// Inspired by tetra4's solution // - https://yukicoder.me/submissions/1149387 #pragma GCC optimize("O3,unroll-loops") #include using namespace std; constexpr int N = 47, R = 1000, M = 400, K = 25; constexpr int INF = 1e9; constexpr int MAX_TIME_SLOTS = 182; constexpr int MAX_FLIGHTS = 2500; struct Flight { int u, s, v, t; }; // スロット(0~180)を "HH:MM" 形式の文字列に変換 string to_time_str(int t) { int h = 6 + t / 12; int m = (t % 12) * 5; char buf[6]; snprintf(buf, sizeof(buf), "%02d:%02d", h, m); return string(buf); } struct Input { array x, y, w; array a, s, b, t; bool valid_dist[N][N]{}; long long weight[N][N]{}; long long total_W = 0; Input() { int _; cin >> _ >> _; for (int i = 0; i < N; ++i) cin >> x[i] >> y[i] >> w[i]; cin >> _; string s_str, t_str; for (int i = 0; i < M; ++i) { cin >> a[i] >> s_str >> b[i] >> t_str; --a[i], --b[i]; s[i] = (stoi(s_str.substr(0, 2)) - 6) * 12 + stoi(s_str.substr(3, 2)) / 5; t[i] = (stoi(t_str.substr(0, 2)) - 6) * 12 + stoi(t_str.substr(3, 2)) / 5; } for (int i = 0; i < N; ++i) { for (int j = 0; j < N; ++j) { if (i == j) continue; long long dx = x[i] - x[j]; long long dy = y[i] - y[j]; if (dx * dx + dy * dy >= (R * R) / 16) { valid_dist[i][j] = true; weight[i][j] = (long long)w[i] * w[j]; total_W += weight[i][j] * 21; } } } } int get_duration(int u, int v) const { double dx = x[u] - x[v]; double dy = y[u] - y[v]; double d = sqrt(dx * dx + dy * dy); double minutes = 60.0 * d / 800.0 + 40.0; return (int)ceil(minutes / 5.0 - 1e-9); } }; // 計算用のワークスペース (生配列で高速化) struct ComputeSciWorkspace { int head[MAX_TIME_SLOTS + 1]; int nxt[MAX_FLIGHTS]; int f_u[MAX_FLIGHTS]; int f_v[MAX_FLIGHTS]; int f_t[MAX_FLIGHTS]; int min_arr[MAX_TIME_SLOTS + 1][N]; }; struct MarginalGainWorkspace { int current_s_ci[N][N][21]; long long edge_gain[N][N][MAX_TIME_SLOTS + 1]; long long dp[N][MAX_TIME_SLOTS + 1]; int nxt_v[N][MAX_TIME_SLOTS + 1]; int dur[N][N]; }; void compute_s_ci(const Input& in, const vector& flights, int s_ci[N][N][21], ComputeSciWorkspace& ws) { for (int u = 0; u < N; ++u) { for (int dst = 0; dst < N; ++dst) { for (int t = 0; t < 21; ++t) { s_ci[u][dst][t] = -INF; } } } memset(ws.head, -1, sizeof(ws.head)); int f_sz = flights.size(); for (int i = 0; i < f_sz; ++i) { int s = flights[i].s; if (s >= 0 && s <= 180) { ws.nxt[i] = ws.head[s]; ws.head[s] = i; ws.f_u[i] = flights[i].u; ws.f_v[i] = flights[i].v; ws.f_t[i] = flights[i].t; } } for (int dst = 0; dst < N; ++dst) { for (int t = 0; t <= 180; ++t) { for (int u = 0; u < N; ++u) ws.min_arr[t][u] = INF; ws.min_arr[t][dst] = t; } for (int t = 180; t >= 0; --t) { if (t + 1 <= 180) { memcpy(ws.min_arr[t], ws.min_arr[t + 1], sizeof(int) * N); ws.min_arr[t][dst] = t; } for (int e = ws.head[t]; e != -1; e = ws.nxt[e]) { int u = ws.f_u[e]; int v = ws.f_v[e]; int arr_time = ws.f_t[e]; if (arr_time <= 180) { if (ws.min_arr[arr_time][v] < ws.min_arr[t][u]) { ws.min_arr[t][u] = ws.min_arr[arr_time][v]; } } } } for (int u = 0; u < N; ++u) { if (u == dst || !in.valid_dist[u][dst]) continue; int t = 180; for (int T_idx = 20; T_idx >= 0; --T_idx) { int T_target = 60 + T_idx * 6; t = min(t, T_target); while (t >= 0 && ws.min_arr[t][u] > T_target) { t--; } if (t >= 0) { s_ci[u][dst][T_idx] = t; } else { break; } } } } } struct RivalSchedule { int s_sq[N][N][21]; RivalSchedule(const Input& in, ComputeSciWorkspace& ws) { vector r_flights; r_flights.reserve(M); for (int i = 0; i < M; ++i) r_flights.push_back({in.a[i], in.s[i], in.b[i], in.t[i]}); compute_s_ci(in, r_flights, s_sq, ws); } }; // ★ ビームサーチ用の状態構造体 struct State { vector> current_paths; vector all_flights; long long score; bool operator<(const State& other) const { return score > other.score; // 降順ソート用 } }; // ★ ビームサーチ版のアルゴリズム vector> solve_beam_search(const Input& in, const RivalSchedule& rival, ComputeSciWorkspace& c_ws, MarginalGainWorkspace& mg_ws) { const int BEAM_WIDTH = 