end(),[](int a,int b){return A[a]>A[b];});\nfor(int v:ord){if(used[v])continue;vectordist(N,-1),par(N,-1);queueq;\nq.push(v);dist[v]=0;int t=v;while(!q.empty()){int u=q.front();q.pop();\nif(dist[u]>dist[t])t=u;if(dist[u]==H)continue;\nfor(int w:adj[u])if(!used[w]&&dist[w]==-1){dist[w]=dist[u]+1;par[w]=u;q.push(w);}}\nvectorpath;for(int c=t;;c=par[c]){path.push_back(c);if(c==v)break;}\nfor(int i=0;i<(int)path.size();i++){used[path[i]]=true;p[path[i]]=(i==0)?-1:path[i-1];}}return p;}\nvoid sa(vector&par,long long&bs,double et){\nvectorht(N);\nauto rh=[&](){vectordeg(N);for(int v=0;vq;for(int v=0;vo;\nwhile(!q.empty()){int v=q.front();q.pop();o.push_back(v);if(par[v]!=-1&&--deg[par[v]]==0)q.push(par[v]);}\nfor(int v:o)ht[v]=(par[v]==-1)?0:ht[par[v]]+1;};rh();\nauto cc=[&](int v,int np)->bool{if(np==-1)return false;for(int c=np;c!=-1;c=par[c])if(c==v)return true;return false;};\nlong long cs=0;for(int v=0;vbp=par;double ss=el();double dur=max(.001,et-ss);\nuniform_real_distributionuf(0,1);\nfor(int it=0;;it++){double t=el();if(t>et)break;double T=2000.0*pow(0.001,(t-ss)/dur);\nint v=rng()%N;if(adj[v].empty())continue;int np;\nif(rng()%50==0)np=-1;else np=adj[v][rng()%adj[v].size()];\nif(np==par[v]||cc(v,np))continue;int nh=(np==-1)?0:ht[np]+1,d=nh-ht[v];\nif(d==0)continue;long long sm=0;int mh=0;\nstackstk;stk.push(v);while(!stk.empty()){int u=stk.top();stk.pop();sm+=A[u];mh=max(mh,ht[u]);\nfor(int w:adj[u])if(par[w]==u)stk.push(w);}\nif(mh+d>H)continue;long long g=(long long)d*sm;\nif(g>0||uf(rng)lb){lb=cs;bp=par;}}}\npar=bp;rh();bs=0;for(int v=0;v>N>>M>>H;A.resize(N);for(int i=0;i>A[i];adj.resize(N);\nfor(int i=0;i>u>>v;adj[u].push_back(v);adj[v].push_back(u);}\nvectorX(N),Y(N);for(int i=0;i>X[i]>>Y[i];\nlong long bs=0;vectorbp(N,-1);auto ts=[&](const vector&p){State st;st.init(p);greedy(st);\nif(st.score>bs){bs=st.score;bp=st.parent;}};\nts(vector(N,-1));\n{vectoro(N);iota(o.begin(),o.end(),0);sort(o.begin(),o.end(),[](int a,int b){return A[a]o(N);iota(o.begin(),o.end(),0);sort(o.begin(),o.end(),[&](int a,int b){\nreturn(X[a]-500)*(X[a]-500)+(Y[a]-500)*(Y[a]-500)<(X[b]-500)*(X[b]-500)+(Y[b]-500)*(Y[b]-500);});\nts(mbfs(o,true));ts(mdfs(o));}\n{vectoro(N);iota(o.begin(),o.end(),0);sort(o.begin(),o.end(),[](int a,int b){return A[a]roots(o.begin(),o.begin()+min(nr,N));\nts(mbfs(roots,true));ts(mdfs(roots));}\nint tr=0;while(el()<0.6){vectoro(N);iota(o.begin(),o.end(),0);shuffle(o.begin(),o.end(),rng);\nif(tr%3==0)ts(mbfs(o,true));else if(tr%3==1)ts(mbfs(o,false));else ts(mdfs(o));tr++;}\nlong long ss;sa(bp,ss,1.7);ts(bp);\nfor(int i=0;i\n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint N;\nvector initial_board;\n\nvoid apply_shift(vector& b, char dir, int idx) {\n if (dir == 'L') { for (int j=0;j0;j--) b[idx][j]=b[idx][j-1]; b[idx][0]='.'; }\n else if (dir == 'U') { for (int i=0;i0;i--) b[i][idx]=b[i-1][idx]; b[0][idx]='.'; }\n}\n\nstruct MoveInfo { char dir; int idx; int amount; double ratio; int oni_removed; };\n\nvector get_candidates(const vector& b) {\n vector cands;\n for (int i=0;i0) cands.push_back(MoveInfo{'L',i,mx+1,(double)cnt/(mx+1),cnt});\n int R=0; for(int j=N-1;j>=0;j--) if(b[i][j]=='o'){R=j+1;break;}\n cnt=0; int mn_r=N; for(int j=R;j0) cands.push_back(MoveInfo{'R',i,N-mn_r,(double)cnt/(N-mn_r),cnt});\n }\n for (int j=0;j0) cands.push_back(MoveInfo{'U',j,mx+1,(double)cnt/(mx+1),cnt});\n int D=0; for(int i=N-1;i>=0;i--) if(b[i][j]=='o'){D=i+1;break;}\n cnt=0; int mn_c=N; for(int i=D;i0) cands.push_back(MoveInfo{'D',j,N-mn_c,(double)cnt/(N-mn_c),cnt});\n }\n return cands;\n}\n\nint count_stuck(const vector& b) {\n int stuck=0;\n for(int i=0;i& b) {\n int score=0;\n for(int i=0;i& b) { int c=0; for(auto& r:b) for(char ch:r) if(ch=='x') c++; return c; }\n\nstruct State { vector board; vector> moves; int cost; int oni_count; double score; };\n\npair>,bool> run_beam(int beam_width) {\n vector beam;\n beam.push_back({initial_board, {}, 0, count_oni(initial_board), 0.0});\n while(true) {\n vector next_beam;\n for(auto& state : beam) {\n if(state.oni_count == 0) return {state.moves, true};\n auto cands = get_candidates(state.board);\n if(cands.empty()) continue;\n sort(cands.begin(), cands.end(), [](const MoveInfo& a, const MoveInfo& b){return a.ratio > b.ratio;});\n int base_s = safety_score(state.board);\n for(int t=0; t 0) continue;\n int no = count_oni(nb);\n auto nm = state.moves;\n for(int k=0;k b.score;});\n if((int)next_beam.size() > beam_width) next_beam.resize(beam_width);\n beam = next_beam;\n }\n sort(beam.begin(), beam.end(), [](const State& a, const State& b){return a.oni_count < b.oni_count || (a.oni_count == b.oni_count && a.cost < b.cost);});\n return {beam[0].moves, beam[0].oni_count == 0};\n}\n\npair>,bool> run_greedy(int strategy, mt19937& rng) {\n vector b=initial_board; vector> moves;\n while(true) {\n int oc=count_oni(b); if(oc==0) return {moves,true};\n auto cands=get_candidates(b); if(cands.empty()) return {moves,false};\n if(strategy==0) sort(cands.begin(),cands.end(),[](const MoveInfo& a,const MoveInfo& b){return a.ratio>b.ratio;});\n else if(strategy==1) sort(cands.begin(),cands.end(),[](const MoveInfo& a,const MoveInfo& b){return a.oni_removed>b.oni_removed||(a.oni_removed==b.oni_removed&&a.amountb.ratio);});\n else shuffle(cands.begin(),cands.end(),rng);\n int best_t=0,best_stuck=N*N; double best_eff=-1e9; int base_s=safety_score(b);\n int cl=min(15,(int)cands.size());\n for(int t=0;t0&&best_stuck==0) continue;\n int sd=safety_score(sim)-base_s; double ef=cands[t].ratio+sd*0.01;\n if(stbest_eff)){best_stuck=st;best_t=t;best_eff=ef;}\n if(st==0&&cands[t].ratio>=1.0) break;\n }\n for(int k=0;k> batch_fallback() {\n vector b=initial_board; vector> moves;\n auto shift=[&](char d,int i){apply_shift(b,d,i);moves.push_back({d,i});};\n struct Oni{int i,j;}; vector onis;\n for(int i=0;i,vector> batches;\n for(int id=0;id<(int)onis.size();id++){\n auto& o=onis[id]; bool us=true,ds=true,ls=true,rs=true;\n for(int k=0;ksecond) Lv=max(Lv,onis[id].j+1);\n if(rit!=batches.end()) for(int id:rit->second) Rv=max(Rv,N-onis[id].j);\n if(Lv>0&&Rv>0){if(2*Lv+Rv<=Lv+2*Rv){for(int k=0;k0){for(int k=0;k0){for(int k=0;ksecond) Uv=max(Uv,onis[id].i+1);\n if(dit!=batches.end()) for(int id:dit->second) Dv=max(Dv,N-onis[id].i);\n if(Uv>0&&Dv>0){if(2*Uv+Dv<=Uv+2*Dv){for(int k=0;k0){for(int k=0;k0){for(int k=0;k>N; initial_board.resize(N);\n for(int i=0;i>initial_board[i];\n mt19937 rng(42); vector> best_moves; int best_cost=1e9;\n auto start=chrono::high_resolution_clock::now();\n auto [bm,bs]=run_beam(10); if(bs&&(int)bm.size()(chrono::high_resolution_clock::now()-start).count()>1500) done=true;\n }\n if(best_moves.empty()) best_moves=batch_fallback();\n for(auto& [d,p]:best_moves) cout<\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, L;\nint T[100];\nint a[100], b[100];\nint best_a[100], best_b[100];\nint best_error = INT_MAX;\nint t_global[100];\nint next_node[2][100];\n\nuint64_t rng_state = 1234567890123456789ULL;\nuint64_t rng64() {\n rng_state ^= rng_state >> 12;\n rng_state ^= rng_state << 25;\n rng_state ^= rng_state >> 27;\n return rng_state * 2685821657736338717ULL;\n}\n\nvoid update_next_node() {\n for (int i = 0; i < N; i++) {\n next_node[0][i] = a[i];\n next_node[1][i] = b[i];\n }\n}\n\nint simulate(int ti[]) {\n memset(ti, 0, sizeof(int) * N);\n int cur = 0;\n for (int w = 0; w < L; w++) {\n int c = ++ti[cur];\n cur = next_node[c & 1][cur];\n }\n int err = 0;\n for (int i = 0; i < N; i++) err += abs(ti[i] - T[i]);\n return err;\n}\n\nvoid try_init(int ai[], int bi[]) {\n memcpy(a, ai, sizeof(a));\n memcpy(b, bi, sizeof(b));\n update_next_node();\n int err = simulate(t_global);\n if (err < best_error) {\n best_error = err;\n memcpy(best_a, a, sizeof(a));\n memcpy(best_b, b, sizeof(b));\n }\n}\n\nvoid greedy_init(int ai[], int bi[], bool avoid_same) {\n int dem[100]; memcpy(dem, T, sizeof(T));\n int cnt[100] = {};\n bool a_ch[100] = {}, b_ch[100] = {};\n for(int i=0; i dem[best] || (dem[j] == dem[best] && T[j] > T[best])) best = j;\n }\n ai[cur] = best; a_ch[cur] = true;\n dem[best] -= (T[cur] + 1) / 2;\n }\n cur = ai[cur];\n } else {\n if (!b_ch[cur]) {\n int best = -1;\n for (int j = 0; j < N; j++) {\n if (j == cur) continue;\n if (avoid_same && a_ch[cur] && j == ai[cur]) continue;\n if (T[j] == 0 && dem[j] <= 0) continue;\n if (best == -1 || dem[j] > dem[best] || (dem[j] == dem[best] && T[j] > T[best])) best = j;\n }\n bi[cur] = best; b_ch[cur] = true;\n dem[best] -= T[cur] / 2;\n }\n cur = bi[cur];\n }\n }\n}\n\nvoid flow_sa(int ai[], int bi[]) {\n int flow_in[100] = {};\n for(int i=0; i> N >> L;\n for (int i = 0; i < N; i++) cin >> T[i];\n \n int ai[100], bi[100];\n \n for (int i = 0; i < N; i++) { ai[i] = (i+1)%N; bi[i] = (i+1)%N; }\n try_init(ai, bi);\n \n greedy_init(ai, bi, true);\n try_init(ai, bi);\n \n greedy_init(ai, bi, false);\n try_init(ai, bi);\n \n memcpy(ai, best_a, sizeof(ai));\n memcpy(bi, best_b, sizeof(bi));\n flow_sa(ai, bi);\n try_init(ai, bi);\n \n memcpy(a, best_a, sizeof(a));\n memcpy(b, best_b, sizeof(b));\n update_next_node();\n int error = simulate(t_global);\n best_error = error;\n \n int order[100];\n iota(order, order + N, 0);\n sort(order, order + N, [](int x, int y) { return T[x] < T[y]; });\n int rank_of[100];\n for (int i = 0; i < N; i++) rank_of[order[i]] = i;\n \n vector nodes_by_T[10001];\n for(int i=0; i 0) nodes_by_T[T[i]].push_back(i);\n \n double start_temp = max(500.0, (double)error / 20.0);\n auto start = chrono::high_resolution_clock::now();\n \n while(true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 1.85) break;\n \n double temp = start_temp * (1.0 - elapsed / 1.85);\n if (temp < 0.01) temp = 0.01;\n \n int old_a[100], old_b[100], old_t_global[100];\n memcpy(old_a, a, sizeof(a));\n memcpy(old_b, b, sizeof(b));\n memcpy(old_t_global, t_global, sizeof(t_global));\n \n int move_type = rng64() % 5;\n int i = -1, j = -1;\n \n if (move_type == 0) {\n i = rng64() % N;\n while(T[i] == 0) i = rng64() % N;\n swap(a[i], b[i]);\n } else if (move_type < 4) {\n i = rng64() % N;\n while(T[i] == 0) i = rng64() % N;\n \n if (nodes_by_T[T[i]].size() > 1) {\n j = nodes_by_T[T[i]][rng64() % nodes_by_T[T[i]].size()];\n while(j == i) j = nodes_by_T[T[i]][rng64() % nodes_by_T[T[i]].size()];\n } else {\n int delta_rank = (rng64() % 5) - 2;\n int new_rank = max(0, min(N - 1, rank_of[i] + delta_rank));\n j = order[new_rank];\n int attempts = 0;\n while(T[j] == 0 || j == i) {\n new_rank = (new_rank + 1) % N;\n j = order[new_rank];\n if (++attempts > N) break;\n }\n if (j == i || T[j] == 0) continue;\n }\n \n if (move_type == 1) swap(a[i], a[j]);\n else if (move_type == 2) swap(b[i], b[j]);\n else swap(a[i], b[j]);\n } else {\n i = rng64() % N;\n while(T[i] == 0) i = rng64() % N;\n bool is_a = rng64() & 1;\n int nv = rng64() % N;\n while(T[nv] == 0) nv = rng64() % N;\n if (is_a) a[i] = nv; else b[i] = nv;\n }\n \n update_next_node();\n int new_error = simulate(t_global);\n double delta = new_error - error;\n \n if (delta <= 0 || (double)(rng64() & 0xFFFF) / 65536.0 < exp(-delta / temp)) {\n error = new_error;\n if (error < best_error) {\n best_error = error;\n memcpy(best_a, a, sizeof(a));\n memcpy(best_b, b, sizeof(b));\n }\n } else {\n memcpy(a, old_a, sizeof(a));\n memcpy(b, old_b, sizeof(b));\n memcpy(t_global, old_t_global, sizeof(t_global));\n }\n }\n \n for (int i = 0; i < N; i++)\n cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nuint64_t xy2d(int n, int x, int y) {\n uint64_t d = 0;\n for (int s = n/2; s > 0; s /= 2) {\n int rx = (x & s) > 0;\n int ry = (y & s) > 0;\n d += (uint64_t)s * s * ((3 * rx) ^ ry);\n if (ry == 0) {\n if (rx == 1) { x = s-1 - x; y = s-1 - y; }\n swap(x, y);\n }\n }\n return d;\n}\n\nint N, M, Q, L, W;\ndouble cx[800], cy[800], ddist[800][800];\nint qcnt = 0;\n\nvector> query(vector& v) {\n if (qcnt >= Q || (int)v.size() < 2) return {};\n qcnt++;\n cout << \"? \" << v.size();\n for (int x : v) cout << \" \" << x;\n cout << endl;\n vector> res(v.size() - 1);\n for (auto& [a, b] : res) cin >> a >> b;\n return res;\n}\n\nint par[800], rnk[800];\nvoid init_dsu() { iota(par, par + N, 0); fill(rnk, rnk + N, 0); }\nint find(int x) { return par[x] == x ? x : par[x] = find(par[x]); }\nbool unite(int x, int y) {\n x = find(x); y = find(y);\n if (x == y) return false;\n if (rnk[x] < rnk[y]) swap(x, y);\n par[y] = x;\n if (rnk[x] == rnk[y]) rnk[x]++;\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n mt19937 rng(1337);\n \n cin >> N >> M >> Q >> L >> W;\n vector G(M);\n for (int& g : G) cin >> g;\n \n for (int i = 0; i < N; i++) {\n int a, b, c, d;\n cin >> a >> b >> c >> d;\n cx[i] = (a + b) / 2.0;\n cy[i] = (c + d) / 2.0;\n }\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n double dx = cx[i] - cx[j], dy = cy[i] - cy[j];\n ddist[i][j] = sqrt(dx*dx + dy*dy);\n }\n \n vector hilbert_idx(N);\n for(int i=0; i ord(N);\n iota(ord.begin(), ord.end(), 0);\n sort(ord.begin(), ord.end(), [&](int a, int b) {\n return hilbert_idx[a] < hilbert_idx[b];\n });\n \n vector cut_cost(N, 0.0);\n for (int j = 1; j < N; j++) {\n cut_cost[j] = ddist[ord[j-1]][ord[j]];\n }\n \n vector p(M);\n iota(p.begin(), p.end(), 0);\n \n if (M <= 20) {\n vector dp(1 << M, -1.0);\n dp[0] = 0.0;\n for (int mask = 0; mask < (1 << M); mask++) {\n if (dp[mask] < -0.5) continue;\n int s = 0;\n for (int i = 0; i < M; i++) if (mask & (1 << i)) s += G[i];\n for (int i = 0; i < M; i++) {\n if (!(mask & (1 << i))) {\n int next_mask = mask | (1 << i);\n int next_s = s + G[i];\n double cost = dp[mask] + (next_s < N ? cut_cost[next_s] : 0.0);\n if (cost > dp[next_mask]) dp[next_mask] = cost;\n }\n }\n }\n int mask = (1 << M) - 1;\n for (int k = M - 1; k >= 0; k--) {\n int s = 0;\n for (int i = 0; i < M; i++) if (mask & (1 << i)) s += G[i];\n for (int i = 0; i < M; i++) {\n if (mask & (1 << i)) {\n int prev_mask = mask ^ (1 << i);\n double cost = dp[prev_mask] + (s < N ? cut_cost[s] : 0.0);\n if (abs(cost - dp[mask]) < 1e-9) {\n p[k] = i;\n mask = prev_mask;\n break;\n }\n }\n }\n }\n } else {\n sort(p.begin(), p.end(), [&](int a, int b) { return G[a] > G[b]; });\n vector prefix(M);\n int s = 0;\n for (int i = 0; i < M; i++) { s += G[p[i]]; prefix[i] = s; }\n \n double current_cost = 0.0;\n for (int i = 0; i < M - 1; i++) current_cost += cut_cost[prefix[i]];\n \n for (int iter = 0; iter < 1000000; iter++) {\n int i = rng() % M;\n int j = rng() % M;\n if (i == j) continue;\n if (i > j) swap(i, j);\n \n double old_cost = 0.0;\n for (int k = i; k < j; k++) old_cost += cut_cost[prefix[k]];\n \n swap(p[i], p[j]);\n int s_prev = (i == 0 ? 0 : prefix[i-1]);\n double new_cost = 0.0;\n for (int k = i; k < j; k++) {\n s_prev += G[p[k]];\n new_cost += cut_cost[s_prev];\n }\n \n if (new_cost > old_cost) {\n s_prev = (i == 0 ? 0 : prefix[i-1]);\n for (int k = i; k < j; k++) {\n s_prev += G[p[k]];\n prefix[k] = s_prev;\n }\n current_cost += (new_cost - old_cost);\n } else {\n swap(p[i], p[j]);\n }\n }\n }\n \n vector> grp(M);\n int curr = 0;\n for (int k = 0; k < M; k++) {\n int group_idx = p[k];\n int sz = G[group_idx];\n for (int j = 0; j < sz; j++) {\n grp[group_idx].push_back(ord[curr++]);\n }\n }\n \n vector proc_order(M);\n iota(proc_order.begin(), proc_order.end(), 0);\n sort(proc_order.begin(), proc_order.end(), [&](int a, int b) {\n return G[a] < G[b];\n });\n \n vector>> ans(M);\n \n for (int k : proc_order) {\n int G_size = grp[k].size();\n if (G_size <= 1) continue;\n \n init_dsu();\n vector> mst;\n \n if (G_size <= L) {\n if (qcnt < Q) mst = query(grp[k]);\n } else {\n int start = 0;\n while (start < G_size) {\n int end = min(start + L, G_size);\n if (end - start < 2) break;\n vector qv(grp[k].begin() + start, grp[k].begin() + end);\n if (qcnt < Q) {\n auto edges = query(qv);\n for (auto& [a, b] : edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n }\n }\n } else {\n break;\n }\n start += L - 1;\n }\n }\n \n if (mst.size() < (size_t)G_size - 1) {\n vector> edges;\n for (int i = 0; i < G_size; i++)\n for (int j = i + 1; j < G_size; j++)\n edges.emplace_back(ddist[grp[k][i]][grp[k][j]], grp[k][i], grp[k][j]);\n sort(edges.begin(), edges.end());\n for (auto& [d, a, b] : edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n }\n if (mst.size() == (size_t)G_size - 1) break;\n }\n }\n ans[k] = mst;\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int i = 0; i < (int)grp[k].size(); i++) cout << grp[k][i] << \" \\n\"[i==(int)grp[k].size()-1];\n for (auto& [a, b] : ans[k]) cout << a << \" \" << b << \"\\n\";\n }\n return 0;\n}","ahc046":"#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N, M;\n cin >> N >> M;\n vector> targets(M);\n for (int i = 0; i < M; i++) cin >> targets[i].first >> targets[i].second;\n \n bool block_grid[20][20] = {};\n int cur_r = targets[0].first, cur_c = targets[0].second;\n vector> actions;\n \n const int DR[] = {-1, 1, 0, 0};\n const int DC[] = {0, 0, -1, 1};\n const char DIR_CHAR[] = {'U', 'D', 'L', 'R'};\n int dir_map[256];\n dir_map['U'] = 0; dir_map['D'] = 1; dir_map['L'] = 2; dir_map['R'] = 3;\n \n bool is_target[20][20] = {};\n for (auto& [r, c] : targets) is_target[r][c] = true;\n \n int dist[20][20][21][21];\n short pr[20][20][21][21];\n short pc[20][20][21][21];\n char pa[20][20][21][21];\n char pd[20][20][21][21];\n short pf[20][20][21][21];\n short pg[20][20][21][21];\n \n struct State { short r, c, ar, ac; };\n State q_arr[176400];\n \n auto is_block_fn = [&](int r, int c, int ar, int ac) {\n if (ar != 20 && r == ar && c == ac) return !block_grid[r][c];\n return block_grid[r][c];\n };\n \n auto bfs = [&](int sr, int sc, int tr, int tc) -> vector> {\n if (sr == tr && sc == tc && !block_grid[sr][sc]) return {};\n \n memset(dist, -1, sizeof(dist));\n int q_sz = 0;\n q_arr[q_sz++] = {(short)sr, (short)sc, 20, 20};\n dist[sr][sc][20][20] = 0;\n \n int found_ar = -1, found_ac = -1;\n \n for (int i = 0; i < q_sz; ++i) {\n auto [r, c, ar, ac] = q_arr[i];\n int d = dist[r][c][ar][ac];\n \n if (r == tr && c == tc && !is_block_fn(r, c, ar, ac)) {\n found_ar = ar; found_ac = ac;\n goto found;\n }\n \n for (int dir = 0; dir < 4; ++dir) {\n int nr = r + DR[dir], nc = c + DC[dir];\n \n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !is_block_fn(nr, nc, ar, ac)) {\n if (dist[nr][nc][ar][ac] == -1) {\n dist[nr][nc][ar][ac] = d + 1;\n pr[nr][nc][ar][ac] = r; pc[nr][nc][ar][ac] = c;\n pa[nr][nc][ar][ac] = 0; pd[nr][nc][ar][ac] = dir;\n pf[nr][nc][ar][ac] = ar; pg[nr][nc][ar][ac] = ac;\n q_arr[q_sz++] = {(short)nr, (short)nc, (short)ar, (short)ac};\n }\n }\n \n int snr = r, snc = c;\n while (true) {\n int nnr = snr + DR[dir], nnc = snc + DC[dir];\n if (nnr < 0 || nnr >= N || nnc < 0 || nnc >= N || is_block_fn(nnr, nnc, ar, ac)) break;\n snr = nnr; snc = nnc;\n }\n if (snr != r || snc != c) {\n if (dist[snr][snc][ar][ac] == -1) {\n dist[snr][snc][ar][ac] = d + 1;\n pr[snr][snc][ar][ac] = r; pc[snr][snc][ar][ac] = c;\n pa[snr][snc][ar][ac] = 1; pd[snr][snc][ar][ac] = dir;\n pf[snr][snc][ar][ac] = ar; pg[snr][snc][ar][ac] = ac;\n q_arr[q_sz++] = {(short)snr, (short)snc, (short)ar, (short)ac};\n }\n }\n \n if (ar == 20) {\n int br = nr, bc = nc;\n if (br >= 0 && br < N && bc >= 0 && bc < N && block_grid[br][bc]) {\n int nar = br, nac = bc;\n if (dist[r][c][nar][nac] == -1) {\n dist[r][c][nar][nac] = d + 1;\n pr[r][c][nar][nac] = r; pc[r][c][nar][nac] = c;\n pa[r][c][nar][nac] = 2; pd[r][c][nar][nac] = dir;\n pf[r][c][nar][nac] = 20; pg[r][c][nar][nac] = 20;\n q_arr[q_sz++] = {(short)r, (short)c, (short)nar, (short)nac};\n }\n }\n }\n }\n }\n return {};\n found:\n vector> path;\n int cr = tr, cc = tc, car = found_ar, cac = found_ac;\n while (cr != sr || cc != sc || car != 20 || cac != 20) {\n int act = pa[cr][cc][car][cac];\n int dir = pd[cr][cc][car][cac];\n int par = pf[cr][cc][car][cac];\n int pac = pg[cr][cc][car][cac];\n int prr = pr[cr][cc][car][cac];\n int prc = pc[cr][cc][car][cac];\n \n path.push_back({act == 0 ? 'M' : (act == 1 ? 'S' : 'A'), DIR_CHAR[dir], cr, cc});\n cr = prr; cc = prc; car = par; cac = pac;\n }\n reverse(path.begin(), path.end());\n return path;\n };\n \n auto is_connected = [&]() -> bool {\n int sr = -1, sc = -1, fc = 0;\n for (int r = 0; r < N; r++)\n for (int c = 0; c < N; c++)\n if (!block_grid[r][c]) { fc++; if (sr < 0) { sr = r; sc = c; } }\n if (fc == 0) return true;\n bool vis[20][20] = {};\n queue> q;\n q.push({sr, sc}); vis[sr][sc] = true; int cnt = 1;\n while (!q.empty()) {\n auto [r, c] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nr = r + DR[d], nc = c + DC[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !block_grid[nr][nc] && !vis[nr][nc]) {\n vis[nr][nc] = true; cnt++; q.push({nr, nc});\n }\n }\n }\n return cnt == fc;\n };\n \n auto can_place = [&](int br, int bc) -> bool {\n if (br < 0 || br >= N || bc < 0 || bc >= N) return false;\n if (block_grid[br][bc]) return false;\n if (is_target[br][bc]) return false;\n block_grid[br][bc] = true;\n bool ok = is_connected();\n block_grid[br][bc] = false;\n return ok;\n };\n \n for (int t = 1; t < M; t++) {\n int tr = targets[t].first, tc = targets[t].second;\n auto path = bfs(cur_r, cur_c, tr, tc);\n for (auto& [act, dir, nr, nc] : path) {\n actions.push_back({act, dir});\n if (act == 'A') {\n int d = dir_map[dir];\n int br = cur_r + DR[d], bc = cur_c + DC[d];\n block_grid[br][bc] = !block_grid[br][bc];\n } else if (act == 'M') {\n int d = dir_map[dir];\n cur_r += DR[d]; cur_c += DC[d];\n } else {\n int d = dir_map[dir];\n int snr = cur_r, snc = cur_c;\n while(true) {\n int nnr = snr + DR[d], nnc = snc + DC[d];\n if(nnr < 0 || nnr >= N || nnc < 0 || nnc >= N || block_grid[nnr][nnc]) break;\n snr = nnr; snc = nnc;\n }\n cur_r = snr; cur_c = snc;\n }\n }\n \n for (int d : {1, 3}) {\n int br = cur_r + DR[d], bc = cur_c + DC[d];\n if (can_place(br, bc)) {\n block_grid[br][bc] = true;\n actions.push_back({'A', DIR_CHAR[d]});\n }\n }\n }\n \n for (auto& [a, d] : actions) cout << a << \" \" << d << \"\\n\";\n return 0;\n}"},"16":{"ahc001":"#include \nusing namespace std;\n\nint n;\nvector x, y, r;\nvector ra, rb, rc, rd;\n\ninline double satisfaction(long long s, long long rv) {\n if (s <= 0 || rv <= 0) return 0;\n double ratio = (double)min(s, rv) / max(s, rv);\n return 1.0 - (1.0 - ratio) * (1.0 - ratio);\n}\n\ndouble compute_score() {\n double s = 0;\n for (int i = 0; i < n; i++)\n s += satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]), r[i]);\n return s;\n}\n\nstruct TNode {\n bool is_leaf; int company; bool vertical; int split_k;\n vector items; int lc, rc_node;\n long long total_r, left_r; int maxL, minR;\n int bL, bB, bR, bT;\n};\nvector tree;\nvector split_offset;\n\nint build_tree(vector items, int L, int B, int R, int T, mt19937& rng, int strategy) {\n int idx = tree.size();\n tree.push_back({});\n if (items.size() == 1) {\n tree[idx] = {true, items[0], false, 0, items, -1, -1, (long long)r[items[0]], 0LL, 0, 0, L,B,R,T};\n return idx;\n }\n int W = R-L, H = T-B;\n long long total_area = (long long)W*H, total_r = 0;\n for (int i : items) total_r += r[i];\n struct Cand { bool vert; int k; double score; };\n vector cands;\n for (int dir = 0; dir < 2; dir++) {\n bool vert = (dir == 0);\n if (vert && W <= 2) continue;\n if (!vert && H <= 2) continue;\n auto sorted = items;\n sort(sorted.begin(), sorted.end(), [&](int i, int j) { return vert ? x[i]= coord[sorted[k]]) continue;\n int mxL = coord[sorted[k-1]], mnR = coord[sorted[k]];\n int lo = vert?L:B, hi = vert?R:T;\n int sp_lo = max(lo+1, mxL+1), sp_hi = min(hi-1, mnR);\n if (sp_lo > sp_hi) continue;\n long long ideal = lo + (long long)(hi-lo)*sum/total_r;\n int sp = max(sp_lo, min(sp_hi, (int)ideal));\n long long area1 = vert ? (long long)(sp-L)*H : (long long)W*(sp-B);\n long long area2 = total_area - area1;\n double sat = satisfaction(area1, sum) + satisfaction(area2, total_r-sum);\n double noise;\n switch(strategy%6) {\n case 0: noise = uniform_real_distribution(0,0.01)(rng); break;\n case 1: noise = uniform_real_distribution(0,0.1)(rng); break;\n case 2: noise = uniform_real_distribution(0,0.5)(rng); break;\n case 3: noise = uniform_real_distribution(0,1.0)(rng); break;\n case 4: sat = -abs((double)sum/total_r-0.5); noise = uniform_real_distribution(0,0.05)(rng); break;\n case 5: sat *= 0.5; noise = uniform_real_distribution(0,0.5)(rng); break;\n }\n cands.push_back({vert, k, sat + noise});\n }\n }\n if (cands.empty()) {\n tree[idx] = {true, items[0], false, 0, items, -1, -1, (long long)r[items[0]], 0LL, 0, 0, L,B,R,T};\n return idx;\n }\n sort(cands.begin(), cands.end(), [](const Cand& a, const Cand& b) { return a.score > b.score; });\n int top = min((int)cands.size(), 3);\n uniform_int_distribution dist(0, top-1);\n const Cand& ch = cands[dist(rng)];\n sort(items.begin(), items.end(), [&](int i, int j) { return ch.vert ? x[i] li(items.begin(), items.begin()+ch.k), ri(items.begin()+ch.k, items.end());\n int lc, rc2;\n if (ch.vert) { lc = build_tree(li,L,B,sp,T,rng,strategy); rc2 = build_tree(ri,sp,B,R,T,rng,strategy); }\n else { lc = build_tree(li,L,B,R,sp,rng,strategy); rc2 = build_tree(ri,L,sp,R,T,rng,strategy); }\n tree[idx] = {false, -1, ch.vert, ch.k, items, lc, rc2, total_r, left_r, mxL, mnR, L,B,R,T};\n return idx;\n}\n\nvoid compute_rects(int idx, int L, int B, int R, int T) {\n if (tree[idx].is_leaf) { int i = tree[idx].company; ra[i]=L; rb[i]=B; rc[i]=R; rd[i]=T; return; }\n int lo = tree[idx].vertical ? L : B, hi = tree[idx].vertical ? R : T;\n long long ideal = lo + (long long)(hi-lo)*tree[idx].left_r/tree[idx].total_r;\n int sp = (int)ideal + split_offset[idx];\n sp = max(sp, tree[idx].maxL+1); sp = min(sp, tree[idx].minR);\n sp = max(sp, lo+1); sp = min(sp, hi-1);\n if (tree[idx].vertical) { compute_rects(tree[idx].lc,L,B,sp,T); compute_rects(tree[idx].rc_node,sp,B,R,T); }\n else { compute_rects(tree[idx].lc,L,B,R,sp); compute_rects(tree[idx].rc_node,L,sp,R,T); }\n}\n\nvoid update_subtree(int idx) {\n if (tree[idx].is_leaf) { int i = tree[idx].company; ra[i]=tree[idx].bL; rb[i]=tree[idx].bB; rc[i]=tree[idx].bR; rd[i]=tree[idx].bT; return; }\n int L=tree[idx].bL, B=tree[idx].bB, R=tree[idx].bR, T=tree[idx].bT;\n int lo = tree[idx].vertical ? L : B, hi = tree[idx].vertical ? R : T;\n long long ideal = lo + (long long)(hi-lo)*tree[idx].left_r/tree[idx].total_r;\n int sp = (int)ideal + split_offset[idx];\n sp = max(sp, tree[idx].maxL+1); sp = min(sp, tree[idx].minR);\n sp = max(sp, lo+1); sp = min(sp, hi-1);\n int lc = tree[idx].lc, rc2 = tree[idx].rc_node;\n if (tree[idx].vertical) {\n tree[lc].bL=L; tree[lc].bB=B; tree[lc].bR=sp; tree[lc].bT=T;\n tree[rc2].bL=sp; tree[rc2].bB=B; tree[rc2].bR=R; tree[rc2].bT=T;\n } else {\n tree[lc].bL=L; tree[lc].bB=B; tree[lc].bR=R; tree[lc].bT=sp;\n tree[rc2].bL=L; tree[rc2].bB=sp; tree[rc2].bR=R; tree[rc2].bT=T;\n }\n update_subtree(lc); update_subtree(rc2);\n}\n\nvoid full_update(int root) { tree[root].bL=0; tree[root].bB=0; tree[root].bR=10000; tree[root].bT=10000; update_subtree(root); }\n\ndouble subtree_score(int idx) {\n double s = 0;\n for (int i : tree[idx].items) s += satisfaction((long long)(rc[i]-ra[i])*(rd[i]-rb[i]), r[i]);\n return s;\n}\n\nvoid optimize_offsets(int root) {\n split_offset.assign(tree.size(), 0);\n compute_rects(root, 0, 0, 10000, 10000);\n double best = compute_score();\n vector internal;\n for (int i = 0; i < (int)tree.size(); i++) if (!tree[i].is_leaf) internal.push_back(i);\n for (int round = 0; round < 15; round++) {\n bool improved = false;\n for (int idx : internal) {\n for (int d : {-1000,-500,-200,-100,-50,-20,-10,-5,-2,-1,1,2,5,10,20,50,100,200,500,1000}) {\n split_offset[idx] += d;\n compute_rects(root, 0, 0, 10000, 10000);\n bool valid = true;\n for (int i = 0; i < n && valid; i++) if (ra[i]>x[i]||rc[i]<=x[i]||rb[i]>y[i]||rd[i]<=y[i]) valid = false;\n if (valid) { double ns = compute_score(); if (ns > best+1e-12) { best=ns; improved=true; continue; } }\n split_offset[idx] -= d;\n }\n }\n if (!improved) break;\n }\n compute_rects(root, 0, 0, 10000, 10000);\n}\n\nvoid sa_offsets(int root, unsigned sa_seed, int max_iter) {\n full_update(root);\n vector internal;\n for (int i = 0; i < (int)tree.size(); i++) if (!tree[i].is_leaf) internal.push_back(i);\n if (internal.empty()) return;\n double cur = compute_score(), best = cur;\n vector best_off = split_offset;\n mt19937 rng(sa_seed);\n uniform_int_distribution idist(0, (int)internal.size()-1);\n uniform_real_distribution adist(0, 1);\n double temp = 0.03;\n for (int iter = 0; iter < max_iter; iter++) {\n int idx = internal[idist(rng)];\n int d;\n if (iter < max_iter/5) d = uniform_int_distribution(-500,500)(rng);\n else if (iter < max_iter*2/5) d = uniform_int_distribution(-100,100)(rng);\n else if (iter < max_iter*4/5) d = uniform_int_distribution(-10,10)(rng);\n else d = uniform_int_distribution(-3,3)(rng);\n if (!d) continue;\n double old_s = subtree_score(idx);\n split_offset[idx] += d;\n update_subtree(idx);\n bool valid = true;\n for (int i : tree[idx].items) if (ra[i]>x[i]||rc[i]<=x[i]||rb[i]>y[i]||rd[i]<=y[i]) { valid = false; break; }\n if (!valid) { split_offset[idx] -= d; update_subtree(idx); continue; }\n double new_s = subtree_score(idx);\n double diff = new_s - old_s;\n if (diff > 0 || adist(rng) < exp(diff/temp)) { cur += diff; if (cur > best) { best = cur; best_off = split_offset; } }\n else { split_offset[idx] -= d; update_subtree(idx); }\n temp *= 0.99997;\n }\n split_offset = best_off; full_update(root);\n}\n\nvoid post_process() {\n for (int i = 0; i < n; i++) {\n while (true) {\n long long area = (long long)(rc[i]-ra[i])*(rd[i]-rb[i]);\n if (area <= r[i]) break;\n double cs = satisfaction(area, r[i]);\n int bd=-1,bdr=0; double bs=cs;\n auto try_s = [&](int dim, int dir) {\n int na=ra[i],nb=rb[i],nc=rc[i],nd=rd[i];\n if(dim==0&&dir==1)nc--;else if(dim==0&&dir==-1)na++;\n else if(dim==1&&dir==1)nd--;else nb++;\n if(na>x[i]||nc<=x[i]||nb>y[i]||nd<=y[i])return;\n if(nc-na<1||nd-nb<1)return;\n double ns=satisfaction((long long)(nc-na)*(nd-nb),r[i]);\n if(ns>bs+1e-12){bs=ns;bd=dim;bdr=dir;}\n };\n try_s(0,1);try_s(0,-1);try_s(1,1);try_s(1,-1);\n if(bd<0)break;\n if(bd==0&&bdr==1)rc[i]--;else if(bd==0&&bdr==-1)ra[i]++;\n else if(bd==1&&bdr==1)rd[i]--;else rb[i]++;\n }\n }\n for (int step : {1000,500,200,100,50,20,10,5,2,1}) {\n bool any = true;\n while (any) {\n any = false;\n vector> order;\n for (int i = 0; i < n; i++) {\n long long area = (long long)(rc[i]-ra[i])*(rd[i]-rb[i]);\n if (area < r[i]) order.push_back({-(1.0-satisfaction(area,r[i])), i});\n }\n sort(order.begin(), order.end());\n for (auto& [_, i] : order) {\n long long area = (long long)(rc[i]-ra[i])*(rd[i]-rb[i]);\n if (area >= r[i]) continue;\n double cs = satisfaction(area, r[i]);\n auto try_e = [&](int dim, int dir) -> bool {\n int na=ra[i],nb=rb[i],nc=rc[i],nd=rd[i];\n if(dim==0&&dir==1)nc+=step;else if(dim==0&&dir==-1)na-=step;\n else if(dim==1&&dir==1)nd+=step;else nb-=step;\n if(na<0||nc>10000||nb<0||nd>10000)return false;\n if(na>x[i]||nc<=x[i]||nb>y[i]||nd<=y[i])return false;\n for(int j=0;jra[j]&&nbrb[j])return false;}\n double ns=satisfaction((long long)(nc-na)*(nd-nb),r[i]);\n if(ns>cs+1e-12){ra[i]=na;rb[i]=nb;rc[i]=nc;rd[i]=nd;return true;}\n return false;\n };\n if(try_e(0,1)||try_e(0,-1)||try_e(1,1)||try_e(1,-1))any=true;\n }\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> n; x.resize(n); y.resize(n); r.resize(n); ra.resize(n); rb.resize(n); rc.resize(n); rd.resize(n);\n for (int i = 0; i < n; i++) cin >> x[i] >> y[i] >> r[i];\n auto start = chrono::steady_clock::now();\n vector indices(n); iota(indices.begin(), indices.end(), 0);\n vector ba(n),bb(n),bc(n),bd(n); double bs=-1;\n vector> candidates;\n \n for (unsigned seed = 0; ; seed++) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now-start).count()>2000) break;\n tree.clear(); split_offset.clear(); mt19937 rng(seed);\n int root = build_tree(indices, 0, 0, 10000, 10000, rng, seed%6);\n optimize_offsets(root);\n post_process();\n double s = compute_score();\n candidates.push_back({s, seed});\n if (s > bs) { bs=s; ba=ra; bb=rb; bc=rc; bd=rd; }\n }\n \n sort(candidates.rbegin(), candidates.rend());\n int top_k = min((int)candidates.size(), 10);\n for (int ci = 0; ci < top_k; ci++) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now-start).count()>4600) break;\n unsigned seed = candidates[ci].second;\n tree.clear(); split_offset.clear(); mt19937 rng(seed);\n int root = build_tree(indices, 0, 0, 10000, 10000, rng, seed%6);\n optimize_offsets(root);\n sa_offsets(root, seed*7919+42, 300000);\n post_process();\n double s = compute_score();\n if (s > bs) { bs=s; ba=ra; bb=rb; bc=rc; bd=rd; }\n }\n \n ra=ba; rb=bb; rc=bc; rd=bd;\n for (int i = 0; i < n; i++) cout << ra[i]<<\" \"<\n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 50;\nint si, sj;\nint T[N][N], P[N][N], tile_total[2500];\nint dx[] = {-1, 1, 0, 0};\nint dy[] = {0, 0, -1, 1};\nchar dc[] = {'U', 'D', 'L', 'R'};\n\nmt19937 rng(42);\nint vis[N][N], tused_arr[2500];\nchar path_buf[3000];\nint best_len = 0;\nchar best_buf[3000];\nlong long best_score = -1;\n\nint extend_path(int ci, int cj, long long& score, int start_len, int eps_x10000, int exit_w_x10, int w2_w_x10, int val_w_x10) {\n int len = start_len;\n while (true) {\n int cands[4], nc = 0;\n int nv_arr[4], ex_arr[4], mne_arr[4];\n for (int d = 0; d < 4; d++) {\n int ni = ci+dx[d], nj = cj+dy[d];\n if (ni<0||ni>=N||nj<0||nj>=N) continue;\n if (vis[ni][nj]) continue;\n if (tused_arr[T[ni][nj]]) continue;\n \n vis[ni][nj] = 1; tused_arr[T[ni][nj]] = 1;\n int ex = 0, mne = 4;\n for (int dd = 0; dd < 4; dd++) {\n int ni2 = ni+dx[dd], nj2 = nj+dy[dd];\n if (ni2<0||ni2>=N||nj2<0||nj2>=N) continue;\n if (vis[ni2][nj2]) continue;\n if (tused_arr[T[ni2][nj2]]) continue;\n ex++;\n vis[ni2][nj2] = 1; tused_arr[T[ni2][nj2]] = 1;\n int ne = 0;\n for (int ddd = 0; ddd < 4; ddd++) {\n int ni3 = ni2+dx[ddd], nj3 = nj2+dy[ddd];\n if (ni3<0||ni3>=N||nj3<0||nj3>=N) continue;\n if (vis[ni3][nj3]) continue;\n if (tused_arr[T[ni3][nj3]]) continue;\n ne++;\n }\n vis[ni2][nj2] = 0; tused_arr[T[ni2][nj2]] = 0;\n if (ne < mne) mne = ne;\n }\n vis[ni][nj] = 0; tused_arr[T[ni][nj]] = 0;\n \n cands[nc] = d;\n ex_arr[nc] = ex;\n mne_arr[nc] = mne;\n nv_arr[nc] = 2 * P[ni][nj] - tile_total[T[ni][nj]];\n nc++;\n }\n if (nc == 0) break;\n \n int chosen;\n if (nc > 1 && (int)(rng() % 10000) < eps_x10000) {\n chosen = cands[rng() % nc];\n } else {\n int bi = 0;\n long long bev = (long long)val_w_x10 * nv_arr[0] + (long long)exit_w_x10 * ex_arr[0] + (long long)w2_w_x10 * mne_arr[0];\n if (ex_arr[0] == 0) bev -= 100000000;\n else if (ex_arr[0] == 1 && mne_arr[0] == 0) bev -= 50000000;\n for (int i = 1; i < nc; i++) {\n long long ev = (long long)val_w_x10 * nv_arr[i] + (long long)exit_w_x10 * ex_arr[i] + (long long)w2_w_x10 * mne_arr[i];\n if (ex_arr[i] == 0) ev -= 100000000;\n else if (ex_arr[i] == 1 && mne_arr[i] == 0) ev -= 50000000;\n if (ev > bev) { bev = ev; bi = i; }\n }\n chosen = cands[bi];\n }\n \n int ni = ci+dx[chosen], nj = cj+dy[chosen];\n vis[ni][nj] = 1; tused_arr[T[ni][nj]] = 1;\n score += P[ni][nj];\n path_buf[len++] = dc[chosen];\n ci = ni; cj = nj;\n }\n return len;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> T[i][j];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> P[i][j];\n \n memset(tile_total, 0, sizeof(tile_total));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) tile_total[T[i][j]] += P[i][j];\n \n auto start_time = chrono::steady_clock::now();\n \n for (int iter = 0; ; iter++) {\n if (iter % 200 == 0) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - start_time).count() > 1700) break;\n }\n \n int eps_x10000 = 100 + rng() % 400;\n int exit_w_x10 = -(30 + rng() % 250);\n int w2_w_x10 = -(10 + rng() % 120);\n int val_w_x10 = 1 + rng() % 10;\n \n int new_len;\n long long new_score;\n \n if (best_len == 0 || iter % 3 == 0) {\n memset(vis, 0, sizeof(vis));\n memset(tused_arr, 0, sizeof(tused_arr));\n vis[si][sj] = 1; tused_arr[T[si][sj]] = 1;\n new_score = P[si][sj];\n new_len = extend_path(si, sj, new_score, 0, eps_x10000, exit_w_x10, w2_w_x10, val_w_x10);\n } else {\n int cut;\n int r = rng() % 10;\n if (r < 2) cut = 0;\n else if (r < 5) cut = rng() % (best_len + 1);\n else cut = max(0, best_len - 1 - (int)(rng() % 80));\n \n for (int k = 0; k < cut; k++) path_buf[k] = best_buf[k];\n \n memset(vis, 0, sizeof(vis));\n memset(tused_arr, 0, sizeof(tused_arr));\n int ci = si, cj = sj;\n vis[ci][cj] = 1; tused_arr[T[ci][cj]] = 1;\n new_score = P[ci][cj];\n for (int k = 0; k < cut; k++) {\n int d = (path_buf[k]=='U')?0:(path_buf[k]=='D')?1:(path_buf[k]=='L')?2:3;\n ci += dx[d]; cj += dy[d];\n vis[ci][cj] = 1; tused_arr[T[ci][cj]] = 1;\n new_score += P[ci][cj];\n }\n \n new_len = extend_path(ci, cj, new_score, cut, eps_x10000, exit_w_x10, w2_w_x10, val_w_x10);\n }\n \n if (new_score > best_score) {\n best_score = new_score;\n best_len = new_len;\n memcpy(best_buf, path_buf, new_len);\n }\n }\n \n for (int i = 0; i < best_len; i++) cout << best_buf[i];\n cout << endl;\n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble row_h[N], col_v[N], row_h_var[N], col_v_var[N];\ndouble h_dev[N][N-1], v_dev[N-1][N], h_dev_var[N][N-1], v_dev_var[N-1][N];\nmt19937 rng(42);\nnormal_distribution norm_dist(0, 1);\n\ndouble get_h_est(int i, int j) { return row_h[i] + h_dev[i][j]; }\ndouble get_v_est(int i, int j) { return col_v[j] + v_dev[i][j]; }\n\npair dijkstra_with_cost(int si, int sj, int ti, int tj, double temperature) {\n double hw[N][N-1], vw[N-1][N];\n for(int i=0; i prev_node[N][N]; bool vis[N][N] = {};\n for(int i=0; i, vector>, greater>> pq;\n pq.push(make_tuple(0.0, si, sj));\n while(!pq.empty()){\n auto [d, i, j] = pq.top(); pq.pop();\n if(vis[i][j]) continue; vis[i][j] = true;\n if(i==ti && j==tj) break;\n if(i > 0 && !vis[i-1][j]) { double w = vw[i-1][j]; if(d+w < dist[i-1][j]) { dist[i-1][j] = d+w; prev_node[i-1][j] = {i,j}; pq.push(make_tuple(dist[i-1][j], i-1, j)); } }\n if(i < N-1 && !vis[i+1][j]) { double w = vw[i][j]; if(d+w < dist[i+1][j]) { dist[i+1][j] = d+w; prev_node[i+1][j] = {i,j}; pq.push(make_tuple(dist[i+1][j], i+1, j)); } }\n if(j > 0 && !vis[i][j-1]) { double w = hw[i][j-1]; if(d+w < dist[i][j-1]) { dist[i][j-1] = d+w; prev_node[i][j-1] = {i,j}; pq.push(make_tuple(dist[i][j-1], i, j-1)); } }\n if(j < N-1 && !vis[i][j+1]) { double w = hw[i][j]; if(d+w < dist[i][j+1]) { dist[i][j+1] = d+w; prev_node[i][j+1] = {i,j}; pq.push(make_tuple(dist[i][j+1], i, j+1)); } }\n }\n string path; double mean_cost = 0; int ci = ti, cj = tj;\n while(ci != si || cj != sj){\n auto [pi, pj] = prev_node[ci][cj];\n if(pi == ci-1) { path += 'D'; mean_cost += get_v_est(ci-1, cj); }\n else if(pi == ci+1) { path += 'U'; mean_cost += get_v_est(ci, cj); }\n else if(pj == cj-1) { path += 'R'; mean_cost += get_h_est(ci, cj-1); }\n else { path += 'L'; mean_cost += get_h_est(ci, cj); }\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return {path, mean_cost};\n}\n\nvoid update(int si, int sj, const string& path, int observed) {\n struct E { char t; int i, j; }; vector edges;\n map hr, vc; int ci = si, cj = sj;\n for(char c : path){\n if(c == 'U') { edges.push_back({'v', ci-1, cj}); vc[cj]++; ci--; }\n else if(c == 'D') { edges.push_back({'v', ci, cj}); vc[cj]++; ci++; }\n else if(c == 'L') { edges.push_back({'h', ci, cj-1}); hr[ci]++; cj--; }\n else { edges.push_back({'h', ci, cj}); hr[ci]++; cj++; }\n }\n double pred = 0;\n for(auto& e : edges) pred += (e.t == 'h') ? get_h_est(e.i, e.j) : get_v_est(e.i, e.j);\n double residual = observed - pred;\n double obs_var = pred * pred / 300.0;\n double S = obs_var;\n for(auto& [i, n] : hr) S += n * n * row_h_var[i];\n for(auto& [j, n] : vc) S += n * n * col_v_var[j];\n for(auto& e : edges) S += (e.t == 'h') ? h_dev_var[e.i][e.j] : v_dev_var[e.i][e.j];\n for(auto& [i, n] : hr) {\n double K = row_h_var[i] * n / S; row_h[i] += K * residual; row_h_var[i] *= (1 - K * n);\n row_h[i] = max(500.0, min(15000.0, row_h[i])); row_h_var[i] = max(100.0, row_h_var[i]);\n }\n for(auto& [j, n] : vc) {\n double K = col_v_var[j] * n / S; col_v[j] += K * residual; col_v_var[j] *= (1 - K * n);\n col_v[j] = max(500.0, min(15000.0, col_v[j])); col_v_var[j] = max(100.0, col_v_var[j]);\n }\n for(auto& e : edges){\n double& dev = (e.t == 'h') ? h_dev[e.i][e.j] : v_dev[e.i][e.j];\n double& dv = (e.t == 'h') ? h_dev_var[e.i][e.j] : v_dev_var[e.i][e.j];\n double K = dv / S; dev += K * residual; dv *= (1 - K);\n dev = max(-5000.0, min(5000.0, dev)); dv = max(100.0, dv);\n }\n}\n\nint main(){\n ios::sync_with_stdio(false); cin.tie(nullptr);\n for(int i=0; i> si >> sj >> ti >> tj;\n double temperature = max(0.0, 1.0 - k / 350.0);\n string best_path; double best_cost = 1e18;\n for(int t=0; t<5; t++){\n auto [path, cost] = dijkstra_with_cost(si, sj, ti, tj, temperature);\n if(cost < best_cost) { best_cost = cost; best_path = path; }\n }\n cout << best_path << endl;\n int obs; cin >> obs; update(si, sj, best_path, obs);\n }\n return 0;\n}","ahc004":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct Entry {\n uint16_t m, pi;\n};\n\nint N, M;\nvector s;\nvector slen;\nvector adj[400][8];\nvector matchCount;\nvector fullMatchCount;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n cin >> N >> M;\n s.resize(M);\n for (int m = 0; m < M; m++) cin >> s[m];\n \n const int NUM_CHARS = 8;\n mt19937 rng(42);\n auto start_time = chrono::high_resolution_clock::now();\n \n slen.resize(M);\n for (int m = 0; m < M; m++) slen[m] = s[m].length();\n \n // Fast EM Initialization\n vector> charProb(N * N);\n for (int i = 0; i < N * N; i++) for (int c = 0; c < NUM_CHARS; c++) charProb[i][c] = 1.0 / NUM_CHARS;\n \n for (int iter = 0; iter < 30; iter++) {\n auto now = chrono::high_resolution_clock::now();\n if (chrono::duration(now - start_time).count() > 0.15) break;\n \n vector> newProb(N * N);\n for (int i = 0; i < N * N; i++) newProb[i].fill(0);\n \n for (int m = 0; m < M; m++) {\n int k = slen[m];\n vector weights(2 * N * N);\n double maxW = 0;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double wH = 1.0, wV = 1.0;\n for (int p = 0; p < k; p++) {\n wH *= charProb[i * N + (j + p) % N][s[m][p] - 'A'];\n wV *= charProb[((i + p) % N) * N + j][s[m][p] - 'A'];\n }\n weights[2 * (i * N + j)] = wH;\n weights[2 * (i * N + j) + 1] = wV;\n if (wH > maxW) maxW = wH;\n if (wV > maxW) maxW = wV;\n }\n }\n \n if (maxW < 1e-300) continue;\n double sumW = 0;\n for (int pi = 0; pi < 2 * N * N; pi++) { weights[pi] /= maxW; sumW += weights[pi]; }\n if (sumW < 1e-300) continue;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double wH = weights[2 * (i * N + j)] / sumW;\n double wV = weights[2 * (i * N + j) + 1] / sumW;\n for (int p = 0; p < k; p++) {\n newProb[i * N + (j + p) % N][s[m][p] - 'A'] += wH;\n newProb[((i + p) % N) * N + j][s[m][p] - 'A'] += wV;\n }\n }\n }\n }\n \n for (int i = 0; i < N * N; i++) {\n double sum = 0;\n for (int c = 0; c < NUM_CHARS; c++) sum += newProb[i][c];\n if (sum > 0) {\n for (int c = 0; c < NUM_CHARS; c++) newProb[i][c] = max(newProb[i][c] / sum, 1e-4);\n double sum2 = 0;\n for (int c = 0; c < NUM_CHARS; c++) sum2 += newProb[i][c];\n for (int c = 0; c < NUM_CHARS; c++) newProb[i][c] /= sum2;\n } else {\n for (int c = 0; c < NUM_CHARS; c++) newProb[i][c] = 1.0 / NUM_CHARS;\n }\n }\n charProb = move(newProb);\n }\n \n vector mat(N, string(N, 'A'));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n double maxP = 0; char best = 'A';\n for (int c = 0; c < NUM_CHARS; c++) if (charProb[i * N + j][c] > maxP) { maxP = charProb[i * N + j][c]; best = 'A' + c; }\n mat[i][j] = best;\n }\n }\n \n // Build Character-Based Adjacency Lists\n for (int m = 0; m < M; m++) {\n int k = slen[m];\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int piH = 2 * (i * N + j);\n for (int p = 0; p < k; p++) adj[i * N + (j + p) % N][s[m][p] - 'A'].push_back({(uint16_t)m, (uint16_t)piH});\n int piV = 2 * (i * N + j) + 1;\n for (int p = 0; p < k; p++) adj[((i + p) % N) * N + j][s[m][p] - 'A'].push_back({(uint16_t)m, (uint16_t)piV});\n }\n }\n }\n \n // Match Counts\n matchCount.resize(M * 800, 0);\n fullMatchCount.resize(M, 0);\n int totalMatched = 0, numDots = 0;\n \n auto recompute = [&]() {\n numDots = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (mat[i][j] == '.') numDots++;\n for (int m = 0; m < M; m++) {\n int k = slen[m]; fullMatchCount[m] = 0;\n int base = m * 800;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n int cH = 0, cV = 0;\n for (int p = 0; p < k; p++) { if (mat[i][(j+p)%N] == s[m][p]) cH++; if (mat[(i+p)%N][j] == s[m][p]) cV++; }\n matchCount[base + 2*(i*N+j)] = cH; matchCount[base + 2*(i*N+j)+1] = cV;\n if (cH == k) fullMatchCount[m]++; if (cV == k) fullMatchCount[m]++;\n }\n }\n totalMatched = 0;\n for (int m = 0; m < M; m++) if (fullMatchCount[m] > 0) totalMatched++;\n };\n \n recompute();\n int bestMatched = totalMatched, bestDots = -1;\n vector bestMat = mat;\n if (totalMatched == M) bestDots = numDots;\n \n // SA Phase\n int stepCount = 0;\n double lastTime = chrono::duration(chrono::high_resolution_clock::now() - start_time).count();\n \n while (true) {\n stepCount++;\n if ((stepCount & 0xFFF) == 0) {\n lastTime = chrono::duration(chrono::high_resolution_clock::now() - start_time).count();\n if (lastTime > 2.7) break;\n }\n double temp = 1.5 * max(0.0, 1.0 - lastTime / 2.8) + 0.01;\n \n int ci = -1, cj = -1;\n char newC;\n int moveType = rng() % 100;\n \n // 15% Multi-cell string-level move\n if (moveType < 15 && totalMatched < M) {\n int start_m = rng() % M;\n int m = -1;\n for (int t = 0; t < M; t++) {\n int rm = (start_m + t) % M;\n if (fullMatchCount[rm] == 0) { m = rm; break; }\n }\n if (m != -1) {\n int k = slen[m], bestMC = -1, bestPi = -1, base = m * 800;\n for (int pi = 0; pi < 2 * N * N; pi++) if (matchCount[base + pi] > bestMC) { bestMC = matchCount[base + pi]; bestPi = pi; }\n if (bestPi != -1) {\n int dir = bestPi % 2, ij = bestPi / 2, si = ij / N, sj = ij % N;\n int deltaMatched = 0, deltaDots = 0;\n char oldChars[13];\n \n for (int p = 0; p < k; p++) {\n int ci2 = dir == 0 ? si : (si + p) % N, cj2 = dir == 0 ? (sj + p) % N : sj;\n int idx2 = ci2 * N + cj2;\n oldChars[p] = mat[ci2][cj2];\n newC = s[m][p];\n if (oldChars[p] == newC) continue;\n if (oldChars[p] == '.') deltaDots--;\n if (oldChars[p] != '.') { for (auto& e : adj[idx2][oldChars[p] - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t oMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = oMC - 1; if (oMC == k2) { if (fullMatchCount[m2] == 1) deltaMatched--; fullMatchCount[m2]--; } } }\n if (newC != '.') { for (auto& e : adj[idx2][newC - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t oMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = oMC + 1; if (oMC + 1 == k2) { if (fullMatchCount[m2] == 0) deltaMatched++; fullMatchCount[m2]++; } } }\n mat[ci2][cj2] = newC;\n }\n \n bool accept = false;\n if (deltaMatched > 0) accept = true;\n else if (deltaMatched == 0) accept = (rng() % 2 == 0);\n else if (totalMatched == M && totalMatched + deltaMatched < M) accept = false;\n else accept = (rng() % 10000 < (int)(exp((double)deltaMatched / temp) * 10000));\n\n if (accept) {\n totalMatched += deltaMatched; numDots += deltaDots;\n if (totalMatched > bestMatched || (totalMatched == M && numDots > bestDots)) { bestMatched = totalMatched; bestMat = mat; if (totalMatched == M) bestDots = numDots; }\n } else {\n for (int p = k - 1; p >= 0; p--) {\n int ci2 = dir == 0 ? si : (si + p) % N, cj2 = dir == 0 ? (sj + p) % N : sj;\n int idx2 = ci2 * N + cj2;\n char nc = s[m][p], oc = oldChars[p];\n if (oc == nc) continue;\n if (nc != '.') { for (auto& e : adj[idx2][nc - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t curMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = curMC - 1; if (curMC == k2) fullMatchCount[m2]--; } }\n if (oc != '.') { for (auto& e : adj[idx2][oc - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t curMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = curMC + 1; if (curMC + 1 == k2) fullMatchCount[m2]++; } }\n mat[ci2][cj2] = oc;\n }\n }\n }\n continue;\n }\n } else if (moveType < 50 && totalMatched < M) {\n // 35% Targeted single-cell move\n int start_m = rng() % M;\n int m = -1;\n for (int t = 0; t < M; t++) {\n int rm = (start_m + t) % M;\n if (fullMatchCount[rm] == 0) { m = rm; break; }\n }\n if (m != -1) {\n int k = slen[m];\n int bestMC = -1, bestPi = -1, base = m * 800;\n for (int pi = 0; pi < 2 * N * N; pi++) if (matchCount[base + pi] > bestMC) { bestMC = matchCount[base + pi]; bestPi = pi; }\n \n if (bestPi != -1) {\n int dir = bestPi % 2, ij = bestPi / 2, si = ij / N, sj = ij % N;\n int mis[13]; int numMis = 0;\n for (int p = 0; p < k; p++) {\n int ci2 = dir == 0 ? si : (si + p) % N, cj2 = dir == 0 ? (sj + p) % N : sj;\n if (mat[ci2][cj2] != s[m][p]) mis[numMis++] = p;\n }\n if (numMis > 0) {\n int p = mis[rng() % numMis];\n ci = dir == 0 ? si : (si + p) % N;\n cj = dir == 0 ? (sj + p) % N : sj;\n newC = s[m][p];\n }\n }\n }\n }\n \n if (ci == -1) {\n ci = rng() % N; cj = rng() % N;\n char oldC = mat[ci][cj];\n if (totalMatched == M && (rng() % 2 == 0)) {\n newC = '.';\n } else {\n if (rng() % 10 < 7) {\n int r = rng() % 8;\n bool found = false;\n for (int t = 0; t < 8; t++) {\n int c = (r + t) % 8;\n if (!adj[ci * N + cj][c].empty() && 'A' + c != oldC) {\n newC = 'A' + c; found = true; break;\n }\n }\n if (!found) {\n newC = 'A' + rng() % 7;\n if (newC >= oldC) newC++;\n }\n } else {\n newC = 'A' + rng() % 7;\n if (newC >= oldC) newC++;\n }\n }\n }\n \n // Single-cell SA evaluation\n int idx = ci * N + cj;\n char oldC = mat[ci][cj];\n if (newC == oldC) continue;\n \n int deltaMatched = 0;\n int deltaDots = (newC == '.' && oldC != '.') ? 1 : ((newC != '.' && oldC == '.') ? -1 : 0);\n \n if (oldC != '.') {\n for (auto& e : adj[idx][oldC - 'A']) {\n int m = e.m, pi = e.pi, k = slen[m];\n if (matchCount[m*800+pi] == k) {\n if (fullMatchCount[m] == 1) deltaMatched--;\n fullMatchCount[m]--;\n }\n matchCount[m*800+pi]--;\n }\n }\n if (newC != '.') {\n for (auto& e : adj[idx][newC - 'A']) {\n int m = e.m, pi = e.pi, k = slen[m];\n matchCount[m*800+pi]++;\n if (matchCount[m*800+pi] == k) {\n if (fullMatchCount[m] == 0) deltaMatched++;\n fullMatchCount[m]++;\n }\n }\n }\n \n bool accept = false;\n if (deltaMatched > 0) accept = true;\n else if (deltaMatched == 0) {\n if (totalMatched == M) {\n if (deltaDots > 0) accept = true;\n else if (deltaDots == 0) accept = (rng() % 2 == 0);\n else accept = (rng() % 10000 < (int)(exp((double)deltaDots / temp) * 10000));\n } else {\n accept = (rng() % 2 == 0);\n }\n }\n else if (totalMatched == M && totalMatched + deltaMatched < M) accept = false;\n else accept = (rng() % 10000 < (int)(exp((double)deltaMatched / temp) * 10000));\n \n if (accept) {\n mat[ci][cj] = newC; totalMatched += deltaMatched; numDots += deltaDots;\n if (totalMatched > bestMatched || (totalMatched == M && numDots > bestDots)) { bestMatched = totalMatched; bestMat = mat; if (totalMatched == M) bestDots = numDots; }\n } else {\n if (newC != '.') { for (auto& e : adj[idx][newC - 'A']) { int m = e.m, pi = e.pi, k = slen[m]; int8_t curMC = matchCount[m*800+pi]; matchCount[m*800+pi] = curMC - 1; if (curMC == k) fullMatchCount[m]--; } }\n if (oldC != '.') { for (auto& e : adj[idx][oldC - 'A']) { int m = e.m, pi = e.pi, k = slen[m]; int8_t curMC = matchCount[m*800+pi]; matchCount[m*800+pi] = curMC + 1; if (curMC + 1 == k) fullMatchCount[m]++; } }\n }\n }\n \n mat = bestMat; recompute();\n \n // Greedy Repair\n for (int rep = 0; rep < 5; rep++) {\n bool anyImproved = false;\n for (int m = 0; m < M; m++) {\n if (fullMatchCount[m] > 0) continue;\n int k = slen[m], bestMC = -1, bestPi = -1, base = m * 800;\n for (int pi = 0; pi < 2 * N * N; pi++) if (matchCount[base + pi] > bestMC) { bestMC = matchCount[base + pi]; bestPi = pi; }\n if (bestPi < 0) continue;\n int dir = bestPi % 2, ij = bestPi / 2, si = ij / N, sj = ij % N;\n int deltaMatched = 0, deltaDots = 0;\n char oldChars[13];\n \n for (int p = 0; p < k; p++) {\n int ci2 = dir == 0 ? si : (si + p) % N, cj2 = dir == 0 ? (sj + p) % N : sj;\n int idx2 = ci2 * N + cj2;\n oldChars[p] = mat[ci2][cj2];\n char nc = s[m][p];\n if (oldChars[p] == nc) continue;\n if (oldChars[p] == '.') deltaDots--;\n if (oldChars[p] != '.') { for (auto& e : adj[idx2][oldChars[p] - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t oMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = oMC - 1; if (oMC == k2) { if (fullMatchCount[m2] == 1) deltaMatched--; fullMatchCount[m2]--; } } }\n if (nc != '.') { for (auto& e : adj[idx2][nc - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t oMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = oMC + 1; if (oMC + 1 == k2) { if (fullMatchCount[m2] == 0) deltaMatched++; fullMatchCount[m2]++; } } }\n mat[ci2][cj2] = nc;\n }\n if (deltaMatched > 0) {\n totalMatched += deltaMatched; numDots += deltaDots;\n anyImproved = true;\n } else {\n for (int p = k - 1; p >= 0; p--) {\n int ci2 = dir == 0 ? si : (si + p) % N, cj2 = dir == 0 ? (sj + p) % N : sj;\n int idx2 = ci2 * N + cj2;\n char nc = s[m][p], oc = oldChars[p];\n if (oc == nc) continue;\n if (nc != '.') { for (auto& e : adj[idx2][nc - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t curMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = curMC - 1; if (curMC == k2) fullMatchCount[m2]--; } }\n if (oc != '.') { for (auto& e : adj[idx2][oc - 'A']) { int m2 = e.m, pi2 = e.pi, k2 = slen[m2]; int8_t curMC = matchCount[m2*800+pi2]; matchCount[m2*800+pi2] = curMC + 1; if (curMC + 1 == k2) fullMatchCount[m2]++; } }\n mat[ci2][cj2] = oc;\n }\n }\n }\n if (totalMatched > bestMatched || (totalMatched == M && numDots > bestDots)) { bestMatched = totalMatched; bestMat = mat; if (totalMatched == M) bestDots = numDots; }\n if (!anyImproved) break;\n }\n \n mat = bestMat; recompute();\n \n // Dot Maximization\n if (totalMatched == M) {\n while (true) {\n int prevDots = numDots;\n for (int ci = 0; ci < N; ci++) {\n for (int cj = 0; cj < N; cj++) {\n if (mat[ci][cj] == '.') continue;\n char oldC2 = mat[ci][cj]; int idx2 = ci * N + cj;\n int deltaM = 0;\n for (auto& e : adj[idx2][oldC2 - 'A']) {\n int m2 = e.m, pi2 = e.pi, k2 = slen[m2];\n if (matchCount[m2*800+pi2] == k2) {\n if (fullMatchCount[m2] == 1) deltaM--;\n }\n }\n if (deltaM == 0) {\n mat[ci][cj] = '.';\n numDots++;\n for (auto& e : adj[idx2][oldC2 - 'A']) {\n int m2 = e.m, pi2 = e.pi, k2 = slen[m2];\n int8_t oldMC = matchCount[m2*800+pi2];\n matchCount[m2*800+pi2] = oldMC - 1;\n if (oldMC == k2) fullMatchCount[m2]--;\n }\n }\n }\n }\n if (numDots == prevDots) break;\n }\n if (numDots > bestDots) { bestDots = numDots; bestMat = mat; }\n }\n \n for (int i = 0; i < N; i++) cout << bestMat[i] << '\\n';\n return 0;\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\nint total_roads;\n\nbool is_road(int i, int j) { return i>=0&&i=0&&j>> vis_from_bit;\n\nvoid precompute_visibility() {\n vis_from_bit.assign(N, vector>(N));\n for(int i=0;i=0&&is_road(i,jj);jj--) vis_from_bit[i][j][i*N+jj] = 1;\n for(int jj=j+1;jj=0&&is_road(ii,j);ii--) vis_from_bit[i][j][ii*N+j] = 1;\n for(int ii=i+1;ii>, vector>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX)), prev(N, vector(N, -1));\n priority_queue>, vector>>, greater<>> pq;\n dist[si][sj] = 0; pq.push({0, {si, sj}});\n while(!pq.empty()) {\n auto [d, p] = pq.top(); pq.pop();\n auto [i, j] = p;\n if(d > dist[i][j]) continue;\n for(int k=0;k<4;k++) {\n int ni = i+di[k], nj = j+dj[k];\n if(is_road(ni, nj)) {\n int nd = d + cell_cost(ni, nj);\n if(nd < dist[ni][nj]) { dist[ni][nj] = nd; prev[ni][nj] = k; pq.push({nd, {ni, nj}}); }\n }\n }\n }\n return {dist, prev};\n}\n\nstring reconstruct(int si, int sj, int ti, int tj, const vector>& prev) {\n if(si==ti && sj==tj) return \"\";\n string path; int ci=ti, cj=tj;\n while(ci!=si || cj!=sj) { int k=prev[ci][cj]; if(k==-1) return \"\"; path+=dc[k]; ci-=di[k]; cj-=dj[k]; }\n reverse(path.begin(), path.end()); return path;\n}\n\nvector> build_greedy(double alpha) {\n bitset<4800> covered = vis_from_bit[si][sj];\n vector> targets;\n int ci = si, cj = sj;\n \n while(covered.count() < total_roads) {\n auto [dist, prev] = dijkstra(ci, cj);\n vector> nodes;\n for(int i=0; i>> tree_acc(N, vector>(N));\n double best_score = -1e-9; int best_idx = -1; bitset<4800> best_acc;\n \n for(auto& [d_val, idx] : nodes) {\n int i = idx / N, j = idx % N;\n if(i == ci && j == cj) {\n tree_acc[i][j] = vis_from_bit[i][j];\n } else if(prev[i][j] != -1) {\n int pi = i - di[prev[i][j]], pj = j - dj[prev[i][j]];\n tree_acc[i][j] = tree_acc[pi][pj] | vis_from_bit[i][j];\n }\n \n bitset<4800> diff = tree_acc[i][j] & ~covered;\n int new_bits = diff.count();\n \n if(new_bits > 0 && dist[i][j] > 0) {\n double score = pow((double)new_bits, alpha) / (double)dist[i][j];\n if(score > best_score) { best_score = score; best_idx = idx; best_acc = tree_acc[i][j]; }\n }\n }\n \n if(best_idx == -1) break;\n int bi = best_idx / N, bj = best_idx % N;\n targets.push_back({bi, bj});\n covered |= best_acc;\n ci = bi; cj = bj;\n }\n return targets;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> si >> sj; grid.resize(N); for(int i=0;i> grid[i];\n precompute_visibility();\n total_roads = 0; for(int i=0;i> pool_set;\n pool_set.insert({si, sj});\n \n vector>> greedy_targets;\n for(double alpha : {0.5, 0.8, 1.0, 1.5, 2.0, 3.0}) {\n auto targets = build_greedy(alpha);\n greedy_targets.push_back(targets);\n for(auto& t : targets) pool_set.insert(t);\n }\n \n vector> all_roads;\n for(int i=0;i 150) {\n vector> T_tmp(pool_set.begin(), pool_set.end());\n shuffle(T_tmp.begin(), T_tmp.end(), rng);\n pool_set.clear();\n pool_set.insert({si, sj});\n for(auto& targets : greedy_targets) for(auto& t : targets) pool_set.insert(t);\n for(auto& p : T_tmp) {\n if(pool_set.size() >= 150) break;\n pool_set.insert(p);\n }\n }\n \n vector> T(pool_set.begin(), pool_set.end());\n int M = T.size(), S = -1;\n map, int> to_idx;\n for(int i=0; i> d(M, vector(M, INT_MAX));\n vector>> path_vis(M, vector>(M));\n vector>> all_prev(M, vector>(N, vector(N, -1)));\n \n for(int u=0; u bs = vis_from_bit[T[u].first][T[u].second];\n int ci = T[v].first, cj = T[v].second;\n while(ci != T[u].first || cj != T[u].second) {\n bs |= vis_from_bit[ci][cj];\n int k = prev[ci][cj]; \n ci -= di[k]; cj -= dj[k];\n }\n path_vis[u][v] = bs;\n }\n }\n \n auto evaluate = [&](const vector& seq) -> pair {\n if(seq.empty()) {\n bitset<4800> cov = vis_from_bit[si][sj];\n int missing = total_roads - cov.count();\n return {(long long)1e8 * missing, missing};\n }\n if(d[S][seq[0]] == INT_MAX || d[seq.back()][S] == INT_MAX) return {1e18, total_roads};\n long long cost = d[S][seq[0]] + d[seq.back()][S];\n bitset<4800> cov = path_vis[S][seq[0]] | path_vis[seq.back()][S];\n for(int i=0; i+1<(int)seq.size(); ++i) {\n if(d[seq[i]][seq[i+1]] == INT_MAX) return {1e18, total_roads};\n cost += d[seq[i]][seq[i+1]];\n cov |= path_vis[seq[i]][seq[i+1]];\n }\n int missing = total_roads - cov.count();\n return {cost + (long long)1e8 * missing, missing};\n };\n \n vector cur_seq;\n long long min_init_cost = 1e18;\n \n auto try_init = [&](vector seq) {\n auto [cost, missing] = evaluate(seq);\n if(missing == 0 && cost < min_init_cost) {\n min_init_cost = cost;\n cur_seq = seq;\n }\n };\n \n for(auto& targets : greedy_targets) {\n vector seq; \n bool valid = true;\n for(auto& t : targets) {\n if(to_idx.count(t)) seq.push_back(to_idx[t]);\n else { valid = false; break; }\n }\n if(valid) try_init(seq);\n }\n \n long long cur_cost = min_init_cost;\n \n if(min_init_cost >= 1e18) {\n bitset<4800> covered = vis_from_bit[si][sj];\n int cur = S; vector used(M, false);\n cur_seq.clear();\n while(covered.count() < total_roads) {\n int best_j = -1; int best_new = -1;\n for(int j=0; j diff = path_vis[cur][j] & ~covered;\n int cnt = diff.count();\n if(cnt > best_new) { best_new = cnt; best_j = j; }\n }\n if(best_new <= 0) break;\n cur_seq.push_back(best_j);\n covered |= path_vis[cur][best_j];\n cur = best_j; used[best_j] = true;\n }\n auto [cost, missing] = evaluate(cur_seq);\n cur_cost = cost;\n }\n \n auto best_seq = cur_seq; long long best_cost = cur_cost;\n \n double T_start = 1000.0, T_end = 0.1;\n auto start_sa = chrono::high_resolution_clock::now();\n double time_limit_sa = 2500.0;\n mt19937 rng_sa(12345); uniform_real_distribution dist01(0.0, 1.0);\n \n while(true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration_cast(now - start_sa).count() / 1000.0;\n if(elapsed > time_limit_sa) break;\n double T_sa = T_start * pow(T_end / T_start, elapsed / time_limit_sa);\n \n int op = rng_sa() % 4;\n bool applied = false;\n \n if (op == 0 && cur_seq.size() >= 2) {\n int l = rng_sa() % cur_seq.size(), r = rng_sa() % cur_seq.size();\n if(l > r) swap(l, r); if(l == r) continue;\n reverse(cur_seq.begin() + l, cur_seq.begin() + r + 1);\n auto [new_cost, new_missing] = evaluate(cur_seq);\n if(new_cost < 1e18) {\n double delta = new_cost - cur_cost;\n if(delta < 0 || dist01(rng_sa) < exp(-delta / T_sa)) {\n cur_cost = new_cost; applied = true;\n if(new_missing == 0 && new_cost < best_cost) { best_cost = new_cost; best_seq = cur_seq; }\n }\n }\n if(!applied) reverse(cur_seq.begin() + l, cur_seq.begin() + r + 1);\n } else if (op == 1 && cur_seq.size() > 1) {\n int i = rng_sa() % cur_seq.size();\n int val = cur_seq[i];\n cur_seq.erase(cur_seq.begin() + i);\n auto [new_cost, new_missing] = evaluate(cur_seq);\n if(new_cost < 1e18) {\n double delta = new_cost - cur_cost;\n if(delta < 0 || dist01(rng_sa) < exp(-delta / T_sa)) {\n cur_cost = new_cost; applied = true;\n if(new_missing == 0 && new_cost < best_cost) { best_cost = new_cost; best_seq = cur_seq; }\n }\n }\n if(!applied) cur_seq.insert(cur_seq.begin() + i, val);\n } else if (op == 2) {\n int x = rng_sa() % M, i = rng_sa() % (cur_seq.size() + 1);\n cur_seq.insert(cur_seq.begin() + i, x);\n auto [new_cost, new_missing] = evaluate(cur_seq);\n if(new_cost < 1e18) {\n double delta = new_cost - cur_cost;\n if(delta < 0 || dist01(rng_sa) < exp(-delta / T_sa)) {\n cur_cost = new_cost; applied = true;\n if(new_missing == 0 && new_cost < best_cost) { best_cost = new_cost; best_seq = cur_seq; }\n }\n }\n if(!applied) cur_seq.erase(cur_seq.begin() + i);\n } else if (op == 3 && cur_seq.size() > 0) {\n int i = rng_sa() % cur_seq.size(), x = rng_sa() % M;\n int old_val = cur_seq[i];\n cur_seq[i] = x;\n auto [new_cost, new_missing] = evaluate(cur_seq);\n if(new_cost < 1e18) {\n double delta = new_cost - cur_cost;\n if(delta < 0 || dist01(rng_sa) < exp(-delta / T_sa)) {\n cur_cost = new_cost; applied = true;\n if(new_missing == 0 && new_cost < best_cost) { best_cost = new_cost; best_seq = cur_seq; }\n }\n }\n if(!applied) cur_seq[i] = old_val;\n }\n }\n \n auto generate_final_route = [&](const vector& seq) -> string {\n string route;\n if (seq.empty()) return route;\n for (int idx = 0; idx < (int)seq.size(); ++idx) {\n int u = (idx == 0) ? S : seq[idx - 1], v = seq[idx];\n route += reconstruct(T[u].first, T[u].second, T[v].first, T[v].second, all_prev[u]);\n }\n route += reconstruct(T[seq.back()].first, T[seq.back()].second, T[S].first, T[S].second, all_prev[seq.back()]);\n return route;\n };\n \n cout << generate_final_route(best_seq) << endl;\n return 0;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint N, M, K, R;\nvector> d, deps, rev_deps;\nvector> skill_est;\nvector crit_path;\nvector task_start, task_done;\nvector>> member_obs;\n\nvector hungarian(const vector>& cost) {\n int n = cost.size(), m = cost[0].size();\n const double INF = 1e18;\n vector u(n+1,0), v(m+1,0);\n vector p(m+1,0), way(m+1,0);\n for (int i = 1; i <= n; i++) {\n p[0] = i; int j0 = 0;\n vector minv(m+1, INF);\n vector used(m+1, false);\n do {\n used[j0] = true;\n int i0 = p[j0], j1 = 0;\n double delta = INF;\n for (int j = 1; j <= m; j++) if (!used[j]) {\n double cur = cost[i0-1][j-1] - u[i0] - v[j];\n if (cur < minv[j]) { minv[j] = cur; way[j] = j0; }\n if (minv[j] < delta) { delta = minv[j]; j1 = j; }\n }\n for (int j = 0; j <= m; j++) {\n if (used[j]) { u[p[j]] += delta; v[j] -= delta; }\n else minv[j] -= delta;\n }\n j0 = j1;\n } while (p[j0] != 0);\n do { int j1 = way[j0]; p[j0] = p[j1]; j0 = j1; } while (j0);\n }\n vector asgn(n, -1);\n for (int j = 1; j <= m; j++) if (p[j] > 0 && p[j] <= n) asgn[p[j]-1] = j-1;\n return asgn;\n}\n\nvoid recompute_crit_path() {\n vector et(N);\n for (int i = 0; i < N; ++i) {\n if (task_done[i] != -1) { et[i] = 0; continue; }\n if (task_start[i] != -1) { et[i] = 0.1; continue; } // Already started, will finish soon\n double min_w = 1e9;\n for (int j = 0; j < M; ++j) {\n double w = 0;\n for (int k = 0; k < K; ++k) w += max(0.0, (double)d[i][k] - skill_est[j][k]);\n min_w = min(min_w, w);\n }\n et[i] = max(1.0, min_w);\n }\n for (int i = N - 1; i >= 0; i--) {\n crit_path[i] = et[i];\n for (int v : rev_deps[i]) crit_path[i] = max(crit_path[i], et[i] + crit_path[v]);\n }\n}\n\nvoid reestimate(int j) {\n auto& ob = member_obs[j];\n if (ob.empty()) return;\n for (int iter = 0; iter < 30; ++iter) {\n for (auto& [task, t] : ob) {\n double w_pred = 0;\n for (int k = 0; k < K; ++k) w_pred += max(0.0, (double)d[task][k] - skill_est[j][k]);\n \n if (t == 1) {\n if (w_pred > 0) {\n for (int k = 0; k < K; ++k) {\n if (d[task][k] > skill_est[j][k]) {\n skill_est[j][k] += 0.3 * (d[task][k] - skill_est[j][k]);\n }\n }\n }\n } else {\n double target_w = t;\n double diff = w_pred - target_w;\n if (abs(diff) < 0.5) continue;\n \n if (w_pred > 0) {\n for (int k = 0; k < K; ++k) {\n if (d[task][k] > skill_est[j][k]) {\n skill_est[j][k] += 0.3 * diff * (d[task][k] - skill_est[j][k]) / w_pred;\n }\n }\n } else { \n double sum_d = 0;\n for (int k = 0; k < K; ++k) sum_d += d[task][k];\n if (sum_d > 0) {\n for (int k = 0; k < K; ++k) {\n skill_est[j][k] += 0.3 * diff * d[task][k] / sum_d;\n }\n }\n }\n }\n }\n for (auto& [task, t] : ob) {\n if (t == 1) {\n for (int k = 0; k < K; ++k) {\n skill_est[j][k] = max(skill_est[j][k], (double)d[task][k]);\n }\n }\n }\n for (int k = 0; k < K; ++k) skill_est[j][k] = max(0.0, skill_est[j][k]);\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> M >> K >> R;\n d.resize(N, vector(K)); deps.resize(N); rev_deps.resize(N);\n for (int i = 0; i < N; i++) for (int k = 0; k < K; k++) cin >> d[i][k];\n for (int r = 0; r < R; r++) { int u, v; cin >> u >> v; u--; v--; deps[v].push_back(u); rev_deps[u].push_back(v); }\n \n crit_path.resize(N, 0); task_start.resize(N, -1); task_done.resize(N, -1);\n skill_est.resize(M, vector(K)); member_obs.resize(M);\n \n for (int k = 0; k < K; k++) {\n vector dk(N); for (int i = 0; i < N; i++) dk[i] = d[i][k];\n sort(dk.begin(), dk.end());\n double init = dk[N/2] * 1.5;\n for (int j = 0; j < M; j++) skill_est[j][k] = init;\n }\n \n vector member_task(M, -1), member_start_day(M, -1);\n set available_tasks; vector deps_rem(N);\n for (int i = 0; i < N; i++) { deps_rem[i] = deps[i].size(); if (!deps_rem[i]) available_tasks.insert(i); }\n \n int current_day = 0;\n while (true) {\n current_day++;\n recompute_crit_path();\n \n vector free_members;\n for (int j = 0; j < M; j++) if (member_task[j] == -1) free_members.push_back(j);\n int fm = free_members.size();\n \n if (fm > 0 && !available_tasks.empty()) {\n vector av(available_tasks.begin(), available_tasks.end());\n sort(av.begin(), av.end(), [&](int a, int b){ return crit_path[a] > crit_path[b]; });\n \n int nr = min((int)av.size(), fm * 5);\n int na = max(nr, fm);\n vector> cost(fm, vector(na, 1e9));\n for (int mi = 0; mi < fm; mi++) { \n int j = free_members[mi];\n for (int ti = 0; ti < nr; ti++) { \n int i = av[ti];\n double w = 0; for (int k = 0; k < K; k++) w += max(0.0, (double)d[i][k]-skill_est[j][k]);\n cost[mi][ti] = max(1.0, w);\n }\n }\n auto asgn = hungarian(cost);\n vector> assigns;\n for (int mi = 0; mi < fm; mi++) { \n int ti = asgn[mi];\n if (ti >= 0 && ti < nr) assigns.push_back({free_members[mi], av[ti]});\n }\n \n cout << assigns.size();\n for (auto [j,i] : assigns) {\n cout << \" \" << (j+1) << \" \" << (i+1);\n member_task[j]=i; member_start_day[j]=current_day; task_start[i]=current_day;\n available_tasks.erase(i);\n }\n cout << endl;\n } else cout << 0 << endl;\n \n int n; cin >> n; if (n == -1) break;\n for (int idx = 0; idx < n; idx++) {\n int j; cin >> j; j--;\n int i = member_task[j], tt = current_day - member_start_day[j] + 1;\n task_done[i] = current_day;\n member_obs[j].push_back({i, tt});\n reestimate(j);\n member_task[j] = -1;\n for (int v : rev_deps[i]) { \n deps_rem[v]--; \n if (deps_rem[v] == 0 && task_start[v] == -1 && task_done[v] == -1) available_tasks.insert(v); \n }\n }\n }\n return 0;\n}","ahc006":"#pragma GCC optimize(\"O3\")\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint a[N], b[N], c[N], d[N];\n\ninline int dist(int x1, int y1, int x2, int y2) { return abs(x1-x2) + abs(y1-y2); }\n\nstruct Xor128 {\n unsigned x = 123456789, y = 362436069, z = 521288629, w = 88675123;\n unsigned next() {\n unsigned t = x ^ (x << 11);\n x = y; y = z; z = w;\n return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));\n }\n int nextInt(int n) { return next() % n; }\n};\n\nXor128 rng;\n\nint route[100];\nint bestRouteArr[100];\nint orders[M];\nint bestOrders[M];\nbool isSelected[N];\nint pos[2000];\nint X[100], Y[100];\n\nvector unselected;\n\nint calcCost() {\n int cost = abs(CX - X[0]) + abs(CY - Y[0]);\n for (int i = 0; i < 2 * M - 1; i++) cost += abs(X[i] - X[i+1]) + abs(Y[i] - Y[i+1]);\n cost += abs(X[2*M-1] - CX) + abs(Y[2*M-1] - CY);\n return cost;\n}\n\nvoid constructRoute() {\n bool vR[50], vD[50];\n memset(vR, 0, sizeof vR); memset(vD, 0, sizeof vD);\n int cx = CX, cy = CY;\n for (int step = 0; step < 2 * M; step++) {\n int best = -1, bestD = INT_MAX;\n for (int i = 0; i < M; i++) {\n if (!vR[i]) { int d2 = dist(cx, cy, a[orders[i]], b[orders[i]]); if (d2 < bestD) { bestD = d2; best = i * 2; } }\n if (vR[i] && !vD[i]) { int d2 = dist(cx, cy, c[orders[i]], d[orders[i]]); if (d2 < bestD) { bestD = d2; best = i * 2 + 1; } }\n }\n route[step] = orders[best / 2] * 2 + (best % 2);\n pos[route[step]] = step;\n if (best % 2 == 0) { vR[best / 2] = true; X[step] = a[orders[best / 2]]; Y[step] = b[orders[best / 2]]; cx = X[step]; cy = Y[step]; }\n else { vD[best / 2] = true; X[step] = c[orders[best / 2]]; Y[step] = d[orders[best / 2]]; cx = X[step]; cy = Y[step]; }\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n for (int i = 0; i < N; i++) cin >> a[i] >> b[i] >> c[i] >> d[i];\n \n auto startTime = chrono::high_resolution_clock::now();\n vector> scores;\n for (int i = 0; i < N; i++) {\n int cost = dist(CX, CY, a[i], b[i]) + dist(a[i], b[i], c[i], d[i]) + dist(c[i], d[i], CX, CY);\n scores.push_back({cost, i});\n }\n sort(scores.begin(), scores.end());\n for (int i = 0; i < M; i++) { orders[i] = scores[i].second; isSelected[orders[i]] = true; }\n unselected.reserve(N);\n for (int i = 0; i < N; i++) if (!isSelected[i]) unselected.push_back(i);\n \n constructRoute();\n int curCost = calcCost(), bestCost = curCost;\n memcpy(bestRouteArr, route, sizeof(route)); memcpy(bestOrders, orders, sizeof(orders));\n \n auto getC = [&](int i) -> pair { if (i < 0 || i >= 2 * M) return {CX, CY}; return {X[i], Y[i]}; };\n \n int iter = 0;\n double temp = 2000.0;\n while (true) {\n if (iter % 1000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - startTime).count();\n if (elapsed > 1.8) break;\n temp = 2000.0 * exp(-5.0 * (elapsed / 1.8));\n }\n iter++;\n auto accept = [&](int Delta) { \n if (Delta <= 0) return true; \n if (Delta >= (int)(temp * 20)) return false;\n unsigned int threshold = (unsigned int)(4294967295.0 * exp(-(double)Delta / temp)); \n return rng.next() < threshold; \n };\n int mt = rng.nextInt(100);\n \n if (mt < 15) { // Insert Move 15%\n int from = rng.nextInt(2 * M);\n int ip = rng.nextInt(2 * M + 1);\n if (ip == from || ip == from + 1) continue;\n int ins = ip > from ? ip - 1 : ip;\n \n int Vx = X[from], Vy = Y[from];\n int sx[103], sy[103];\n sx[0] = CX; sy[0] = CY;\n int s_idx = 1;\n for (int idx = 0; idx < 2 * M; idx++) {\n if (idx == from) continue;\n sx[s_idx] = X[idx]; sy[s_idx] = Y[idx]; s_idx++;\n }\n sx[s_idx] = CX; sy[s_idx] = CY;\n \n int Delta1 = dist(sx[ins], sy[ins], Vx, Vy) + dist(Vx, Vy, sx[ins+1], sy[ins+1]) - dist(sx[ins], sy[ins], sx[ins+1], sy[ins+1]);\n \n auto [p_from_1_x, p_from_1_y] = getC(from - 1); \n auto [p_from1_x, p_from1_y] = getC(from + 1);\n int Delta2 = dist(p_from_1_x, p_from_1_y, p_from1_x, p_from1_y) - (dist(p_from_1_x, p_from_1_y, X[from], Y[from]) + dist(X[from], Y[from], p_from1_x, p_from1_y));\n \n int Delta = Delta1 + Delta2;\n int p_counterpart = pos[route[from] ^ 1];\n int p_other_new = p_counterpart - (p_counterpart > from ? 1 : 0);\n bool valid = true;\n if (route[from] % 2 == 0) { if (ins > p_other_new) valid = false; }\n else { if (ins <= p_other_new) valid = false; }\n \n if (valid && accept(Delta)) {\n curCost += Delta;\n int val = route[from];\n for (int i = from; i < 2 * M - 1; i++) { route[i] = route[i+1]; X[i] = X[i+1]; Y[i] = Y[i+1]; pos[route[i]] = i; }\n for (int i = 2 * M - 1; i > ins; i--) { route[i] = route[i-1]; X[i] = X[i-1]; Y[i] = Y[i-1]; pos[route[i]] = i; }\n route[ins] = val; X[ins] = Vx; Y[ins] = Vy; pos[val] = ins;\n if (curCost < bestCost) { bestCost = curCost; memcpy(bestRouteArr, route, sizeof(route)); memcpy(bestOrders, orders, sizeof(orders)); }\n }\n } else if (mt < 35) { // Smart Order Swap 20%\n int k_idx = rng.nextInt(M); int k = orders[k_idx];\n if (unselected.empty()) continue;\n int p1 = pos[k*2], p2 = pos[k*2+1]; if (p1 > p2) swap(p1, p2);\n int savings = 0;\n if (p2 == p1 + 1) {\n auto [xm1, ym1] = getC(p1-1); auto [xp2, yp2] = getC(p2+1);\n savings = dist(xm1, ym1, X[p1], Y[p1]) + dist(X[p1], Y[p1], X[p2], Y[p2]) + dist(X[p2], Y[p2], xp2, yp2) - dist(xm1, ym1, xp2, yp2);\n } else {\n auto [xm1, ym1] = getC(p1-1); auto [xp1, yp1] = getC(p1+1);\n auto [xm2, ym2] = getC(p2-1); auto [xp2, yp2] = getC(p2+1);\n savings = (dist(xm1, ym1, X[p1], Y[p1]) + dist(X[p1], Y[p1], xp1, yp1) - dist(xm1, ym1, xp1, yp1))\n + (dist(xm2, ym2, X[p2], Y[p2]) + dist(X[p2], Y[p2], xp2, yp2) - dist(xm2, ym2, xp2, yp2));\n }\n int shrunk_X[100], shrunk_Y[100], shrunk_route[100]; int s_idx = 0;\n for (int idx = 0; idx < 2 * M; idx++) { if (idx == p1 || idx == p2) continue; shrunk_route[s_idx] = route[idx]; shrunk_X[s_idx] = X[idx]; shrunk_Y[s_idx] = Y[idx]; s_idx++; }\n \n int sx[103], sy[103];\n sx[0] = CX; sy[0] = CY;\n for (int i = 0; i < s_idx; i++) { sx[i+1] = shrunk_X[i]; sy[i+1] = shrunk_Y[i]; }\n sx[s_idx+1] = CX; sy[s_idx+1] = CY;\n\n int best_us_idx = -1, best_new_k = -1, best_Delta = 1e9, best_ins_i = -1, best_ins_j = -1;\n int trials = min(5, (int)unselected.size());\n for(int t = 0; t < trials; t++) {\n int us_idx = rng.nextInt(unselected.size()); int new_k = unselected[us_idx];\n int X_new1 = a[new_k], Y_new1 = b[new_k], X_new2 = c[new_k], Y_new2 = d[new_k];\n int cost_D[103];\n for (int j = 0; j <= s_idx; j++) { cost_D[j] = dist(sx[j], sy[j], X_new2, Y_new2) + dist(X_new2, Y_new2, sx[j+1], sy[j+1]) - dist(sx[j], sy[j], sx[j+1], sy[j+1]); }\n int min_cost_D_from[103], min_idx_D_from[103];\n min_cost_D_from[s_idx + 1] = 1e9; min_idx_D_from[s_idx + 1] = -1;\n for (int j = s_idx; j >= 0; j--) { if (cost_D[j] < min_cost_D_from[j + 1]) { min_cost_D_from[j] = cost_D[j]; min_idx_D_from[j] = j; } else { min_cost_D_from[j] = min_cost_D_from[j + 1]; min_idx_D_from[j] = min_idx_D_from[j + 1]; } }\n int current_best_cost = 1e9, current_best_i = -1, current_best_j = -1;\n for (int i = 0; i <= s_idx; i++) {\n int cost_P = dist(sx[i], sy[i], X_new1, Y_new1) + dist(X_new1, Y_new1, sx[i+1], sy[i+1]) - dist(sx[i], sy[i], sx[i+1], sy[i+1]);\n int cost_same = cost_P + dist(X_new1, Y_new1, X_new2, Y_new2) + dist(X_new2, Y_new2, sx[i+1], sy[i+1]) - dist(X_new1, Y_new1, sx[i+1], sy[i+1]);\n if (cost_same < current_best_cost) { current_best_cost = cost_same; current_best_i = i; current_best_j = i; }\n if (i + 1 <= s_idx) { int cost_next = cost_P + cost_D[i+1]; if (cost_next < current_best_cost) { current_best_cost = cost_next; current_best_i = i; current_best_j = i + 1; } }\n if (i + 2 <= s_idx) { int cost_far = cost_P + min_cost_D_from[i + 2]; if (cost_far < current_best_cost) { current_best_cost = cost_far; current_best_i = i; current_best_j = min_idx_D_from[i + 2]; } }\n }\n int Delta = current_best_cost - savings;\n if(Delta < best_Delta) { best_Delta = Delta; best_us_idx = us_idx; best_new_k = new_k; best_ins_i = current_best_i; best_ins_j = current_best_j; }\n }\n if (accept(best_Delta)) {\n curCost += best_Delta;\n int new_k = best_new_k, us_idx = best_us_idx;\n int X_new1 = a[new_k], Y_new1 = b[new_k], X_new2 = c[new_k], Y_new2 = d[new_k];\n int new_route[100], new_X[100], new_Y[100]; int n_idx = 0;\n for (int idx = 0; idx < s_idx; idx++) {\n if (idx == best_ins_i) { new_route[n_idx] = new_k * 2; new_X[n_idx] = X_new1; new_Y[n_idx] = Y_new1; n_idx++; }\n if (idx == best_ins_j) { new_route[n_idx] = new_k * 2 + 1; new_X[n_idx] = X_new2; new_Y[n_idx] = Y_new2; n_idx++; }\n new_route[n_idx] = shrunk_route[idx]; new_X[n_idx] = shrunk_X[idx]; new_Y[n_idx] = shrunk_Y[idx]; n_idx++;\n }\n if (s_idx == best_ins_i) { new_route[n_idx] = new_k * 2; new_X[n_idx] = X_new1; new_Y[n_idx] = Y_new1; n_idx++; }\n if (s_idx == best_ins_j) { new_route[n_idx] = new_k * 2 + 1; new_X[n_idx] = X_new2; new_Y[n_idx] = Y_new2; n_idx++; }\n \n memcpy(route, new_route, sizeof(route)); memcpy(X, new_X, sizeof(X)); memcpy(Y, new_Y, sizeof(Y));\n for (int idx = 0; idx < 2 * M; idx++) pos[route[idx]] = idx;\n isSelected[k] = false; isSelected[new_k] = true; orders[k_idx] = new_k;\n unselected[us_idx] = unselected.back(); unselected.pop_back(); unselected.push_back(k);\n if (curCost < bestCost) { bestCost = curCost; memcpy(bestRouteArr, route, sizeof(route)); memcpy(bestOrders, orders, sizeof(orders)); }\n }\n } else if (mt < 50) { // Order Re-insert 15%\n int k_idx = rng.nextInt(M); int k = orders[k_idx];\n int p1 = pos[k*2], p2 = pos[k*2+1]; if (p1 > p2) swap(p1, p2);\n int savings = 0;\n if (p2 == p1 + 1) {\n auto [xm1, ym1] = getC(p1-1); auto [xp2, yp2] = getC(p2+1);\n savings = dist(xm1, ym1, X[p1], Y[p1]) + dist(X[p1], Y[p1], X[p2], Y[p2]) + dist(X[p2], Y[p2], xp2, yp2) - dist(xm1, ym1, xp2, yp2);\n } else {\n auto [xm1, ym1] = getC(p1-1); auto [xp1, yp1] = getC(p1+1);\n auto [xm2, ym2] = getC(p2-1); auto [xp2, yp2] = getC(p2+1);\n savings = (dist(xm1, ym1, X[p1], Y[p1]) + dist(X[p1], Y[p1], xp1, yp1) - dist(xm1, ym1, xp1, yp1))\n + (dist(xm2, ym2, X[p2], Y[p2]) + dist(X[p2], Y[p2], xp2, yp2) - dist(xm2, ym2, xp2, yp2));\n }\n int shrunk_X[100], shrunk_Y[100], shrunk_route[100]; int s_idx = 0;\n for (int idx = 0; idx < 2 * M; idx++) { if (idx == p1 || idx == p2) continue; shrunk_route[s_idx] = route[idx]; shrunk_X[s_idx] = X[idx]; shrunk_Y[s_idx] = Y[idx]; s_idx++; }\n \n int sx[103], sy[103];\n sx[0] = CX; sy[0] = CY;\n for (int i = 0; i < s_idx; i++) { sx[i+1] = shrunk_X[i]; sy[i+1] = shrunk_Y[i]; }\n sx[s_idx+1] = CX; sy[s_idx+1] = CY;\n \n int X_new1 = a[k], Y_new1 = b[k], X_new2 = c[k], Y_new2 = d[k];\n int cost_D[103];\n for (int j = 0; j <= s_idx; j++) { cost_D[j] = dist(sx[j], sy[j], X_new2, Y_new2) + dist(X_new2, Y_new2, sx[j+1], sy[j+1]) - dist(sx[j], sy[j], sx[j+1], sy[j+1]); }\n int min_cost_D_from[103], min_idx_D_from[103];\n min_cost_D_from[s_idx + 1] = 1e9; min_idx_D_from[s_idx + 1] = -1;\n for (int j = s_idx; j >= 0; j--) { if (cost_D[j] < min_cost_D_from[j + 1]) { min_cost_D_from[j] = cost_D[j]; min_idx_D_from[j] = j; } else { min_cost_D_from[j] = min_cost_D_from[j + 1]; min_idx_D_from[j] = min_idx_D_from[j + 1]; } }\n int best_cost = 1e9, best_ins_i = -1, best_ins_j = -1;\n for (int i = 0; i <= s_idx; i++) {\n int cost_P = dist(sx[i], sy[i], X_new1, Y_new1) + dist(X_new1, Y_new1, sx[i+1], sy[i+1]) - dist(sx[i], sy[i], sx[i+1], sy[i+1]);\n int cost_same = cost_P + dist(X_new1, Y_new1, X_new2, Y_new2) + dist(X_new2, Y_new2, sx[i+1], sy[i+1]) - dist(X_new1, Y_new1, sx[i+1], sy[i+1]);\n if (cost_same < best_cost) { best_cost = cost_same; best_ins_i = i; best_ins_j = i; }\n if (i + 1 <= s_idx) { int cost_next = cost_P + cost_D[i+1]; if (cost_next < best_cost) { best_cost = cost_next; best_ins_i = i; best_ins_j = i + 1; } }\n if (i + 2 <= s_idx) { int cost_far = cost_P + min_cost_D_from[i + 2]; if (cost_far < best_cost) { best_cost = cost_far; best_ins_i = i; best_ins_j = min_idx_D_from[i + 2]; } }\n }\n int Delta = best_cost - savings;\n if (accept(Delta)) {\n curCost += Delta;\n int new_route[100], new_X[100], new_Y[100]; int n_idx = 0;\n for (int idx = 0; idx < s_idx; idx++) {\n if (idx == best_ins_i) { new_route[n_idx] = k * 2; new_X[n_idx] = X_new1; new_Y[n_idx] = Y_new1; n_idx++; }\n if (idx == best_ins_j) { new_route[n_idx] = k * 2 + 1; new_X[n_idx] = X_new2; new_Y[n_idx] = Y_new2; n_idx++; }\n new_route[n_idx] = shrunk_route[idx]; new_X[n_idx] = shrunk_X[idx]; new_Y[n_idx] = shrunk_Y[idx]; n_idx++;\n }\n if (s_idx == best_ins_i) { new_route[n_idx] = k * 2; new_X[n_idx] = X_new1; new_Y[n_idx] = Y_new1; n_idx++; }\n if (s_idx == best_ins_j) { new_route[n_idx] = k * 2 + 1; new_X[n_idx] = X_new2; new_Y[n_idx] = Y_new2; n_idx++; }\n \n memcpy(route, new_route, sizeof(route)); memcpy(X, new_X, sizeof(X)); memcpy(Y, new_Y, sizeof(Y));\n for (int idx = 0; idx < 2 * M; idx++) pos[route[idx]] = idx;\n if (curCost < bestCost) { bestCost = curCost; memcpy(bestRouteArr, route, sizeof(route)); memcpy(bestOrders, orders, sizeof(orders)); }\n }\n } else if (mt < 65) { // Order Swap Move 15%\n int k1_idx = rng.nextInt(M); int k2_idx = rng.nextInt(M - 1); if (k2_idx >= k1_idx) k2_idx++;\n int k1 = orders[k1_idx], k2 = orders[k2_idx];\n int p1 = pos[k1*2], p2 = pos[k1*2+1];\n int p3 = pos[k2*2], p4 = pos[k2*2+1];\n int min_p = min({p1, p2, p3, p4});\n int max_p = max({p1, p2, p3, p4});\n \n int old_cost = 0;\n for (int i = min_p - 1; i <= max_p; i++) {\n auto [x1, y1] = getC(i);\n auto [x2, y2] = getC(i+1);\n old_cost += dist(x1, y1, x2, y2);\n }\n \n route[p1] = k2*2; X[p1] = a[k2]; Y[p1] = b[k2];\n route[p2] = k2*2+1; X[p2] = c[k2]; Y[p2] = d[k2];\n route[p3] = k1*2; X[p3] = a[k1]; Y[p3] = b[k1];\n route[p4] = k1*2+1; X[p4] = c[k1]; Y[p4] = d[k1];\n pos[k1*2] = p3; pos[k1*2+1] = p4;\n pos[k2*2] = p1; pos[k2*2+1] = p2;\n \n int new_cost = 0;\n for (int i = min_p - 1; i <= max_p; i++) {\n auto [x1, y1] = getC(i);\n auto [x2, y2] = getC(i+1);\n new_cost += dist(x1, y1, x2, y2);\n }\n \n int Delta = new_cost - old_cost;\n if (accept(Delta)) {\n curCost += Delta;\n swap(orders[k1_idx], orders[k2_idx]);\n if (curCost < bestCost) { bestCost = curCost; memcpy(bestRouteArr, route, sizeof(route)); memcpy(bestOrders, orders, sizeof(orders)); }\n } else {\n route[p1] = k1*2; X[p1] = a[k1]; Y[p1] = b[k1];\n route[p2] = k1*2+1; X[p2] = c[k1]; Y[p2] = d[k1];\n route[p3] = k2*2; X[p3] = a[k2]; Y[p3] = b[k2];\n route[p4] = k2*2+1; X[p4] = c[k2]; Y[p4] = d[k2];\n pos[k1*2] = p1; pos[k1*2+1] = p2;\n pos[k2*2] = p3; pos[k2*2+1] = p4;\n }\n } else if (mt < 75) { // Route Swap 10%\n int i = rng.nextInt(2 * M), j = rng.nextInt(2 * M - 1); if (j >= i) j++; if (i > j) swap(i, j);\n int u = route[i], v = route[j]; if (u == (v ^ 1)) continue;\n bool valid = true;\n if (u % 2 == 0) { if (pos[u ^ 1] <= j) valid = false; } \n else { if (pos[u ^ 1] > j) valid = false; }\n if (v % 2 == 0) { if (pos[v ^ 1] <= i) valid = false; } \n else { if (pos[v ^ 1] > i) valid = false; }\n if (!valid) continue;\n auto [xim1, yim1] = getC(i - 1);\n auto [xj1, yj1] = getC(j + 1);\n int Delta = 0;\n if (j == i + 1) {\n Delta = (dist(xim1, yim1, X[j], Y[j]) + dist(X[j], Y[j], X[i], Y[i]) + dist(X[i], Y[i], xj1, yj1)) - (dist(xim1, yim1, X[i], Y[i]) + dist(X[i], Y[i], X[j], Y[j]) + dist(X[j], Y[j], xj1, yj1));\n } else {\n auto [xi1, yi1] = getC(i + 1);\n auto [xjm1, yjm1] = getC(j - 1);\n Delta = (dist(xim1, yim1, X[j], Y[j]) + dist(X[j], Y[j], xi1, yi1) + dist(xjm1, yjm1, X[i], Y[i]) + dist(X[i], Y[i], xj1, yj1)) - (dist(xim1, yim1, X[i], Y[i]) + dist(X[i], Y[i], xi1, yi1) + dist(xjm1, yjm1, X[j], Y[j]) + dist(X[j], Y[j], xj1, yj1));\n }\n if (accept(Delta)) {\n curCost += Delta; swap(route[i], route[j]); swap(X[i], X[j]); swap(Y[i], Y[j]); pos[route[i]] = i; pos[route[j]] = j;\n if (curCost < bestCost) { bestCost = curCost; memcpy(bestRouteArr, route, sizeof(route)); memcpy(bestOrders, orders, sizeof(orders)); }\n }\n } else { // 2-opt 25%\n int l = rng.nextInt(2 * M - 1), r = l + 1 + rng.nextInt(2 * M - 1 - l);\n bool valid = true; for (int i = l; i <= r; i++) { int p_other = pos[route[i] ^ 1]; if (p_other >= l && p_other <= r) { valid = false; break; } }\n if (valid) {\n auto [xl1, yl1] = getC(l - 1); auto [xl, yl] = getC(l); auto [xr, yr] = getC(r); auto [xr1, yr1] = getC(r + 1);\n int Delta = (dist(xl1, yl1, xr, yr) + dist(xl, yl, xr1, yr1)) - (dist(xl1, yl1, xl, yl) + dist(xr, yr, xr1, yr1));\n if (accept(Delta)) {\n curCost += Delta; reverse(route + l, route + r + 1); reverse(X + l, X + r + 1); reverse(Y + l, Y + r + 1);\n for (int i = l; i <= r; i++) pos[route[i]] = i;\n if (curCost < bestCost) { bestCost = curCost; memcpy(bestRouteArr, route, sizeof(route)); memcpy(bestOrders, orders, sizeof(orders)); }\n }\n }\n }\n }\n \n cout << M; for(int i = 0; i < M; i++) cout << \" \" << bestOrders[i] + 1; cout << endl;\n int bestX_arr[100], bestY_arr[100];\n for (int i = 0; i < 2 * M; i++) { int node = bestRouteArr[i]; int k = node / 2; if (node % 2 == 0) { bestX_arr[i] = a[k]; bestY_arr[i] = b[k]; } else { bestX_arr[i] = c[k]; bestY_arr[i] = d[k]; } }\n cout << 2 * M + 2 << \" \" << CX << \" \" << CY;\n for(int i = 0; i < 2 * M; i++) cout << \" \" << bestX_arr[i] << \" \" << bestY_arr[i];\n cout << \" \" << CX << \" \" << CY << endl;\n \n return 0;\n}","ahc007":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct UnionFind {\n vector parent, rank_;\n int components;\n \n UnionFind(int n) : parent(n), rank_(n, 0), components(n) {\n for (int i = 0; i < n; i++) parent[i] = i;\n }\n \n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n \n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n components--;\n return true;\n }\n \n bool connected(int x, int y) {\n return find(x) == find(y);\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n vector x(N), y(N);\n vector u(M), v(M);\n vector d(M);\n \n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dist = sqrt((double)(x[u[i]] - x[v[i]]) * (x[u[i]] - x[v[i]]) + \n (double)(y[u[i]] - y[v[i]]) * (y[u[i]] - y[v[i]]));\n d[i] = max(1, (int)round(dist));\n }\n \n // Compute reference MST using d_i\n vector order(M);\n for (int i = 0; i < M; i++) order[i] = i;\n sort(order.begin(), order.end(), [&](int a, int b) { return d[a] < d[b]; });\n \n UnionFind refUF(N);\n vector inRefMST(M, false);\n for (int idx : order) {\n if (refUF.unite(u[idx], v[idx])) {\n inRefMST[idx] = true;\n }\n }\n \n // Process edges online\n UnionFind uf(N);\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int adopt = 0;\n \n if (!uf.connected(u[i], v[i])) {\n if (inRefMST[i]) {\n // Always accept reference MST edges - guarantees connectivity\n adopt = 1;\n uf.unite(u[i], v[i]);\n } else {\n // Accept non-MST edges only if they're cheap enough\n // to potentially replace expensive MST edges\n double percentile = (double)(l - d[i]) / (2.0 * d[i]);\n percentile = max(0.0, min(1.0, percentile));\n \n int remaining = M - i - 1;\n int needed = uf.components - 1;\n double safety = (needed > 0) ? (double)remaining / needed : 999.0;\n \n double threshold;\n if (safety >= 5) threshold = 0.3;\n else if (safety >= 3) threshold = 0.4;\n else if (safety >= 2) threshold = 0.5;\n else threshold = 0.65;\n \n if (percentile <= threshold) {\n adopt = 1;\n uf.unite(u[i], v[i]);\n }\n }\n }\n \n cout << adopt << endl;\n }\n \n return 0;\n}","ahc008":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int SIZE = 30;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\n\nint N, M;\nvector px, py, pt;\nvector hx, hy;\nbool wall[SIZE][SIZE];\n\nbool inBounds(int x, int y) { return x >= 0 && x < SIZE && y >= 0 && y < SIZE; }\n\nvoid bfs(int sx, int sy, int dist[SIZE][SIZE]) {\n memset(dist, -1, sizeof(int) * SIZE * SIZE);\n if (!inBounds(sx, sy) || wall[sx][sy]) return;\n queue> q;\n dist[sx][sy] = 0;\n q.push({sx, sy});\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && dist[nx][ny] == -1) {\n dist[nx][ny] = dist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n}\n\ndouble petThreatWeight(int t) {\n switch(t) { case 1: return 1.0; case 2: return 1.5; case 3: return 2.0; case 4: return 2.5; case 5: return 2.0; default: return 1.0; }\n}\n\ndouble petSpeed(int t) {\n switch(t) { case 1: return 1.0; case 2: return 2.0; case 3: return 3.0; case 4: return 2.0; case 5: return 2.0; default: return 1.0; }\n}\n\nbool petAdjacentTo(int x, int y, const vector& ppx, const vector& ppy) {\n for (int i = 0; i < N; i++) {\n if (ppx[i] == x && ppy[i] == y) return true;\n for (int d = 0; d < 4; d++)\n if (ppx[i] == x + dx[d] && ppy[i] == y + dy[d]) return true;\n }\n return false;\n}\n\nbool humanAt(int x, int y, const vector& hhx, const vector& hhy) {\n for (int i = 0; i < M; i++)\n if (hhx[i] == x && hhy[i] == y) return true;\n return false;\n}\n\ndouble computeScoreWithDist(int dist[SIZE][SIZE]) {\n int area = 0;\n double effectivePets = 0;\n bool enclosed = true;\n \n for (int i = 0; i < SIZE; i++)\n for (int j = 0; j < SIZE; j++)\n if (dist[i][j] >= 0) {\n area++;\n if (enclosed) {\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (inBounds(ni, nj) && !wall[ni][nj] && dist[ni][nj] < 0) {\n enclosed = false; break;\n }\n }\n }\n }\n \n for (int i = 0; i < N; i++)\n if (dist[px[i]][py[i]] >= 0) effectivePets += 1.0;\n\n if (enclosed && effectivePets > 0) effectivePets += 20.0;\n\n int boundaryDist[SIZE][SIZE];\n memset(boundaryDist, -1, sizeof(int) * SIZE * SIZE);\n queue> q;\n for (int x = 0; x < SIZE; x++)\n for (int y = 0; y < SIZE; y++)\n if (dist[x][y] < 0 && !wall[x][y]) {\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && dist[nx][ny] >= 0) {\n if (boundaryDist[x][y] == -1) { boundaryDist[x][y] = 1; q.push({x, y}); }\n break;\n }\n }\n }\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && boundaryDist[nx][ny] == -1 && dist[nx][ny] < 0) {\n boundaryDist[nx][ny] = boundaryDist[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n \n for (int i = 0; i < N; i++) {\n if (dist[px[i]][py[i]] >= 0) continue;\n int d = boundaryDist[px[i]][py[i]];\n if (d >= 1) effectivePets += petThreatWeight(pt[i]) * 0.2 * exp(-0.25 * d);\n }\n \n return (double)area / 900.0 * pow(2.0, -effectivePets);\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N;\n px.resize(N); py.resize(N); pt.resize(N);\n for (int i = 0; i < N; i++) { cin >> px[i] >> py[i] >> pt[i]; px[i]--; py[i]--; }\n cin >> M;\n hx.resize(M); hy.resize(M);\n for (int i = 0; i < M; i++) { cin >> hx[i] >> hy[i]; hx[i]--; hy[i]--; }\n memset(wall, false, sizeof(wall));\n\n for (int turn = 0; turn < 300; turn++) {\n vector startPx = px, startPy = py, startHx = hx, startHy = hy;\n string actions(M, '.');\n bool newWall[SIZE][SIZE] = {};\n\n for (int i = 0; i < M; i++) {\n int myHx = startHx[i], myHy = startHy[i];\n int distBefore[SIZE][SIZE];\n bfs(myHx, myHy, distBefore);\n double curScore = computeScoreWithDist(distBefore);\n \n char bestAction = '.';\n double bestScore = curScore;\n\n for (int d = 0; d < 4; d++) {\n int wx = myHx + dx[d], wy = myHy + dy[d];\n if (inBounds(wx, wy) && !wall[wx][wy] && !newWall[wx][wy] &&\n !petAdjacentTo(wx, wy, startPx, startPy) && !humanAt(wx, wy, startHx, startHy)) {\n wall[wx][wy] = true;\n int distAfter[SIZE][SIZE];\n bfs(myHx, myHy, distAfter);\n double newScore = computeScoreWithDist(distAfter);\n \n bool separated = false;\n for (int j = 0; j < N; j++)\n if (distBefore[px[j]][py[j]] >= 0 && distAfter[px[j]][py[j]] < 0) {\n newScore += 0.12;\n separated = true;\n }\n \n if (separated) {\n for (int dd = 0; dd < 4; dd++) {\n int nx = wx + dx[dd], ny = wy + dy[dd];\n if (!inBounds(nx, ny) || wall[nx][ny] || newWall[nx][ny]) newScore += 0.002;\n }\n }\n \n for (int j = 0; j < N; j++) {\n if (distBefore[px[j]][py[j]] >= 0) {\n int hDist = abs(myHx - px[j]) + abs(myHy - py[j]);\n int wDistPet = abs(wx - px[j]) + abs(wy - py[j]);\n int wDistHuman = abs(wx - myHx) + abs(wy - myHy);\n if (wDistHuman + wDistPet <= hDist + 2)\n newScore += 0.025;\n }\n }\n \n for (int j = 0; j < N; j++) {\n if (distBefore[px[j]][py[j]] < 0) {\n int wDistPet = abs(wx - px[j]) + abs(wy - py[j]);\n if (wDistPet <= 4) newScore += 0.012 * (5 - wDistPet);\n }\n }\n \n wall[wx][wy] = false;\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"udlr\"[d]; }\n }\n }\n \n for (int d = 0; d < 4; d++) {\n int nx = myHx + dx[d], ny = myHy + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && !newWall[nx][ny]) {\n int distAfter[SIZE][SIZE];\n bfs(nx, ny, distAfter);\n double newScore = computeScoreWithDist(distAfter);\n if (newScore > bestScore) { bestScore = newScore; bestAction = \"UDLR\"[d]; }\n }\n }\n \n if (bestAction == '.') {\n double bestUrgency = -1e9;\n int bestTargetX = -1, bestTargetY = -1;\n \n for (int x = 0; x < SIZE; x++)\n for (int y = 0; y < SIZE; y++)\n if (distBefore[x][y] < 0 && !wall[x][y] && !newWall[x][y]) {\n bool adjToRegion = false;\n int minHDist = 999;\n for (int dd = 0; dd < 4; dd++) {\n int nx = x + dx[dd], ny = y + dy[dd];\n if (inBounds(nx, ny) && distBefore[nx][ny] >= 0) {\n adjToRegion = true;\n minHDist = min(minHDist, distBefore[nx][ny] + 1);\n }\n }\n if (!adjToRegion) continue;\n if (petAdjacentTo(x, y, startPx, startPy)) continue;\n \n double minPetArrival = 1e9;\n for (int j = 0; j < N; j++) {\n if (distBefore[startPx[j]][startPy[j]] >= 0) continue;\n double arrival = (abs(startPx[j] - x) + abs(startPy[j] - y)) / petSpeed(pt[j]);\n minPetArrival = min(minPetArrival, arrival);\n }\n \n double urgency = -minPetArrival * 8 - minHDist;\n if (urgency > bestUrgency) {\n bestUrgency = urgency;\n int tx = -1, ty = -1, td = 999;\n for (int dd = 0; dd < 4; dd++) {\n int nx = x + dx[dd], ny = y + dy[dd];\n if (inBounds(nx, ny) && distBefore[nx][ny] >= 0 && distBefore[nx][ny] < td) {\n td = distBefore[nx][ny]; tx = nx; ty = ny;\n }\n }\n bestTargetX = tx; bestTargetY = ty;\n }\n }\n \n if (bestTargetX >= 0) {\n int bestMoveDist = abs(myHx - bestTargetX) + abs(myHy - bestTargetY);\n char bestMove = '.';\n for (int d = 0; d < 4; d++) {\n int nx = myHx + dx[d], ny = myHy + dy[d];\n if (inBounds(nx, ny) && !wall[nx][ny] && !newWall[nx][ny]) {\n int dist = abs(nx - bestTargetX) + abs(ny - bestTargetY);\n if (dist < bestMoveDist) { bestMoveDist = dist; bestMove = \"UDLR\"[d]; }\n }\n }\n if (bestMove != '.') bestAction = bestMove;\n }\n \n if (bestAction == '.') {\n int boundaryDist2[SIZE][SIZE];\n int firstDir[SIZE][SIZE];\n memset(boundaryDist2, -1, sizeof(int) * SIZE * SIZE);\n memset(firstDir, -1, sizeof(int) * SIZE * SIZE);\n queue> q;\n \n for (int x = 0; x < SIZE; x++)\n for (int y = 0; y < SIZE; y++)\n if (distBefore[x][y] >= 0) {\n bool isBd = false;\n for (int dd = 0; dd < 4; dd++) {\n int nnx = x + dx[dd], nny = y + dy[dd];\n if (!inBounds(nnx, nny) || wall[nnx][nny]) isBd = true;\n }\n if (isBd) { boundaryDist2[x][y] = 0; q.push({x, y}); }\n }\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int dd = 0; dd < 4; dd++) {\n int nnx = x + dx[dd], nny = y + dy[dd];\n if (inBounds(nnx, nny) && !wall[nnx][nny] && boundaryDist2[nnx][nny] == -1 && distBefore[nnx][nny] >= 0) {\n boundaryDist2[nnx][nny] = boundaryDist2[x][y] + 1;\n if (boundaryDist2[x][y] == 0) {\n if (x == nnx-1) firstDir[nnx][nny] = 0;\n else if (x == nnx+1) firstDir[nnx][nny] = 1;\n else if (y == nny-1) firstDir[nnx][nny] = 2;\n else firstDir[nnx][nny] = 3;\n } else firstDir[nnx][nny] = firstDir[x][y];\n q.push({nnx, nny});\n }\n }\n }\n \n if (boundaryDist2[myHx][myHy] > 0 && firstDir[myHx][myHy] >= 0) {\n int dd = firstDir[myHx][myHy];\n int nnx = myHx + dx[dd], nny = myHy + dy[dd];\n if (inBounds(nnx, nny) && !wall[nnx][nny] && !newWall[nnx][nny])\n bestAction = \"UDLR\"[dd];\n }\n }\n }\n \n actions[i] = bestAction;\n switch (actions[i]) {\n case 'u': newWall[myHx-1][myHy]=true; wall[myHx-1][myHy]=true; break;\n case 'd': newWall[myHx+1][myHy]=true; wall[myHx+1][myHy]=true; break;\n case 'l': newWall[myHx][myHy-1]=true; wall[myHx][myHy-1]=true; break;\n case 'r': newWall[myHx][myHy+1]=true; wall[myHx][myHy+1]=true; break;\n case 'U': hx[i]=myHx-1; hy[i]=myHy; break;\n case 'D': hx[i]=myHx+1; hy[i]=myHy; break;\n case 'L': hx[i]=myHx; hy[i]=myHy-1; break;\n case 'R': hx[i]=myHx; hy[i]=myHy+1; break;\n }\n }\n \n cout << actions << endl;\n for (int i = 0; i < N; i++) {\n string move; cin >> move;\n for (char c : move) {\n if (c=='U') px[i]--; else if (c=='D') px[i]++;\n else if (c=='L') py[i]--; else if (c=='R') py[i]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\nint si,sj,ti,tj;double p;int ti_idx;\nint md[400][4];double fv[400][202];int c2d[256];\nmt19937 rng(42);\n\ndouble pr_arr[201][400];\ndouble W[201][400];\n\nvoid init(){\n vectorh(20),v(19);for(int i=0;i<20;i++)cin>>h[i];for(int i=0;i<19;i++)cin>>v[i];\n ti_idx=ti*20+tj;int di[]={-1,1,0,0},dj[]={0,0,-1,1};\n for(int i=0;i<20;i++)for(int j=0;j<20;j++){int idx=i*20+j;\n for(int d=0;d<4;d++){int ni=i+di[d],nj=j+dj[d];bool bl=(ni<0||ni>=20||nj<0||nj>=20);\n if(!bl){if(d==0&&i>0&&v[i-1][j]=='1')bl=true;else if(d==1&&v[i][j]=='1')bl=true;\n else if(d==2&&j>0&&h[i][j-1]=='1')bl=true;else if(d==3&&h[i][j]=='1')bl=true;}\n if(bl){ni=i;nj=j;}md[idx][d]=ni*20+nj;}}\n memset(fv,0,sizeof(fv));\n for(int t=200;t>=1;t--)for(int idx=0;idx<400;idx++){\n if(idx==ti_idx){fv[idx][t]=0;continue;}\n double b=0;for(int d=0;d<4;d++){int ni=md[idx][d];\n double sc=p*fv[idx][t+1];if(ni==ti_idx)sc+=(1-p)*(401-t);else sc+=(1-p)*fv[ni][t+1];\n b=max(b,sc);}fv[idx][t]=b;}}\n\ndouble compute_score(const string&s){\n double pr[400]={},np[400];pr[si*20+sj]=1;double es=0;\n for(int t=0;t<(int)s.size();t++){int d=c2d[(unsigned char)s[t]];memset(np,0,sizeof(np));\n for(int i=0;i<400;i++){if(pr[i]<1e-18)continue;\n if(i==ti_idx)continue;\n np[i]+=p*pr[i];int ni=md[i][d];\n if(ni==ti_idx)es+=(1-p)*pr[i]*(400-t);else np[ni]+=(1-p)*pr[i];}\n memcpy(pr,np,sizeof(pr));}return es;}\n\nstring bfs_path(){int dist[400],pdir[400];memset(dist,-1,sizeof(dist));\n queueq;int start=si*20+sj;q.push(start);dist[start]=0;\n while(!q.empty()){int idx=q.front();q.pop();if(idx==ti_idx)break;\n for(int d=0;d<4;d++){int ni=md[idx][d];if(ni!=idx&&dist[ni]==-1){dist[ni]=dist[idx]+1;pdir[ni]=d;q.push(ni);}}}\n string path;int idx=ti_idx;int di[]={-1,1,0,0},dj[]={0,0,-1,1};\n while(idx!=start){int d=pdir[idx];path=string(1,\"UDLR\"[d])+path;idx=(idx/20-di[d])*20+(idx%20-dj[d]);}return path;}\n\nstring beam_search(int B, double noise=0.0){\n vector pr_flat(B * 400, 0.0);\n vector acc(B, 0.0);\n vector> act(B);\n int cur_B = 1;\n pr_flat[si*20+sj] = 1.0;\n\n for(int t=0; t<200; ++t){\n vector>> scores;\n scores.reserve(cur_B * 4);\n for(int i=0; i 0) h += uniform_real_distribution(-noise, noise)(rng);\n scores.push_back({h, {i, d}});\n }\n }\n int next_B = min(B, (int)scores.size());\n if(next_B == 0) break;\n if(next_B < (int)scores.size()) {\n nth_element(scores.begin(), scores.begin() + next_B - 1, scores.end(), [](const auto& a, const auto& b){\n return a.first > b.first;\n });\n }\n\n vector npr_flat(next_B * 400, 0.0);\n vector nacc(next_B, 0.0);\n vector> nact(next_B);\n\n for(int k=0; k bsc) {\n bsc = acc[i];\n br = \"\";\n for(int t=0;t<200;++t) br += \"UDLR\"[act[i][t]];\n }\n }\n return br;\n}\n\nvoid coordinate_descent(string& best) {\n int L = best.size();\n \n for(int pass=0; pass<50; ++pass) {\n memset(pr_arr[0], 0, sizeof(pr_arr[0]));\n pr_arr[0][si*20+sj] = 1.0;\n for(int t=0; t=0; --t) {\n int dd = c2d[(unsigned char)best[t]];\n for(int i=0; i<400; ++i) {\n if(i == ti_idx) { W[t][i] = 0; continue; }\n double val = p * W[t+1][i];\n int ni = md[i][dd];\n if(ni == ti_idx) val += (1-p) * (400 - t);\n else val += (1-p) * W[t+1][ni];\n W[t][i] = val;\n }\n }\n \n bool changed = false;\n for(int pos=L-1; pos>=0; --pos) {\n int current_d = c2d[(unsigned char)best[pos]];\n double current_score = 0;\n for(int i=0; i<400; ++i) {\n if(i == ti_idx) continue;\n double pr_i = pr_arr[pos][i];\n if(pr_i < 1e-18) continue;\n double val = p * W[pos+1][i];\n int ni = md[i][current_d];\n if(ni == ti_idx) val += (1-p) * (400 - pos);\n else val += (1-p) * W[pos+1][ni];\n current_score += pr_i * val;\n }\n \n double best_new_score = current_score;\n int best_d = current_d;\n \n for(int d=0; d<4; ++d) {\n if(d == current_d) continue;\n double new_score = 0;\n for(int i=0; i<400; ++i) {\n if(i == ti_idx) continue;\n double pr_i = pr_arr[pos][i];\n if(pr_i < 1e-18) continue;\n double val = p * W[pos+1][i];\n int ni = md[i][d];\n if(ni == ti_idx) val += (1-p) * (400 - pos);\n else val += (1-p) * W[pos+1][ni];\n new_score += pr_i * val;\n }\n if(new_score > best_new_score + 1e-9) {\n best_new_score = new_score;\n best_d = d;\n }\n }\n \n if(best_d != current_d) {\n changed = true;\n best[pos] = \"UDLR\"[best_d];\n }\n \n int final_d = c2d[(unsigned char)best[pos]];\n for(int i=0; i<400; ++i) {\n if(i == ti_idx) { W[pos][i] = 0; continue; }\n double val = p * W[pos+1][i];\n int ni = md[i][final_d];\n if(ni == ti_idx) val += (1-p) * (400 - pos);\n else val += (1-p) * W[pos+1][ni];\n W[pos][i] = val;\n }\n }\n if(!changed) break;\n }\n}\n\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n c2d['U']=0;c2d['D']=1;c2d['L']=2;c2d['R']=3;\n cin>>si>>sj>>ti>>tj>>p;init();\n string best; double bs = 0;\n \n auto optimize = [&](string s) {\n if(s.size() < 200) {\n double pr[400] = {}; pr[si*20+sj] = 1;\n for(char c : s) {\n int d = c2d[(unsigned char)c];\n double np[400] = {};\n for(int i=0; i<400; ++i) { if(pr[i]<1e-18) continue; if(i==ti_idx) continue; np[i] += p*pr[i]; int ni=md[i][d]; if(ni!=ti_idx) np[ni]+=(1-p)*pr[i]; }\n memcpy(pr, np, sizeof(pr));\n }\n for(int t=s.size(); t<200; t++) {\n double bsc2 = -1; int ba = 0;\n for(int d=0; d<4; d++) {\n double rp = 0; double np[400] = {};\n for(int i=0; i<400; ++i) { if(pr[i]<1e-18) continue; if(i==ti_idx) continue; np[i] += p*pr[i]; int ni=md[i][d]; if(ni==ti_idx) rp+=(1-p)*pr[i]; else np[ni]+=(1-p)*pr[i]; }\n double sc = rp * (400 - t); for(int i=0; i<400; ++i) sc += np[i] * fv[i][t+2];\n if(sc > bsc2) { bsc2 = sc; ba = d; }\n }\n s += \"UDLR\"[ba];\n double np[400] = {};\n for(int i=0; i<400; ++i) { if(pr[i]<1e-18) continue; if(i==ti_idx) continue; np[i] += p*pr[i]; int ni=md[i][ba]; if(ni!