3; const int BRANCHES = 15; for (int u = 0; u < N; ++u) { for (int v = 0; v < N; ++v) { mg_ws.dur[u][v] = (u != v) ? in.get_duration(u, v) : 0; } } vector beam; State init_state; init_state.score = 0; beam.push_back(init_state); for (int k = 0; k < K; ++k) { vector next_beam; for (const auto& state : beam) { // 現在の状態に対する s_ci を計算 compute_s_ci(in, state.all_flights, mg_ws.current_s_ci, c_ws); memset(mg_ws.edge_gain, 0, sizeof(mg_ws.edge_gain)); // 高速な枝刈り付き限界利益計算 for (int u = 0; u < N; ++u) { for (int dst = 0; dst < N; ++dst) { if (!in.valid_dist[u][dst]) continue; long long w = in.weight[u][dst]; for (int T_idx = 0; T_idx < 21; ++T_idx) { int s_sq_val = rival.s_sq[u][dst][T_idx]; int s_ci_val = mg_ws.current_s_ci[u][dst][T_idx]; if (s_ci_val > s_sq_val) continue; int min_s = max(0, s_sq_val + 1); int T_target = 60 + T_idx * 6; for (int v = 0; v < N; ++v) { if (u == v) continue; int max_t = (v == dst) ? T_target : mg_ws.current_s_ci[v][dst][T_idx]; if (max_t < 0) continue; int max_s = min(180 - mg_ws.dur[u][v], max_t - mg_ws.dur[u][v]); if (min_s <= max_s) { mg_ws.edge_gain[u][v][min_s] += w; if (max_s + 1 <= 180) { mg_ws.edge_gain[u][v][max_s + 1] -= w; } } } } } } // いもす法展開 for (int u = 0; u < N; ++u) { for (int v = 0; v < N; ++v) { if (u == v) continue; long long current_val = 0; long long* gain_uv = mg_ws.edge_gain[u][v]; for (int s = 0; s <= 180; ++s) { current_val += gain_uv[s]; gain_uv[s] = current_val; } } } memset(mg_ws.dp, 0, sizeof(mg_ws.dp)); memset(mg_ws.nxt_v, -1, sizeof(mg_ws.nxt_v)); for (int t = 180; t >= 0; --t) { for (int u = 0; u < N; ++u) { if (t + 1 <= 180) { mg_ws.dp[u][t] = mg_ws.dp[u][t + 1]; mg_ws.nxt_v[u][t] = -1; } for (int v = 0; v < N; ++v) { if (u == v) continue; int t_next = t + mg_ws.dur[u][v]; if (t_next <= 180) { long long gain = mg_ws.edge_gain[u][v][t]; if (gain + mg_ws.dp[v][t_next] > mg_ws.dp[u][t]) { mg_ws.dp[u][t] = gain + mg_ws.dp[v][t_next]; mg_ws.nxt_v[u][t] = v; } } } } } // ★ ビームサーチの分岐: 利益が高い順に開始都市をソート vector> start_cands; for (int u = 0; u < N; ++u) { start_cands.emplace_back(mg_ws.dp[u][0], u); } sort(start_cands.rbegin(), start_cands.rend()); // 上位 BRANCHES 個からパスを生成 for (int i = 0; i < min(N, BRANCHES); ++i) { int start_u = start_cands[i].second; vector path; int curr_u = start_u, curr_t = 0; while (curr_t <= 180) { int next_city = mg_ws.nxt_v[curr_u][curr_t]; if (next_city != -1) { int d = mg_ws.dur[curr_u][next_city]; path.push_back({curr_u, curr_t, next_city, curr_t + d}); curr_u = next_city; curr_t += d; } else { curr_t += 1; } } State nstate = state; nstate.current_paths.push_back(path); for (const auto& f : path) { nstate.all_flights.push_back(f); } // 分岐先のスコアを正確に評価 compute_s_ci(in, nstate.all_flights, mg_ws.current_s_ci, c_ws); long long v_ci = 0; for (int u = 0; u < N; ++u) { for (int dst = 0; dst < N; ++dst) { if (!in.valid_dist[u][dst]) continue; long long w = in.weight[u][dst]; for (int T_idx = 0; T_idx < 21; ++T_idx) { if (mg_ws.current_s_ci[u][dst][T_idx] > rival.s_sq[u][dst][T_idx]) { v_ci += w; } } } } nstate.score = (long long)(1000000.0 * (double)v_ci / in.total_W); next_beam.push_back(nstate); } } // ビームをスコア降順でソート sort(next_beam.begin(), next_beam.end()); beam.clear(); for (const auto& s : next_beam) { // スコアが全く同じ(実質的に同じルート)ものは除外して多様性を確保 if (beam.empty() || beam.back().score != s.score) { beam.push_back(s); if (beam.size() == BEAM_WIDTH) break; } } } return beam[0].current_paths; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); Input in; auto c_ws = make_unique(); auto mg_ws = make_unique(); RivalSchedule rival(in, *c_ws); auto circle_flights = solve_beam_search(in, rival, *c_ws, *mg_ws); for (int k = 0; k < K; ++k) { cout << circle_flights[k].size() << "\n"; for (const auto& f : circle_flights[k]) { cout << f.u + 1 << " " << to_time_str(f.s) << " " << f.v + 1 << " " << to_time_str(f.t) << "\n"; } } return 0; }