=ti_idx) np[ni]+=(1-p)*pr[i]; }\n memcpy(pr, np, sizeof(pr));\n }\n }\n coordinate_descent(s);\n double sc = compute_score(s);\n if(sc > bs) { bs = sc; best = s; }\n };\n \n string sp = bfs_path();\n optimize(sp);\n \n for(int r=2; r<=5; r++) {\n string s;\n for(int i=0; i(1, 5)(rng);\n for(int j=0; j(0, 199)(rng);\n s[pos] = \"UDLR\"[uniform_int_distribution(0, 3)(rng)];\n }\n optimize(s);\n }\n \n for(int i=0; i<30; ++i) {\n string s = best;\n int pos = uniform_int_distribution(0, 180)(rng);\n int len = uniform_int_distribution(5, 20)(rng);\n for(int j=pos; j(0, 3)(rng)];\n optimize(s);\n }\n \n cout<\nusing namespace std;\n\nconst int N = 30;\nint orig[N][N], cur[N][N], rot[N][N];\nconstexpr int di[]={0,-1,0,1}, dj[]={-1,0,1,0};\nconstexpr int to[8][4]={{1,0,-1,-1},{3,-1,-1,0},{-1,-1,3,2},{-1,2,1,-1},{1,0,3,2},{3,2,1,0},{2,-1,0,-1},{-1,3,-1,1}};\nconstexpr int rt[8][4]={{0,1,2,3},{1,2,3,0},{2,3,0,1},{3,0,1,2},{4,5,4,5},{5,4,5,4},{6,7,6,7},{7,6,7,6}};\n\nint cycle_counts[2002] = {};\nset active_lengths;\nlong long total_loop_edges = 0;\n\nint vm[N][N][4]; \nunsigned int vcnt=0;\n\nvoid update_cycle_counts(int len, int delta) {\n if (delta == 1) {\n if (cycle_counts[len] == 0) active_lengths.insert(len);\n cycle_counts[len]++;\n total_loop_edges += len;\n } else {\n cycle_counts[len]--;\n total_loop_edges -= len;\n if (cycle_counts[len] == 0) active_lengths.erase(len);\n }\n}\n\nvoid init_cycle_counts() {\n memset(cycle_counts, 0, sizeof(cycle_counts));\n active_lengths.clear();\n total_loop_edges = 0;\n \n ++vcnt;\n if (vcnt == 0) { memset(vm, 0, sizeof(vm)); vcnt = 1; }\n \n for (int i=0; i= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == si && nj == sj && nd == sd) { is_cycle = true; break; }\n if (vm[ni][nj][nd] == vcnt) break;\n if (len > 2000) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n update_cycle_counts(len, 1);\n }\n }\n }\n}\n\nvoid update_tile(int i, int j, int new_t) {\n int old_t = cur[i][j];\n if (old_t == new_t) return;\n\n bool visited_old[4] = {false, false, false, false};\n for (int d = 0; d < 4; d++) {\n if (visited_old[d] || to[old_t][d] == -1) continue;\n int len = 0;\n int ci = i, cj = j, cd = d;\n bool is_cycle = false;\n while (true) {\n int t2 = (ci == i && cj == j) ? old_t : cur[ci][cj];\n int d2 = to[t2][cd];\n if (d2 == -1) break;\n if (ci == i && cj == j) { visited_old[cd] = true; visited_old[d2] = true; }\n int ni = ci + di[d2], nj = cj + dj[d2];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == i && nj == j && nd == d) { is_cycle = true; break; }\n if (len > 2000) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n update_cycle_counts(len, -1);\n }\n }\n\n cur[i][j] = new_t;\n bool visited_new[4] = {false, false, false, false};\n for (int d = 0; d < 4; d++) {\n if (visited_new[d] || to[new_t][d] == -1) continue;\n int len = 0;\n int ci = i, cj = j, cd = d;\n bool is_cycle = false;\n while (true) {\n int t2 = (ci == i && cj == j) ? new_t : cur[ci][cj];\n int d2 = to[t2][cd];\n if (d2 == -1) break;\n if (ci == i && cj == j) { visited_new[cd] = true; visited_new[d2] = true; }\n int ni = ci + di[d2], nj = cj + dj[d2];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) break;\n len++;\n int nd = (d2 + 2) % 4;\n if (ni == i && nj == j && nd == d) { is_cycle = true; break; }\n if (len > 2000) break;\n ci = ni; cj = nj; cd = nd;\n }\n if (is_cycle) {\n update_cycle_counts(len, 1);\n }\n }\n}\n\nlong long get_score() {\n if (active_lengths.empty()) return 0;\n auto it = active_lengths.rbegin();\n int L1 = *it;\n if (cycle_counts[L1] >= 2) return (long long)L1 * L1;\n if (active_lengths.size() == 1) return 0;\n int L2 = *next(it);\n return (long long)L1 * L2;\n}\n\nlong long get_sa_energy() {\n if (active_lengths.empty()) return 0;\n auto it = active_lengths.rbegin();\n int L1 = *it;\n \n if (cycle_counts[L1] >= 2) {\n return (long long)L1 * L1 * 1000 + total_loop_edges;\n }\n if (active_lengths.size() == 1) {\n return total_loop_edges;\n }\n int L2 = *next(it);\n return (long long)L1 * L2 * 1000 + total_loop_edges;\n}\n\nint lmatch(int i, int j) {\n int t = cur[i][j], m = 0;\n for (int d = 0; d < 4; d++) {\n if (to[t][d] == -1) continue;\n int ni = i + di[d], nj = j + dj[d];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) continue;\n if (to[cur[ni][nj]][(d + 2) % 4] != -1) m++;\n }\n return m;\n}\n\nvoid greedy_match() {\n for (int pass = 0; pass < 10; pass++) {\n bool ch = false;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n int br = rot[i][j], bm = lmatch(i, j);\n for (int r = 0; r < 4; r++) {\n if (r == rot[i][j]) continue;\n cur[i][j] = rt[orig[i][j]][r];\n int m = lmatch(i, j);\n if (m > bm) { bm = m; br = r; ch = true; }\n }\n rot[i][j] = br; cur[i][j] = rt[orig[i][j]][br];\n }\n if (!ch) break;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(0);\n for (int i = 0; i < N; i++) { string s; cin >> s; for (int j = 0; j < N; j++) orig[i][j] = s[j] - '0'; }\n mt19937 rng(42);\n long long gbest = 0; int grot[N][N] = {};\n auto t0 = chrono::steady_clock::now();\n bool have_best = false;\n\n for (int trial = 0; ; trial++) {\n double elapsed = chrono::duration(chrono::steady_clock::now() - t0).count();\n if (elapsed > 1.5) break;\n\n if (have_best && trial % 2 == 1) {\n memcpy(rot, grot, sizeof(rot));\n int np = 20 + rng() % 80;\n for (int k = 0; k < np; k++) { int i = rng() % N, j = rng() % N; rot[i][j] = rng() % 4; }\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cur[i][j] = rt[orig[i][j]][rot[i][j]];\n greedy_match();\n } else {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { rot[i][j] = rng() % 4; cur[i][j] = rt[orig[i][j]][rot[i][j]]; }\n greedy_match();\n }\n\n init_cycle_counts();\n long long current_energy = get_sa_energy();\n long long best_score = get_score();\n int brot[N][N]; memcpy(brot, rot, sizeof(rot));\n\n for (int iter = 0; ; iter++) {\n if (iter % 10000 == 0) {\n if (chrono::duration(chrono::steady_clock::now() - t0).count() > 1.7) break;\n }\n double frac = min(iter / 2000000.0, 1.0);\n double temp = 50000.0 * pow(0.00002, frac);\n int idx = (rng() >> 2) % 900, i = idx / N, j = idx % N;\n int old_r = rot[i][j];\n int new_r = (rng() >> 12) & 3;\n if (old_r == new_r) continue;\n int new_t = rt[orig[i][j]][new_r];\n if (new_t == cur[i][j]) continue;\n\n update_tile(i, j, new_t);\n long long new_energy = get_sa_energy();\n long long diff = new_energy - current_energy;\n\n if (diff >= 0 || (double)(rng() & 0xFFFF) / 65536.0 < exp((double)diff / temp)) {\n current_energy = new_energy;\n rot[i][j] = new_r;\n long long true_score = get_score();\n if (true_score > best_score) {\n best_score = true_score;\n memcpy(brot, rot, sizeof(rot));\n }\n } else {\n update_tile(i, j, rt[orig[i][j]][old_r]);\n rot[i][j] = old_r;\n }\n }\n\n if (best_score > gbest) {\n gbest = best_score;\n memcpy(grot, brot, sizeof(grot));\n have_best = true;\n }\n }\n\n memcpy(rot, grot, sizeof(rot));\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cur[i][j] = rt[orig[i][j]][rot[i][j]];\n init_cycle_counts();\n long long current_score = get_score();\n\n for (int pass = 0; pass < 10; pass++) {\n bool imp = false;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n int old_t = cur[i][j];\n int best_new_t = old_t;\n long long best_local_score = current_score;\n int best_new_r = rot[i][j];\n\n for (int r = 0; r < 4; r++) {\n int new_t = rt[orig[i][j]][r];\n if (new_t == old_t) continue;\n update_tile(i, j, new_t);\n long long new_score = get_score();\n if (new_score > best_local_score) {\n best_local_score = new_score;\n best_new_t = new_t;\n best_new_r = r;\n }\n update_tile(i, j, old_t);\n }\n\n if (best_new_t != old_t) {\n update_tile(i, j, best_new_t);\n rot[i][j] = best_new_r;\n current_score = best_local_score;\n imp = true;\n }\n }\n if (!imp) break;\n }\n\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cout << rot[i][j];\n cout << endl;\n\n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N,T,board[10][10],init_board[10][10],er,ec,init_er,init_ec;\nint target[10][10],tile_count[16];\nint best_board[10][10],best_er_b,best_ec_b;\nconst int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\nconst int BS[]={2,8,1,4},BN[]={8,2,4,1};\nconst char DC_C[]={'U','D','L','R'};\nconst int REV[]={1,0,3,2};\n\nint par2[100],sz2[100],edg2[100];\nint find2(int x){while(par2[x]!=x)x=par2[x]=par2[par2[x]];return x;}\nvoid unite2(int x,int y){\n x=find2(x);y=find2(y);\n if(x==y){edg2[x]++;return;}\n if(sz2[x]> el;\n for(int i=0;i par(N*N),rnk(N*N,0);iota(par.begin(),par.end(),0);\n function f=[&](int x)->int{return par[x]==x?x:par[x]=f(par[x]);};\n memset(target,0,sizeof(target));\n for(auto&[w,u,v]:el){\n int pu=f(u),pv=f(v);\n if(pu!=pv){\n int r1=u/N,c1=u%N,r2=v/N,c2=v%N;\n if(r2==r1+1){target[r1][c1]|=8;target[r2][c2]|=2;}\n else{target[r1][c1]|=4;target[r2][c2]|=1;}\n if(rnk[pu]=0&&r=0&&c=0&&r=0&&c>N>>T;memset(tile_count,0,sizeof(tile_count));\n for(int i=0;i>s;for(int j=0;j='0'&&c<='9')?c-'0':c-'a'+10;if(board[i][j])tile_count[board[i][j]]++;else{init_er=i;init_ec=j;}}}\n memcpy(init_board,board,sizeof(board));er=init_er;ec=init_ec;\n int gbm=max_tree();string gbm_moves;\n memcpy(best_board,init_board,sizeof(init_board));best_er_b=init_er;best_ec_b=init_ec;\n auto start=chrono::high_resolution_clock::now();\n\n // Phase 1: SA from initial board\n for(int trial=0;;trial++){\n auto now=chrono::high_resolution_clock::now();\n if(chrono::duration_cast(now-start).count()>1800)break;\n mt19937 rng(42+trial*137);\n memcpy(board,init_board,sizeof(board));er=init_er;ec=init_ec;\n int skip_r=rng()%N,skip_c=rng()%N;\n gen_target(rng,skip_r,skip_c);\n if(match_ub()(now2-start).count()>1800)break;}\n long long dv[4];\n for(int d=0;d<4;d++){\n int nr=er+DR[d],nc=ec+DC[d];\n if(nr<0||nr>=N||nc<0||nc>=N){dv[d]=-1e18;continue;}\n int X=board[nr][nc],dm=0;\n if(target[nr][nc]&&(X&target[nr][nc])==target[nr][nc])dm--;\n if(target[er][ec]&&(X&target[er][ec])==target[er][ec])dm++;\n int dcc=0,dtc=0;\n for(int dd=0;dd<4;dd++){\n int r=er+DR[dd],c=ec+DC[dd];\n if(r>=0&&r=0&&c=0&&r=0&&cbv){bv=dv[d];bd=d;}\n if(bd==-1)break;int ch;\n if(bv>0){ch=bd;stale=0;}\n else{stale++;double delta=(double)bv/1000.0;\n if(exp(delta/max(temp,0.01))>(double)rng()/(double)UINT32_MAX)ch=bd;\n else{int v[4],nv=0;for(int d=0;d<4;d++){if(dv[d]<=-1e18)continue;if(ld>=0&&d==REV[ld])continue;v[nv++]=d;}\n if(!nv)for(int d=0;d<4;d++)if(dv[d]>-1e18)v[nv++]=d;if(!nv)break;ch=v[rng()%nv];}}\n apply_move(ch,cm,cc,tc);mv+=DC_C[ch];ld=ch;\n if(chk%25==0){int mx=max_tree();if(mx>bm){bm=mx;bi=mv.size();stale=0;save_best(tb,tber,tbec);}if(mx==N*N-1)break;}\n temp*=cool;\n if(stale>250){\n for(int w=0;w<15&&(int)mv.size()=0&&nr2=0&&nc2=0&&d==REV[ld])continue;v[nv++]=d;}}\n if(!nv)for(int d=0;d<4;d++){int nr2=er+DR[d],nc2=ec+DC[d];if(nr2>=0&&nr2=0&&nc2bm){bm=mx;bi=mv.size();save_best(tb,tber,tbec);}\n }\n }\n {int mx=max_tree();if(mx>bm){bm=mx;bi=mv.size();save_best(tb,tber,tbec);}}\n if(bm>gbm){gbm=bm;gbm_moves=mv.substr(0,bi);memcpy(best_board,tb,sizeof(tb));best_er_b=tber;best_ec_b=tbec;}\n if(gbm==N*N-1)break;\n }\n\n // Phase 2: SA from best state with actual empty position\n for(int trial2=0;;trial2++){\n auto now=chrono::high_resolution_clock::now();\n if(chrono::duration_cast(now-start).count()>2850)break;\n mt19937 rng2(77777+trial2*137);\n memcpy(board,best_board,sizeof(best_board));er=best_er_b;ec=best_ec_b;\n // Use actual empty square position for target generation\n int skip_r=best_er_b,skip_c=best_ec_b;\n if(trial2%3==0){skip_r=rng2()%N;skip_c=rng2()%N;}\n gen_target(rng2,skip_r,skip_c);\n if(match_ub()(now2-start).count()>2850)break;}\n long long dv[4];\n for(int d=0;d<4;d++){\n int nr=er+DR[d],nc=ec+DC[d];\n if(nr<0||nr>=N||nc<0||nc>=N){dv[d]=-1e18;continue;}\n int X=board[nr][nc],dm=0;\n if(target[nr][nc]&&(X&target[nr][nc])==target[nr][nc])dm--;\n if(target[er][ec]&&(X&target[er][ec])==target[er][ec])dm++;\n int dcc=0,dtc=0;\n for(int dd=0;dd<4;dd++){\n int r=er+DR[dd],c=ec+DC[dd];\n if(r>=0&&r=0&&c=0&&r=0&&cbv){bv=dv[d];bd=d;}\n if(bd==-1)break;int ch;\n if(bv>0){ch=bd;stale2=0;}\n else{stale2++;double delta=(double)bv/1000.0;\n if(exp(delta/max(temp2,0.01))>(double)rng2()/(double)UINT32_MAX)ch=bd;\n else{int v[4],nv=0;for(int d=0;d<4;d++){if(dv[d]<=-1e18)continue;if(ld2>=0&&d==REV[ld2])continue;v[nv++]=d;}\n if(!nv)for(int d=0;d<4;d++)if(dv[d]>-1e18)v[nv++]=d;if(!nv)break;ch=v[rng2()%nv];}}\n apply_move(ch,cm,cc,tc);mv2+=DC_C[ch];ld2=ch;\n if(chk2%20==0){int mx=max_tree();if(mx>bm2){bm2=mx;bi2=mv2.size();stale2=0;save_best(tb2,tber2,tbec2);}if(mx==N*N-1)break;}\n temp2*=cool2;\n if(stale2>200){\n for(int w=0;w<12&&(int)mv2.size()=0&&nr2=0&&nc2=0&&d==REV[ld2])continue;v[nv++]=d;}}\n if(!nv)for(int d=0;d<4;d++){int nr2=er+DR[d],nc2=ec+DC[d];if(nr2>=0&&nr2=0&&nc2bm2){bm2=mx;bi2=mv2.size();save_best(tb2,tber2,tbec2);}\n }\n }\n {int mx=max_tree();if(mx>bm2){bm2=mx;bi2=mv2.size();save_best(tb2,tber2,tbec2);}}\n if(bm2>gbm){gbm=bm2;gbm_moves+=mv2.substr(0,bi2);memcpy(best_board,tb2,sizeof(tb2));best_er_b=tber2;best_ec_b=tbec2;}\n if(gbm==N*N-1)break;\n }\n\n if((int)gbm_moves.size()>T)gbm_moves=gbm_moves.substr(0,T);\n cout<\nusing namespace std;\ntypedef long long ll;\n\nint N, K;\nint a_arr[11];\nvector px, py;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> K;\n for (int d = 1; d <= 10; d++) cin >> a_arr[d];\n px.resize(N); py.resize(N);\n for (int i = 0; i < N; i++) cin >> px[i] >> py[i];\n \n auto start = chrono::steady_clock::now();\n \n struct Line { ll la, lb, lc, p1x, p1y, p2x, p2y; };\n vector lines, best_lines;\n int best_overall = 0;\n \n auto make_line = [&](ll x1, ll y1, ll x2, ll y2) -> Line {\n if (x1 == x2 && y1 == y2) x2++;\n return {y2-y1, x1-x2, x2*y1-x1*y2, x1, y1, x2, y2};\n };\n \n auto make_sep = [&](int i, int j) -> Line {\n ll dx = py[i]-py[j], dy = px[j]-px[i];\n ll g = __gcd(abs(dx), abs(dy)); if(g>0){dx/=g;dy/=g;}\n if(dx==0&&dy==0) dx=1;\n ll mx2=px[i]+px[j], my2=py[i]+py[j];\n for(int r=0;r<4;r++){\n ll cx=(mx2+(r&1))/2, cy=(my2+((r>>1)&1))/2;\n Line l=make_line(cx,cy,cx+dx,cy+dy);\n ll vi=l.la*px[i]+l.lb*py[i]+l.lc, vj=l.la*px[j]+l.lb*py[j]+l.lc;\n if(vi!=0&&vj!=0&&(vi>0)!=(vj>0)) return l;\n }\n return make_line(mx2/2,my2/2,mx2/2+dx,my2/2+dy);\n };\n \n auto compute_gm = [&]() -> vector> {\n int nl = lines.size();\n map,int> smap;\n vector> gm;\n for(int i=0;i0){if(j<64)h1|=1LL<second].push_back(i);\n }\n }\n return gm;\n };\n \n auto score_gm = [&](vector>& gm) -> int {\n int pc[11]={};\n for(auto& m:gm){int sz=m.size();if(sz>=1&&sz<=10)pc[sz]++;}\n int s=0; for(int d=1;d<=10;d++) s+=min(a_arr[d],pc[d]); return s;\n };\n \n auto eval_cand = [&](Line& l, vector>& gm) -> int {\n int pc[11]={};\n for(auto& m:gm){\n int pos=0,neg=0;\n for(int i:m){\n ll val=l.la*px[i]+l.lb*py[i]+l.lc;\n if(val>0)pos++;else if(val<0)neg++;\n }\n if(pos>=1&&pos<=10)pc[pos]++;\n if(neg>=1&&neg<=10)pc[neg]++;\n }\n int s=0; for(int d=1;d<=10;d++) s+=min(a_arr[d],pc[d]); return s;\n };\n \n auto gen_cands = [&](vector>& gm, int max_cands=400) -> vector {\n int pc[11]={};\n for(auto& m:gm){int sz=m.size();if(sz>=1&&sz<=10)pc[sz]++;}\n vector cands;\n set> seen;\n auto add=[&](Line l){\n if((int)cands.size()>=max_cands) return;\n ll a=l.la,b=l.lb,c=l.lc;\n ll g=__gcd(__gcd(abs(a),abs(b)),abs(c));\n if(g>0){a/=g;b/=g;c/=g;}\n if(a<0||(a==0&&b<0)||(a==0&&b==0&&c<0)){a=-a;b=-b;c=-c;}\n if(seen.insert({a,b,c}).second) cands.push_back(l);\n };\n // Sort groups by priority\n vector> order;\n for(int i=0;i<(int)gm.size();i++){\n int sz=gm[i].size();\n if(sz<=1) continue;\n bool need=(sz>10)||(sz<=10&&pc[sz]>a_arr[sz]);\n if(!need) for(int p=1;p=max_cands) break;\n }\n return cands;\n };\n \n // Phase 1: Greedy\n for(int iter=0;iter(chrono::steady_clock::now()-start).count()>0.8) break;\n auto gm=compute_gm();\n int cs=score_gm(gm);\n if(cs>best_overall){best_overall=cs;best_lines=lines;}\n int mx=0;for(int d=1;d<=10;d++)mx+=a_arr[d];\n if(cs==mx) break;\n auto cands=gen_cands(gm,400);\n if(cands.empty()) break;\n int bs=cs,bi=-1;\n for(int i=0;i<(int)cands.size();i++){\n int s=eval_cand(cands[i],gm);\n if(s>bs){bs=s;bi=i;}\n }\n if(bi>=0) lines.push_back(cands[bi]);\n else {\n int max_sz=1,max_i=-1;\n for(int i=0;i<(int)gm.size();i++)\n if((int)gm[i].size()>max_sz){max_sz=gm[i].size();max_i=i;}\n if(max_sz>1&&(int)lines.size()best_overall){best_overall=s;best_lines=lines;}}\n \n // Phase 2: Local search\n mt19937 rng(42);\n int no_imp=0;\n while(chrono::duration(chrono::steady_clock::now()-start).count()<2.85){\n int nl=lines.size();\n if(nl==0) break;\n bool improved=false;\n \n // Try adding a line\n if((int)lines.size()bs){bs=s;bi=i;}\n }\n if(bi>=0){lines.push_back(cands[bi]);improved=true;}\n }\n }\n \n // Try replacing a line\n if(!improved&&nl>0){\n int idx=rng()%nl;\n auto old=lines[idx];\n lines[idx]=lines.back();lines.pop_back();\n auto gm=compute_gm();\n int cs=score_gm(gm);\n auto cands=gen_cands(gm,300);\n cands.push_back(old);\n int bs=cs,bi=(int)cands.size()-1;\n for(int i=0;i<(int)cands.size()-1;i++){\n int s=eval_cand(cands[i],gm);\n if(s>bs){bs=s;bi=i;}\n }\n lines.push_back(cands[bi]);\n if(bs>cs) improved=true;\n }\n \n auto gm=compute_gm();\n int ns=score_gm(gm);\n if(ns>best_overall){best_overall=ns;best_lines=lines;no_imp=0;}\n else if(improved) no_imp=0;\n else no_imp++;\n \n if(no_imp>60){\n lines=best_lines;\n int nl2=lines.size();\n if(nl2>3){\n int rc=2+rng()%4;\n shuffle(lines.begin(),lines.end(),rng);\n lines.resize(max(0,(int)lines.size()-rc));\n for(int iter2=0;iter2(chrono::steady_clock::now()-start).count()>2.85) break;\n auto gm2=compute_gm();\n int cs2=score_gm(gm2);\n auto cands2=gen_cands(gm2,300);\n if(cands2.empty()) break;\n int bs2=cs2,bi2=-1;\n for(int i=0;i<(int)cands2.size();i++){\n int s=eval_cand(cands2[i],gm2);\n if(s>bs2){bs2=s;bi2=i;}\n }\n if(bi2>=0) lines.push_back(cands2[bi2]);\n else break;\n }\n gm=compute_gm();ns=score_gm(gm);\n if(ns>best_overall){best_overall=ns;best_lines=lines;}\n }\n no_imp=0;\n }\n }\n \n lines=best_lines;\n cout<\n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, M;\nvector> has_dot;\nvector> ops;\nmap>> segs[4];\n\nvector dots_y[65];\nvector dots_x[65];\nvector dots_u[130];\nvector dots_v[130];\nvector pt_idx[65];\nvector> existing_dots;\n\nset candidates;\nvector>> empty_pts_vec;\n\nint seg_type(int x1,int y1,int x2,int y2){\n if(y1==y2)return 0;\n if(x1==x2)return 1;\n if(x2-x1==y2-y1)return 2;\n return 3;\n}\nint line_id(int t,int x,int y){\n if(t==0)return y;\n if(t==1)return x;\n if(t==2)return x-y;\n return x+y;\n}\nint line_coord(int t,int x,int y){\n if(t==0||t==2||t==3)return x;\n return y;\n}\n\nbool check_overlap(int t, int lid, int s, int e) {\n if (s > e) swap(s, e);\n auto it = segs[t].find(lid);\n if (it == segs[t].end()) return false;\n auto& st = it->second;\n auto jt = st.upper_bound({s, 1e9});\n if (jt != st.begin()) {\n auto kt = prev(jt);\n if (kt->second > s) return true;\n }\n if (jt != st.end()) {\n if (jt->first < e) return true;\n }\n return false;\n}\n\nvoid add_seg(int t, int lid, int s, int e) {\n if (s > e) swap(s, e);\n auto& st = segs[t][lid];\n auto it = st.upper_bound({s, 1e9});\n if (it != st.begin()) {\n auto kt = prev(it);\n if (kt->second >= s) {\n s = min(s, kt->first);\n e = max(e, kt->second);\n st.erase(kt);\n }\n }\n it = st.upper_bound({s, 1e9});\n while (it != st.end() && it->first <= e) {\n e = max(e, it->second);\n it = st.erase(it);\n }\n st.insert({s, e});\n}\n\nbool has_perim_overlap(int x1,int y1,int x2,int y2,int x3,int y3,int x4,int y4){\n int e[4][4]={{x1,y1,x2,y2},{x2,y2,x3,y3},{x3,y3,x4,y4},{x4,y4,x1,y1}};\n for(int i=0;i<4;i++){\n int t=seg_type(e[i][0],e[i][1],e[i][2],e[i][3]);\n int lid=line_id(t,e[i][0],e[i][1]);\n int s=line_coord(t,e[i][0],e[i][1]);\n int ee=line_coord(t,e[i][2],e[i][3]);\n if(check_overlap(t,lid,s,ee))return true;\n }\n return false;\n}\n\nvoid add_perim(int x1,int y1,int x2,int y2,int x3,int y3,int x4,int y4){\n int e[4][4]={{x1,y1,x2,y2},{x2,y2,x3,y3},{x3,y3,x4,y4},{x4,y4,x1,y1}};\n for(int i=0;i<4;i++){\n int t=seg_type(e[i][0],e[i][1],e[i][2],e[i][3]);\n int lid=line_id(t,e[i][0],e[i][1]);\n int s=line_coord(t,e[i][0],e[i][1]);\n int ee=line_coord(t,e[i][2],e[i][3]);\n add_seg(t,lid,s,ee);\n }\n}\n\nbool valid_rect_axis(int ex, int ey, int x1, int y1) {\n for (int px = min(ex, x1) + 1; px < max(ex, x1); ++px) {\n if (has_dot[px][ey]) return false;\n if (has_dot[px][y1]) return false;\n }\n for (int py = min(ey, y1) + 1; py < max(ey, y1); ++py) {\n if (has_dot[ex][py]) return false;\n if (has_dot[x1][py]) return false;\n }\n if (has_perim_overlap(ex, ey, ex, y1, x1, y1, x1, ey)) return false;\n return true;\n}\n\nbool valid_rect_45(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n auto chk = [&](int ax, int ay, int bx, int by) {\n int dx = (bx > ax) ? 1 : -1;\n int dy = (by > ay) ? 1 : -1;\n int steps = abs(bx - ax);\n for (int i = 1; i < steps; ++i) {\n int px = ax + i * dx;\n int py = ay + i * dy;\n if (has_dot[px][py]) return true;\n }\n return false;\n };\n if (chk(x1, y1, x2, y2) || chk(x2, y2, x3, y3) || chk(x3, y3, x4, y4) || chk(x4, y4, x1, y1)) return false;\n if (has_perim_overlap(x1, y1, x2, y2, x3, y3, x4, y4)) return false;\n return true;\n}\n\nvector sorted_by_dist(const vector& v, int center) {\n vector res = v;\n sort(res.begin(), res.end(), [&](int a, int b) {\n return abs(a - center) < abs(b - center);\n });\n return res;\n}\n\npair, int> find_best_rect(int ex, int ey) {\n int best_cost = 1e9;\n array best_r = {-1};\n \n auto ys = sorted_by_dist(dots_x[ex], ey);\n auto xs = sorted_by_dist(dots_y[ey], ex);\n \n for (int y1 : ys) {\n int cost_y = abs(y1 - ey);\n if (cost_y >= best_cost) break;\n for (int x1 : xs) {\n int cost_x = abs(x1 - ex);\n int cost = cost_y + cost_x;\n if (cost >= best_cost) break;\n if (has_dot[x1][y1]) {\n if (valid_rect_axis(ex, ey, x1, y1)) {\n best_cost = cost;\n best_r = {ex, ey, ex, y1, x1, y1, x1, ey};\n }\n }\n }\n }\n \n int eu = ex + ey;\n int ev = ex - ey;\n auto vs = sorted_by_dist(dots_u[eu], ev);\n auto us = sorted_by_dist(dots_v[ev + N], eu);\n \n for (int v2 : vs) {\n if ((eu + v2) % 2 != 0) continue;\n int xp2 = (eu + v2) / 2;\n int yp2 = (eu - v2) / 2;\n if (xp2 < 0 || xp2 >= N || yp2 < 0 || yp2 >= N) continue;\n int cost_v = abs(v2 - ev);\n if (cost_v >= best_cost) break;\n \n for (int u3 : us) {\n if ((u3 + ev) % 2 != 0) continue;\n int xp4 = (u3 + ev) / 2;\n int yp4 = (u3 - ev) / 2;\n if (xp4 < 0 || xp4 >= N || yp4 < 0 || yp4 >= N) continue;\n \n int xp3 = (u3 + v2) / 2;\n int yp3 = (u3 - v2) / 2;\n if (xp3 < 0 || xp3 >= N || yp3 < 0 || yp3 >= N) continue;\n \n int cost_u = abs(u3 - eu);\n int cost = cost_v + cost_u;\n if (cost >= best_cost) break;\n \n if (has_dot[xp3][yp3]) {\n if (valid_rect_45(ex, ey, xp2, yp2, xp3, yp3, xp4, yp4)) {\n best_cost = cost;\n best_r = {ex, ey, xp2, yp2, xp3, yp3, xp4, yp4};\n }\n }\n }\n }\n \n return {best_r, best_cost};\n}\n\nvoid add_cand(int x, int y) {\n if (x >= 0 && x < N && y >= 0 && y < N && !has_dot[x][y]) {\n int idx = pt_idx[x][y];\n if (idx != -1) {\n candidates.insert(idx);\n }\n }\n}\n\nvoid add_cand_uv(int u, int v) {\n if ((u + v) % 2 != 0) return;\n int x = (u + v) / 2;\n int y = (u - v) / 2;\n add_cand(x, y);\n}\n\nvoid add_candidates(int x, int y) {\n int u = x + y;\n int v = x - y;\n \n for (int ex : dots_y[y]) {\n for (int ey : dots_x[x]) {\n add_cand(ex, ey); // Opposite axis-aligned\n }\n }\n for (int ex2 : dots_y[y]) {\n for (int ey : dots_x[ex2]) {\n add_cand(x, ey); // Adjacent axis-aligned, share x\n }\n }\n for (int ey2 : dots_x[x]) {\n for (int ex : dots_y[ey2]) {\n add_cand(ex, y); // Adjacent axis-aligned, share y\n }\n }\n \n for (int eu : dots_v[v + N]) {\n for (int ev : dots_u[u]) {\n add_cand_uv(eu, ev); // Opposite 45-degree\n }\n }\n for (int eu2 : dots_v[v + N]) {\n for (int ev : dots_u[eu2]) {\n add_cand_uv(u, ev); // Adjacent 45-degree, share u\n }\n }\n for (int ev2 : dots_u[u]) {\n for (int eu : dots_v[ev2 + N]) {\n add_cand_uv(eu, v); // Adjacent 45-degree, share v\n }\n }\n}\n\nint main(){\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n cin >> N >> M;\n has_dot.assign(N, vector(N, false));\n \n int c = (N - 1) / 2;\n \n for(int i=0;i> initial_dots(M);\n for(int i=0;i> x >> y;\n has_dot[x][y] = true;\n dots_x[x].push_back(y);\n dots_y[y].push_back(x);\n int u = x + y;\n int v = x - y;\n dots_u[u].push_back(v);\n dots_v[v + N].push_back(u);\n initial_dots[i] = {x, y};\n }\n \n for(int x=0;x\n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 10;\nint grid[N][N];\nint flavors[101];\nmt19937 rng(42);\n\nvoid applyTilt(int g[N][N], int d) {\n if (d == 0) { for (int c = 0; c < N; c++) { int w = 0; for (int r = 0; r < N; r++) if (g[r][c]) { if (w != r) { g[w][c] = g[r][c]; g[r][c] = 0; } w++; } } }\n else if (d == 1) { for (int c = 0; c < N; c++) { int w = N-1; for (int r = N-1; r >= 0; r--) if (g[r][c]) { if (w != r) { g[w][c] = g[r][c]; g[r][c] = 0; } w--; } } }\n else if (d == 2) { for (int r = 0; r < N; r++) { int w = 0; for (int c = 0; c < N; c++) if (g[r][c]) { if (w != c) { g[r][w] = g[r][c]; g[r][c] = 0; } w++; } } }\n else { for (int r = 0; r < N; r++) { int w = N-1; for (int c = N-1; c >= 0; c--) if (g[r][c]) { if (w != c) { g[r][w] = g[r][c]; g[r][c] = 0; } w--; } } }\n}\n\nint getScore(int g[N][N]) {\n bool vis[N][N] = {}; int s = 0;\n constexpr int dr[] = {-1,1,0,0}, dc[] = {0,0,-1,1};\n int q[N*N], fr, bk;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) {\n if (!vis[r][c] && g[r][c]) {\n int fl = g[r][c], sz = 0; fr = 0; bk = 0;\n q[bk++] = r*N+c; vis[r][c] = true;\n while (fr < bk) { int id = q[fr++], cr = id/N, cc = id%N; sz++;\n for (int d = 0; d < 4; d++) { int nr = cr+dr[d], nc = cc+dc[d];\n if (nr>=0&&nr=0&&nc= 100) return getScore(orig);\n int nf = flavors[turn + 1];\n long long total = 0; int count = 0;\n int g[N][N]; memcpy(g, orig, sizeof(g));\n int saved[N][N];\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) {\n if (g[r][c] == 0) {\n g[r][c] = nf;\n int bestS = 0;\n for (int d = 0; d < 4; d++) {\n memcpy(saved, g, sizeof(saved));\n applyTilt(g, d);\n int s = getScore(g);\n bestS = max(bestS, s);\n memcpy(g, saved, sizeof(saved));\n }\n total += bestS;\n g[r][c] = 0;\n count++;\n }\n }\n return count > 0 ? total / count : getScore(orig);\n}\n\nlong long runMC(int startT, int base[N][N]) {\n int sim[N][N]; memcpy(sim, base, sizeof(sim));\n for (int t = startT; t <= 100; t++) {\n int er[100], ec[100], cnt = 0;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) if (!sim[r][c]) { er[cnt] = r; ec[cnt] = c; cnt++; }\n if (!cnt) break;\n int idx = rng() % cnt;\n sim[er[idx]][ec[idx]] = flavors[t];\n int bestS = -1, bestD = 0, sv[N][N];\n for (int d = 0; d < 4; d++) { memcpy(sv, sim, sizeof(sv)); applyTilt(sim, d); int s = getScore(sim); if (s > bestS) { bestS = s; bestD = d; } memcpy(sim, sv, sizeof(sv)); }\n applyTilt(sim, bestD);\n }\n return getScore(sim);\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n for (int i = 1; i <= 100; i++) cin >> flavors[i];\n memset(grid, 0, sizeof(grid));\n const char dirChars[] = \"FBLR\";\n const int dirPrio[] = {4, 1, 2, 3};\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n int pos = 1;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) if (!grid[r][c]) { if (pos == p) { grid[r][c] = flavors[t]; goto placed; } pos++; }\n placed:;\n \n int scores[4], adjs[4];\n int saved[N][N]; memcpy(saved, grid, sizeof(grid));\n for (int d = 0; d < 4; d++) {\n applyTilt(grid, d);\n scores[d] = getScore(grid);\n adjs[d] = getAdj(grid);\n memcpy(grid, saved, sizeof(grid));\n }\n \n int maxScore = *max_element(scores, scores + 4);\n vector tied; for (int d = 0; d < 4; d++) if (scores[d] == maxScore) tied.push_back(d);\n \n int bestDir;\n if (tied.size() == 1) {\n bestDir = tied[0];\n } else {\n long long ply1[4] = {};\n for (int d : tied) {\n applyTilt(grid, d);\n ply1[d] = compute1Ply(grid, t);\n memcpy(grid, saved, sizeof(grid));\n }\n long long maxPly = -1; for (int d : tied) maxPly = max(maxPly, ply1[d]);\n vector tied2; for (int d : tied) if (ply1[d] == maxPly) tied2.push_back(d);\n \n if (tied2.size() == 1) {\n bestDir = tied2[0];\n } else {\n int maxAdj = -1; for (int d : tied2) maxAdj = max(maxAdj, adjs[d]);\n vector tied3; for (int d : tied2) if (adjs[d] == maxAdj) tied3.push_back(d);\n \n if (tied3.size() == 1) {\n bestDir = tied3[0];\n } else if (t >= 40) {\n int numSims = max(3, min(10, (100 - t) / 5));\n long long mcBest = -1; bestDir = tied3[0];\n for (int d : tied3) {\n int tmp[N][N]; memcpy(tmp, grid, sizeof(grid)); applyTilt(tmp, d);\n long long total = 0;\n for (int s = 0; s < numSims; s++) total += runMC(t + 1, tmp);\n if (total > mcBest) { mcBest = total; bestDir = d; }\n }\n } else {\n bestDir = tied3[0];\n for (int d : tied3) if (dirPrio[d] < dirPrio[bestDir]) bestDir = d;\n }\n }\n }\n \n applyTilt(grid, bestDir);\n cout << dirChars[bestDir] << '\\n'; cout.flush();\n }\n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nuint64_t sm64(uint64_t x) {\n x += 0x9e3779b97f4a7c15ULL;\n x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9ULL;\n x = (x ^ (x >> 27)) * 0x94d049bb133111ebULL;\n return x ^ (x >> 31);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int M; double eps;\n cin >> M >> eps;\n \n auto genFp = [&](int N, int code) -> vector {\n int maxE = N*(N-1)/2;\n vector ed(N, (N-1.0)*eps);\n int edges = 0;\n if (N <= 14) {\n for(int j=1; j> (j-1)) & 1){\n edges += j;\n for(int i=0; i> (j-1)) & 1) : ((h2 >> (j-65)) & 1);\n if(bj){\n edges += j;\n for(int i=0; i fp(N+1);\n fp[0] = edges*(1.0-2.0*eps) + maxE*eps;\n for(int i=0; i& a, const vector& b, double dVE, double dVD, int N) -> double {\n double d = (a[0]-b[0]); d = d*d/dVE;\n for(int i=1; i<=N; i++){ double df = a[i]-b[i]; d += df*df/dVD; }\n return d;\n };\n \n auto evaluateN = [&](int Nt) -> double {\n double dVD = max(0.001, (Nt-1.0)*eps*(1.0-eps));\n double dVE = max(0.001, (double)(Nt*(Nt-1)/2)*eps*(1.0-eps));\n int NCt = (Nt <= 14) ? min(4000, (1 << (Nt-1))) : 4000;\n if(NCt < M) return -1e18;\n \n vector> fps(NCt);\n for(int c=0; c used(NCt, false);\n vector minD(NCt, 1e18);\n used[0] = true;\n for(int c=1; c bestD){ bestD = minD[c]; best = c; }\n if(best < 0) return -1e18;\n used[best] = true; dMin = min(dMin, bestD);\n for(int c=0; cbestScore){bestScore=s;bestN=n;} }\n for(int n=21; n<=40; n+=2){ double s=evaluateN(n); if(s>bestScore){bestScore=s;bestN=n;} }\n for(int n=44; n<=70; n+=4){ double s=evaluateN(n); if(s>bestScore){bestScore=s;bestN=n;} }\n for(int n=75; n<=100; n+=5){ double s=evaluateN(n); if(s>bestScore){bestScore=s;bestN=n;} }\n for(int n=max(4,bestN-3); n<=min(100,bestN+3); n++){ double s=evaluateN(n); if(s>bestScore){bestScore=s;bestN=n;} }\n \n int N = bestN;\n int maxE = N*(N-1)/2;\n double dVD = max(0.001, (N-1.0)*eps*(1.0-eps));\n double dVE = max(0.001, (double)maxE*eps*(1.0-eps));\n auto eidx = [&](int i, int j)->int{ if(i>j) swap(i,j); return i*(2*N-i-1)/2+(j-i-1); };\n \n int NC = (N <= 14) ? (1 << (N-1)) : 15000;\n vector> cfp(NC);\n for(int c=0; c sel; vector minD(NC, 1e18); vector used(NC, false);\n sel.push_back(0); used[0] = true;\n for(int c=1; cbestD){bestD=minD[c];best=c;}\n if(best<0) break;\n sel.push_back(best); used[best]=true;\n for(int c=0; c> (j-1)) & 1) for(int i=0; i> (j-1)) & 1) : ((h2 >> (j-65)) & 1);\n if(bj) for(int i=0; i> gefp(M, vector(N+1));\n for(int k=0; k> H;\n int hE = count(H.begin(), H.end(), '1');\n vector hd(N, 0);\n for(int i=0; i\nusing namespace std;\ntypedef long long ll;\ntypedef pair pli;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N,M,D,K; cin>>N>>M>>D>>K;\n vector u(M),v(M),w(M);\n vector>> adj(N);\n for(int i=0;i>u[i]>>v[i]>>w[i];u[i]--;v[i]--;adj[u[i]].push_back({i,v[i]});adj[v[i]].push_back({i,u[i]});}\n vector x(N),y(N);\n for(int i=0;i>x[i]>>y[i];\n\n int S=min(N,100);\n vector betw(M,0);\n for(int si=0;si dist(N,LLONG_MAX);vector pe(N,-1);\n dist[s]=0;priority_queue,greater> pq;pq.push({0,s});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>dist[nd])continue;for(auto[ei,nx]:adj[nd]){ll nd2=d+w[ei];if(nd2 ss(N,1);vector> ch(N);\n for(int t=0;t ord={s};for(int i=0;i<(int)ord.size();i++)for(int c:ch[ord[i]])ord.push_back(c);\n for(int i=(int)ord.size()-1;i>0;i--){int nd=ord[i];int o=(u[pe[nd]]==nd)?v[pe[nd]]:u[pe[nd]];ss[o]+=ss[nd];}\n for(int t=0;t> apsp(N,vector(N,LLONG_MAX));\n for(int s=0;s,greater> pq;pq.push({0,s});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>apsp[s][nd])continue;for(auto[ei,nx]:adj[nd]){ll nd2=d+w[ei];if(nd2 det(M,0);\n for(int ei=0;ei impact(M);\n for(int i=0;i> conflicts(M);\n vector dist(N);vector pe(N);\n for(int ei=0;ei,greater> pq;pq.push({0,u[ei]});\n while(!pq.empty()){auto[d,nd]=pq.top();pq.pop();if(d>dist[nd])continue;for(auto[ej,nx]:adj[nd]){if(ej==ei)continue;ll nd2=d+w[ej];if(nd2 order(M);iota(order.begin(),order.end(),0);\n sort(order.begin(),order.end(),[&](int a,int b){return impact[a]>impact[b];});\n\n vector r(M,-1),dc(D,0);vector day_imp(D,0);\n for(int ei:order){\n double bs=1e18;int bd=-1;\n for(int d=0;d=K)continue;double sc=0;for(int ej:conflicts[ei])if(r[ej]==d)sc+=impact[ei]*impact[ej];sc+=day_imp[d]*1e-4;if(sc(now-t0).count()>5.0)break;\n int ei=rng()%M;int od=r[ei];double cs=0;for(int ej:conflicts[ei])if(r[ej]==od)cs+=impact[ei]*impact[ej];\n int bd=-1;double bi=0;for(int d=0;d=K)continue;double ns=0;for(int ej:conflicts[ei])if(r[ej]==d)ns+=impact[ei]*impact[ej];double imp=cs-ns+((day_imp[od]-impact[ei])-(day_imp[d]+impact[ei]))*1e-4;if(imp>bi){bi=imp;bd=d;}}\n if(bd!=-1){r[ei]=bd;dc[od]--;dc[bd]++;day_imp[od]-=impact[ei];day_imp[bd]+=impact[ei];}}\n\n for(int i=0;i\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\nint D;\nusing Point=tuple;\nusing Array3D=vector>>;\n\nchrono::high_resolution_clock::time_point start_time;\n\nvector readSil(){vectors(D);for(int i=0;i>s[i];return s;}\nArray3D buildMF(const vector&f,const vector&r){Array3D b(D,vector>(D,vector(D,0)));for(int x=0;x> findComp(const Array3D&b){\n Array3D vis(D,vector>(D,vector(D,0)));vector>cs;\n const int dx[]={1,-1,0,0,0,0},dy[]={0,0,1,-1,0,0},dz[]={0,0,0,0,1,-1};\n for(int x=0;xc;queueq;q.push({x,y,z});vis[x][y][z]=1;\n while(!q.empty()){auto[cx,cy,cz]=q.front();q.pop();c.push_back({cx,cy,cz});\n for(int d=0;d<6;d++){int nx=cx+dx[d],ny=cy+dy[d],nz=cz+dz[d];\n if(0<=nx&&nx> findSubComp(const vector& vox){\n Array3D vs(D, vector>(D, vector(D, 0)));\n Array3D vis(D, vector>(D, vector(D, 0)));\n for(auto& [x,y,z] : vox) vs[x][y][z] = 1;\n vector> cs;\n const int dx[]={1,-1,0,0,0,0},dy[]={0,0,1,-1,0,0},dz[]={0,0,0,0,1,-1};\n for(auto& [x,y,z] : vox){\n if(vis[x][y][z]) continue;\n vector c; queue q; q.push({x,y,z}); vis[x][y][z] = 1;\n while(!q.empty()){\n auto [cx,cy,cz] = q.front(); q.pop(); c.push_back({cx,cy,cz});\n for(int d=0;d<6;d++){\n int nx=cx+dx[d], ny=cy+dy[d], nz=cz+dz[d];\n if(0<=nx&&nx>> genRots(){\n vector>>rots;int B[6][3]={{1,0,0},{-1,0,0},{0,1,0},{0,-1,0},{0,0,1},{0,0,-1}};\n for(int i=0;i<6;i++)for(int j=0;j<6;j++){if(i/2==j/2)continue;int cr[3];\n cr[0]=B[i][1]*B[j][2]-B[i][2]*B[j][1];cr[1]=B[i][2]*B[j][0]-B[i][0]*B[j][2];cr[2]=B[i][0]*B[j][1]-B[i][1]*B[j][0];\n int dt=B[i][0]*(B[j][1]*cr[2]-B[j][2]*cr[1])-B[i][1]*(B[j][0]*cr[2]-B[j][2]*cr[0])+B[i][2]*(B[j][0]*cr[1]-B[j][1]*cr[0]);\n if(dt!=1)continue;rots.push_back({{B[i][0],B[i][1],B[i][2]},{B[j][0],B[j][1],B[j][2]},{cr[0],cr[1],cr[2]}});}\n return rots;\n}\n\nPoint appR(const vector>&M,const Point&p){auto[x,y,z]=p;return{M[0][0]*x+M[0][1]*y+M[0][2]*z,M[1][0]*x+M[1][1]*y+M[1][2]*z,M[2][0]*x+M[2][1]*y+M[2][2]*z};}\n\nvectorcanon(const vector&comp,const vector>>&rots){vectorbest;for(auto&M:rots){vectorr;for(auto&p:comp)r.push_back(appR(M,p));int mX=INT_MAX,mY=INT_MAX,mZ=INT_MAX;for(auto&[x,y,z]:r){mX=min(mX,x);mY=min(mY,y);mZ=min(mZ,z);}for(auto&[x,y,z]:r){x-=mX;y-=mY;z-=mZ;}sort(r.begin(),r.end());if(best.empty()||r>>& rots, int& nextId) {\n Array3D U0(D, vector>(D, vector(D, 0)));\n Array3D U1(D, vector>(D, vector(D, 0)));\n for(int x=0;x, vector> cm1;\n for (int j=0; j o0(n0); for (int i=0; i c0[b].size();});\n \n vector u1(n1, false);\n for (int i : o0) {\n auto cn = canon(c0[i], rots);\n auto it = cm1.find(cn);\n if (it != cm1.end()) for (int j : it->second) if (!u1[j]) {\n int id = nextId++;\n for (auto [x,y,z] : c0[i]) a0[x][y][z] = id;\n for (auto [x,y,z] : c1[j]) a1[x][y][z] = id;\n u1[j] = true; break;\n }\n }\n}\n\nbool doOneGlobalPartial(Array3D& a0, Array3D& a1, const Array3D& b0, const Array3D& b1, const vector>>& rots, int& nextId) {\n Array3D U0(D, vector>(D, vector(D, 0)));\n Array3D U1(D, vector>(D, vector(D, 0)));\n vector P1;\n for(int x=0;x b.size();});\n \n int bestO = 1, bestRi = -1, bestTx = 0, bestTy = 0, bestTz = 0;\n int bestCompIdx = -1;\n vector> rotsComp(comps0.size());\n \n const int OFF = 30, S = 61;\n vector tc(S*S*S, 0);\n \n for (int c_idx = 0; c_idx < (int)comps0.size(); c_idx++) {\n auto& comp = comps0[c_idx];\n if (comp.size() <= bestO) break;\n \n for (int ri = 0; ri < 24; ri++) {\n vector rot;\n for (auto& p : comp) rot.push_back(appR(rots[ri], p));\n int mX=INT_MAX, mY=INT_MAX, mZ=INT_MAX;\n for (auto& [x,y,z] : rot) { mX=min(mX,x); mY=min(mY,y); mZ=min(mZ,z); }\n for (auto& [x,y,z] : rot) { x-=mX; y-=mY; z-=mZ; }\n \n fill(tc.begin(), tc.end(), 0);\n int local_max = 0, local_tx = 0, local_ty = 0, local_tz = 0;\n for (auto& [sx,sy,sz] : rot) \n for (auto& [px,py,pz] : P1) {\n int kx = px-sx + OFF, ky = py-sy + OFF, kz = pz-sz + OFF;\n int idx = kx + ky*S + kz*S*S;\n tc[idx]++;\n if (tc[idx] > local_max) {\n local_max = tc[idx]; local_tx = kx - OFF; local_ty = ky - OFF; local_tz = kz - OFF;\n }\n }\n if (local_max > bestO) {\n bestO = local_max; bestRi = ri;\n bestTx = local_tx; bestTy = local_ty; bestTz = local_tz;\n bestCompIdx = c_idx;\n rotsComp[c_idx] = rot;\n if (bestO == comp.size()) break;\n }\n }\n }\n \n if (bestCompIdx != -1) {\n auto& comp = comps0[bestCompIdx];\n auto& rot = rotsComp[bestCompIdx];\n \n vector so, to;\n for (int i=0; i<(int)comp.size(); i++) {\n auto [rx,ry,rz] = rot[i];\n int tx=rx+bestTx, ty=ry+bestTy, tz=rz+bestTz;\n if (0<=tx&&tx= 2) {\n if (best_sc_idx == -1 || scs[i].size() > scs[best_sc_idx].size()) {\n best_sc_idx = i;\n }\n }\n }\n \n if (best_sc_idx != -1) {\n map s2i; for (int i=0; i<(int)so.size(); i++) s2i[so[i]] = i;\n int id = nextId++;\n for (auto& p : scs[best_sc_idx]) {\n int i = s2i[p];\n auto [sx,sy,sz] = so[i]; auto [tx,ty,tz] = to[i];\n a0[sx][sy][sz] = id; a1[tx][ty][tz] = id;\n }\n return true;\n }\n }\n return false;\n}\n\nvoid doSimpleIntersection(Array3D& a0, Array3D& a1, const Array3D& b0, const Array3D& b1, int& nextId) {\n Array3D U0(D, vector>(D, vector(D, 0)));\n Array3D U1(D, vector>(D, vector(D, 0)));\n for(int x=0;x>(D, vector(D, 0)));\n for(int x=0;x> D;\n vector> f(2), r(2);\n for (int i = 0; i < 2; i++) { f[i] = readSil(); r[i] = readSil(); }\n \n auto rots = genRots();\n auto b0 = buildMF(f[0], r[0]), b1 = buildMF(f[1], r[1]);\n Array3D a0(D, vector>(D, vector(D, 0)));\n Array3D a1(D, vector>(D, vector(D, 0)));\n int nid = 1;\n \n doExactMatch(a0, a1, b0, b1, rots, nid);\n while (chrono::duration_cast(chrono::high_resolution_clock::now() - start_time).count() < 4500) {\n bool changed = doOneGlobalPartial(a0, a1, b0, b1, rots, nid);\n if (changed) { doExactMatch(a0, a1, b0, b1, rots, nid); continue; }\n changed = doOneGlobalPartial(a1, a0, b1, b0, rots, nid);\n if (changed) { doExactMatch(a0, a1, b0, b1, rots, nid); continue; }\n break;\n }\n doSimpleIntersection(a0, a1, b0, b1, nid);\n doExactMatch(a0, a1, b0, b1, rots, nid);\n \n Array3D U0(D, vector>(D, vector(D, 0)));\n Array3D U1(D, vector>(D, vector(D, 0)));\n for(int x=0;x id_remap;\n int next_remap_id = 1;\n for(int x=0;x\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) cin >> x[i] >> y[i];\n \n vector>> adj(N);\n vector eu(M), ev(M), ew(M);\n for (int j = 0; j < M; j++) {\n cin >> eu[j] >> ev[j] >> ew[j];\n eu[j]--; ev[j]--;\n adj[eu[j]].push_back({ev[j], j});\n adj[ev[j]].push_back({eu[j], j});\n }\n \n vector a(K), b(K);\n for (int k = 0; k < K; k++) cin >> a[k] >> b[k];\n \n const int PMAX = 5000;\n const long long PMAXSQ = (long long)PMAX * PMAX;\n \n vector> rsq(K, vector(N));\n for (int k = 0; k < K; k++)\n for (int i = 0; i < N; i++) {\n long long dx = a[k] - x[i], dy = b[k] - y[i];\n rsq[k][i] = dx * dx + dy * dy;\n }\n \n vector> clo(K);\n for (int k = 0; k < K; k++) {\n vector> v;\n for (int i = 0; i < N; i++)\n if (rsq[k][i] <= PMAXSQ) v.push_back({rsq[k][i], i});\n sort(v.begin(), v.end());\n int cnt = min(30, (int)v.size());\n clo[k].resize(cnt);\n for (int j = 0; j < cnt; j++) clo[k][j] = v[j].second;\n }\n \n vector sp(N, LLONG_MAX);\n vector par(N, -1), pe(N, -1);\n sp[0] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, 0});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > sp[u]) continue;\n for (auto [v, e] : adj[u])\n if (sp[u] + ew[e] < sp[v]) {\n sp[v] = sp[u] + ew[e]; par[v] = u; pe[v] = e;\n pq.push({sp[v], v});\n }\n }\n \n vector> pth(N);\n for (int i = 1; i < N; i++) {\n int c = i;\n while (c) { pth[i].push_back(pe[c]); c = par[c]; }\n }\n \n auto calcP = [](long long sq) -> int {\n if (sq <= 0) return 0;\n int p = max(1, (int)ceil(sqrt((double)sq) - 1e-9));\n while ((long long)p * p < sq) p++;\n return min(p, 5000);\n };\n \n auto compute_sph = [&](const vector& P_arr) -> pair> {\n vector act;\n for (int i = 0; i < N; i++) if (P_arr[i] > 0) act.push_back(i);\n if (act.empty()) return {0, vector(M, 0)};\n vector B(M, 0);\n vector in_tree(N, false);\n in_tree[0] = true;\n set rem(act.begin(), act.end());\n rem.erase(0);\n long long ec = 0;\n while (!rem.empty()) {\n vector d(N, LLONG_MAX);\n vector prev(N, -1), preve(N, -1);\n priority_queue, vector>, greater<>> pq2;\n for (int v = 0; v < N; v++) if (in_tree[v]) { d[v] = 0; pq2.push({0, v}); }\n while (!pq2.empty()) {\n auto [dd, u] = pq2.top(); pq2.pop();\n if (dd > d[u]) continue;\n for (auto [v, e] : adj[u])\n if (d[u] + ew[e] < d[v]) {\n d[v] = d[u] + ew[e]; prev[v] = u; preve[v] = e;\n pq2.push({d[v], v});\n }\n }\n long long bd = LLONG_MAX; int bt = -1;\n for (int t : rem) if (d[t] < bd) { bd = d[t]; bt = t; }\n int v = bt;\n while (v != -1 && !in_tree[v]) { B[preve[v]] = 1; in_tree[v] = true; v = prev[v]; }\n ec += bd; rem.erase(bt);\n }\n return {ec, B};\n };\n \n vector asgn(K);\n vector> vr(N);\n vector pos_in_vr(K);\n vector vmx(N, 0);\n \n for (int k = 0; k < K; k++) {\n asgn[k] = clo[k][0];\n pos_in_vr[k] = vr[asgn[k]].size();\n vr[asgn[k]].push_back(k);\n vmx[asgn[k]] = max(vmx[asgn[k]], rsq[k][asgn[k]]);\n }\n \n vector P(N);\n long long pcost = 0;\n for (int i = 0; i < N; i++) { P[i] = calcP(vmx[i]); pcost += (long long)P[i] * P[i]; }\n \n vector eref(M, 0);\n long long ecost = 0;\n for (int i = 1; i < N; i++)\n if (P[i] > 0)\n for (int e : pth[i]) { if (!eref[e]) ecost += ew[e]; eref[e]++; }\n \n long long cost = pcost + ecost;\n vector best_asgn = asgn;\n long long best_cost = cost;\n \n mt19937 rng(42);\n uniform_real_distribution<> unif(0.0, 1.0);\n auto t0 = chrono::high_resolution_clock::now();\n \n while (true) {\n double el = chrono::duration(chrono::high_resolution_clock::now() - t0).count();\n if (el > 1.4) break;\n double temp = 5e6 * pow(0.01, el / 1.4);\n \n int k = rng() % K;\n int ov = asgn[k];\n int nv = clo[k][rng() % clo[k].size()];\n if (nv == ov) continue;\n \n long long nmx_ov = vmx[ov];\n if (rsq[k][ov] == vmx[ov]) {\n nmx_ov = 0;\n for (int r : vr[ov]) if (r != k) nmx_ov = max(nmx_ov, rsq[r][ov]);\n }\n int nPov = calcP(nmx_ov);\n long long nmx_nv = max(vmx[nv], rsq[k][nv]);\n int nPnv = calcP(nmx_nv);\n \n long long dpc = (long long)nPov*nPov - (long long)P[ov]*P[ov]\n + (long long)nPnv*nPnv - (long long)P[nv]*P[nv];\n \n long long dec = 0;\n if (P[ov] > 0 && nPov == 0)\n for (int e : pth[ov]) { eref[e]--; if (!eref[e]) dec -= ew[e]; }\n if (P[nv] == 0 && nPnv > 0)\n for (int e : pth[nv]) { if (!eref[e]) dec += ew[e]; eref[e]++; }\n \n long long nc = cost + dpc + dec;\n if (nc < cost || unif(rng) < exp(-(double)(nc - cost) / temp)) {\n int pk = pos_in_vr[k];\n if (pk < (int)vr[ov].size() - 1) {\n int last = vr[ov].back();\n vr[ov][pk] = last; pos_in_vr[last] = pk;\n }\n vr[ov].pop_back();\n pos_in_vr[k] = vr[nv].size();\n vr[nv].push_back(k);\n vmx[ov] = nmx_ov; vmx[nv] = nmx_nv;\n P[ov] = nPov; P[nv] = nPnv;\n pcost += dpc; ecost += dec; asgn[k] = nv; cost = nc;\n if (cost < best_cost) { best_cost = cost; best_asgn = asgn; }\n } else {\n if (P[nv] == 0 && nPnv > 0) for (int e : pth[nv]) eref[e]--;\n if (P[ov] > 0 && nPov == 0) for (int e : pth[ov]) eref[e]++;\n }\n }\n \n // Restore best state\n asgn = best_asgn;\n for (int i = 0; i < N; i++) vr[i].clear();\n fill(vmx.begin(), vmx.end(), 0);\n for (int k = 0; k < K; k++) {\n pos_in_vr[k] = vr[asgn[k]].size();\n vr[asgn[k]].push_back(k);\n vmx[asgn[k]] = max(vmx[asgn[k]], rsq[k][asgn[k]]);\n }\n for (int i = 0; i < N; i++) P[i] = calcP(vmx[i]);\n pcost = 0;\n for (int i = 0; i < N; i++) pcost += (long long)P[i]*P[i];\n \n // Greedy power optimization (no deactivation) BEFORE deactivation\n {\n bool gimproved = true;\n while (gimproved) {\n gimproved = false;\n for (int k = 0; k < K; k++) {\n int ov = asgn[k];\n if (P[ov] == 0) continue;\n long long best_saving = 0; int best_nv = -1;\n for (int nv : clo[k]) {\n if (nv == ov || P[nv] == 0) continue;\n long long nmx_ov2 = vmx[ov];\n if (rsq[k][ov] == vmx[ov]) {\n nmx_ov2 = 0;\n for (int r : vr[ov]) if (r != k) nmx_ov2 = max(nmx_ov2, rsq[r][ov]);\n }\n int nPov2 = calcP(nmx_ov2);\n if (nPov2 == 0) continue;\n long long nmx_nv2 = max(vmx[nv], rsq[k][nv]);\n int nPnv2 = calcP(nmx_nv2);\n long long old_c = (long long)P[ov]*P[ov] + (long long)P[nv]*P[nv];\n long long new_c = (long long)nPov2*nPov2 + (long long)nPnv2*nPnv2;\n if (new_c < old_c && old_c - new_c > best_saving) {\n best_saving = old_c - new_c; best_nv = nv;\n }\n }\n if (best_nv != -1) {\n int pk = pos_in_vr[k];\n if (pk < (int)vr[ov].size() - 1) {\n int last = vr[ov].back();\n vr[ov][pk] = last; pos_in_vr[last] = pk;\n }\n vr[ov].pop_back();\n pos_in_vr[k] = vr[best_nv].size();\n vr[best_nv].push_back(k);\n if (rsq[k][ov] == vmx[ov]) {\n vmx[ov] = 0;\n for (int r : vr[ov]) vmx[ov] = max(vmx[ov], rsq[r][ov]);\n }\n P[ov] = calcP(vmx[ov]);\n vmx[best_nv] = max(vmx[best_nv], rsq[k][best_nv]);\n P[best_nv] = calcP(vmx[best_nv]);\n asgn[k] = best_nv; gimproved = true;\n }\n }\n }\n pcost = 0;\n for (int i = 0; i < N; i++) pcost += (long long)P[i]*P[i];\n }\n \n // SPH vertex deactivation (ordered by sp[v] descending)\n auto [sph_ec, sph_B] = compute_sph(P);\n long long cur_total = pcost + sph_ec;\n \n vector deact_order;\n for (int v = 1; v < N; v++) if (P[v] > 0) deact_order.push_back(v);\n sort(deact_order.begin(), deact_order.end(), [&](int a, int b) { return sp[a] > sp[b]; });\n \n for (int pass = 0; pass < 5; pass++) {\n bool improved = false;\n for (int v : deact_order) {\n if (P[v] == 0 || vr[v].empty()) continue;\n vector> reassigns;\n bool feasible = true;\n for (int k : vr[v]) {\n long long best_inc = LLONG_MAX; int best_nv = -1;\n for (int nv : clo[k]) if (nv != v && P[nv] > 0) {\n long long nmx = max(vmx[nv], rsq[k][nv]);\n int nPnv = calcP(nmx);\n long long inc = (long long)nPnv*nPnv - (long long)P[nv]*P[nv];\n if (inc < best_inc) { best_inc = inc; best_nv = nv; }\n }\n if (best_nv == -1) { feasible = false; break; }\n reassigns.push_back({k, best_nv});\n }\n if (!feasible) continue;\n vector nvmx = vmx; nvmx[v] = 0;\n for (auto& [k, nv] : reassigns) nvmx[nv] = max(nvmx[nv], rsq[k][nv]);\n vector nP(N); long long npc = 0;\n for (int i = 0; i < N; i++) { nP[i] = calcP(nvmx[i]); npc += (long long)nP[i]*nP[i]; }\n auto [nec, nB] = compute_sph(nP);\n if (npc + nec < cur_total) {\n for (auto& [k, nv] : reassigns) {\n int pk = pos_in_vr[k];\n if (pk < (int)vr[asgn[k]].size() - 1) {\n int last = vr[asgn[k]].back();\n vr[asgn[k]][pk] = last; pos_in_vr[last] = pk;\n }\n vr[asgn[k]].pop_back();\n asgn[k] = nv; pos_in_vr[k] = vr[nv].size(); vr[nv].push_back(k);\n }\n vr[v].clear(); P = nP; vmx = nvmx; pcost = npc;\n cur_total = npc + nec; sph_B = nB; improved = true;\n }\n }\n if (!improved) break;\n }\n \n // Final greedy power optimization (no deactivation)\n {\n bool gimproved = true;\n while (gimproved) {\n gimproved = false;\n for (int k = 0; k < K; k++) {\n int ov = asgn[k];\n if (P[ov] == 0) continue;\n long long best_saving = 0; int best_nv = -1;\n for (int nv : clo[k]) {\n if (nv == ov || P[nv] == 0) continue;\n long long nmx_ov2 = vmx[ov];\n if (rsq[k][ov] == vmx[ov]) {\n nmx_ov2 = 0;\n for (int r : vr[ov]) if (r != k) nmx_ov2 = max(nmx_ov2, rsq[r][ov]);\n }\n int nPov2 = calcP(nmx_ov2);\n if (nPov2 == 0) continue;\n long long nmx_nv2 = max(vmx[nv], rsq[k][nv]);\n int nPnv2 = calcP(nmx_nv2);\n long long old_c = (long long)P[ov]*P[ov] + (long long)P[nv]*P[nv];\n long long new_c = (long long)nPov2*nPov2 + (long long)nPnv2*nPnv2;\n if (new_c < old_c && old_c - new_c > best_saving) {\n best_saving = old_c - new_c; best_nv = nv;\n }\n }\n if (best_nv != -1) {\n int pk = pos_in_vr[k];\n if (pk < (int)vr[ov].size() - 1) {\n int last = vr[ov].back();\n vr[ov][pk] = last; pos_in_vr[last] = pk;\n }\n vr[ov].pop_back();\n pos_in_vr[k] = vr[best_nv].size();\n vr[best_nv].push_back(k);\n if (rsq[k][ov] == vmx[ov]) {\n vmx[ov] = 0;\n for (int r : vr[ov]) vmx[ov] = max(vmx[ov], rsq[r][ov]);\n }\n P[ov] = calcP(vmx[ov]);\n vmx[best_nv] = max(vmx[best_nv], rsq[k][best_nv]);\n P[best_nv] = calcP(vmx[best_nv]);\n asgn[k] = best_nv; gimproved = true;\n }\n }\n }\n }\n \n tie(sph_ec, sph_B) = compute_sph(P);\n for (int i = 0; i < N; i++) cout << P[i] << \" \\n\"[i == N-1];\n for (int j = 0; j < M; j++) cout << sph_B[j] << \" \\n\"[j == M-1];\n return 0;\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint grid[N][N];\nvector> swaps;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++)\n for (int y = 0; y <= x; y++)\n cin >> grid[x][y];\n \n auto siftDown = [&](int x, int y) {\n while (x < N - 1) {\n int lv = grid[x+1][y], rv = grid[x+1][y+1], cv = grid[x][y];\n if (cv <= lv && cv <= rv) break;\n if (lv <= rv) {\n swap(grid[x][y], grid[x+1][y]);\n swaps.push_back({x, y, x+1, y});\n x++;\n } else {\n swap(grid[x][y], grid[x+1][y+1]);\n swaps.push_back({x, y, x+1, y+1});\n x++; y++;\n }\n if (swaps.size() >= 9999) return;\n }\n };\n \n // Heapify: bottom to top, full sift-down\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n siftDown(x, y);\n if (swaps.size() >= 9999) goto done;\n }\n }\n \n // Iteratively fix remaining violations\n // (caused by triangular grid's dual-parent structure)\n for (int iter = 0; iter < 500; iter++) {\n bool any = false;\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n if (grid[x][y] > grid[x+1][y] || grid[x][y] > grid[x+1][y+1]) {\n any = true;\n // One-step fix: swap parent with smaller child\n if (grid[x+1][y] <= grid[x+1][y+1]) {\n swap(grid[x][y], grid[x+1][y]);\n swaps.push_back({x, y, x+1, y});\n } else {\n swap(grid[x][y], grid[x+1][y+1]);\n swaps.push_back({x, y, x+1, y+1});\n }\n if (swaps.size() >= 9999) goto done;\n }\n }\n }\n if (!any) break;\n }\n \ndone:\n cout << swaps.size() << \"\\n\";\n for (auto& s : swaps)\n cout << s[0] << \" \" << s[1] << \" \" << s[2] << \" \" << s[3] << \"\\n\";\n \n return 0;\n}","toyota2023summer-final":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int D, N;\n cin >> D >> N;\n \n vector> is_obstacle(D, vector(D, false));\n for (int i = 0; i < N; i++) {\n int ri, rj;\n cin >> ri >> rj;\n is_obstacle[ri][rj] = true;\n }\n \n int entrance_i = 0, entrance_j = (D - 1) / 2;\n \n // Compute shortest path distance from entrance avoiding obstacles\n vector> dist(D, vector(D, -1));\n queue> q;\n q.push({entrance_i, entrance_j});\n dist[entrance_i][entrance_j] = 0;\n \n const int di[] = {-1, 1, 0, 0};\n const int dj[] = {0, 0, -1, 1};\n \n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && dist[ni][nj] == -1 && !is_obstacle[ni][nj]) {\n dist[ni][nj] = dist[i][j] + 1;\n q.push({ni, nj});\n }\n }\n }\n \n int M = 0;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (!(i == entrance_i && j == entrance_j) && !is_obstacle[i][j])\n M++;\n \n struct Cell { int i, j, dist, degree, rank; };\n vector C(M);\n vector> cell_index(D, vector(D, -1));\n \n int idx = 0;\n for (int i = 0; i < D; i++) {\n for (int j = 0; j < D; j++) {\n if (!(i == entrance_i && j == entrance_j) && !is_obstacle[i][j]) {\n C[idx].i = i; C[idx].j = j; C[idx].dist = dist[i][j];\n cell_index[i][j] = idx++;\n }\n }\n }\n \n // Calculate internal degrees (only counting valid container neighbors)\n for (int k = 0; k < M; k++) {\n C[k].degree = 0;\n for (int d = 0; d < 4; d++) {\n int ni = C[k].i + di[d], nj = C[k].j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && cell_index[ni][nj] != -1) {\n C[k].degree++;\n }\n }\n }\n \n // Sort primarily by BFS distance, then by degree descending (hubs first), then coordinates\n sort(C.begin(), C.end(), [&](const Cell& a, const Cell& b) {\n if (a.dist != b.dist) return a.dist < b.dist;\n if (a.degree != b.degree) return a.degree > b.degree;\n if (a.i != b.i) return a.i < b.i;\n return a.j < b.j;\n });\n \n for (int k = 0; k < M; k++) C[k].rank = k;\n \n set available_cells_set;\n for (int k = 0; k < M; k++) available_cells_set.insert(k);\n \n vector> container_at(D, vector(D, -1));\n vector> is_empty(D, vector(D, true));\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (is_obstacle[i][j]) is_empty[i][j] = false;\n \n for (int d = 0; d < M; d++) {\n int t; cin >> t;\n \n // Find Articulation Points dynamically using Tarjan's Algorithm\n int dfs_timer = 0;\n vector> tin(D, vector(D, -1)), low(D, vector(D, -1));\n vector> is_ap(D, vector(D, false));\n \n auto dfs = [&](auto& self, int i, int j, int pi, int pj) -> void {\n tin[i][j] = low[i][j] = dfs_timer++;\n int children = 0;\n for (int dd = 0; dd < 4; dd++) {\n int ni = i + di[dd], nj = j + dj[dd];\n if (ni < 0 || ni >= D || nj < 0 || nj >= D || !is_empty[ni][nj]) continue;\n if (tin[ni][nj] == -1) {\n self(self, ni, nj, i, j);\n low[i][j] = min(low[i][j], low[ni][nj]);\n if (low[ni][nj] >= tin[i][j] && (pi != -1 || pj != -1)) is_ap[i][j] = true;\n children++;\n } else if (!(ni == pi && nj == pj)) {\n low[i][j] = min(low[i][j], tin[ni][nj]);\n }\n }\n if (pi == -1 && pj == -1 && children > 1) is_ap[i][j] = true;\n };\n dfs(dfs, entrance_i, entrance_j, -1, -1);\n \n // Filter Safe Cells and Find Best Match based on BFS Rank\n vector> safe_with_rank; // {rank, index in C}\n for (int k : available_cells_set) {\n if (available_cells_set.size() == 1 || !is_ap[C[k].i][C[k].j]) {\n safe_with_rank.push_back({C[k].rank, k});\n }\n }\n sort(safe_with_rank.begin(), safe_with_rank.end());\n \n int best_k = -1, best_diff = M + 1, best_rank = -1;\n int target_rank = t;\n auto it = lower_bound(safe_with_rank.begin(), safe_with_rank.end(), make_pair(target_rank, -1));\n \n if (it != safe_with_rank.end()) {\n int diff = abs(it->first - target_rank);\n if (diff < best_diff || (diff == best_diff && it->first > best_rank)) {\n best_diff = diff; best_k = it->second; best_rank = it->first;\n }\n }\n if (it != safe_with_rank.begin()) {\n --it; int diff = abs(it->first - target_rank);\n if (diff < best_diff || (diff == best_diff && it->first > best_rank)) {\n best_diff = diff; best_k = it->second; best_rank = it->first;\n }\n }\n \n if (best_k == -1) { best_k = *available_cells_set.begin(); best_rank = C[best_k].rank; }\n \n available_cells_set.erase(best_k);\n cout << C[best_k].i << \" \" << C[best_k].j << endl;\n container_at[C[best_k].i][C[best_k].j] = t;\n is_empty[C[best_k].i][C[best_k].j] = false;\n }\n \n // Transport phase: Greedily remove the smallest numbered accessible container\n for (int iter = 0; iter < M; iter++) {\n vector> reachable(D, vector(D, false));\n queue> bfs_q;\n bfs_q.push({entrance_i, entrance_j});\n reachable[entrance_i][entrance_j] = true;\n while (!bfs_q.empty()) {\n auto [i, j] = bfs_q.front(); bfs_q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + di[d], nj = j + dj[d];\n if (ni >= 0 && ni < D && nj >= 0 && nj < D && !reachable[ni][nj] && is_empty[ni][nj]) {\n reachable[ni][nj] = true; bfs_q.push({ni, nj});\n }\n }\n }\n int min_t = M + 1, min_i = -1, min_j = -1;\n for (int i = 0; i < D; i++)\n for (int j = 0; j < D; j++)\n if (container_at[i][j] >= 0) {\n bool acc = false;\n for (int d = 0; d < 4; d++) { int ni = i + di[d], nj = j + dj[d]; if (ni >= 0 && ni < D && nj >= 0 && nj < D && is_empty[ni][nj] && reachable[ni][nj]) { acc = true; break; } }\n if (acc && container_at[i][j] < min_t) { min_t = container_at[i][j]; min_i = i; min_j = j; }\n }\n cout << min_i << \" \" << min_j << endl;\n is_empty[min_i][min_j] = true; container_at[min_i][min_j] = -1;\n }\n \n return 0;\n}","ahc024":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nconst int N = 50, M = 100;\nconst int dx[] = {0, 0, 1, -1};\nconst int dy[] = {1, -1, 0, 0};\n\nint n, m;\nint grid[N][N], orig[N][N], best_grid[N][N];\nint bestE = -1;\nint ac[M+1][M+1], orig_ac[M+1][M+1];\nbool is_req[M+1][M+1];\nbool is_interior[M+1];\nint color_cnt[M+1], orig_color_cnt[M+1];\nmt19937 rng(42);\n\nint vis[N][N];\nint timer = 0;\nint bfs_q_x[N*N];\nint bfs_q_y[N*N];\n\nbool ok(int x, int y) { return 0 <= x && x < n && 0 <= y && y < n; }\n\nvoid creq() {\n memset(ac, 0, sizeof(ac));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) {\n if (j + 1 < n && orig[i][j] != orig[i][j+1])\n ac[min(orig[i][j], orig[i][j+1])][max(orig[i][j], orig[i][j+1])]++;\n if (i + 1 < n && orig[i][j] != orig[i+1][j])\n ac[min(orig[i][j], orig[i+1][j])][max(orig[i][j], orig[i+1][j])]++;\n if (i == 0) ac[0][orig[i][j]]++;\n if (i == n - 1) ac[0][orig[i][j]]++;\n if (j == 0) ac[0][orig[i][j]]++;\n if (j == n - 1) ac[0][orig[i][j]]++;\n }\n memset(is_req, 0, sizeof(is_req));\n for (int a = 0; a <= m; a++)\n for (int b = a; b <= m; b++)\n if (ac[a][b] > 0) is_req[a][b] = true;\n memcpy(orig_ac, ac, sizeof(ac));\n \n memset(is_interior, true, sizeof(is_interior));\n is_interior[0] = false;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (i == 0 || i == n - 1 || j == 0 || j == n - 1)\n is_interior[orig[i][j]] = false;\n}\n\nbool is_articulation_point(int i, int j, int c) {\n if (color_cnt[c] <= 2) return false;\n \n int c_neighs_x[4], c_neighs_y[4];\n int c_neighs_cnt = 0;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == c) {\n c_neighs_x[c_neighs_cnt] = ni;\n c_neighs_y[c_neighs_cnt] = nj;\n c_neighs_cnt++;\n }\n }\n if (c_neighs_cnt <= 1) return false;\n \n if (timer == INT_MAX) { memset(vis, 0, sizeof(vis)); timer = 1; }\n timer++;\n int head = 0, tail = 0;\n bfs_q_x[tail] = c_neighs_x[0];\n bfs_q_y[tail] = c_neighs_y[0];\n tail++;\n vis[c_neighs_x[0]][c_neighs_y[0]] = timer;\n \n int found_count = 1;\n bool found[4] = {false};\n found[0] = true;\n \n while (head < tail) {\n int x = bfs_q_x[head];\n int y = bfs_q_y[head];\n head++;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (ok(nx, ny) && vis[nx][ny] != timer && grid[nx][ny] == c && !(nx == i && ny == j)) {\n vis[nx][ny] = timer;\n bfs_q_x[tail] = nx;\n bfs_q_y[tail] = ny;\n tail++;\n for (int k = 1; k < c_neighs_cnt; k++) {\n if (nx == c_neighs_x[k] && ny == c_neighs_y[k] && !found[k]) {\n found[k] = true;\n found_count++;\n }\n }\n if (found_count == c_neighs_cnt) return false;\n }\n }\n }\n return true;\n}\n\nbool check_0_connect(int i, int j) {\n int zero_neighs_x[4], zero_neighs_y[4];\n int zero_neighs_cnt = 0;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == 0) {\n zero_neighs_x[zero_neighs_cnt] = ni;\n zero_neighs_y[zero_neighs_cnt] = nj;\n zero_neighs_cnt++;\n }\n }\n if (zero_neighs_cnt == 0) return true;\n \n if (timer == INT_MAX) { memset(vis, 0, sizeof(vis)); timer = 1; }\n timer++;\n int head = 0, tail = 0;\n bfs_q_x[tail] = zero_neighs_x[0];\n bfs_q_y[tail] = zero_neighs_y[0];\n tail++;\n vis[zero_neighs_x[0]][zero_neighs_y[0]] = timer;\n bool reached_bnd = (zero_neighs_x[0] == 0 || zero_neighs_x[0] == n - 1 || zero_neighs_y[0] == 0 || zero_neighs_y[0] == n - 1);\n \n while (head < tail) {\n int x = bfs_q_x[head];\n int y = bfs_q_y[head];\n head++;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (ok(nx, ny) && vis[nx][ny] != timer && grid[nx][ny] == 0 && !(nx == i && ny == j)) {\n vis[nx][ny] = timer;\n bfs_q_x[tail] = nx;\n bfs_q_y[tail] = ny;\n tail++;\n if (nx == 0 || nx == n - 1 || ny == 0 || ny == n - 1) reached_bnd = true;\n }\n }\n }\n if (!reached_bnd) return false;\n for (int k = 1; k < zero_neighs_cnt; k++) {\n if (vis[zero_neighs_x[k]][zero_neighs_y[k]] != timer) return false;\n }\n return true;\n}\n\nbool is_valid_move(int i, int j, int nc) {\n int oc = grid[i][j];\n if (oc == nc) return false;\n \n if (nc == 0 && is_interior[oc]) return false;\n \n if (nc == 0) {\n bool adj_to_zero = (i == 0 || i == n - 1 || j == 0 || j == n - 1);\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == 0) adj_to_zero = true;\n }\n if (!adj_to_zero) return false;\n } else {\n bool has_nc = false;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == nc) has_nc = true;\n }\n if (!has_nc) return false;\n }\n \n int deltas_arr_a[10], deltas_arr_b[10];\n int d_vals[10] = {0};\n int d_cnt = 0;\n \n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj)) {\n int nb = grid[ni][nj];\n if (oc != nb) {\n int a = min(oc, nb), b = max(oc, nb);\n bool found = false;\n for(int k=0; k 0) {\n if (oc != 0) {\n int a = 0, b = oc;\n bool found = false;\n for(int k=0; k 0 && !is_req[a][b]) return false;\n }\n \n if (oc != 0) {\n if (color_cnt[oc] == 1) return false;\n if (is_articulation_point(i, j, oc)) return false;\n } else {\n if (!check_0_connect(i, j)) return false;\n }\n \n return true;\n}\n\nvoid apply_move(int i, int j, int nc) {\n int oc = grid[i][j];\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj)) {\n int nb = grid[ni][nj];\n if (oc != nb) ac[min(oc, nb)][max(oc, nb)]--;\n if (nc != nb) ac[min(nc, nb)][max(nc, nb)]++;\n }\n }\n int bnd_cnt = 0;\n if (i == 0) bnd_cnt++;\n if (i == n - 1) bnd_cnt++;\n if (j == 0) bnd_cnt++;\n if (j == n - 1) bnd_cnt++;\n if (bnd_cnt > 0) {\n if (oc != 0) ac[0][oc] -= bnd_cnt;\n if (nc != 0) ac[0][nc] += bnd_cnt;\n }\n grid[i][j] = nc;\n color_cnt[oc]--;\n color_cnt[nc]++;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> n >> m;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) {\n cin >> orig[i][j];\n }\n \n memset(orig_color_cnt, 0, sizeof(orig_color_cnt));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++) orig_color_cnt[orig[i][j]]++;\n \n creq();\n \n memcpy(grid, orig, sizeof(grid));\n memcpy(ac, orig_ac, sizeof(ac));\n memcpy(color_cnt, orig_color_cnt, sizeof(color_cnt));\n \n int E = 0;\n bestE = 0;\n memcpy(best_grid, grid, sizeof(grid));\n \n vector active_cells;\n vector is_active(n * n, false);\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n bool active = (i == 0 || i == n - 1 || j == 0 || j == n - 1);\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[i][j] != grid[ni][nj]) active = true;\n }\n if (active) {\n int idx = i * n + j;\n active_cells.push_back(idx);\n is_active[idx] = true;\n }\n }\n }\n \n auto start = chrono::high_resolution_clock::now();\n uniform_real_distribution prob_dist(0.0, 1.0);\n \n long long iterations = 0;\n double T = 0.5;\n double elapsed = 0.0;\n \n while (true) {\n if (iterations % 10000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n elapsed = chrono::duration(now - start).count();\n if (elapsed > 1.8) break;\n T = max(0.1, 0.5 - 0.4 * (elapsed / 1.8));\n }\n iterations++;\n \n if (active_cells.empty()) break;\n int idx = active_cells[rng() % active_cells.size()];\n int i = idx / n, j = idx % n;\n \n bool active = (i == 0 || i == n - 1 || j == 0 || j == n - 1);\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[i][j] != grid[ni][nj]) { active = true; break; }\n }\n if (!active) continue;\n \n int oc = grid[i][j];\n \n int nc = -1;\n if (oc == 0) {\n int options[5]; int opt_cnt = 0;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] != 0) {\n options[opt_cnt++] = grid[ni][nj];\n }\n }\n if (opt_cnt > 0) nc = options[rng() % opt_cnt];\n } else {\n bool can_be_zero = !is_interior[oc];\n if (can_be_zero) {\n bool adj_to_zero = (i == 0 || i == n - 1 || j == 0 || j == n - 1);\n if (!adj_to_zero) {\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] == 0) { adj_to_zero = true; break; }\n }\n }\n if (!adj_to_zero) can_be_zero = false;\n }\n \n if (can_be_zero) {\n if (rng() % 10 < 8) {\n nc = 0;\n } else {\n int options[5]; int opt_cnt = 0;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] != oc && grid[ni][nj] != 0) {\n options[opt_cnt++] = grid[ni][nj];\n }\n }\n if (opt_cnt > 0) nc = options[rng() % opt_cnt];\n else nc = 0;\n }\n } else {\n int options[5]; int opt_cnt = 0;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj) && grid[ni][nj] != oc && grid[ni][nj] != 0) {\n options[opt_cnt++] = grid[ni][nj];\n }\n }\n if (opt_cnt > 0) nc = options[rng() % opt_cnt];\n }\n }\n \n if (nc != -1 && oc != nc) {\n if (is_valid_move(i, j, nc)) {\n int delta_E = (nc == 0 ? 1 : (oc == 0 ? -1 : 0));\n double prob_accept = 1.0;\n if (delta_E < 0) {\n prob_accept = exp(delta_E / T);\n }\n if (prob_dist(rng) < prob_accept) {\n apply_move(i, j, nc);\n E += delta_E;\n if (E > bestE) {\n bestE = E;\n memcpy(best_grid, grid, sizeof(grid));\n }\n \n auto update_active = [&](int x, int y) {\n int nidx = x * n + y;\n bool nactive = (x == 0 || x == n - 1 || y == 0 || y == n - 1);\n for (int dd = 0; dd < 4; dd++) {\n int nx = x + dx[dd], ny = y + dy[dd];\n if (ok(nx, ny) && grid[x][y] != grid[nx][ny]) { nactive = true; break; }\n }\n if (nactive && !is_active[nidx]) {\n active_cells.push_back(nidx);\n is_active[nidx] = true;\n }\n };\n \n update_active(i, j);\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ok(ni, nj)) {\n update_active(ni, nj);\n }\n }\n }\n }\n }\n }\n \n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << best_grid[i][j];\n if (j < n - 1) cout << \" \";\n }\n cout << \"\\n\";\n }\n return 0;\n}","ahc025":"#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, D, Q;\nint qc = 0;\nint cmp[105][105];\n\nchar do_query(int a, int b) {\n if (cmp[a][b] == -1) return '<';\n if (cmp[a][b] == 1) return '>';\n if (cmp[a][b] == 2) return '=';\n if (qc >= Q) return '=';\n qc++;\n cout << \"1 1 \" << a << \" \" << b << endl;\n char res; cin >> res;\n if (res == '<') { cmp[a][b] = -1; cmp[b][a] = 1; }\n else if (res == '>') { cmp[a][b] = 1; cmp[b][a] = -1; }\n else if (res == '=') { cmp[a][b] = 2; cmp[b][a] = 2; }\n return res;\n}\n\nchar do_query_sets(const vector& L, const vector& R) {\n if (L.empty() || R.empty()) return '=';\n cout << L.size() << \" \" << R.size();\n for (int x : L) cout << \" \" << x;\n for (int x : R) cout << \" \" << x;\n cout << endl;\n char res; cin >> res;\n qc++;\n return res;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n vector items(N);\n for (int i = 0; i < N; i++) items[i] = i;\n \n // Phase 1: Heap Sort to find heavy items efficiently\n for (int i = 1; i < N && qc < Q; i++) {\n int cur = i;\n while (cur > 0 && qc < Q) {\n int par = (cur - 1) / 2;\n char res = do_query(items[cur], items[par]);\n if (res == '>') { swap(items[cur], items[par]); cur = par; }\n else break;\n }\n }\n for (int i = N - 1; i > 0 && qc < Q; i--) {\n swap(items[0], items[i]);\n int cur = 0;\n while (qc < Q) {\n int l = 2 * cur + 1, r = 2 * cur + 2, largest = cur;\n if (l < i) { if (do_query(items[l], items[largest]) == '>') largest = l; }\n if (r < i) { if (do_query(items[r], items[largest]) == '>') largest = r; }\n if (largest != cur) { swap(items[cur], items[largest]); cur = largest; }\n else break;\n }\n }\n \n // Phase 2: Initial LPT Assignment\n vector ew(N);\n double cur_ew = 0;\n for (int i = 0; i < N; i++) { cur_ew += 1.0 / (N - i); ew[items[i]] = cur_ew; }\n \n vector sum_g(D, 0);\n vector> group_items(D);\n vector asgn(N);\n \n for (int i = N - 1; i >= 0; i--) {\n int item = items[i], mg = 0;\n for (int g = 1; g < D; g++) if (sum_g[g] < sum_g[mg]) mg = g;\n asgn[item] = mg; sum_g[mg] += ew[item]; group_items[mg].push_back(item);\n }\n \n // Phase 3: Exact Local Search with Real Queries\n while (qc < Q) {\n int A = 0; bool abort = false;\n for (int g = 1; g < D; g++) {\n if (qc >= Q) { abort = true; break; }\n if (do_query_sets(group_items[g], group_items[A]) == '>') A = g;\n }\n if (abort) break;\n \n int B = 0;\n for (int g = 1; g < D; g++) {\n if (qc >= Q) { abort = true; break; }\n if (do_query_sets(group_items[g], group_items[B]) == '<') B = g;\n }\n if (abort) break;\n if (A == B) break;\n \n vector& items_A = group_items[A];\n vector& items_B = group_items[B];\n bool improved = false;\n \n // Try single moves from A to B\n sort(items_A.begin(), items_A.end(), [&](int x, int y){ return ew[x] < ew[y]; });\n for (int idx = 0; idx < min(5, (int)items_A.size()); idx++) {\n if ((int)items_A.size() <= 1) break;\n int i = items_A[idx];\n vector L = items_B;\n vector R = items_A;\n R.erase(find(R.begin(), R.end(), i));\n \n if (qc >= Q) break;\n char res = do_query_sets(L, R);\n if (res == '<' || res == '=') {\n items_A.erase(find(items_A.begin(), items_A.end(), i));\n items_B.push_back(i); asgn[i] = B;\n sum_g[A] -= ew[i]; sum_g[B] += ew[i];\n improved = true; break;\n }\n }\n \n if (!improved) {\n // Try swaps between A and B\n if (items_A.size() > 1 && items_B.size() > 1) {\n sort(items_A.begin(), items_A.end(), [&](int x, int y){ return ew[x] > ew[y]; });\n sort(items_B.begin(), items_B.end(), [&](int x, int y){ return ew[x] < ew[y]; });\n for (int idx_i = 0; idx_i < min(5, (int)items_A.size()) && !improved; idx_i++) {\n for (int idx_j = 0; idx_j < min(5, (int)items_B.size()); idx_j++) {\n int i = items_A[idx_i], j = items_B[idx_j];\n if (cmp[i][j] != 1) { if (qc >= Q) { abort = true; break; } if (do_query(i, j) != '>') continue; }\n \n vector L = items_B; L.erase(find(L.begin(), L.end(), j));\n vector R = items_A; R.erase(find(R.begin(), R.end(), i));\n \n if (qc >= Q) { abort = true; break; }\n char res = do_query_sets(L, R);\n if (res == '<' || res == '=') {\n items_A.erase(find(items_A.begin(), items_A.end(), i));\n items_A.push_back(j);\n items_B.erase(find(items_B.begin(), items_B.end(), j));\n items_B.push_back(i);\n asgn[i] = B; asgn[j] = A;\n sum_g[A] += ew[j] - ew[i]; sum_g[B] += ew[i] - ew[j];\n improved = true; break;\n }\n }\n if (abort) break;\n }\n }\n }\n if (!improved || abort) break;\n }\n \n // Waste remaining queries safely\n while (qc < Q) { cout << \"1 1 0 1\" << endl; char res; cin >> res; qc++; }\n \n for (int i = 0; i < N; i++) cout << asgn[i] << \" \\n\"[i==N-1];\n return 0;\n}","ahc026":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint n, m;\nvector> init_stacks;\n\npair>> solve(int nezi_ord, int inv_ord) {\n vector> stacks = init_stacks;\n vector box_stack(n + 1), box_pos(n + 1);\n for (int i = 0; i < m; i++)\n for (int j = 0; j < (int)stacks[i].size(); j++) {\n box_stack[stacks[i][j]] = i;\n box_pos[stacks[i][j]] = j;\n }\n \n int total_energy = 0;\n vector> ops;\n \n for (int v = 1; v <= n; v++) {\n int sid = box_stack[v], pos = box_pos[v];\n \n while ((int)stacks[sid].size() > pos + 1) {\n int top_idx = stacks[sid].size() - 1;\n \n int run_start = top_idx;\n while (run_start > pos + 1 && stacks[sid][run_start - 1] > stacks[sid][run_start])\n run_start--;\n \n int max_in_run = stacks[sid][run_start];\n for (int s = run_start + 1; s <= top_idx; s++)\n max_in_run = max(max_in_run, stacks[sid][s]);\n \n bool has_ne_zi = false;\n for (int d = 0; d < m; d++) {\n if (d == sid || stacks[d].empty()) continue;\n if (stacks[d].back() > max_in_run) { has_ne_zi = true; break; }\n }\n \n bool has_empty = false;\n for (int d = 0; d < m; d++)\n if (d != sid && stacks[d].empty()) { has_empty = true; break; }\n \n int chunk_start;\n \n if (has_ne_zi) {\n chunk_start = run_start;\n } else {\n chunk_start = -1;\n for (int cs = run_start + 1; cs <= top_idx; cs++) {\n int cmax = stacks[sid][cs];\n for (int s = cs + 1; s <= top_idx; s++)\n cmax = max(cmax, stacks[sid][s]);\n \n bool found = false;\n for (int d = 0; d < m; d++) {\n if (d == sid || stacks[d].empty()) continue;\n if (stacks[d].back() > cmax) { found = true; break; }\n }\n if (found) { chunk_start = cs; break; }\n }\n \n if (chunk_start == -1 && has_empty) chunk_start = run_start;\n \n if (chunk_start == -1) {\n for (int cs = run_start + 1; cs <= top_idx; cs++) {\n int cmax = stacks[sid][cs];\n for (int s = cs + 1; s <= top_idx; s++)\n cmax = max(cmax, stacks[sid][s]);\n \n bool found = false;\n for (int d = 0; d < m; d++) {\n if (d == sid) continue;\n if (stacks[d].empty() || stacks[d].back() > cmax) { found = true; break; }\n }\n if (found) { chunk_start = cs; break; }\n }\n }\n \n if (chunk_start == -1) chunk_start = run_start;\n }\n \n int chunk_size = top_idx - chunk_start + 1;\n int chunk_max = stacks[sid][chunk_start];\n for (int s = chunk_start + 1; s <= top_idx; s++)\n chunk_max = max(chunk_max, stacks[sid][s]);\n \n int dest = -1;\n int bp = 4, bs = INT_MAX;\n \n for (int d = 0; d < m; d++) {\n if (d == sid) continue;\n int p, sub;\n if (stacks[d].empty()) {\n bool ne_zi = false;\n for (int d2 = 0; d2 < m; d2++) {\n if (d2 == sid || stacks[d2].empty()) continue;\n if (stacks[d2].back() > chunk_max) { ne_zi = true; break; }\n }\n p = ne_zi ? 2 : 1;\n sub = 0;\n } else {\n int td = stacks[d].back();\n if (td > chunk_max) {\n p = 0;\n sub = nezi_ord ? -td : td;\n } else {\n int ca = 0;\n for (int s = chunk_start; s <= top_idx; s++)\n if (stacks[sid][s] > td) ca++;\n p = 3;\n sub = ca * 1000 + (inv_ord ? td : -td);\n }\n }\n if (p < bp || (p == bp && sub < bs)) { bp = p; bs = sub; dest = d; }\n }\n if (dest == -1) dest = (sid + 1) % m;\n \n int u = stacks[sid][chunk_start];\n ops.push_back({u, dest + 1});\n total_energy += chunk_size + 1;\n \n vector moved(stacks[sid].begin() + chunk_start, stacks[sid].end());\n stacks[sid].resize(chunk_start);\n stacks[dest].insert(stacks[dest].end(), moved.begin(), moved.end());\n \n for (int j = 0; j < (int)moved.size(); j++) {\n box_stack[moved[j]] = dest;\n box_pos[moved[j]] = stacks[dest].size() - moved.size() + j;\n }\n }\n \n ops.push_back({v, 0});\n stacks[sid].pop_back();\n }\n \n return {total_energy, ops};\n}\n\nint main() {\n cin >> n >> m;\n init_stacks.resize(m);\n for (int i = 0; i < m; i++) {\n init_stacks[i].resize(n / m);\n for (int j = 0; j < n / m; j++)\n cin >> init_stacks[i][j];\n }\n \n int best_energy = INT_MAX;\n vector> best_ops;\n \n for (int nezi = 0; nezi < 2; nezi++) {\n for (int inv = 0; inv < 2; inv++) {\n auto [energy, ops] = solve(nezi, inv);\n if (energy < best_energy) {\n best_energy = energy;\n best_ops = ops;\n }\n }\n }\n \n for (auto& op : best_ops)\n cout << op.first << \" \" << op.second << endl;\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\nchar dir_char[] = {'R', 'D', 'L', 'U'};\n\nbool can_move(int i, int j, int dir) {\n int ni = i + dx[dir], nj = j + dy[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0 && v[i][j] == '1') return false;\n if (dir == 1 && h[i][j] == '1') return false;\n if (dir == 2 && v[i][nj] == '1') return false;\n if (dir == 3 && h[ni][j] == '1') return false;\n return true;\n}\n\nint get_dir(char c) {\n if (c == 'R') return 0;\n if (c == 'D') return 1;\n if (c == 'L') return 2;\n return 3; // 'U'\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1); v.resize(N); d.resize(N, vector(N));\n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> d[i][j];\n \n int total_cells = N * N;\n vector all_dist(total_cells * total_cells, -1);\n vector all_prev_dir(total_cells * total_cells, -1);\n\n auto get_dist = [&](int si, int sj, int ei, int ej) -> int& {\n return all_dist[(si * N + sj) * total_cells + (ei * N + ej)];\n };\n auto get_prev = [&](int si, int sj, int ei, int ej) -> int& {\n return all_prev_dir[(si * N + sj) * total_cells + (ei * N + ej)];\n };\n\n // Precompute BFS from all cells\n for (int si = 0; si < N; ++si) {\n for (int sj = 0; sj < N; ++sj) {\n queue> q;\n get_dist(si, sj, si, sj) = 0;\n q.push({si, sj});\n while (!q.empty()) {\n auto [ci, cj] = q.front(); q.pop();\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(ci, cj, dir)) continue;\n int ni = ci + dx[dir], nj = cj + dy[dir];\n if (get_dist(si, sj, ni, nj) == -1) { \n get_dist(si, sj, ni, nj) = get_dist(si, sj, ci, cj) + 1; \n get_prev(si, sj, ni, nj) = (dir + 2) % 4; // Direction to go BACK\n q.push({ni, nj}); \n }\n }\n }\n }\n }\n\n auto get_path = [&](int si, int sj, int ei, int ej) -> string {\n string path_back;\n int ci = ei, cj = ej;\n while (ci != si || cj != sj) {\n int dir = get_prev(si, sj, ci, cj);\n path_back += dir_char[dir];\n ci += dx[dir];\n cj += dy[dir];\n }\n string path_to;\n for (int k = (int)path_back.size() - 1; k >= 0; --k) {\n char c = path_back[k];\n if (c == 'R') path_to += 'L';\n else if (c == 'D') path_to += 'U';\n else if (c == 'L') path_to += 'R';\n else path_to += 'D';\n }\n return path_to;\n };\n \n // Build DFS tour\n string base_tour;\n base_tour.reserve(N * N * 2);\n vector> visited(N, vector(N, false));\n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n for (int dir = 0; dir < 4; dir++) {\n if (!can_move(i, j, dir)) continue;\n int ni = i + dx[dir], nj = j + dy[dir];\n if (!visited[ni][nj]) {\n base_tour += dir_char[dir];\n dfs(ni, nj);\n base_tour += dir_char[(dir + 2) % 4];\n }\n }\n };\n dfs(0, 0);\n \n int L = base_tour.size();\n vector> positions(L + 1);\n positions[0] = {0, 0};\n for (int t = 0; t < L; t++) {\n int dir = get_dir(base_tour[t]);\n positions[t+1] = {positions[t].first + dx[dir], positions[t].second + dy[dir]};\n }\n \n // Find closest insertion point on base tour for detours\n vector best_step(N * N, 0), best_cost(N * N, INT_MAX);\n for (int t = 0; t < L; t++) {\n auto [pi, pj] = positions[t];\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (pi == i && pj == j) continue;\n int cost = 2 * get_dist(pi, pj, i, j);\n if (cost < best_cost[i * N + j]) { best_cost[i * N + j] = cost; best_step[i * N + j] = t; }\n }\n }\n \n // Correctly calculate visits per cycle (t=0 to L-1)\n vector visit_count(N * N, 0);\n for (int t = 0; t < L; t++) { auto [i, j] = positions[t]; visit_count[i * N + j]++; }\n \n double S_factor = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) S_factor += (double)d[i][j] / visit_count[i * N + j];\n \n using Cell = tuple;\n priority_queue pq;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (i == 0 && j == 0) continue;\n int k = visit_count[i * N + j], cost = best_cost[i * N + j];\n if (cost == 0 || cost >= INT_MAX) continue;\n pq.push({(double)d[i][j] / ((long long)k * (k + 1)) / cost, i, j});\n }\n \n struct Detour { int step; int i; int j; };\n vector detours;\n int current_L = L;\n \n while (!pq.empty() && current_L < 100000) {\n auto [p, i, j] = pq.top(); pq.pop();\n int k = visit_count[i * N + j], cost = best_cost[i * N + j];\n if (cost >= INT_MAX) continue;\n double new_p = (double)d[i][j] / ((long long)k * (k + 1)) / cost;\n if (abs(new_p - p) > 1e-9) { pq.push({new_p, i, j}); continue; }\n \n if (current_L + cost > 100000) continue;\n \n // Benefit-cost check\n double benefit = (double)d[i][j] * (current_L + cost) / ((long long)k * (k + 1));\n double detour_cost_val = (double)cost * S_factor;\n if (benefit <= detour_cost_val) break; // No more beneficial detours possible\n \n int step = best_step[i * N + j];\n \n detours.push_back({step, i, j});\n current_L += cost;\n S_factor -= (double)d[i][j] / k;\n visit_count[i * N + j]++;\n S_factor += (double)d[i][j] / visit_count[i * N + j];\n int nk = visit_count[i * N + j];\n pq.push({(double)d[i][j] / ((long long)nk * (nk + 1)) / cost, i, j});\n }\n \n sort(detours.begin(), detours.end(), [](const auto& a, const auto& b) { return a.step < b.step; });\n \n string result;\n result.reserve(100000);\n int detour_idx = 0;\n for (int t = 0; t <= L; t++) {\n while (detour_idx < (int)detours.size() && detours[detour_idx].step == t) {\n auto [step, i, j] = detours[detour_idx];\n auto [pi, pj] = positions[step];\n string path_to = get_path(pi, pj, i, j);\n string path_back;\n for (int k2 = (int)path_to.size() - 1; k2 >= 0; k2--) {\n char c = path_to[k2];\n path_back += (c == 'R') ? 'L' : (c == 'D') ? 'U' : (c == 'L') ? 'R' : 'D';\n }\n result += path_to;\n result += path_back;\n detour_idx++;\n }\n if (t < L) result += base_tour[t];\n }\n \n cout << result << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint main(){\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N,M; cin>>N>>M;\n int si,sj; cin>>si>>sj;\n vector A(N);\n for(int i=0;i>A[i];\n vector t(M);\n for(int i=0;i>t[i];\n vector>> cp(26);\n for(int i=0;i> cd(26,vector(26,0));\n for(int c1=0;c1<26;c1++) for(int c2=0;c2<26;c2++){\n int md=INT_MAX;\n for(auto&[i1,j1]:cp[c1]) for(auto&[i2,j2]:cp[c2]) md=min(md,abs(i1-i2)+abs(j1-j2));\n cd[c1][c2]=md;\n }\n vector> ov(M,vector(M,0));\n for(int i=0;i=1;l--){ bool ok=true; for(int k=0;k> fail(M,vector(6,0));\n for(int k=0;k0&&t[k][f]!=t[k][i-1]) f=fail[k][f]; if(t[k][f]==t[k][i-1]) f++; fail[k][i]=f;}\n auto buildS=[&](const vector&o)->string{ string s=t[o[0]];\n for(int i=1;i<(int)o.size();i++){ int mx=min(5,(int)s.size()),a=0;\n for(int l=mx;l>=1;l--){ bool ok=true; for(int k=0;k&o)->int{ int tv=0; for(int i=1;i<(int)o.size();i++) tv+=ov[o[i-1]][o[i]]; return tv;};\n mt19937 rng(42);\n auto greedyR=[&](int st,unsigned seed)->vector{ mt19937 lr(seed); vectoro; o.push_back(st);\n vectoru(M,false); u[st]=true; for(int s=1;sc;\n for(int j=0;jbo){bo=ov[l][j];c.clear();c.push_back(j);}\n else if(ov[l][j]==bo) c.push_back(j);} o.push_back(c[lr()%c.size()]); u[o.back()]=true;} return o;};\n auto twoOpt=[&](vectoro)->vector{ bool imp=true; while(imp){ imp=false;\n for(int i=0;i0){os+=ov[o[i-1]][o[i]];ns+=ov[o[i-1]][o[i+1]];}\n os+=ov[o[i]][o[i+1]]; ns+=ov[o[i+1]][o[i]]; if(i+2os){swap(o[i],o[i+1]);imp=true;}}} return o;};\n auto orOpt=[&](vectoro)->vector{ for(int it=0;it<10;it++){ bool imp=false;\n for(int i=0;i0) rd-=ov[o[i-1]][w]; if(i0&&iint{return(k0)?gr(j-1):-1,D=(jbd){bd=rd+id;bk=j;}}\n if(bk!=i){ vectorrm; for(int k=0;ko,unsigned seed)->vector{ int curOv=totalOv(o); int bestOv=curOv; auto bestO=o;\n mt19937 saRng(seed); uniform_int_distributiondistI(0,M-1); uniform_real_distributiondistD(0.0,1.0);\n double temp=3.0; for(int it=0;it<300000;it++){ temp*=0.99998;\n if(saRng()%3==0){ int i=distI(saRng),j=distI(saRng); if(i==j) continue; int w=o[i],rd=0;\n if(i>0) rd-=ov[o[i-1]][w]; if(i0&&iint{return(k0)?gr(j-1):-1,D=(j0||distD(saRng)bestOv){bestOv=curOv;bestO=o;}}}\n else{ int i=distI(saRng),j=distI(saRng); if(i==j) continue; if(i>j) swap(i,j); int delta=0;\n if(j==i+1){ if(i>0){delta-=ov[o[i-1]][o[i]];delta+=ov[o[i-1]][o[j]];}\n delta-=ov[o[i]][o[j]]; delta+=ov[o[j]][o[i]]; if(j+10){delta-=ov[o[i-1]][o[i]];delta+=ov[o[i-1]][o[j]];}\n if(i+10){delta-=ov[o[j-1]][o[j]];delta+=ov[o[j-1]][o[i]];}\n if(j+10||distD(saRng)bestOv){bestOv=curOv;bestO=o;}}}} return bestO;};\n const int INF=1e9;\n auto dpStep=[&](const vector&cur, vector& nx, char c){ \n fill(nx.begin(), nx.end(), INF); int ci=c-'A';\n for(int q=0;q<225;q++){ if(cur[q]>=INF) continue; int qi=q/15,qj=q%15;\n for(auto&[pi,pj]:cp[ci]){ int p=pi*15+pj; int nc=cur[q]+abs(pi-qi)+abs(pj-qj)+1; if(ncstring{ \n vectorcur(225,INF), nx(225); cur[si*15+sj]=0; string S; vectorused(M,false);\n if(forceFirst>=0){ for(char c:t[forceFirst]) { dpStep(cur, nx, c); swap(cur, nx); } S+=t[forceFirst]; used[forceFirst]=true;}\n for(int step=(forceFirst>=0?1:0);step>cands;\n for(int j=0;j=1;l--){ bool ok=true; for(int k=0;kbestNx(225); string bestExt;\n for(int k=0;k=1;l--){ bool ok=true; for(int kk=0;kkstring{ vectorml(M,0); vectormatched(M,false); int nm=0;\n string S; int ci=si,cj=sj; while(nm0&&t[k][l]!=('A'+c)) l=fail[k][l]; if(t[k][l]==('A'+c)) l++;\n if(l==5) comp++; else if(l>ml[k]) adv+=(l-ml[k]);}\n double score=comp*w1+adv*w2-md*w3; if(score>bscore){bscore=score;bchar=c;bpi=pi;bpj=pj;}}\n S+=('A'+bchar); ci=bpi; cj=bpj;\n for(int k=0;k0&&t[k][l]!=('A'+bchar)) l=fail[k][l]; if(t[k][l]==('A'+bchar)) l++; ml[k]=l;\n if(l==5){matched[k]=true;nm++;}}} return S;};\n auto dpCharGreedy=[&]()->string{ \n vectorcur(225,INF), nx(225), bestNx(225); cur[si*15+sj]=0; string S;\n vectorml(M,0); vectormatched(M,false); int nm=0;\n while(nm0&&t[k][l]!=('A'+c)) l=fail[k][l]; if(t[k][l]==('A'+c)) l++;\n if(l==5) comp++; else if(l>ml[k]) adv+=(l-ml[k]);}\n bool better=false; if(comp>bestComp) better=true; else if(comp==bestComp){if(costbestAdv) better=true;}\n if(better){bestComp=comp;bestAdv=adv;bestCost=cost;bchar=c;swap(bestNx,nx);}}\n S+=('A'+bchar); swap(cur,bestNx);\n for(int k=0;k0&&t[k][l]!=('A'+bchar)) l=fail[k][l]; if(t[k][l]==('A'+bchar)) l++; ml[k]=l;\n if(l==5){matched[k]=true;nm++;}}} return S;};\n vectorcandidates; vector>>cs;\n for(int s=0;sint{ int L=s.size(); vectorcur(225,INF), nx(225); cur[si*15+sj]=0;\n for(int i=0;i>>dp(L+1,vector>(225,{INF,-1})); dp[0][si*15+sj]={0,-1};\n for(int i=0;i=INF) continue; int qi=q/15,qj=q%15;\n for(auto&[pi,pj]:cp[ci]){ int p=pi*15+pj; int nc=dp[i][q].first+abs(pi-qi)+abs(pj-qj)+1;\n if(ncpp(L); int cr=be; for(int i=L-1;i>=0;i--){pp[i]=cr;cr=dp[i+1][cr].second;}\n for(int i=0;i\nusing namespace std;\n\nconst int MAX_POS = 500;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nvector max_di, max_dj;\nvector>> positions;\nvector>>> pos_cells;\nvector>> cell_pos;\nint known[25][25];\nint query_count = 0;\ndouble current_cost = 0.0;\nvector> lw;\ndouble cov_val[25][25];\ndouble prob_oil_val[25][25];\n\nint drill_cell(int i, int j) {\n cout << \"q 1 \" << i << \" \" << j << '\\n';\n cout.flush();\n int v; cin >> v;\n known[i][j] = v;\n query_count++;\n current_cost += 1.0;\n return v;\n}\n\nint divine_cells(vector>& cells) {\n int k = cells.size();\n cout << \"q \" << k;\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << '\\n';\n cout.flush();\n int v; cin >> v;\n query_count++;\n current_cost += 1.0 / sqrt(k);\n return v;\n}\n\nbool submit_answer(vector>& cells) {\n sort(cells.begin(), cells.end());\n cells.erase(unique(cells.begin(), cells.end()), cells.end());\n cout << \"a \" << cells.size();\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << '\\n';\n cout.flush();\n int r; cin >> r;\n if (r == 0) {\n query_count++;\n current_cost += 1.0;\n }\n return r == 1;\n}\n\nvoid normalize_weights(int k) {\n double mx = -1e9;\n int sz = positions[k].size();\n for (int p = 0; p < sz; p++) if (lw[k][p] > mx) mx = lw[k][p];\n double total = 0;\n for (int p = 0; p < sz; p++) {\n if (lw[k][p] > mx - 50.0) total += exp(lw[k][p] - mx);\n }\n if (total < 1e-30) {\n for (int p = 0; p < sz; p++) lw[k][p] = 0.0;\n } else {\n for (int p = 0; p < sz; p++) {\n if (lw[k][p] < mx - 50.0) lw[k][p] = -1e9;\n else lw[k][p] -= mx;\n }\n }\n}\n\nvoid compute_prob_and_cov() {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n cov_val[i][j] = 0;\n prob_oil_val[i][j] = 1.0;\n }\n for (int k = 0; k < M; k++) {\n double mx = -1e9;\n int sz = positions[k].size();\n for (int p = 0; p < sz; p++) if (lw[k][p] > mx) mx = lw[k][p];\n double total = 0;\n double wt[MAX_POS];\n for (int p = 0; p < sz; p++) {\n wt[p] = exp(lw[k][p] - mx);\n total += wt[p];\n }\n if (total < 1e-30) continue;\n for (int p = 0; p < sz; p++) {\n double w = wt[p] / total;\n if (w < 1e-9) continue;\n for (auto& [ci, cj] : pos_cells[k][p]) {\n cov_val[ci][cj] += w;\n prob_oil_val[ci][cj] *= max(0.0, 1.0 - w);\n }\n }\n }\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) {\n cov_val[i][j] = known[i][j];\n prob_oil_val[i][j] = (known[i][j] > 0 ? 1.0 : 0.0);\n } else {\n prob_oil_val[i][j] = 1.0 - prob_oil_val[i][j];\n }\n }\n}\n\nvoid update_divine(const vector>& qcells, int obs) {\n int ksz = qcells.size();\n double sigma2 = ksz * eps * (1 - eps);\n \n int cnts[25][MAX_POS];\n for (int k = 0; k < M; k++) {\n memset(cnts[k], 0, sizeof(int) * positions[k].size());\n for (auto& [i, j] : qcells) {\n for (int p : cell_pos[k][i * N + j]) {\n cnts[k][p]++;\n }\n }\n }\n \n double E_X[25], Var_X[25];\n for (int k = 0; k < M; k++) {\n double mx = -1e9;\n int sz = positions[k].size();\n for (int p = 0; p < sz; p++) if (lw[k][p] > mx) mx = lw[k][p];\n double total = 0;\n double wt[MAX_POS];\n for (int p = 0; p < sz; p++) {\n wt[p] = exp(lw[k][p] - mx);\n total += wt[p];\n }\n if (total < 1e-30) { E_X[k] = 0; Var_X[k] = 0; continue; }\n \n double EX = 0, EX2 = 0;\n for (int p = 0; p < sz; p++) {\n wt[p] /= total;\n double c = cnts[k][p];\n EX += wt[p] * c;\n EX2 += wt[p] * c * c;\n }\n E_X[k] = EX;\n Var_X[k] = EX2 - EX * EX;\n if (Var_X[k] < 0) Var_X[k] = 0;\n }\n \n double total_E = 0, total_Var = 0;\n for (int k = 0; k < M; k++) {\n total_E += E_X[k];\n total_Var += Var_X[k];\n }\n \n for (int k = 0; k < M; k++) {\n double S_others = total_E - E_X[k];\n double Var_others = total_Var - Var_X[k];\n if (Var_others < 0) Var_others = 0;\n \n double total_var = sigma2 + Var_others * (1 - 2 * eps) * (1 - 2 * eps);\n if (total_var < sigma2) total_var = sigma2;\n \n int sz = positions[k].size();\n for (int p = 0; p < sz; p++) {\n double ev = S_others + cnts[k][p];\n double mean = ksz * eps + ev * (1 - 2 * eps);\n double diff = obs - mean;\n double penalty = diff * diff / (2 * total_var);\n if (penalty > 10.0) penalty = 10.0;\n lw[k][p] += -penalty;\n }\n normalize_weights(k);\n }\n compute_prob_and_cov();\n}\n\nvoid update_drill(int i, int j, int obs) {\n if (obs == 0) {\n for (int k = 0; k < M; k++) {\n for (int p : cell_pos[k][i * N + j]) lw[k][p] = -1e9;\n normalize_weights(k);\n }\n } else if (obs == M) {\n for (int k = 0; k < M; k++) {\n for (int p = 0; p < (int)positions[k].size(); p++) {\n if (!binary_search(cell_pos[k][i * N + j].begin(), cell_pos[k][i * N + j].end(), p)) {\n lw[k][p] = -1e9;\n }\n }\n normalize_weights(k);\n }\n } else {\n double fc_arr[25];\n for (int k = 0; k < M; k++) {\n double mx = -1e9;\n int sz = positions[k].size();\n for (int p = 0; p < sz; p++) if (lw[k][p] > mx) mx = lw[k][p];\n double total = 0;\n double wt[MAX_POS];\n for (int p = 0; p < sz; p++) {\n wt[p] = exp(lw[k][p] - mx);\n total += wt[p];\n }\n if (total < 1e-30) { fc_arr[k] = 0; continue; }\n double covers = 0;\n for (int p : cell_pos[k][i * N + j]) covers += wt[p];\n fc_arr[k] = covers / total;\n }\n \n for (int k = 0; k < M; k++) {\n double P[25];\n memset(P, 0, sizeof(P));\n P[0] = 1.0;\n for (int m = 0; m < M; m++) {\n if (m == k) continue;\n double p_m = max(0.0, min(1.0, fc_arr[m]));\n double q_m = 1.0 - p_m;\n for (int jj = M - 1; jj >= 0; jj--) {\n P[jj] = P[jj] * q_m + (jj > 0 ? P[jj-1] * p_m : 0.0);\n }\n }\n \n int sz = positions[k].size();\n for (int p = 0; p < sz; p++) {\n bool covers = binary_search(cell_pos[k][i * N + j].begin(), cell_pos[k][i * N + j].end(), p);\n int base = covers ? 1 : 0;\n double likelihood = 0.0;\n if (obs - base >= 0 && obs - base < M) {\n likelihood = P[obs - base];\n }\n if (likelihood < 1e-9) likelihood = 1e-9;\n double penalty = -log(likelihood);\n if (penalty > 10.0) penalty = 10.0;\n lw[k][p] += -penalty;\n }\n normalize_weights(k);\n }\n }\n compute_prob_and_cov();\n}\n\nvector> get_answer() {\n vector> ans;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] > 0) ans.push_back({i, j});\n else if (known[i][j] < 0 && prob_oil_val[i][j] > 0.5) ans.push_back({i, j});\n }\n sort(ans.begin(), ans.end());\n return ans;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> M >> eps;\n shapes.resize(M);\n for (int k = 0; k < M; k++) {\n int d; cin >> d;\n shapes[k].resize(d);\n for (int l = 0; l < d; l++) cin >> shapes[k][l].first >> shapes[k][l].second;\n }\n max_di.resize(M); max_dj.resize(M);\n for (int k = 0; k < M; k++) {\n max_di[k] = max_dj[k] = 0;\n for (auto& [i, j] : shapes[k]) { max_di[k] = max(max_di[k], i); max_dj[k] = max(max_dj[k], j); }\n }\n cell_pos.resize(M, vector>(N * N));\n for (int k = 0; k < M; k++) {\n vector> pos;\n vector>> cells;\n int pidx = 0;\n for (int di = 0; di <= N - 1 - max_di[k]; di++)\n for (int dj = 0; dj <= N - 1 - max_dj[k]; dj++) {\n pos.push_back({di, dj});\n vector> c;\n for (auto& [i, j] : shapes[k]) {\n int ci = di + i, cj = dj + j;\n c.push_back({ci, cj});\n cell_pos[k][ci * N + cj].push_back(pidx);\n }\n cells.push_back(c);\n pidx++;\n }\n positions.push_back(pos);\n pos_cells.push_back(cells);\n }\n memset(known, -1, sizeof(known));\n for (int k = 0; k < M; k++) lw.push_back(vector(positions[k].size(), 0.0));\n compute_prob_and_cov();\n \n for (int i = 0; i < N && query_count < 2*N*N - 1; i++) {\n vector> cells;\n for (int j = 0; j < N; j++) if (known[i][j] < 0) cells.push_back({i, j});\n if (cells.size() >= 2) update_divine(cells, divine_cells(cells));\n else if (cells.size() == 1) update_drill(cells[0].first, cells[0].second, drill_cell(cells[0].first, cells[0].second));\n }\n for (int j = 0; j < N && query_count < 2*N*N - 1; j++) {\n vector> cells;\n for (int i = 0; i < N; i++) if (known[i][j] < 0) cells.push_back({i, j});\n if (cells.size() >= 2) update_divine(cells, divine_cells(cells));\n else if (cells.size() == 1) update_drill(cells[0].first, cells[0].second, drill_cell(cells[0].first, cells[0].second));\n }\n \n int targeted_count = 0;\n while (query_count < 2*N*N - 1 && targeted_count < 30) {\n int best_k = -1; double max_ent = -1;\n for (int k = 0; k < M; k++) {\n double mx = -1e9;\n for (auto& l : lw[k]) if (l > mx) mx = l;\n double total = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) total += exp(lw[k][p] - mx);\n if (total < 1e-30) continue;\n double ent = 0;\n for (int p = 0; p < (int)positions[k].size(); p++) {\n double prob = exp(lw[k][p] - mx) / total;\n if (prob > 1e-9 && prob < 1 - 1e-9) ent -= prob * log(prob);\n }\n if (ent > max_ent) { max_ent = ent; best_k = k; }\n }\n if (best_k == -1 || max_ent < 0.1) break;\n \n int best_p = max_element(lw[best_k].begin(), lw[best_k].end()) - lw[best_k].begin();\n if (lw[best_k][best_p] < -1e8) break;\n vector> qcells;\n for (auto& cell : pos_cells[best_k][best_p]) {\n if (known[cell.first][cell.second] < 0) qcells.push_back(cell);\n }\n if (qcells.size() >= 2) {\n update_divine(qcells, divine_cells(qcells));\n targeted_count++;\n } else if (qcells.size() == 1) {\n update_drill(qcells[0].first, qcells[0].second, drill_cell(qcells[0].first, qcells[0].second));\n targeted_count++;\n } else break;\n }\n \n vector> last_ans;\n while (query_count < 2 * N * N - 1) {\n double exp_err = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) continue;\n double p = prob_oil_val[i][j];\n exp_err += min(p, 1 - p);\n }\n \n vector> ans = get_answer();\n \n bool should_answer = (exp_err < 1.0 || query_count >= 2 * N * N - 1);\n \n if (should_answer && ans != last_ans) {\n if (submit_answer(ans)) return 0;\n last_ans = ans;\n }\n \n if (!should_answer || ans == last_ans) {\n int bi = -1, bj = -1; double bent = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (known[i][j] >= 0) continue;\n double p = max(0.001, min(0.999, prob_oil_val[i][j]));\n double ent = -p*log(p) - (1-p)*log(1-p);\n if (ent > bent) { bent = ent; bi = i; bj = j; }\n }\n if (bi < 0) break;\n update_drill(bi, bj, drill_cell(bi, bj));\n }\n }\n \n if (query_count < 2 * N * N) {\n vector> final_ans = get_answer();\n submit_answer(final_ans);\n }\n return 0;\n}","ahc031":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint W, D, N;\nvector> a;\n\nlong long day_def(int d, const vector& h) {\n long long c = 0;\n for (int k = 0; k < N; k++) { int area = h[k] * W; if (a[d][k] > area) c += 100LL * (a[d][k] - area); }\n return c;\n}\n\nvoid get_bounds(const vector& h, vector& b) {\n b.resize(N - 1); int y = 0;\n for (int k = 0; k < N - 1; k++) { y += h[k]; b[k] = y; }\n}\n\nlong long bound_diff(const vector& b1, const vector& b2) {\n int i = 0, j = 0; long long c = 0;\n while (i < (int)b1.size() && j < (int)b2.size()) {\n if (b1[i] == b2[j]) { i++; j++; } else if (b1[i] < b2[j]) { c++; i++; } else { c++; j++; }\n }\n c += (int)b1.size() - i + (int)b2.size() - j; return c;\n}\n\nvector greedy_day(int d) {\n vector h(N, 1); int rem = W - N;\n while (rem > 0) {\n int bk = -1; long long br = -1;\n for (int k = 0; k < N; k++) { int df = max(0, a[d][k] - h[k] * W); int nd = max(0, a[d][k] - (h[k] + 1) * W); long long r = df - nd;\n if (r > br || (r == br && bk >= 0 && a[d][k] > a[d][bk])) { br = r; bk = k; } }\n if (bk == -1 || br == 0) { int mx = -1; for (int k = 0; k < N; k++) if (a[d][k] > mx) { mx = a[d][k]; bk = k; } }\n if (bk == -1) break; h[bk]++; rem--;\n }\n return h;\n}\n\nvector adjust_toward(int d, vector h, int max_iter=300) {\n for (int iter = 0; iter < max_iter; iter++) {\n int bk = -1; long long br = -1;\n for (int k = 0; k < N; k++) { int df = max(0, a[d][k] - h[k] * W); int nd = max(0, a[d][k] - (h[k] + 1) * W); long long r = df - nd; if (r > br) { br = r; bk = k; } }\n if (bk == -1 || br == 0) break;\n int bk2 = -1; long long min_inc = LLONG_MAX;\n for (int k = 0; k < N; k++) { if (h[k] > 1 && k != bk) { int od = max(0, a[d][k] - h[k] * W); int nd = max(0, a[d][k] - (h[k] - 1) * W); if (nd - od < min_inc) { min_inc = nd - od; bk2 = k; } } }\n if (bk2 == -1) break; h[bk]++; h[bk2]--;\n }\n return h;\n}\n\nlong long total_cost(const vector>& h) {\n long long c = 0;\n for (int d = 0; d < D; d++) c += day_def(d, h[d]);\n for (int d = 1; d < D; d++) { vector b1, b2; get_bounds(h[d-1], b1); get_bounds(h[d], b2); c += bound_diff(b1, b2) * W; }\n return c;\n}\n\nint main(){\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> W >> D >> N;\n a.resize(D, vector(N));\n for (int d = 0; d < D; d++) for (int k = 0; k < N; k++) cin >> a[d][k];\n \n mt19937 rng(42); uniform_real_distribution uni(0, 1);\n \n vector fixed_h(N, 1);\n { int rem = W - N; while (rem > 0) { int bk = -1; long long bs = -1;\n for (int k = 0; k < N; k++) { long long td = 0, ntd = 0; for (int d = 0; d < D; d++) { td += max(0, a[d][k] - fixed_h[k] * W); ntd += max(0, a[d][k] - (fixed_h[k] + 1) * W); } if (td - ntd > bs) { bs = td - ntd; bk = k; } }\n if (bk == -1) break; fixed_h[bk]++; rem--; } }\n \n { vector ch = fixed_h; long long cc = 0; for (int d = 0; d < D; d++) cc += day_def(d, ch);\n long long bc = cc; auto st = chrono::steady_clock::now();\n for (int it = 0; it < 200000; it++) { if (it % 20000 == 0) { double el = chrono::duration(chrono::steady_clock::now() - st).count(); if (el > 0.05) break; }\n int k1 = (int)(rng() % N), k2 = (int)(rng() % N); if (k1 == k2 || ch[k1] <= 1) continue;\n long long delta = 0; for (int d = 0; d < D; d++) { delta += 100LL*(max(0,a[d][k1]-(ch[k1]-1)*W)-max(0,a[d][k1]-ch[k1]*W)); delta += 100LL*(max(0,a[d][k2]-(ch[k2]+1)*W)-max(0,a[d][k2]-ch[k2]*W)); }\n double el = chrono::duration(chrono::steady_clock::now() - st).count();\n double temp = 5e6*max(1e-4,1.0-el/0.05); if (delta <= 0 || exp(-(double)delta/temp) > uni(rng)) { ch[k1]--; ch[k2]++; cc += delta; if (cc < bc) { bc = cc; fixed_h = ch; } } } }\n \n vector> greedy_seq(D);\n for (int d = 0; d < D; d++) greedy_seq[d] = greedy_day(d);\n \n auto gen_cands = [&](bool use_dp_res, const vector>& dp_res) {\n vector>> cands(D);\n for (int d = 0; d < D; d++) {\n cands[d].push_back(greedy_seq[d]);\n cands[d].push_back(fixed_h);\n cands[d].push_back(adjust_toward(d, fixed_h));\n \n for (int dd = max(0, d-3); dd <= min(D-1, d+3); dd++) {\n if (dd == d) continue;\n cands[d].push_back(adjust_toward(d, greedy_seq[dd]));\n for (int i = 0; i < 3; i++) {\n vector h = greedy_seq[dd]; int rem = 2 + (int)(rng() % 8);\n for (int j = 0; j < rem; j++) { int k1 = (int)(rng()%N), k2 = (int)(rng()%N); if (k1!=k2 && h[k1]>1) { h[k1]--; h[k2]++; } }\n cands[d].push_back(adjust_toward(d, h, 50));\n }\n }\n \n // Morph from adjacent greedy\n for (int dd : {d-1, d+1}) {\n if (dd < 0 || dd >= D) continue;\n vector h = greedy_seq[dd];\n vector src_b, tgt_b;\n get_bounds(greedy_seq[dd], src_b);\n get_bounds(greedy_seq[d], tgt_b);\n for (int step = 0; step < 25; step++) {\n int best_b = -1, best_diff = 0;\n for (int b = 0; b < N-1; b++) { int diff = tgt_b[b] - src_b[b]; if (abs(diff) > abs(best_diff)) { best_diff = diff; best_b = b; } }\n if (best_b == -1 || best_diff == 0) break;\n int dir = (best_diff > 0) ? 1 : -1;\n int kd = (dir > 0) ? best_b + 1 : best_b;\n int ki = (dir > 0) ? best_b : best_b + 1;\n if (h[kd] <= 1) break;\n h[kd]--; h[ki]++; src_b[best_b] += dir;\n h = adjust_toward(d, h, 3);\n get_bounds(h, src_b);\n cands[d].push_back(h);\n }\n }\n \n // Add DP result as candidate\n if (use_dp_res) {\n cands[d].push_back(dp_res[d]);\n // Also adjust DP result of adjacent days\n for (int dd : {d-1, d+1}) {\n if (dd < 0 || dd >= D) continue;\n cands[d].push_back(adjust_toward(d, dp_res[dd]));\n }\n }\n \n // Common boundary positions\n {\n vector> all_bnds(D);\n for (int dd = 0; dd < D; dd++) get_bounds(greedy_seq[dd], all_bnds[dd]);\n for (int b = 0; b < N-1; b++) {\n vector positions;\n for (int dd = 0; dd < D; dd++) positions.push_back(all_bnds[dd][b]);\n sort(positions.begin(), positions.end());\n // Try median position\n int med = positions[D/2];\n vector h = greedy_seq[d];\n vector hb; get_bounds(h, hb);\n int shift = med - hb[b];\n if (shift != 0 && b+1 < N && h[b] + shift >= 1 && h[b+1] - shift >= 1) {\n h[b] += shift; h[b+1] -= shift;\n cands[d].push_back(adjust_toward(d, h, 20));\n }\n }\n }\n \n vector min_h(N); int sum_min = 0;\n for (int k = 0; k < N; k++) { min_h[k] = (a[d][k] + W - 1) / W; sum_min += min_h[k]; }\n int extra = W - sum_min;\n if (extra >= 0) { cands[d].push_back(adjust_toward(d, min_h)); }\n else {\n vector ch = min_h; int rem = -extra;\n while (rem > 0) { int bk = -1; long long mi = LLONG_MAX; for (int k = 0; k < N; k++) if (ch[k]>1) { int od=max(0,a[d][k]-ch[k]*W),nd=max(0,a[d][k]-(ch[k]-1)*W); if(nd-od> valid; for (auto& c : cands[d]) { if ((int)c.size()!=N) continue; bool ok=true; int s=0; for(int k=0;k 120) { sort(cands[d].begin(), cands[d].end(), [&](const vector& x, const vector& y) { return day_def(d, x) < day_def(d, y); }); cands[d].resize(120); }\n }\n return cands;\n };\n \n // First DP pass\n auto cands = gen_cands(false, vector>());\n \n auto run_dp = [&](vector>>& cands) -> vector> {\n vector ksz(D); int maxK = 0;\n for (int d = 0; d < D; d++) { ksz[d] = cands[d].size(); maxK = max(maxK, ksz[d]); }\n vector> dp(D, vector(maxK, LLONG_MAX)); vector> par(D, vector(maxK, -1));\n vector> cdef(D); vector>> cbnd(D);\n for (int d = 0; d < D; d++) { cdef[d].resize(ksz[d]); cbnd[d].resize(ksz[d]); for (int i = 0; i < ksz[d]; i++) { cdef[d][i] = day_def(d, cands[d][i]); get_bounds(cands[d][i], cbnd[d][i]); } }\n for (int k = 0; k < ksz[0]; k++) dp[0][k] = cdef[0][k];\n for (int d = 1; d < D; d++) for (int k = 0; k < ksz[d]; k++) for (int j = 0; j < ksz[d-1]; j++) { if (dp[d-1][j] == LLONG_MAX) continue; long long cost = dp[d-1][j] + bound_diff(cbnd[d-1][j], cbnd[d][k]) * W + cdef[d][k]; if (cost < dp[d][k]) { dp[d][k] = cost; par[d][k] = j; } }\n long long best_dp = LLONG_MAX; int best_k = -1;\n for (int k = 0; k < ksz[D-1]; k++) if (dp[D-1][k] < best_dp) { best_dp = dp[D-1][k]; best_k = k; }\n vector> res(D); { int ck = best_k; for (int d = D-1; d >= 0; d--) { res[d] = cands[d][ck]; ck = par[d][ck]; } }\n return res;\n };\n \n auto dp_res = run_dp(cands);\n \n // Second DP pass with DP result as candidates\n {\n auto cands2 = gen_cands(true, dp_res);\n auto dp_res2 = run_dp(cands2);\n if (total_cost(dp_res2) < total_cost(dp_res)) dp_res = dp_res2;\n }\n \n auto sa_run = [&](vector> cur_h, double time_limit, int seed) -> pair>> {\n mt19937 lr(seed); uniform_real_distribution lu(0, 1);\n vector> cb(D); vector pc(D, 0);\n for (int d = 0; d < D; d++) get_bounds(cur_h[d], cb[d]);\n for (int d = 1; d < D; d++) pc[d] = bound_diff(cb[d-1], cb[d]) * W;\n long long cc = 0; for (int d = 0; d < D; d++) cc += day_def(d, cur_h[d]); for (int d = 1; d < D; d++) cc += pc[d];\n long long bc = cc; vector> bh = cur_h;\n auto st = chrono::steady_clock::now(); long long it = 0; double el = 0;\n while (true) { \n if (++it % 5000 == 0) { el = chrono::duration(chrono::steady_clock::now() - st).count(); if (el > time_limit) break; }\n int mt = (int)(lr() % 100);\n if (mt < 25) {\n int d=(int)(lr()%D), b=(int)(lr()%(N-1)), dir = (lr()%2)?1:-1;\n int kd = (dir>0)?b+1:b, ki = (dir>0)?b:b+1;\n if (cur_h[d][kd] <= 1) continue;\n long long dd = 100LL*(max(0,a[d][kd]-(cur_h[d][kd]-1)*W)-max(0,a[d][kd]-cur_h[d][kd]*W)) + 100LL*(max(0,a[d][ki]-(cur_h[d][ki]+1)*W)-max(0,a[d][ki]-cur_h[d][ki]*W));\n cur_h[d][kd]--; cur_h[d][ki]++; cb[d][b] += dir;\n long long npd = (d>0?bound_diff(cb[d-1],cb[d])*W:0) + (d0?pc[d]:0) + (d lu(lr)) { cc += delta; if(d>0)pc[d]=bound_diff(cb[d-1],cb[d])*W; if(d0)?1:-1;\n int kd=(dir>0)?b+1:b, ki=(dir>0)?b:b+1; if(cur_h[d][kd]<=1)continue;\n long long dd=100LL*(max(0,a[d][kd]-(cur_h[d][kd]-1)*W)-max(0,a[d][kd]-cur_h[d][kd]*W))+100LL*(max(0,a[d][ki]-(cur_h[d][ki]+1)*W)-max(0,a[d][ki]-cur_h[d][ki]*W));\n cur_h[d][kd]--;cur_h[d][ki]++;cb[d][b]+=dir;\n long long npd=(d>0?bound_diff(cb[d-1],cb[d])*W:0)+(d0?pc[d]:0)+(dlu(lr)){cc+=delta;if(d>0)pc[d]=bound_diff(cb[d-1],cb[d])*W;if(d0?bound_diff(cb[d-1],cb[d])*W:0)+(d0?pc[d]:0)+(dlu(lr)){cc+=delta;if(d>0)pc[d]=bound_diff(cb[d-1],cb[d])*W;if(d0)?1:-1;\n int kd=(dir>0)?b+1:b, ki=(dir>0)?b:b+1;\n if(cur_h[d][kd]<=u)continue;\n long long dd=100LL*(max(0,a[d][kd]-(cur_h[d][kd]-u)*W)-max(0,a[d][kd]-cur_h[d][kd]*W))+100LL*(max(0,a[d][ki]-(cur_h[d][ki]+u)*W)-max(0,a[d][ki]-cur_h[d][ki]*W));\n cur_h[d][kd]-=u;cur_h[d][ki]+=u;cb[d][b]+=dir*u;\n long long npd=(d>0?bound_diff(cb[d-1],cb[d])*W:0)+(d0?pc[d]:0)+(dlu(lr)){cc+=delta;if(d>0)pc[d]=bound_diff(cb[d-1],cb[d])*W;if(d0?bound_diff(cb[d-1],cb[d])*W:0)+(d0?pc[d]:0)+(dlu(lr)){cc+=delta;if(d>0)pc[d]=bound_diff(cb[d-1],cb[d])*W;if(d0)?1:-1; int dir_d1=-dir_d;\n int kd_d=(dir_d>0)?b+1:b, ki_d=(dir_d>0)?b:b+1;\n int kd_d1=(dir_d1>0)?b+1:b, ki_d1=(dir_d1>0)?b:b+1;\n if(cur_h[d][kd_d]<=1||cur_h[d+1][kd_d1]<=1)continue;\n long long dd=100LL*(max(0,a[d][kd_d]-(cur_h[d][kd_d]-1)*W)-max(0,a[d][kd_d]-cur_h[d][kd_d]*W))+100LL*(max(0,a[d][ki_d]-(cur_h[d][ki_d]+1)*W)-max(0,a[d][ki_d]-cur_h[d][ki_d]*W));\n dd+=100LL*(max(0,a[d+1][kd_d1]-(cur_h[d+1][kd_d1]-1)*W)-max(0,a[d+1][kd_d1]-cur_h[d+1][kd_d1]*W))+100LL*(max(0,a[d+1][ki_d1]-(cur_h[d+1][ki_d1]+1)*W)-max(0,a[d+1][ki_d1]-cur_h[d+1][ki_d1]*W));\n cur_h[d][kd_d]--;cur_h[d][ki_d]++;cb[d][b]+=dir_d;\n cur_h[d+1][kd_d1]--;cur_h[d+1][ki_d1]++;cb[d+1][b]+=dir_d1;\n long long npd=0; if(d>0)npd+=bound_diff(cb[d-1],cb[d])*W; npd+=bound_diff(cb[d],cb[d+1])*W; if(d+10)opd+=pc[d]; opd+=pc[d+1]; if(d+1lu(lr)){cc+=delta;if(d>0)pc[d]=bound_diff(cb[d-1],cb[d])*W;pc[d+1]=bound_diff(cb[d],cb[d+1])*W;if(d+1>>> starts;\n starts.push_back({total_cost(dp_res), dp_res});\n starts.push_back({total_cost(vector>(D, fixed_h)), vector>(D, fixed_h)});\n starts.push_back({total_cost(greedy_seq), greedy_seq});\n sort(starts.begin(), starts.end());\n \n long long gbc = starts[0].first; vector> gbh = starts[0].second;\n auto tst = chrono::steady_clock::now(); double tb = 2.8;\n \n for (int s = 0; s < min(3, (int)starts.size()); s++) {\n double el = chrono::duration(chrono::steady_clock::now() - tst).count();\n double al = (s == 0) ? tb * 0.85 : tb * 0.10;\n if (el + al > tb) al = tb - el;\n if (al < 0.03) break;\n auto [cost, h] = sa_run(starts[s].second, al, 42 + s * 7919);\n if (cost < gbc) { gbc = cost; gbh = h; }\n }\n \n for (int d = 0; d < D; d++) { int y = 0; for (int k = 0; k < N; k++) { cout << y << \" 0 \" << y + gbh[d][k] << \" \" << W << \"\\n\"; y += gbh[d][k]; } }\n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long MOD = 998244353;\n\nlong long bmod[81];\nlong long a[81];\nlong long s_val[180];\nint ops[81];\nint op_p[81];\nint op_q[81];\nint L = 0;\n\nint best_ops[81], best_op_p[81], best_op_q[81];\nint best_L = 0;\nlong long best_total_score = 0;\n\nlong long best_score[9][10];\nlong long best_counts[9][10][20];\nlong long current_counts[20];\n\nstruct FastRNG {\n unsigned long long x = 123456789, y = 362436069, z = 521288629;\n unsigned long long operator()() {\n unsigned long long t;\n x ^= x << 16; x ^= x >> 5; x ^= x << 1;\n t = x; x = y; y = z; z = t ^ x ^ y;\n return z;\n }\n};\n\nFastRNG rng;\n\nvoid dfs(int m, int remaining_ops, long long current_values[9], int used_ops, int subgrid_idx) {\n long long score = 0;\n for (int i = 0; i < 9; i++) score += current_values[i];\n if (score > best_score[subgrid_idx][used_ops]) {\n best_score[subgrid_idx][used_ops] = score;\n memcpy(best_counts[subgrid_idx][used_ops], current_counts, sizeof(current_counts));\n }\n \n if (remaining_ops == 0 || m == 20) return;\n\n dfs(m + 1, remaining_ops, current_values, used_ops, subgrid_idx);\n\n for (int i = 1; i <= remaining_ops; i++) {\n current_counts[m]++;\n for (int j = 0; j < 9; j++) {\n current_values[j] += s_val[m * 9 + j];\n if (current_values[j] >= MOD) current_values[j] -= MOD;\n }\n dfs(m + 1, remaining_ops - i, current_values, used_ops + i, subgrid_idx);\n }\n for (int i = 1; i <= remaining_ops; i++) {\n current_counts[m]--;\n for (int j = 0; j < 9; j++) {\n current_values[j] -= s_val[m * 9 + j];\n if (current_values[j] < 0) current_values[j] += MOD;\n }\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K;\n cin >> N >> M >> K;\n \n for (int i = 0; i < 81; i++) cin >> a[i];\n for (int m = 0; m < 20; m++)\n for (int i = 0; i < 9; i++)\n cin >> s_val[m * 9 + i];\n \n auto start_time = chrono::high_resolution_clock::now();\n \n // Phase 1: Exhaustive search for optimal independent subgrid configurations\n for (int j = 0; j < 9; j++) {\n int pj = (j / 3) * 3;\n int qj = (j % 3) * 3;\n long long initial_values[9];\n for (int i = 0; i < 3; i++) {\n for (int jj = 0; jj < 3; jj++) {\n initial_values[i * 3 + jj] = a[(pj + i) * 9 + (qj + jj)];\n }\n }\n memset(current_counts, 0, sizeof(current_counts));\n memset(best_score[j], 0, sizeof(best_score[j]));\n dfs(0, 9, initial_values, 0, j);\n }\n \n // Phase 2: Knapsack DP to distribute operations optimally\n long long dp[10][82];\n int choice[10][82];\n memset(dp, -1, sizeof(dp));\n dp[0][0] = 0;\n for (int i = 0; i < 9; i++) {\n for (int k = 0; k <= 81; k++) {\n if (dp[i][k] < 0) continue;\n for (int kj = 0; kj <= 9; kj++) {\n if (k + kj <= 81) {\n if (dp[i][k] + best_score[i][kj] > dp[i+1][k+kj]) {\n dp[i+1][k+kj] = dp[i][k] + best_score[i][kj];\n choice[i+1][k+kj] = kj;\n }\n }\n }\n }\n }\n \n long long max_total_score = 0;\n int best_total_k = 0;\n for (int k = 0; k <= 81; k++) {\n if (dp[9][k] > max_total_score) {\n max_total_score = dp[9][k];\n best_total_k = k;\n }\n }\n \n int current_k = best_total_k;\n int optimal_k[9];\n for (int i = 8; i >= 0; i--) {\n int kj = choice[i+1][current_k];\n optimal_k[i] = kj;\n current_k -= kj;\n }\n \n // Build initial board and operations array from DP results\n for (int i = 0; i < 81; i++) bmod[i] = a[i];\n L = 0;\n for (int j = 0; j < 9; j++) {\n int pj = (j / 3) * 3;\n int qj = (j % 3) * 3;\n int kj = optimal_k[j];\n for (int m = 0; m < 20; m++) {\n for (int c = 0; c < best_counts[j][kj][m]; c++) {\n ops[L] = m;\n op_p[L] = pj;\n op_q[L] = qj;\n for (int i = 0; i < 3; i++) {\n for (int jj = 0; jj < 3; jj++) {\n int u = (pj + i) * 9 + (qj + jj);\n long long nv = bmod[u] + s_val[m * 9 + i * 3 + jj];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n L++;\n }\n }\n }\n \n long long score = 0;\n for (int i = 0; i < 81; i++) score += bmod[i];\n \n best_total_score = score;\n best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n \n // Phase 3: Simulated Annealing for overlapping synergies\n double start_temp = 1e10, end_temp = 1e4;\n auto sa_start_time = chrono::high_resolution_clock::now();\n double sa_time_limit = 1.9 - chrono::duration(sa_start_time - start_time).count();\n \n int iter = 0;\n while (true) {\n iter++;\n if (iter % 10000 == 0) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - sa_start_time).count();\n if (elapsed > sa_time_limit) break;\n }\n \n double temp = start_temp * pow(end_temp / start_temp, min(1.0, chrono::duration(chrono::high_resolution_clock::now() - sa_start_time).count() / sa_time_limit));\n \n int move_type = rng() % 100;\n long long delta = 0;\n \n if (move_type < 20 && L < K) {\n int new_m = rng() % 20;\n int new_p = rng() % 7;\n int new_q = rng() % 7;\n \n long long old_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) old_score += bmod[(new_p + i) * 9 + (new_q + j)];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] + s_val[new_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) new_score += bmod[(new_p + i) * 9 + (new_q + j)];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[L] = new_m; op_p[L] = new_p; op_q[L] = new_q;\n L++;\n score += delta;\n if (score > best_total_score) {\n best_total_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] - s_val[new_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n }\n } else if (move_type < 30 && L > 0) {\n int idx = rng() % L;\n int old_m = ops[idx], old_p = op_p[idx], old_q = op_q[idx];\n \n long long old_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) old_score += bmod[(old_p + i) * 9 + (old_q + j)];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] - s_val[old_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) new_score += bmod[(old_p + i) * 9 + (old_q + j)];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[idx] = ops[L - 1]; op_p[idx] = op_p[L - 1]; op_q[idx] = op_q[L - 1];\n L--;\n score += delta;\n if (score > best_total_score) {\n best_total_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] + s_val[old_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n } else if (L > 0) {\n int idx = rng() % L;\n int old_m = ops[idx], old_p = op_p[idx], old_q = op_q[idx];\n \n int r = rng() % 5;\n int new_m = old_m, new_p = old_p, new_q = old_q;\n if (r == 0) new_m = rng() % 20;\n else if (r == 1) new_p = rng() % 7;\n else if (r == 2) new_q = rng() % 7;\n else if (r == 3) { new_p = rng() % 7; new_q = rng() % 7; }\n else { new_m = rng() % 20; new_p = rng() % 7; new_q = rng() % 7; }\n \n if (new_m == old_m && new_p == old_p && new_q == old_q) continue;\n \n bool affected[81] = {false};\n int affected_list[18];\n int affected_count = 0;\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n if (!affected[u]) { affected[u] = true; affected_list[affected_count++] = u; }\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n if (!affected[u]) { affected[u] = true; affected_list[affected_count++] = u; }\n }\n \n long long old_score = 0;\n for (int k = 0; k < affected_count; k++) old_score += bmod[affected_list[k]];\n \n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] - s_val[old_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] + s_val[new_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n \n long long new_score = 0;\n for (int k = 0; k < affected_count; k++) new_score += bmod[affected_list[k]];\n \n delta = new_score - old_score;\n \n if (delta >= 0 || (delta / temp > -20 && exp(delta / temp) > (double)(rng() % 1000000) / 1000000.0)) {\n ops[idx] = new_m; op_p[idx] = new_p; op_q[idx] = new_q;\n score += delta;\n if (score > best_total_score) {\n best_total_score = score; best_L = L;\n memcpy(best_ops, ops, L * sizeof(int));\n memcpy(best_op_p, op_p, L * sizeof(int));\n memcpy(best_op_q, op_q, L * sizeof(int));\n }\n } else {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (new_p + i) * 9 + (new_q + j);\n long long nv = bmod[u] - s_val[new_m * 9 + i * 3 + j];\n if (nv < 0) nv += MOD;\n bmod[u] = nv;\n }\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n int u = (old_p + i) * 9 + (old_q + j);\n long long nv = bmod[u] + s_val[old_m * 9 + i * 3 + j];\n if (nv >= MOD) nv -= MOD;\n bmod[u] = nv;\n }\n }\n for (int k = 0; k < affected_count; k++) affected[affected_list[k]] = false;\n }\n }\n \n cout << best_L << \"\\n\";\n for (int i = 0; i < best_L; i++)\n cout << best_ops[i] << \" \" << best_op_p[i] << \" \" << best_op_q[i] << \"\\n\";\n \n return 0;\n}","ahc033":"#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N], grid[N][N];\nbool dispatched[N*N];\nint nxt_recv[N];\nint lr, lc, lh;\nint total_disp;\n\nint next_exp(int g) {\n for (int j = 0; j < N; j++)\n if (!dispatched[N*g+j]) return N*g+j;\n return -1;\n}\n\nint main() {\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> A[i][j];\n \n memset(grid, -1, sizeof(grid));\n fill(dispatched, dispatched+N*N, false);\n fill(nxt_recv, nxt_recv+N, 0);\n lr = 0; lc = 0; lh = -1; total_disp = 0;\n \n vector acts(N);\n // Turn 0: bomb small cranes to prevent deadlocks\n for (int i = 0; i < N; i++) acts[i] += (i ? 'B' : '.');\n \n // Receive turn 0\n for (int i = 0; i < N; i++)\n if (nxt_recv[i] < N) grid[i][0] = A[i][nxt_recv[i]++];\n \n for (int t = 1; total_disp < N*N && (int)acts[0].size() < 9999; t++) {\n // Step 1: Receive\n for (int i = 0; i < N; i++) {\n if (nxt_recv[i] < N && grid[i][0] == -1 && !(lr == i && lc == 0 && lh >= 0)) {\n grid[i][0] = A[i][nxt_recv[i]++];\n }\n }\n \n // Step 2: Large crane action\n char act = '.';\n if (lh >= 0) {\n // Holding: Deliver directly to the correct dispatch gate\n int g = lh / N;\n int tr = g, tc = N - 1;\n \n if (lr == tr && lc == tc) {\n act = 'Q'; \n grid[tr][tc] = lh; \n lh = -1;\n } else {\n if (lr < tr) { lr++; act = 'D'; }\n else if (lr > tr) { lr--; act = 'U'; }\n else if (lc < tc) { lc++; act = 'R'; }\n else { lc--; act = 'L'; }\n }\n } else {\n // Not holding: Pick up the best available container\n int bc = -1, bs = INT_MAX, br = -1, bcc = -1;\n for (int r = 0; r < N; r++) {\n for (int c = 0; c < N; c++) {\n if (grid[r][c] < 0) continue;\n int co = grid[r][c], g = co / N, e = next_exp(g);\n int d = abs(lr - r) + abs(lc - c);\n int s;\n \n if (e >= 0 && e == co) s = -10000 + d; // Expected container (minimizes M1)\n else if (c == 0 && nxt_recv[r] < N) {\n int nc = A[r][nxt_recv[r]], ng = nc / N, ne = next_exp(ng);\n s = (ne >= 0 && ne == nc) ? -5000 + d : -1000 + d; // Blocks expected container\n } else if (c == 0) {\n s = -500 + d; // Blocks receiving gate\n } else {\n s = d + 500; // Other (shouldn't exist in this strategy)\n }\n \n if (s < bs) { bs = s; bc = co; br = r; bcc = c; }\n }\n }\n \n if (bc >= 0) {\n if (lr == br && lc == bcc) {\n act = 'P'; \n lh = bc; \n grid[br][bcc] = -1;\n } else {\n if (lr < br) { lr++; act = 'D'; }\n else if (lr > br) { lr--; act = 'U'; }\n else if (lc < bcc) { lc++; act = 'R'; }\n else { lc--; act = 'L'; }\n }\n }\n }\n \n acts[0] += act;\n for (int i = 1; i < N; i++) acts[i] += '.';\n \n // Step 3: Dispatch\n for (int i = 0; i < N; i++) {\n if (grid[i][N-1] >= 0) {\n dispatched[grid[i][N-1]] = true;\n grid[i][N-1] = -1;\n total_disp++;\n }\n }\n }\n \n int ml = 0;\n for (int i = 0; i < N; i++) ml = max(ml, (int)acts[i].size());\n for (int i = 0; i < N; i++) {\n while ((int)acts[i].size() < ml) acts[i] += '.';\n cout << acts[i] << endl;\n }\n return 0;\n}","ahc034":"#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\ntypedef long long ll;\n\nstruct Edge { int to, rev; ll cap, cost; };\n\nvoid add_edge(vector>& g, int f, int t, ll cap, ll cost) {\n g[f].push_back({t, (int)g[t].size(), cap, cost});\n g[t].push_back({f, (int)g[f].size() - 1, 0, -cost});\n}\n\nll min_cost_flow(vector>& g, int s, int t, ll mf) {\n int n = g.size();\n vector h(n, 0);\n ll res = 0, flow = 0;\n while (flow < mf) {\n priority_queue, vector>, greater<>> pq;\n vector dist(n, 1e18);\n vector pv(n), pe(n);\n dist[s] = 0; pq.push({0, s});\n while (!pq.empty()) {\n auto [d, v] = pq.top(); pq.pop();\n if (dist[v] < d) continue;\n for (int i = 0; i < (int)g[v].size(); i++) {\n Edge& e = g[v][i];\n if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {\n dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];\n pv[e.to] = v; pe[e.to] = i;\n pq.push({dist[e.to], e.to});\n }\n }\n }\n if (dist[t] == 1e18) break;\n for (int v = 0; v < n; v++) if (dist[v] < 1e18) h[v] += dist[v];\n ll d = mf - flow;\n for (int v = t; v != s; v = pv[v]) d = min(d, g[pv[v]][pe[v]].cap);\n flow += d; res += d * h[t];\n for (int v = t; v != s; v = pv[v]) {\n Edge& e = g[pv[v]][pe[v]]; e.cap -= d;\n g[v][e.rev].cap += d;\n }\n }\n return res;\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int n; cin >> n;\n vector> H(n, vector(n));\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) cin >> H[i][j];\n \n auto h = H;\n \n vector> src, snk;\n vector> sid(n, vector(n, -1)), kid(n, vector(n, -1));\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {\n if (H[i][j] > 0) { sid[i][j] = src.size(); src.push_back({i, j}); }\n else if (H[i][j] < 0) { kid[i][j] = snk.size(); snk.push_back({i, j}); }\n }\n int P = src.size(), M = snk.size();\n \n vector> flow(P, vector(M, 0));\n if (P > 0 && M > 0) {\n int S = 0, T = P + M + 1;\n vector> g(P + M + 2);\n int total_supply = 0;\n for (int i = 0; i < P; i++) {\n add_edge(g, S, 1 + i, H[src[i].first][src[i].second], 0);\n total_supply += H[src[i].first][src[i].second];\n }\n for (int j = 0; j < M; j++) add_edge(g, 1 + P + j, T, -H[snk[j].first][snk[j].second], 0);\n for (int i = 0; i < P; i++) {\n auto [si, sj] = src[i];\n for (int j = 0; j < M; j++) {\n auto [ti, tj] = snk[j];\n ll d = abs(si - ti) + abs(sj - tj);\n add_edge(g, 1 + i, 1 + P + j, H[src[i].first][src[i].second], d);\n }\n }\n min_cost_flow(g, S, T, total_supply);\n for (int i = 0; i < P; i++)\n for (auto& e : g[1 + i])\n if (e.to >= 1 + P && e.to < 1 + P + M)\n flow[i][e.to - 1 - P] = (int)g[e.to][e.rev].cap;\n }\n \n vector>> src_snks(P);\n for (int i = 0; i < P; i++) {\n auto [si, sj] = src[i];\n for (int j = 0; j < M; j++) {\n if (flow[i][j] > 0) {\n auto [ti, tj] = snk[j];\n int d = abs(si - ti) + abs(sj - tj);\n src_snks[i].push_back({d, j});\n }\n }\n sort(src_snks[i].begin(), src_snks[i].end());\n }\n\n auto trip_cost = [&](int i, int r, int c) -> ll {\n auto [si, sj] = src[i];\n int soil = H[si][sj];\n if (soil <= 0) return LLONG_MAX;\n ll cost = (ll)(abs(r-si)+abs(c-sj)) * 100 + soil;\n int cur_load = soil, cr = si, cc = sj;\n for (auto& [d0, j] : src_snks[i]) {\n if (cur_load <= 0) break;\n auto [ti, tj] = snk[j];\n int dd = abs(cr-ti)+abs(cc-tj);\n int amt = min(flow[i][j], cur_load);\n cost += (ll)dd * (100 + cur_load) + amt;\n cur_load -= amt; cr = ti; cc = tj;\n }\n if (cur_load > 0) cost += (ll)40 * (100 + cur_load) + cur_load;\n return cost;\n };\n \n vector src_rem(P);\n for (int i = 0; i < P; i++) src_rem[i] = H[src[i].first][src[i].second];\n \n vector ops;\n int r = 0, c = 0, load = 0, cur_src = -1;\n \n while (ops.size() < 100000) {\n if (h[r][c] > 0 && sid[r][c] >= 0 && src_rem[sid[r][c]] > 0) {\n int s = sid[r][c];\n ops.push_back(\"+\" + to_string(h[r][c]));\n load += h[r][c]; src_rem[s] = 0; h[r][c] = 0; cur_src = s;\n }\n while (h[r][c] < 0 && load > 0) {\n int d = min(load, -h[r][c]);\n ops.push_back(\"-\" + to_string(d));\n load -= d; h[r][c] += d;\n }\n \n bool any_left = false;\n for (int i = 0; i < P; i++) if (src_rem[i] > 0) any_left = true;\n for (int i = 0; i < n && !any_left; i++) for (int j = 0; j < n && !any_left; j++) if (h[i][j] != 0) any_left = true;\n if (!any_left && load == 0) break;\n\n int br = -1, bc = -1; ll bcost = LLONG_MAX;\n if (load > 0) {\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (h[i][j] < 0) {\n int d = abs(r - i) + abs(c - j);\n int absorb = min(-h[i][j], load);\n ll cost = (ll)d * (100 + load) - 30LL * absorb;\n if (cost < bcost) { bcost = cost; br = i; bc = j; }\n }\n } else {\n cur_src = -1;\n for (int i = 0; i < P; i++) {\n if (src_rem[i] <= 0) continue;\n ll cost = trip_cost(i, r, c);\n if (cost < bcost) { bcost = cost; br = src[i].first; bc = src[i].second; cur_src = i; }\n }\n if (br == -1) {\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (h[i][j] != 0) {\n int d = abs(r - i) + abs(c - j);\n ll cost = (ll)d * 100;\n if (cost < bcost) { bcost = cost; br = i; bc = j; }\n }\n }\n }\n if (br == -1) break;\n if (br < r) { r--; ops.push_back(\"U\"); }\n else if (br > r) { r++; ops.push_back(\"D\"); }\n else if (bc < c) { c--; ops.push_back(\"L\"); }\n else { c++; ops.push_back(\"R\"); }\n }\n for (auto& op : ops) cout << op << \"\\n\";\n}","ahc035":"#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct RNG {\n unsigned long long s[2];\n RNG(unsigned long long s1=0x123456789ABCDEF0ULL,unsigned long long s2=0xFEDCBA9876543210ULL):s{s1,s2}{}\n unsigned long long next(){unsigned long long s1=s[0],s0=s[1],r=s0+s1;s[0]=s0;s1^=s1<<23;s[1]=s1^s0^(s1>>18)^(s0>>5);return r;}\n int nextInt(int n){return (int)(next()%(unsigned long long)n);}\n double nextDouble(){return (double)(next()>>11)*0x1.0p-53;}\n};\n\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n const int N=6,M=15,SC=60,GS=36,NE=60;\n int n,mm,t;cin>>n>>mm>>t;\n int X[SC][M];for(int i=0;i>X[i][j];\n int eu[NE],ev[NE],ei=0;\n for(int i=0;ibestScore){bestScore=sc;memcpy(bestGrid,g,sizeof(int)*GS);memset(bestUsed,0,sizeof(bestUsed));for(int i=0;ibsc){bsc=sc;bs=s;}}\n g[pos]=bs;u[bs]=true;pf[pos]=true;}\n };\n \n // Strategy 0: center-first greedy\n {int g[GS]={};bool u[SC]={};bool pf[GS]={};greedyFill(g,u,pf,po);trySol(g);}\n // Strategy 1: best-pair-first greedy\n {int g[GS]={};bool u[SC]={};bool pf[GS]={};\n int ba=0,bb=1,bp=pot[0][1];for(int i=0;ibp){bp=pot[i][j];ba=i;bb=j;}\n g[14]=ba;u[ba]=true;pf[14]=true;g[15]=bb;u[bb]=true;pf[15]=true;greedyFill(g,u,pf,po);trySol(g);}\n // Strategy 2: value-sorted placement\n {int g[GS];int ss[SC];iota(ss,ss+SC,0);sort(ss,ss+SC,[&](int a,int b){return val[a]>val[b];});for(int i=0;i0;i--){int j=tmpRng.nextInt(i+1);swap(order[i],order[j]);}int g[GS]={};bool u[SC]={};bool pf[GS]={};greedyFill(g,u,pf,order);trySol(g);}\n \n // Phase 1: SA with 500->10 over 80ms\n {\n int grid[GS];memcpy(grid,bestGrid,sizeof(int)*GS);\n bool used[SC];memcpy(used,bestUsed,sizeof(bool)*SC);\n int un[SC-GS];int unc=bestUnc;memcpy(un,bestUn,sizeof(int)*unc);\n int cs=bestScore,bs=cs;int bg[GS];memcpy(bg,grid,sizeof(int)*GS);\n auto st=chrono::high_resolution_clock::now();double invT=1.0/500.0;\n for(int iter=0;iter<200000000;iter++){\n if((iter&0x3FFF)==0){auto el=chrono::duration_cast(chrono::high_resolution_clock::now()-st).count();if(el>80000)break;double p=(double)el/180000.0;double tmp=500.0*pow(10.0/500.0,p);invT=1.0/tmp;}\n if(rng.next()%5>0){int i=rng.nextInt(GS),j=rng.nextInt(GS);if(i==j)continue;int delta=0;for(int k=0;k=0){cs+=delta;if(cs>bs){bs=cs;memcpy(bg,grid,sizeof(int)*GS);}}else{int idx=(int)((double)(-delta)*invT*100.0);if(idxbs){bs=cs;memcpy(bg,grid,sizeof(int)*GS);}}else swap(grid[i],grid[j]);}}\n else{int pos=rng.nextInt(GS);int ui=rng.nextInt(unc);int ns=un[ui],os=grid[pos];int delta=0;for(int k=0;k=0){cs+=delta;used[os]=false;used[ns]=true;un[ui]=os;if(cs>bs){bs=cs;memcpy(bg,grid,sizeof(int)*GS);}}else{int idx=(int)((double)(-delta)*invT*100.0);if(idxbs){bs=cs;memcpy(bg,grid,sizeof(int)*GS);}}else grid[pos]=os;}}\n }\n if(bs>bestScore){bestScore=bs;memcpy(bestGrid,bg,sizeof(int)*GS);memset(bestUsed,0,sizeof(bestUsed));for(int i=0;i0.1 over 100ms\n {\n int grid[GS];memcpy(grid,bestGrid,sizeof(int)*GS);\n bool used[SC];memset(used,0,sizeof(used));for(int i=0;i(chrono::high_resolution_clock::now()-st).count();if(el>100000)break;double p=(double)el/180000.0;double tmp=100.0*pow(0.1/100.0,p);invT=1.0/tmp;}\n if(rng.next()%5>0){int i=rng.nextInt(GS),j=rng.nextInt(GS);if(i==j)continue;int delta=0;for(int k=0;k=0){cs+=delta;if(cs>bs){bs=cs;memcpy(bg,grid,sizeof(int)*GS);}}else{int idx=(int)((double)(-delta)*invT*100.0);if(idxbs){bs=cs;memcpy(bg,grid,sizeof(int)*GS);}}else swap(grid[i],grid[j]);}}\n else{int pos=rng.nextInt(GS);int ui=rng.nextInt(unc);int ns=un[ui],os=grid[pos];int delta=0;for(int k=0;k=0){cs+=delta;used[os]=false;used[ns]=true;un[ui]=os;if(cs>bs){bs=cs;memcpy(bg,grid,sizeof(int)*GS);}}else{int idx=(int)((double)(-delta)*invT*100.0);if(idxbs){bs=cs;memcpy(bg,grid,sizeof(int)*GS);}}else grid[pos]=os;}}\n }\n if(bs>bestScore){bestScore=bs;memcpy(bestGrid,bg,sizeof(int)*GS);}\n }\n \n for(int i=0;i>X[i][j];\n }return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nint dx[] = {0, 1, 0, -1};\nint dy[] = {1, 0, -1, 0};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n \n vector s(N), t(N);\n for (int i = 0; i < N; i++) cin >> s[i];\n for (int i = 0; i < N; i++) cin >> t[i];\n \n int Vp = V;\n vector len(Vp, 1);\n int idx = 1;\n for (int l = 1; idx < Vp; l++) {\n int cnt = (l <= 2 && Vp >= 10) ? 2 : 1;\n for (int k = 0; k < cnt && idx < Vp; k++) {\n len[idx++] = min(l, N / 2);\n }\n }\n \n cout << Vp << \"\\n\";\n for (int i = 1; i < Vp; i++) cout << 0 << \" \" << len[i] << \"\\n\";\n \n vector> grid(N, vector(N)), target(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n grid[i][j] = s[i][j] - '0';\n target[i][j] = t[i][j] - '0';\n }\n \n vector> sources, targets;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n if (grid[i][j] && !target[i][j]) sources.push_back({i, j});\n if (!grid[i][j] && target[i][j]) targets.push_back({i, j});\n }\n \n int Mm = sources.size();\n if (Mm == 0) {\n cout << N/2 << \" \" << N/2 << \"\\n\";\n return 0;\n }\n \n // Cluster sources\n vector s_cluster(Mm, -1);\n int num_s_clusters = 0;\n for (int i = 0; i < Mm; i++) {\n if (s_cluster[i] != -1) continue;\n queue q; q.push(i); s_cluster[i] = num_s_clusters;\n while (!q.empty()) {\n int u = q.front(); q.pop();\n for (int v = 0; v < Mm; v++) {\n if (s_cluster[v] != -1) continue;\n if (abs(sources[u].first - sources[v].first) + abs(sources[u].second - sources[v].second) <= 6) {\n s_cluster[v] = num_s_clusters; q.push(v);\n }\n }\n }\n num_s_clusters++;\n }\n\n // Cluster targets\n vector t_cluster(Mm, -1);\n int num_t_clusters = 0;\n for (int i = 0; i < Mm; i++) {\n if (t_cluster[i] != -1) continue;\n queue q; q.push(i); t_cluster[i] = num_t_clusters;\n while (!q.empty()) {\n int u = q.front(); q.pop();\n for (int v = 0; v < Mm; v++) {\n if (t_cluster[v] != -1) continue;\n if (abs(targets[u].first - targets[v].first) + abs(targets[u].second - targets[v].second) <= 6) {\n t_cluster[v] = num_t_clusters; q.push(v);\n }\n }\n }\n num_t_clusters++;\n }\n \n vector> s_center(num_s_clusters, {0, 0});\n vector s_count(num_s_clusters, 0);\n for (int i = 0; i < Mm; i++) {\n s_center[s_cluster[i]].first += sources[i].first;\n s_center[s_cluster[i]].second += sources[i].second;\n s_count[s_cluster[i]]++;\n }\n for (int i = 0; i < num_s_clusters; i++) { s_center[i].first /= s_count[i]; s_center[i].second /= s_count[i]; }\n \n vector> t_center(num_t_clusters, {0, 0});\n vector t_count(num_t_clusters, 0);\n for (int i = 0; i < Mm; i++) {\n t_center[t_cluster[i]].first += targets[i].first;\n t_center[t_cluster[i]].second += targets[i].second;\n t_count[t_cluster[i]]++;\n }\n for (int i = 0; i < num_t_clusters; i++) { t_center[i].first /= t_count[i]; t_center[i].second /= t_count[i]; }\n \n vector cluster_match(num_s_clusters, -1);\n vector t_cluster_used(num_t_clusters, false);\n vector s_cluster_order(num_s_clusters);\n iota(s_cluster_order.begin(), s_cluster_order.end(), 0);\n sort(s_cluster_order.begin(), s_cluster_order.end(), [&](int a, int b) { return s_count[a] > s_count[b]; });\n \n for (int i : s_cluster_order) {\n long long best_dist = 1e18; int best_t = -1;\n for (int j = 0; j < num_t_clusters; j++) {\n if (t_cluster_used[j]) continue;\n long long dist = abs(s_center[i].first - t_center[j].first) + abs(s_center[i].second - t_center[j].second);\n if (dist < best_dist) { best_dist = dist; best_t = j; }\n }\n if (best_t != -1) { cluster_match[i] = best_t; t_cluster_used[best_t] = true; }\n }\n \n vector match(Mm, -1);\n vector sused(Mm, false), tused(Mm, false);\n \n for (int i = 0; i < num_s_clusters; i++) {\n if (cluster_match[i] == -1) continue;\n int j = cluster_match[i];\n vector s_indices, t_indices;\n for (int k = 0; k < Mm; k++) {\n if (s_cluster[k] == i) s_indices.push_back(k);\n if (t_cluster[k] == j) t_indices.push_back(k);\n }\n vector> pairs;\n for (int si : s_indices) {\n for (int ti : t_indices) {\n if (tused[ti]) continue;\n pairs.push_back({abs(sources[si].first - targets[ti].first) + abs(sources[si].second - targets[ti].second), si, ti});\n }\n }\n sort(pairs.begin(), pairs.end());\n for (auto& [d, si, ti] : pairs) {\n if (!sused[si] && !tused[ti]) { match[si] = ti; sused[si] = true; tused[ti] = true; }\n }\n }\n \n vector> pairs;\n for (int i = 0; i < Mm; i++) {\n if (sused[i]) continue;\n for (int j = 0; j < Mm; j++) {\n if (tused[j]) continue;\n pairs.push_back({abs(sources[i].first - targets[j].first) + abs(sources[i].second - targets[j].second), i, j});\n }\n }\n sort(pairs.begin(), pairs.end());\n for (auto& [d, i, j] : pairs) {\n if (!sused[i] && !tused[j]) { match[i] = j; sused[i] = true; tused[j] = true; }\n }\n \n int best_cluster = max_element(s_count.begin(), s_count.end()) - s_count.begin();\n int rx = s_center[best_cluster].first;\n int ry = s_center[best_cluster].second;\n cout << rx << \" \" << ry << \"\\n\";\n \n vector dir(Vp, 0);\n vector available_s(Mm, true);\n vector finger_state(Vp, 0); // 0: IDLE, 1: TO_SOURCE, 2: TO_TARGET\n vector finger_task(Vp, -1);\n vector f_target_x(Vp), f_target_y(Vp), f_target_dir(Vp);\n vector ops;\n \n auto get_best_station = [&](int rx, int ry, int f, int cell_x, int cell_y) {\n int best_cost = INT_MAX, best_nx = -1, best_ny = -1, best_dir = -1;\n for (int d = 0; d < 4; d++) {\n int nx = cell_x - dx[d] * len[f], ny = cell_y - dy[d] * len[f];\n if (0 <= nx && nx < N && 0 <= ny && ny < N) {\n int dist = abs(rx - nx) + abs(ry - ny);\n int rot = min((dir[f] - d + 4) % 4, (d - dir[f] + 4) % 4);\n int cost = max(dist, rot);\n if (cost < best_cost) { best_cost = cost; best_nx = nx; best_ny = ny; best_dir = d; }\n }\n }\n return make_tuple(best_nx, best_ny, best_dir, best_cost);\n };\n \n while (true) {\n // 1. Update target stations dynamically based on current root position\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 1) {\n int s_idx = finger_task[f];\n auto [nx, ny, d, cost] = get_best_station(rx, ry, f, sources[s_idx].first, sources[s_idx].second);\n if (nx != -1) { f_target_x[f] = nx; f_target_y[f] = ny; f_target_dir[f] = d; }\n } else if (finger_state[f] == 2) {\n int t_idx = match[finger_task[f]];\n auto [nx, ny, d, cost] = get_best_station(rx, ry, f, targets[t_idx].first, targets[t_idx].second);\n if (nx != -1) { f_target_x[f] = nx; f_target_y[f] = ny; f_target_dir[f] = d; }\n }\n }\n\n // 2. Assign idle fingers\n bool any_idle = false;\n for (int f = 1; f < Vp; f++) if (finger_state[f] == 0) { any_idle = true; break; }\n \n if (any_idle) {\n int min_cost_to_pending = INT_MAX;\n for (int f2 = 1; f2 < Vp; f2++) {\n if (finger_state[f2] != 0) {\n int dist = abs(rx - f_target_x[f2]) + abs(ry - f_target_y[f2]);\n int rot = min((dir[f2] - f_target_dir[f2] + 4) % 4, (f_target_dir[f2] - dir[f2] + 4) % 4);\n int cost = max(dist, rot);\n min_cost_to_pending = min(min_cost_to_pending, cost);\n }\n }\n int max_accept_cost = (min_cost_to_pending == INT_MAX) ? INT_MAX : min_cost_to_pending + 6;\n\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) {\n int min_cost = INT_MAX, best_s = -1, b_nx, b_ny, b_dir;\n for (int i = 0; i < Mm; i++) {\n if (!available_s[i]) continue;\n auto [nx, ny, d, cost] = get_best_station(rx, ry, f, sources[i].first, sources[i].second);\n if (cost < min_cost && cost <= max_accept_cost) {\n min_cost = cost; best_s = i; b_nx = nx; b_ny = ny; b_dir = d;\n }\n }\n if (best_s != -1) {\n finger_state[f] = 1; finger_task[f] = best_s; available_s[best_s] = false;\n f_target_x[f] = b_nx; f_target_y[f] = b_ny; f_target_dir[f] = b_dir;\n }\n }\n }\n }\n\n // 3. Check if any finger is at its target station (must stay to execute action)\n bool must_stay = false;\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] != 0) {\n int dist = abs(rx - f_target_x[f]) + abs(ry - f_target_y[f]);\n int rot = min((dir[f] - f_target_dir[f] + 4) % 4, (f_target_dir[f] - dir[f] + 4) % 4);\n if (dist == 0 && rot == 0) {\n must_stay = true;\n break;\n }\n }\n }\n\n // 4. Find best move (Greedy TSP towards the most urgent station)\n int best_f = -1;\n int min_cost = INT_MAX;\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n int dist = abs(rx - f_target_x[f]) + abs(ry - f_target_y[f]);\n int rot = min((dir[f] - f_target_dir[f] + 4) % 4, (f_target_dir[f] - dir[f] + 4) % 4);\n int cost = max(dist, rot);\n if (cost < min_cost) {\n min_cost = cost;\n best_f = f;\n }\n }\n\n int best_move = 0;\n if (!must_stay && best_f != -1) {\n if (rx < f_target_x[best_f]) best_move = 1; // D\n else if (rx > f_target_x[best_f]) best_move = 2; // U\n else if (ry < f_target_y[best_f]) best_move = 3; // R\n else if (ry > f_target_y[best_f]) best_move = 4; // L\n }\n\n // 5. Construct operation string\n string op(2 * Vp, '.');\n if (best_move == 1) { op[0] = 'D'; rx++; }\n else if (best_move == 2) { op[0] = 'U'; rx--; }\n else if (best_move == 3) { op[0] = 'R'; ry++; }\n else if (best_move == 4) { op[0] = 'L'; ry--; }\n\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n if (dir[f] != f_target_dir[f]) {\n int diff = (f_target_dir[f] - dir[f] + 4) % 4;\n if (diff <= 2) { op[f] = 'R'; dir[f] = (dir[f] + 1) % 4; }\n else { op[f] = 'L'; dir[f] = (dir[f] + 3) % 4; }\n }\n }\n\n for (int f = 1; f < Vp; f++) {\n if (finger_state[f] == 0) continue;\n if (rx == f_target_x[f] && ry == f_target_y[f] && dir[f] == f_target_dir[f]) {\n op[Vp + f] = 'P';\n if (finger_state[f] == 1) {\n int s_idx = finger_task[f];\n grid[sources[s_idx].first][sources[s_idx].second] = 0;\n finger_state[f] = 2;\n } else {\n int s_idx = finger_task[f]; int t_idx = match[s_idx];\n grid[targets[t_idx].first][targets[t_idx].second] = 1;\n finger_state[f] = 0;\n }\n }\n }\n ops.push_back(op);\n\n // 6. Check termination\n bool any_pending = false, any_available = false;\n for (int f = 1; f < Vp; f++) if (finger_state[f] != 0) any_pending = true;\n for (int i = 0; i < Mm; i++) if (available_s[i]) any_available = true;\n if (!any_pending && !any_available) break;\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc039":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nstruct GridRect { int score, x1, y1, x2, y2; };\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N; cin >> N;\n vector fx(2*N), fy(2*N), val(2*N);\n for (int i = 0; i < 2*N; i++) {\n cin >> fx[i] >> fy[i];\n val[i] = (i < N) ? 1 : -1;\n }\n \n int GS = 700, CS = 143;\n vector> grid(GS, vector(GS, 0));\n for (int i = 0; i < 2*N; i++) {\n int gx = min(fx[i] / CS, GS - 1);\n int gy = min(fy[i] / CS, GS - 1);\n grid[gx][gy] += val[i];\n }\n \n vector grid_rects;\n for (int gx1 = 0; gx1 < GS; gx1++) {\n vector col_sums(GS, 0);\n for (int gx2 = gx1; gx2 < GS; gx2++) {\n for (int gy = 0; gy < GS; gy++) {\n col_sums[gy] += grid[gx2][gy];\n }\n int cur = 0, best = 0, cy1 = 0, by1 = 0, by2 = -1;\n for (int gy2 = 0; gy2 < GS; gy2++) {\n cur += col_sums[gy2];\n if (cur > best) { best = cur; by1 = cy1; by2 = gy2; }\n if (cur < 0) { cur = 0; cy1 = gy2 + 1; }\n }\n if (best > 0) grid_rects.push_back({best, gx1, by1, gx2, by2});\n }\n }\n sort(grid_rects.begin(), grid_rects.end(), [](const GridRect& a, const GridRect& b) { return a.score > b.score; });\n \n int best_exact_score = 0;\n int final_x1 = 0, final_y1 = 0, final_x2 = 0, final_y2 = 0;\n for (int k = 0; k < min(20, (int)grid_rects.size()); k++) {\n int bestX1 = grid_rects[k].x1 * CS;\n int bestY1 = grid_rects[k].y1 * CS;\n int bestX2 = min((grid_rects[k].x2 + 1) * CS, 100000);\n int bestY2 = min((grid_rects[k].y2 + 1) * CS, 100000);\n \n for (int iter = 0; iter < 20; iter++) {\n for (int dim = 0; dim < 2; dim++) {\n vector> ev;\n for (int i = 0; i < 2 * N; i++) {\n bool inside = (dim == 0) ? (fx[i] >= bestX1 && fx[i] <= bestX2) : (fy[i] >= bestY1 && fy[i] <= bestY2);\n if (inside) ev.push_back({(dim == 0) ? fy[i] : fx[i], val[i]});\n }\n sort(ev.begin(), ev.end());\n \n // Group coordinates to fix the 1D overestimation bug\n vector> ev_unique;\n for (int i = 0; i < (int)ev.size(); i++) {\n if (i > 0 && ev[i].first == ev[i-1].first) {\n ev_unique.back().second += ev[i].second;\n } else {\n ev_unique.push_back(ev[i]);\n }\n }\n \n int bs = -1000000000, b1 = (dim == 0) ? bestY1 : bestX1, b2 = (dim == 0) ? bestY2 : bestX2;\n int mp = 0, mpi = -1, pfx = 0;\n for (int j = 0; j <= (int)ev_unique.size(); j++) {\n int s = pfx - mp;\n if (s > bs) {\n bs = s;\n b1 = (mpi == -1) ? 0 : ev_unique[mpi].first;\n b2 = (j == (int)ev_unique.size()) ? 100000 : ev_unique[j - 1].first;\n }\n if (pfx < mp) {\n mp = pfx;\n mpi = j;\n }\n if (j < (int)ev_unique.size()) pfx += ev_unique[j].second;\n }\n \n if (dim == 0) { bestY1 = b1; bestY2 = b2; } else { bestX1 = b1; bestX2 = b2; }\n }\n }\n \n int current_score = 0;\n for (int i = 0; i < 2 * N; i++) {\n if (fx[i] >= bestX1 && fx[i] <= bestX2 && fy[i] >= bestY1 && fy[i] <= bestY2) {\n current_score += val[i];\n }\n }\n \n if (current_score > best_exact_score) {\n best_exact_score = current_score;\n final_x1 = bestX1; final_y1 = bestY1;\n final_x2 = bestX2; final_y2 = bestY2;\n }\n }\n \n if (best_exact_score > 0) {\n cout << 4 << \"\\n\" << final_x1 << \" \" << final_y1 << \"\\n\"\n << final_x2 << \" \" << final_y1 << \"\\n\"\n << final_x2 << \" \" << final_y2 << \"\\n\"\n << final_x1 << \" \" << final_y2 << \"\\n\";\n } else {\n cout << 4 << \"\\n50000 50000\\n50001 50000\\n50001 50001\\n50000 50001\\n\";\n }\n \n return 0;\n}","ahc040":"#include \nusing namespace std;\nint N,T,sigma;\nvectorw_obs,h_obs;\nvectorw_est,h_est;\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n cin>>N>>T>>sigma;\n w_obs.resize(N);h_obs.resize(N);w_est.resize(N);h_est.resize(N);\n for(int i=0;i>w_obs[i]>>h_obs[i];w_est[i]=w_obs[i];h_est[i]=h_obs[i];}\n mt19937 rng(42);\n auto start=chrono::steady_clock::now();\n int ne=(T>=20)?4:(T>=8?2:0);\n for(int t=0;t(now-start).count()>2700)break;\n vectorwc(N),hc(N);\n for(int i=0;ipx,py,pw,ph;vectorplc;vector>out;\n long long cW=0,cH=0;\n bool is_est=(t=4&&t>=2);\n for(int i=0;irx)ry=max(ry,py[j]+ph[j]);\n long long nW=max(cW,rx+rw),nH=max(cH,ry+rh),s=nW+nH;\n switch(strat){\n case 1:s+=abs(nW-nH)/4;break;case 2:s+=abs(nW-nH)/2;break;\n case 3:s+=abs(nW-nH);break;case 4:s=max(nW,nH)*2;break;\n case 5:s=nW*3+nH;break;case 6:s=nW+nH*3;break;\n case 7:s+=abs(nW-nH)*3/4;break;case 8:s+=abs(nW-nH)/8;break;\n case 9:{long long w=nW*nH;for(int j=0;jry)rx=max(rx,px[j]+pw[j]);\n long long nW=max(cW,rx+rw),nH=max(cH,ry+rh),s=nW+nH;\n switch(strat){\n case 1:s+=abs(nW-nH)/4;break;case 2:s+=abs(nW-nH)/2;break;\n case 3:s+=abs(nW-nH);break;case 4:s=max(nW,nH)*2;break;\n case 5:s=nW*3+nH;break;case 6:s=nW+nH*3;break;\n case 7:s+=abs(nW-nH)*3/4;break;case 8:s+=abs(nW-nH)/8;break;\n case 9:{long long w=nW*nH;for(int j=0;j>Wp>>Hp;\n if(is_est){\n bool ir=(t%2==0),iro=(ne>=4&&t>=2);\n if(ir){\n double ws=0;for(int i=0;i>vh;for(int i=0;i>vw;for(int i=0;i(out[j]);\n if(px[j]+pw[j]==cW&&rc>0){double es=We/rc*lr;if(rot)h_est[o]=max(1.0,h_est[o]+es);else w_est[o]=max(1.0,w_est[o]+es);}\n if(py[j]+ph[j]==cH&&bc>0){double es=He/bc*lr;if(rot)w_est[o]=max(1.0,w_est[o]+es);else h_est[o]=max(1.0,h_est[o]+es);}\n }\n double glr=0.05;\n for(int i=0;i\nusing namespace std;\nint N, M, H;\nvector A;\nvector> adj;\nmt19937 rng(42);\nchrono::steady_clock::time_point T0;\ndouble el() { return chrono::duration(chrono::steady_clock::now() - T0).count(); }\n\nstruct State {\n vector parent, height, sub_max_h, q, deg;\n vector sub_sum;\n long long score;\n\n void recompute() {\n int head = 0, tail = 0;\n for (int i = 0; i < N; i++) deg[i] = 0;\n for (int i = 0; i < N; i++) if (parent[i] != -1) deg[parent[i]]++;\n for (int i = 0; i < N; i++) if (deg[i] == 0) q[tail++] = i;\n while (head < tail) { \n int v = q[head++]; \n if (parent[v] != -1) { \n deg[parent[v]]--; \n if (deg[parent[v]] == 0) q[tail++] = parent[v]; \n }\n }\n for (int i = tail - 1; i >= 0; i--) {\n int v = q[i]; \n height[v] = (parent[v] == -1) ? 0 : height[parent[v]] + 1; \n sub_sum[v] = A[v]; sub_max_h[v] = height[v]; \n }\n score = 0;\n for (int i = 0; i < tail; i++) {\n int v = q[i]; \n if (parent[v] != -1) { \n sub_sum[parent[v]] += sub_sum[v]; \n sub_max_h[parent[v]] = max(sub_max_h[parent[v]], sub_max_h[v]); \n }\n score += (long long)(height[v] + 1) * A[v];\n }\n }\n \n bool creates_cycle(int v, int np) { \n if (np == -1) return false; \n for (int c = np; c != -1; c = parent[c]) if (c == v) return true; \n return false; \n }\n \n void apply_move(int v, int np) {\n int op = parent[v]; parent[v] = np;\n int delta = (np == -1) ? -height[v] : (height[np] + 1 - height[v]);\n if (delta != 0) { \n vector stk; stk.push_back(v); \n while (!stk.empty()) { \n int u = stk.back(); stk.pop_back(); \n height[u] += delta; \n sub_max_h[u] += delta; \n for (int c : adj[u]) if (parent[c] == u) stk.push_back(c); \n } \n }\n vector ancs; \n for (int c = op; c != -1; c = parent[c]) ancs.push_back(c); \n for (int c = np; c != -1; c = parent[c]) ancs.push_back(c);\n sort(ancs.begin(), ancs.end(), [this](int a, int b) { return height[a] > height[b]; }); \n ancs.erase(unique(ancs.begin(), ancs.end()), ancs.end());\n for (int c : ancs) { \n sub_sum[c] = A[c]; sub_max_h[c] = height[c]; \n for (int ch : adj[c]) if (parent[ch] == c) { \n sub_sum[c] += sub_sum[ch]; \n sub_max_h[c] = max(sub_max_h[c], sub_max_h[ch]); \n } \n }\n }\n \n void init(const vector& p) {\n parent = p; height.resize(N); sub_sum.resize(N); sub_max_h.resize(N); q.resize(N); deg.resize(N);\n recompute();\n }\n};\n\nvoid greedy(State& st) { \n while (true) { \n long long bg = 0; int bv = -1, bu = -1; \n for (int v = 0; v < N; v++) for (int u : adj[v]) { \n if (u == st.parent[v]) continue; \n if (st.creates_cycle(v, u)) continue;\n int nh = st.height[u] + 1, d = nh - st.height[v]; \n if (d <= 0 || st.sub_max_h[v] + d > H) continue; \n long long g = (long long)d * st.sub_sum[v]; \n if (g > bg) { bg = g; bv = v; bu = u; } \n } \n if (bv == -1) break; \n st.parent[bv] = bu;\n st.recompute();\n } \n}\n\nvoid sa(State& st, double et) { \n double ss = el(); double dur = max(0.001, et - ss); \n uniform_real_distribution uf(0, 1); \n long long lb = st.score; vector bp = st.parent; \n double T = 5000.0;\n for (int it = 0; ; it++) { \n if (it % 1000 == 0) { \n double t = el(); if (t > et) break; \n T = 5000.0 * exp(-20.0 * (t - ss) / dur); \n st.recompute();\n }\n int v = rng() % N; \n int np;\n if (rng() % 20 == 0) np = -1;\n else { if (adj[v].empty()) continue; np = adj[v][rng() % adj[v].size()]; }\n \n if (np == st.parent[v]) continue; \n if (st.creates_cycle(v, np)) continue;\n \n int nh = (np == -1) ? 0 : st.height[np] + 1; \n int d = nh - st.height[v]; \n if (st.sub_max_h[v] + d > H) continue; \n \n long long g = (long long)d * st.sub_sum[v]; \n if (g > 0 || uf(rng) < exp((double)g / T)) { \n st.apply_move(v, np); \n st.score += g; \n if (st.score > lb) { lb = st.score; bp = st.parent; } \n } \n } \n st.parent = bp; st.recompute();\n}\n\nvector bfs_sol(const vector& ro, bool by_b) { vector p(N, -1), h(N, 0); vector vis(N); for (int r : ro) { if (vis[r]) continue; queue q; q.push(r); vis[r] = true; p[r] = -1; h[r] = 0; while (!q.empty()) { int u = q.front(); q.pop(); if (h[u] >= H) continue; vector nb = adj[u]; if (by_b) sort(nb.begin(), nb.end(), [](int a, int b) { return A[a] < A[b]; }); else shuffle(nb.begin(), nb.end(), rng); for (int v : nb) { if (vis[v]) continue; vis[v] = true; p[v] = u; h[v] = h[u] + 1; q.push(v); } } } return p; }\nvector dfs_sol(const vector& ro) { vector p(N, -1), h(N, 0); vector vis(N); for (int r : ro) { if (vis[r]) continue; vis[r] = true; p[r] = -1; h[r] = 0; function dfs = [&](int u) { if (h[u] >= H) return; vector nb = adj[u]; sort(nb.begin(), nb.end(), [](int a, int b) { return A[a] < A[b]; }); for (int v : nb) { if (vis[v]) continue; vis[v] = true; p[v] = u; h[v] = h[u] + 1; dfs(v); } }; dfs(r); } return p; }\nvector chain_sol() { vector p(N, -1); vector used(N); vector ord(N); iota(ord.begin(), ord.end(), 0); sort(ord.begin(), ord.end(), [](int a, int b) { return A[a] > A[b]; }); for (int v : ord) { if (used[v]) continue; vector dist(N, -1), par(N, -1); queue q; q.push(v); dist[v] = 0; int tgt = v; while (!q.empty()) { int u = q.front(); q.pop(); if (dist[u] > dist[tgt]) tgt = u; if (dist[u] == H) continue; for (int w : adj[u]) if (!used[w] && dist[w] == -1) { dist[w] = dist[u] + 1; par[w] = u; q.push(w); } } vector path; for (int c = tgt;; c = par[c]) { path.push_back(c); if (c == v) break; } for (int i = 0; i < (int)path.size(); i++) { used[path[i]] = true; p[path[i]] = (i == 0) ? -1 : path[i - 1]; } } return p; }\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr); T0 = chrono::steady_clock::now();\n cin >> N >> M >> H; A.resize(N); for (int i = 0; i < N; i++) cin >> A[i]; adj.resize(N);\n for (int i = 0; i < M; i++) { int u, v; cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); }\n vector X(N), Y(N); for (int i = 0; i < N; i++) cin >> X[i] >> Y[i];\n long long bs = 0; vector bp(N, -1); State st;\n auto try_sol = [&](const vector& p) { st.init(p); greedy(st); if (st.score > bs) { bs = st.score; bp = st.parent; } };\n try_sol(vector(N, -1));\n { vector o(N); iota(o.begin(), o.end(), 0); sort(o.begin(), o.end(), [](int a, int b) { return A[a] < A[b]; }); try_sol(bfs_sol(o, true)); try_sol(dfs_sol(o)); }\n try_sol(chain_sol());\n { vector o(N); iota(o.begin(), o.end(), 0); sort(o.begin(), o.end(), [&](int a, int b) { return (X[a]-500)*(X[a]-500)+(Y[a]-500)*(Y[a]-500) < (X[b]-500)*(X[b]-500)+(Y[b]-500)*(Y[b]-500); }); try_sol(bfs_sol(o, true)); try_sol(dfs_sol(o)); }\n while (el() < 0.4) { vector o(N); iota(o.begin(), o.end(), 0); shuffle(o.begin(), o.end(), rng); if (rng() % 2) try_sol(bfs_sol(o, rng() % 2)); else try_sol(dfs_sol(o)); }\n st.init(bp); sa(st, 1.6); greedy(st); if (st.score > bs) { bs = st.score; bp = st.parent; }\n for (int i = 0; i < N; i++) cout << bp[i] << (i == N - 1 ? \"\\n\" : \" \");\n return 0;\n}","ahc042":"#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint N;\nvector initial_board;\n\nvoid apply_shift(vector& b, char dir, int idx) {\n if(dir=='L'){for(int j=0;j0;j--)b[idx][j]=b[idx][j-1];b[idx][0]='.';}\n else if(dir=='U'){for(int i=0;i0;i--)b[i][idx]=b[i-1][idx];b[0][idx]='.';}\n}\n\nstruct MoveInfo{char dir;int idx;int amount;double ratio;int oni_removed;};\n\nvector get_candidates(const vector& b){\n vector cands;\n for(int i=0;i0){int cnt=0,mx=-1;for(int j=0;j0)cands.push_back(MoveInfo{'L',i,mx+1,(double)cnt/(mx+1),cnt});}\n int R=0;for(int j=N-1;j>=0;j--)if(b[i][j]=='o'){R=j+1;break;}\n if(R0)cands.push_back(MoveInfo{'R',i,N-lo,(double)cnt/(N-lo),cnt});}\n }\n for(int j=0;j0){int cnt=0,mx=-1;for(int i=0;i0)cands.push_back(MoveInfo{'U',j,mx+1,(double)cnt/(mx+1),cnt});}\n int D=0;for(int i=N-1;i>=0;i--)if(b[i][j]=='o'){D=i+1;break;}\n if(D0)cands.push_back(MoveInfo{'D',j,N-lo,(double)cnt/(N-lo),cnt});}\n }\n return cands;\n}\n\nint count_oni(const vector& b){int c=0;for(auto&r:b)for(char ch:r)if(ch=='x')c++;return c;}\n\npair compute_safety(const vector& b){\n int stuck=0;double score=0;\n for(int i=0;i> batch_from_board(const vector& board_in){\n vector b=board_in;\n vector> moves;\n auto shift=[&](char d,int i){apply_shift(b,d,i);moves.push_back({d,i});};\n struct Oni{int i,j;};vector onis;\n for(int i=0;i>> oni_dirs(onis.size());\n for(int id=0;id<(int)onis.size();id++){\n auto& o=onis[id];bool us=true,ds=true,ls=true,rs=true;\n for(int k=0;k assign(onis.size(),0);\n for(int id=0;id<(int)onis.size();id++){\n char bd=0;int bc=1e9;\n for(auto& kv:oni_dirs[id])if(kv.second,int> mx_map;\n for(int id=0;id<(int)onis.size();id++){\n char d=assign[id];if(!d)continue;\n int idx=(d=='L'||d=='R')?onis[id].i:onis[id].j;\n for(auto& kv:oni_dirs[id])if(kv.first==d){\n auto key=make_pair(d,idx);mx_map[key]=max(mx_map[key],kv.second);break;\n }\n }\n return mx_map;\n };\n \n // Local search to minimize total moves (considering combined shifts)\n auto compute_total=[&](){\n auto mx_map=compute_batches();\n int total=0;\n for(int i=0;i0&&Rv>0)total+=min(2*Lv+Rv,Lv+2*Rv);\n else total+=2*(Lv+Rv);\n }\n for(int j=0;j0&&Dv>0)total+=min(2*Uv+Dv,Uv+2*Dv);\n else total+=2*(Uv+Dv);\n }\n return total;\n };\n \n for(int iter=0;iter<200;iter++){\n bool improved=false;\n for(int id=0;id<(int)onis.size();id++){\n if(oni_dirs[id].size()<=1)continue;\n int old_c=compute_total();\n char old_d=assign[id];\n for(auto& kv:oni_dirs[id]){\n if(kv.first==old_d)continue;\n assign[id]=kv.first;\n int new_c=compute_total();\n if(new_c0&&Rv>0){\n if(2*Lv+Rv<=Lv+2*Rv){for(int k=0;k0){for(int k=0;k0){for(int k=0;k0&&Dv>0){\n if(2*Uv+Dv<=Uv+2*Dv){for(int k=0;k0){for(int k=0;k0){for(int k=0;k>,bool> run_greedy(int strategy,mt19937& rng){\n vector b=initial_board;vector> moves;\n while(true){\n int oc=count_oni(b);if(oc==0)return {moves,true};\n auto cands=get_candidates(b);\n if(cands.empty()){\n // Phase 2: batch for remaining from current state\n auto bm=batch_from_board(b);\n moves.insert(moves.end(),bm.begin(),bm.end());\n return {moves,count_oni(b)==0};\n }\n if(strategy==0)sort(cands.begin(),cands.end(),[](const MoveInfo&a,const MoveInfo&b){return a.ratio>b.ratio;});\n else if(strategy==1)sort(cands.begin(),cands.end(),[](const MoveInfo&a,const MoveInfo&b){return a.oni_removed>b.oni_removed||(a.oni_removed==b.oni_removed&&a.amountb.ratio);});\n else shuffle(cands.begin(),cands.end(),rng);\n auto[base_stuck,base_safety]=compute_safety(b);\n int best_t=-1;double best_score=-1e18;\n int cl=min(20,(int)cands.size());\n for(int t=0;tbest_score){best_score=score;best_t=t;}\n }\n if(best_t<0)return {moves,false};\n for(int k=0;k>N;initial_board.resize(N);\n for(int i=0;i>initial_board[i];\n mt19937 rng(42);vector> best_moves;int best_cost=1e9;\n auto start=chrono::high_resolution_clock::now();\n bool done=false;\n for(int s=0;s<4&&!done;s++)for(int t=0;t<300&&!done;t++){\n rng.seed(42+s*1000+t);auto[m,ok]=run_greedy(s,rng);\n if(ok&&(int)m.size()(chrono::high_resolution_clock::now()-start).count()>1800)done=true;\n }\n // Also try pure batch\n auto bm=batch_from_board(initial_board);if((int)bm.size()\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint N, L;\nint T[100];\nint a[100], b[100];\nint best_a[100], best_b[100];\nint best_error = INT_MAX;\nint t_global[100];\nint next_node[2][100];\n\nuint64_t rng_state = 1234567890123456789ULL;\nuint64_t rng64() {\n rng_state ^= rng_state >> 12;\n rng_state ^= rng_state << 25;\n rng_state ^= rng_state >> 27;\n return rng_state * 2685821657736338717ULL;\n}\n\nvoid update_next_node() {\n for (int i = 0; i < N; i++) {\n next_node[0][i] = a[i];\n next_node[1][i] = b[i];\n }\n}\n\nint simulate(int ti[]) {\n memset(ti, 0, sizeof(int) * N);\n int cur = 0;\n for (int w = 0; w < L; w++) {\n int c = ++ti[cur];\n cur = next_node[c & 1][cur];\n }\n int err = 0;\n for (int i = 0; i < N; i++) err += abs(ti[i] - T[i]);\n return err;\n}\n\nvoid try_init(int ai[], int bi[]) {\n memcpy(a, ai, sizeof(a));\n memcpy(b, bi, sizeof(b));\n update_next_node();\n int err = simulate(t_global);\n if (err < best_error) {\n best_error = err;\n memcpy(best_a, a, sizeof(a));\n memcpy(best_b, b, sizeof(b));\n }\n}\n\nvoid greedy_init(int ai[], int bi[], bool avoid_same) {\n int dem[100]; memcpy(dem, T, sizeof(T));\n int cnt[100] = {};\n bool a_ch[100] = {}, b_ch[100] = {};\n for(int i=0; i dem[best] || (dem[j] == dem[best] && T[j] > T[best])) best = j;\n }\n ai[cur] = best; a_ch[cur] = true;\n dem[best] -= (T[cur] + 1) / 2;\n }\n cur = ai[cur];\n } else {\n if (!b_ch[cur]) {\n int best = -1;\n for (int j = 0; j < N; j++) {\n if (j == cur) continue;\n if (avoid_same && a_ch[cur] && j == ai[cur]) continue;\n if (T[j] == 0 && dem[j] <= 0) continue;\n if (best == -1 || dem[j] > dem[best] || (dem[j] == dem[best] && T[j] > T[best])) best = j;\n }\n bi[cur] = best; b_ch[cur] = true;\n dem[best] -= T[cur] / 2;\n }\n cur = bi[cur];\n }\n }\n}\n\nvoid flow_sa(int ai[], int bi[]) {\n int flow_in[100] = {};\n for(int i=0; i> N >> L;\n for (int i = 0; i < N; i++) cin >> T[i];\n \n int ai[100], bi[100];\n \n for (int i = 0; i < N; i++) { ai[i] = (i+1)%N; bi[i] = (i+1)%N; }\n try_init(ai, bi);\n \n greedy_init(ai, bi, true);\n try_init(ai, bi);\n \n greedy_init(ai, bi, false);\n try_init(ai, bi);\n \n memcpy(ai, best_a, sizeof(ai));\n memcpy(bi, best_b, sizeof(bi));\n flow_sa(ai, bi);\n try_init(ai, bi);\n \n memcpy(a, best_a, sizeof(a));\n memcpy(b, best_b, sizeof(b));\n update_next_node();\n int error = simulate(t_global);\n best_error = error;\n \n int order[100];\n iota(order, order + N, 0);\n sort(order, order + N, [](int x, int y) { return T[x] < T[y]; });\n int rank_of[100];\n for (int i = 0; i < N; i++) rank_of[order[i]] = i;\n \n vector nodes_by_T[10001];\n for(int i=0; i 0) nodes_by_T[T[i]].push_back(i);\n \n double start_temp = max(500.0, (double)error / 20.0);\n auto start = chrono::high_resolution_clock::now();\n \n while(true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 1.85) break;\n \n double temp = start_temp * (1.0 - elapsed / 1.85);\n if (temp < 0.01) temp = 0.01;\n \n int old_a[100], old_b[100], old_t_global[100];\n memcpy(old_a, a, sizeof(a));\n memcpy(old_b, b, sizeof(b));\n memcpy(old_t_global, t_global, sizeof(t_global));\n \n int move_type = rng64() % 5;\n int i = -1, j = -1;\n \n if (move_type == 0) {\n i = rng64() % N;\n while(T[i] == 0) i = rng64() % N;\n swap(a[i], b[i]);\n } else if (move_type < 4) {\n i = rng64() % N;\n while(T[i] == 0) i = rng64() % N;\n \n if (nodes_by_T[T[i]].size() > 1) {\n j = nodes_by_T[T[i]][rng64() % nodes_by_T[T[i]].size()];\n while(j == i) j = nodes_by_T[T[i]][rng64() % nodes_by_T[T[i]].size()];\n } else {\n int delta_rank = (rng64() % 5) - 2;\n int new_rank = max(0, min(N - 1, rank_of[i] + delta_rank));\n j = order[new_rank];\n int attempts = 0;\n while(T[j] == 0 || j == i) {\n new_rank = (new_rank + 1) % N;\n j = order[new_rank];\n if (++attempts > N) break;\n }\n if (j == i || T[j] == 0) continue;\n }\n \n if (move_type == 1) swap(a[i], a[j]);\n else if (move_type == 2) swap(b[i], b[j]);\n else swap(a[i], b[j]);\n } else {\n i = rng64() % N;\n while(T[i] == 0) i = rng64() % N;\n bool is_a = rng64() & 1;\n int nv = rng64() % N;\n while(T[nv] == 0) nv = rng64() % N;\n if (is_a) a[i] = nv; else b[i] = nv;\n }\n \n update_next_node();\n int new_error = simulate(t_global);\n double delta = new_error - error;\n \n if (delta <= 0 || (double)(rng64() & 0xFFFF) / 65536.0 < exp(-delta / temp)) {\n error = new_error;\n if (error < best_error) {\n best_error = error;\n memcpy(best_a, a, sizeof(a));\n memcpy(best_b, b, sizeof(b));\n }\n } else {\n memcpy(a, old_a, sizeof(a));\n memcpy(b, old_b, sizeof(b));\n memcpy(t_global, old_t_global, sizeof(t_global));\n }\n }\n \n for (int i = 0; i < N; i++)\n cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nuint64_t xy2d(int n, int x, int y) {\n uint64_t d = 0;\n for (int s = n/2; s > 0; s /= 2) {\n int rx = (x & s) > 0;\n int ry = (y & s) > 0;\n d += (uint64_t)s * s * ((3 * rx) ^ ry);\n if (ry == 0) {\n if (rx == 1) { x = s-1 - x; y = s-1 - y; }\n swap(x, y);\n }\n }\n return d;\n}\n\nint N, M, Q, L, W;\ndouble cx[800], cy[800], ddist[800][800];\nint idist[800][800];\nint qcnt = 0;\n\nvector> query(vector& v) {\n if (qcnt >= Q || (int)v.size() < 2) return {};\n qcnt++;\n cout << \"? \" << v.size();\n for (int x : v) cout << \" \" << x;\n cout << endl;\n vector> res(v.size() - 1);\n for (auto& [a, b] : res) cin >> a >> b;\n return res;\n}\n\nint par[800], rnk[800];\nvoid init_dsu() { iota(par, par + N, 0); fill(rnk, rnk + N, 0); }\nint find(int x) { return par[x] == x ? x : par[x] = find(par[x]); }\nbool unite(int x, int y) {\n x = find(x); y = find(y);\n if (x == y) return false;\n if (rnk[x] < rnk[y]) swap(x, y);\n par[y] = x;\n if (rnk[x] == rnk[y]) rnk[x]++;\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n mt19937 rng(1337);\n \n cin >> N >> M >> Q >> L >> W;\n vector G(M);\n for (int& g : G) cin >> g;\n \n for (int i = 0; i < N; i++) {\n int a, b, c, d;\n cin >> a >> b >> c >> d;\n cx[i] = (a + b) / 2.0;\n cy[i] = (c + d) / 2.0;\n }\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n double dx = cx[i] - cx[j], dy = cy[i] - cy[j];\n ddist[i][j] = sqrt(dx*dx + dy*dy);\n idist[i][j] = (int)floor(sqrt(dx*dx + dy*dy));\n }\n \n vector ord(N);\n iota(ord.begin(), ord.end(), 0);\n sort(ord.begin(), ord.end(), [](int a, int b) {\n return xy2d(32768, (int)cx[a], (int)cy[a]) < xy2d(32768, (int)cx[b], (int)cy[b]);\n });\n \n vector cut_cost(N, 0);\n for (int j = 1; j < N; j++) {\n cut_cost[j] = idist[ord[j-1]][ord[j]];\n }\n \n vector p(M);\n iota(p.begin(), p.end(), 0);\n \n if (M <= 20) {\n vector dp(1 << M, -1);\n dp[0] = 0;\n for (int mask = 0; mask < (1 << M); mask++) {\n if (dp[mask] < 0) continue;\n int s = 0;\n for (int i = 0; i < M; i++) if (mask & (1 << i)) s += G[i];\n for (int i = 0; i < M; i++) {\n if (!(mask & (1 << i))) {\n int next_mask = mask | (1 << i);\n int next_s = s + G[i];\n int cost = dp[mask] + (next_s < N ? cut_cost[next_s] : 0);\n if (cost > dp[next_mask]) dp[next_mask] = cost;\n }\n }\n }\n int mask = (1 << M) - 1;\n for (int k = M - 1; k >= 0; k--) {\n int s = 0;\n for (int i = 0; i < M; i++) if (mask & (1 << i)) s += G[i];\n for (int i = 0; i < M; i++) {\n if (mask & (1 << i)) {\n int prev_mask = mask ^ (1 << i);\n int cost = dp[prev_mask] + (s < N ? cut_cost[s] : 0);\n if (cost == dp[mask]) {\n p[k] = i;\n mask = prev_mask;\n break;\n }\n }\n }\n }\n } else {\n sort(p.begin(), p.end(), [&](int a, int b) { return G[a] > G[b]; });\n vector prefix(M);\n int s = 0;\n for (int i = 0; i < M; i++) { s += G[p[i]]; prefix[i] = s; }\n \n if (M > 1) {\n for (int iter = 0; iter < 2500000; iter++) {\n int i = rng() % M;\n int len = (iter < 2000000) ? 1 : (rng() % 5 + 1);\n int j = min(i + len, M - 1);\n if (i == j) continue;\n \n long long old_cost = 0;\n for (int kk = i; kk < j; kk++) old_cost += cut_cost[prefix[kk]];\n \n swap(p[i], p[j]);\n int s_prev = (i == 0 ? 0 : prefix[i-1]);\n long long new_cost = 0;\n for (int kk = i; kk < j; kk++) {\n s_prev += G[p[kk]];\n new_cost += cut_cost[s_prev];\n }\n \n if (new_cost > old_cost) {\n s_prev = (i == 0 ? 0 : prefix[i-1]);\n for (int kk = i; kk < j; kk++) {\n s_prev += G[p[kk]];\n prefix[kk] = s_prev;\n }\n } else {\n swap(p[i], p[j]);\n }\n }\n }\n }\n \n vector> grp(M);\n int curr = 0;\n for (int k = 0; k < M; k++) {\n int group_idx = p[k];\n int sz = G[group_idx];\n for (int j = 0; j < sz; j++) {\n grp[group_idx].push_back(ord[curr++]);\n }\n }\n \n vector proc_order(M);\n iota(proc_order.begin(), proc_order.end(), 0);\n sort(proc_order.begin(), proc_order.end(), [&](int a, int b) {\n if (G[a] <= L && G[b] > L) return true;\n if (G[a] > L && G[b] <= L) return false;\n if (G[a] <= L && G[b] <= L) return G[a] < G[b];\n return G[a] > G[b];\n });\n \n vector>> ans(M);\n \n for (int k : proc_order) {\n int G_size = grp[k].size();\n if (G_size <= 1) continue;\n \n init_dsu();\n vector> mst;\n \n vector> est_edges;\n for (int i = 0; i < G_size; i++)\n for (int j = i + 1; j < G_size; j++) {\n int u = grp[k][i], v = grp[k][j];\n est_edges.emplace_back(idist[u][v], min(u, v), max(u, v));\n }\n sort(est_edges.begin(), est_edges.end());\n \n vector par_l(G_size);\n iota(par_l.begin(), par_l.end(), 0);\n auto find_l = [&](auto& self, int x) -> int {\n return par_l[x] == x ? x : par_l[x] = self(self, par_l[x]);\n };\n \n vector> adj_local(G_size);\n map local_id;\n for (int i = 0; i < G_size; ++i) local_id[grp[k][i]] = i;\n \n for (auto& [d, a, b] : est_edges) {\n int la = local_id[a], lb = local_id[b];\n int ra = find_l(find_l, la), rb = find_l(find_l, lb);\n if (ra != rb) {\n par_l[ra] = rb;\n adj_local[la].push_back(lb);\n adj_local[lb].push_back(la);\n }\n }\n \n if (G_size <= L) {\n if (qcnt < Q) mst = query(grp[k]);\n } else {\n int root = 0;\n vector parent_local(G_size, -1);\n vector order;\n queue q_bfs;\n q_bfs.push(root);\n parent_local[root] = root;\n while(!q_bfs.empty()) {\n int u = q_bfs.front(); q_bfs.pop();\n order.push_back(u);\n for(int v : adj_local[u]) {\n if(v != parent_local[u]) {\n parent_local[v] = u;\n q_bfs.push(v);\n }\n }\n }\n \n vector> chunks_local_ids;\n int target_size = max(2, L / 2);\n \n function(int)> decomp = [&](int u) -> vector {\n vector nodes_without_u;\n for (int v : adj_local[u]) {\n if (v == parent_local[u]) continue;\n auto sub_nodes = decomp(v);\n for (int x : sub_nodes) nodes_without_u.push_back(x);\n }\n \n if ((int)nodes_without_u.size() >= target_size) {\n int ptr = 0;\n while (ptr + target_size <= (int)nodes_without_u.size()) {\n vector chunk_local_ids;\n for (int i = 0; i < target_size; ++i) {\n chunk_local_ids.push_back(nodes_without_u[ptr + i]);\n }\n chunk_local_ids.push_back(u);\n chunks_local_ids.push_back(chunk_local_ids);\n ptr += target_size;\n }\n \n vector remaining;\n for (int i = ptr; i < (int)nodes_without_u.size(); ++i) {\n remaining.push_back(nodes_without_u[i]);\n }\n remaining.push_back(u);\n return remaining;\n } else {\n nodes_without_u.push_back(u);\n return nodes_without_u;\n }\n };\n \n auto remaining = decomp(root);\n if ((int)remaining.size() > 1) {\n chunks_local_ids.push_back(remaining);\n }\n \n vector> chunks;\n for (auto& chunk_local_ids : chunks_local_ids) {\n vector chunk;\n for (int x : chunk_local_ids) chunk.push_back(grp[k][x]);\n \n vector in_chunk_set(N, false);\n for (int x : chunk) in_chunk_set[x] = true;\n \n vector min_dist_to_chunk(N, 1e18);\n for (int c : grp[k]) {\n if (in_chunk_set[c]) continue;\n for (int x : chunk) min_dist_to_chunk[c] = min(min_dist_to_chunk[c], ddist[c][x]);\n }\n \n priority_queue, vector>, greater>> pq_crossing;\n for (int u_local : chunk_local_ids) {\n for (int v_local : adj_local[u_local]) {\n int u = grp[k][u_local], v = grp[k][v_local];\n if (!in_chunk_set[v]) {\n pq_crossing.push({idist[u][v], v});\n }\n }\n }\n \n while ((int)chunk.size() < L) {\n bool added = false;\n while (!pq_crossing.empty()) {\n auto [d, v] = pq_crossing.top();\n pq_crossing.pop();\n if (!in_chunk_set[v]) {\n chunk.push_back(v);\n in_chunk_set[v] = true;\n for (int w_local : adj_local[local_id[v]]) {\n int w = grp[k][w_local];\n if (!in_chunk_set[w]) {\n pq_crossing.push({idist[v][w], w});\n }\n }\n added = true;\n break;\n }\n }\n \n if (!added) {\n double min_d = 1e18; int best = -1;\n for (int c : grp[k]) {\n if (in_chunk_set[c]) continue;\n if (min_dist_to_chunk[c] < min_d) {\n min_d = min_dist_to_chunk[c];\n best = c;\n }\n }\n if (best == -1) break;\n chunk.push_back(best);\n in_chunk_set[best] = true;\n for (int c : grp[k]) {\n if (!in_chunk_set[c]) {\n min_dist_to_chunk[c] = min(min_dist_to_chunk[c], ddist[c][best]);\n }\n }\n }\n }\n chunks.push_back(chunk);\n }\n \n for (auto& chunk : chunks) {\n if (qcnt >= Q) break;\n auto edges = query(chunk);\n for (auto& [a, b] : edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n }\n }\n }\n }\n \n if (mst.size() < (size_t)G_size - 1) {\n for (auto& [d, a, b] : est_edges) {\n if (unite(a, b)) {\n mst.emplace_back(a, b);\n }\n if (mst.size() == (size_t)G_size - 1) break;\n }\n }\n ans[k] = mst;\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int i = 0; i < (int)grp[k].size(); i++) cout << grp[k][i] << \" \\n\"[i==(int)grp[k].size()-1];\n for (auto& [a, b] : ans[k]) cout << min(a, b) << \" \" << max(a, b) << \"\\n\";\n }\n return 0;\n}","ahc046":"#include \n#include \n#include \n#include \n#include \n#include \n#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n int N, M;\n cin >> N >> M;\n vector> targets(M);\n for (int i = 0; i < M; i++) cin >> targets[i].first >> targets[i].second;\n \n bool block_grid[20][20] = {};\n int cur_r = targets[0].first, cur_c = targets[0].second;\n vector> actions;\n \n const int DR[] = {-1, 1, 0, 0};\n const int DC[] = {0, 0, -1, 1};\n const char DIR_CHAR[] = {'U', 'D', 'L', 'R'};\n int dir_map[256];\n dir_map['U'] = 0; dir_map['D'] = 1; dir_map['L'] = 2; dir_map['R'] = 3;\n \n bool is_target[20][20] = {};\n for (auto& [r, c] : targets) is_target[r][c] = true;\n \n int vis0[20][20];\n int dist0[20][20];\n int cur_token0 = 0;\n \n auto bfs_dist_0_flip = [&](int sr, int sc, int tr, int tc) -> int {\n if (sr == tr && sc == tc) return 0;\n cur_token0++;\n pair q_arr[400];\n int q_sz = 0;\n q_arr[q_sz++] = {sr, sc}; \n vis0[sr][sc] = cur_token0; \n dist0[sr][sc] = 0;\n for (int i = 0; i < q_sz; ++i) {\n auto [r, c] = q_arr[i];\n int d = dist0[r][c];\n for (int dir = 0; dir < 4; ++dir) {\n int nr = r + DR[dir], nc = c + DC[dir];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !block_grid[nr][nc] && vis0[nr][nc] != cur_token0) {\n vis0[nr][nc] = cur_token0; \n dist0[nr][nc] = d + 1;\n if (nr == tr && nc == tc) return d + 1; \n q_arr[q_sz++] = {nr, nc};\n }\n int snr = r, snc = c;\n while (true) { \n int nnr = snr + DR[dir], nnc = snc + DC[dir]; \n if (nnr < 0 || nnr >= N || nnc < 0 || nnc >= N || block_grid[nnr][nnc]) break; \n snr = nnr; snc = nnc; \n }\n if (vis0[snr][snc] != cur_token0) {\n vis0[snr][snc] = cur_token0; \n dist0[snr][snc] = d + 1;\n if (snr == tr && snc == tc) return d + 1; \n q_arr[q_sz++] = {snr, snc};\n }\n }\n }\n return 1e9;\n };\n\n auto bfs_0_flip = [&](int sr, int sc, int tr, int tc) -> vector> {\n if (sr == tr && sc == tc) return {};\n int dist[20][20]; memset(dist, -1, sizeof(dist));\n int pr[20][20], pc[20][20]; memset(pr, -1, sizeof(pr)); memset(pc, -1, sizeof(pc));\n char pa[20][20], pd[20][20]; memset(pa, 0, sizeof(pa)); memset(pd, 0, sizeof(pd));\n \n pair q_arr[400];\n int q_sz = 0;\n q_arr[q_sz++] = {sr, sc}; dist[sr][sc] = 0;\n \n for (int i = 0; i < q_sz; ++i) {\n auto [r, c] = q_arr[i];\n for (int d = 0; d < 4; d++) {\n int nr = r + DR[d], nc = c + DC[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !block_grid[nr][nc] && dist[nr][nc] == -1) {\n dist[nr][nc] = dist[r][c] + 1;\n pr[nr][nc] = r; pc[nr][nc] = c; pa[nr][nc] = 0; pd[nr][nc] = d;\n if (nr == tr && nc == tc) goto found;\n q_arr[q_sz++] = {nr, nc};\n }\n int snr = r, snc = c;\n while (true) {\n int nnr = snr + DR[d], nnc = snc + DC[d];\n if (nnr < 0 || nnr >= N || nnc < 0 || nnc >= N || block_grid[nnr][nnc]) break;\n snr = nnr; snc = nnc;\n }\n if (dist[snr][snc] == -1) {\n dist[snr][snc] = dist[r][c] + 1;\n pr[snr][snc] = r; pc[snr][snc] = c; pa[snr][snc] = 1; pd[snr][snc] = d;\n if (snr == tr && snc == tc) goto found;\n q_arr[q_sz++] = {snr, snc};\n }\n }\n }\n return {};\n found:\n vector> path;\n int cr = tr, cc = tc;\n while (cr != sr || cc != sc) {\n path.push_back({pa[cr][cc] ? 'S' : 'M', DIR_CHAR[pd[cr][cc]]});\n int rr = pr[cr][cc], rc = pc[cr][cc]; cr = rr; cc = rc;\n }\n reverse(path.begin(), path.end());\n return path;\n };\n \n auto is_connected = [&]() -> bool {\n int sr = -1, sc = -1, fc = 0;\n for (int r = 0; r < N; r++) for (int c = 0; c < N; c++) if (!block_grid[r][c]) { fc++; if (sr < 0) { sr = r; sc = c; } }\n if (fc == 0) return true;\n bool vis_c[20][20] = {}; \n pair q_arr[400];\n int q_sz = 0;\n q_arr[q_sz++] = {sr, sc}; vis_c[sr][sc] = true; int cnt = 1;\n for (int i = 0; i < q_sz; ++i) {\n auto [r, c] = q_arr[i];\n for (int d = 0; d < 4; d++) { \n int nr = r + DR[d], nc = c + DC[d]; \n if (nr >= 0 && nr < N && nc >= 0 && nc < N && !block_grid[nr][nc] && !vis_c[nr][nc]) { \n vis_c[nr][nc] = true; cnt++; q_arr[q_sz++] = {nr, nc}; \n } \n }\n }\n return cnt == fc;\n };\n \n auto can_place = [&](int br, int bc) -> bool {\n if (br < 0 || br >= N || bc < 0 || bc >= N || block_grid[br][bc] || is_target[br][bc]) return false;\n block_grid[br][bc] = true; bool ok = is_connected(); block_grid[br][bc] = false; return ok;\n };\n \n auto place_blocks = [&](int t_start) {\n is_target[cur_r][cur_c] = false;\n for (int iter = 0; iter < 4; ++iter) {\n int best_d = -1, best_benefit = -1e9;\n for (int d = 0; d < 4; d++) {\n int br = cur_r + DR[d], bc = cur_c + DC[d];\n if (can_place(br, bc)) {\n int total_benefit = 0; int cr = cur_r, cc = cur_c;\n for (int k = t_start; k < M; ++k) {\n int orig = bfs_dist_0_flip(cr, cc, targets[k].first, targets[k].second);\n block_grid[br][bc] = true; \n int new_d = bfs_dist_0_flip(cr, cc, targets[k].first, targets[k].second); \n block_grid[br][bc] = false;\n total_benefit += orig - new_d; \n cr = targets[k].first; cc = targets[k].second;\n }\n if (total_benefit > best_benefit) {\n best_benefit = total_benefit;\n best_d = d;\n }\n }\n }\n if (best_d != -1 && best_benefit >= 2) { \n int br = cur_r + DR[best_d], bc = cur_c + DC[best_d]; \n block_grid[br][bc] = true; \n actions.push_back({'A', DIR_CHAR[best_d]}); \n } else break;\n }\n };\n \n place_blocks(1);\n \n for (int t = 1; t < M; t++) {\n int tr = targets[t].first, tc = targets[t].second;\n auto path = bfs_0_flip(cur_r, cur_c, tr, tc);\n for (auto& [act, dir] : path) {\n actions.push_back({act, dir});\n if (act == 'M') {\n int d = dir_map[dir];\n cur_r += DR[d]; cur_c += DC[d];\n } else {\n int d = dir_map[dir];\n int snr = cur_r, snc = cur_c;\n while (true) {\n int nnr = snr + DR[d], nnc = snc + DC[d];\n if (nnr < 0 || nnr >= N || nnc < 0 || nnc >= N || block_grid[nnr][nnc]) break;\n snr = nnr; snc = nnc;\n }\n cur_r = snr; cur_c = snc;\n }\n }\n place_blocks(t + 1);\n }\n \n for (auto& [a, d] : actions) cout << a << \" \" << d << \"\\n\";\n return 0;\n}"}}}