#include using namespace std; const int N = 47; const int MF = 400; const int K = 25; const int TMIN = 360; const int TMAX = 1260; const int NT = 21; const int NINF = -1000000; int cx[N], cy[N], cw[N]; int sqa_[MF], sqb_[MF], sqs_[MF], sqt_[MF]; int ft[N][N]; bool vp[N][N]; int tgt[NT]; int ssq[N][N][NT]; mt19937 rng(42); int parse_time(const char* s) { return (s[0]-'0')*600 + (s[1]-'0')*60 + (s[3]-'0')*10 + (s[4]-'0'); } string fmt(int t) { char b[6]; b[0]='0'+t/600; t%=600; b[1]='0'+t/60; t%=60; b[2]=':'; b[3]='0'+t/10; b[4]='0'+t%10; b[5]=0; return string(b); } int cft(double d) { return ((int)ceil((60.0*d/800.0+40.0)/5.0))*5; } void compute_sq() { struct E { int arr, dep, from; }; vector rev[N]; for (int i = 0; i < MF; i++) rev[sqb_[i]].push_back({sqt_[i], sqs_[i], sqa_[i]}); for (int i = 0; i < N; i++) sort(rev[i].begin(), rev[i].end(), [](auto& a, auto& b){ return a.arr > b.arr; }); for (int ti = 0; ti < NT; ti++) { int T = tgt[ti]; for (int j = 0; j < N; j++) { int best[N]; fill(best, best+N, NINF); best[j] = T; priority_queue> pq; pq.push({T, j}); while (!pq.empty()) { auto [at, c] = pq.top(); pq.pop(); if (at < best[c]) continue; for (auto& e : rev[c]) { if (e.arr > at) continue; if (e.dep > best[e.from]) { best[e.from] = e.dep; pq.push({e.dep, e.from}); } } } for (int i = 0; i < N; i++) ssq[i][j][ti] = best[i]; } } } struct Flight { int from, to, dep, arr; }; struct Plane { vector fs; }; vector build(const vector& cities, int start) { vector fs; int ct = start; for (int i = 0; i+1 < (int)cities.size(); i++) { int a = cities[i], b = cities[i+1]; if (a == b) continue; int d = ((ct+4)/5)*5; if (d < TMIN) d = TMIN; int ar = d + ft[a][b]; if (ar > TMAX) break; fs.push_back({a, b, d, ar}); ct = ar; } return fs; } bool valid(const Plane& p) { for (int j = 0; j < (int)p.fs.size(); j++) { auto& f = p.fs[j]; if (f.from == f.to || f.dep < TMIN || f.arr > TMAX) return false; if (f.dep%5 || f.arr%5) return false; if (f.arr - f.dep != ft[f.from][f.to]) return false; if (j > 0 && (p.fs[j-1].to != f.from || p.fs[j-1].arr > f.dep)) return false; } return true; } // ========================================================= // BF-based evaluation // ========================================================= struct CF { int from, to, dep, arr; }; CF sorted_flights[500]; int nf; void collect_sorted(const vector& planes) { nf = 0; for (auto& p : planes) for (auto& f : p.fs) sorted_flights[nf++] = {f.from, f.to, f.dep, f.arr}; sort(sorted_flights, sorted_flights+nf, [](auto& a, auto& b){ return a.arr > b.arr; }); } int best_ci[NT][N][N]; long long spp[NT][N]; long long score_for(int j, int ti, const int* best) { long long s = 0; for (int i = 0; i < N; i++) if (vp[i][j] && best[i] > ssq[i][j][ti]) s += (long long)cw[i]*cw[j]; return s; } void bf_solve(int j, int ti, int* best_out) { fill(best_out, best_out+N, NINF); best_out[j] = tgt[ti]; for (int round = 0; round < 8; round++) { bool changed = false; for (int fi = 0; fi < nf; fi++) { auto& f = sorted_flights[fi]; if (f.arr <= best_out[f.to] && f.dep > best_out[f.from]) { best_out[f.from] = f.dep; changed = true; } } if (!changed) break; } } long long eval_full(const vector& planes) { collect_sorted(planes); long long total = 0; for (int ti = 0; ti < NT; ti++) { for (int j = 0; j < N; j++) { bf_solve(j, ti, best_ci[ti][j]); spp[ti][j] = score_for(j, ti, best_ci[ti][j]); total += spp[ti][j]; } } return total; } struct Change { int ti, j; int old_best[N]; long long old_spp; }; Change changes[NT*N]; int nchanges; long long eval_incr(const vector& planes, long long old_score) { collect_sorted(planes); long long total = old_score; nchanges = 0; int new_best[N]; for (int ti = 0; ti < NT; ti++) { for (int j = 0; j < N; j++) { bf_solve(j, ti, new_best); if (memcmp(new_best, best_ci[ti][j], sizeof(int)*N) == 0) continue; Change& ch = changes[nchanges++]; ch.ti = ti; ch.j = j; memcpy(ch.old_best, best_ci[ti][j], sizeof(int)*N); ch.old_spp = spp[ti][j]; long long new_s = score_for(j, ti, new_best); total += new_s - spp[ti][j]; spp[ti][j] = new_s; memcpy(best_ci[ti][j], new_best, sizeof(int)*N); } } return total; } // Partial eval for specific time slots only long long eval_incr_partial(const vector& planes, long long old_score, const int* ti_list, int ti_cnt) { collect_sorted(planes); long long total = old_score; nchanges = 0; int new_best[N]; for (int k = 0; k < ti_cnt; k++) { int ti = ti_list[k]; for (int j = 0; j < N; j++) { bf_solve(j, ti, new_best); if (memcmp(new_best, best_ci[ti][j], sizeof(int)*N) == 0) continue; Change& ch = changes[nchanges++]; ch.ti = ti; ch.j = j; memcpy(ch.old_best, best_ci[ti][j], sizeof(int)*N); ch.old_spp = spp[ti][j]; long long new_s = score_for(j, ti, new_best); total += new_s - spp[ti][j]; spp[ti][j] = new_s; memcpy(best_ci[ti][j], new_best, sizeof(int)*N); } } return total; } void rollback() { for (int i = 0; i < nchanges; i++) { auto& ch = changes[i]; memcpy(best_ci[ch.ti][ch.j], ch.old_best, sizeof(int)*N); spp[ch.ti][ch.j] = ch.old_spp; } } // ========================================================= // Greedy initial solution: backward construction // // Strategy: For each plane, build schedule from back to front. // 1. Pick a "final destination" (high-population city) // 2. Set deadline = TMAX (21:00) // 3. Repeatedly prepend flights: // - For current position (city c, must depart by time t), // pick the source city a that maximizes score contribution // of the flight a->c arriving at or before t // - Update c = a, t = dep time of that flight // - Stop when we reach TMIN // ========================================================= // Quick heuristic: weight of a direct flight a->b arriving at arr // = sum over valid (i, b, ti) where arr <= tgt[ti] and dep > ssq[i][b][ti] // of w_i * w_b // But for greedy construction, we simplify: value of flight a->b = // sum over ti where arr <= tgt[ti] of (w_a * w_b if dep > ssq[a][b][ti]) // plus general "connectivity value" for transfer potential long long flight_value(int a, int b, int dep, int arr) { if (a == b || !vp[a][b]) return 0; long long val = 0; // Direct value: does this flight beat square for (a->b, ti)? for (int ti = 0; ti < NT; ti++) { if (arr <= tgt[ti] && dep > ssq[a][b][ti]) { val += (long long)cw[a] * cw[b]; } } // Transfer value: this flight brings passengers to b // Other flights from b can then continue - approximate value // by connectivity bonus weighted by city population val += (long long)cw[a] * cw[b] / 10; // small bonus for connectivity return val; } // Backward greedy construction: build flights from back to front // Each plane gets a hub. Schedule is built as: // ... -> spoke -> hub -> spoke -> hub -> final_dest // where flights are prepended, ensuring timing constraints. void greedy_init(vector& planes) { // Hub assignments for 25 planes (same distribution as original) // 8 planes hub=0, 6 planes hub=1, 5 planes hub=2, 6 planes hub=0 (extended) int hub_assign[K]; for (int i = 0; i < 8; i++) hub_assign[i] = 0; for (int i = 8; i < 14; i++) hub_assign[i] = 1; for (int i = 14; i < 19; i++) hub_assign[i] = 2; for (int i = 19; i < 25; i++) hub_assign[i] = 0; // For spoke selection, rank cities by value relative to each hub // value(hub, spoke) = w_hub * w_spoke * (number of ti where direct flight beats sq) struct SpokeVal { int city; long long val; }; for (int p = 0; p < K; p++) { int hub = hub_assign[p]; // Compute spoke values for this hub vector spokes; for (int s = 0; s < N; s++) { if (s == hub || !vp[hub][s]) continue; long long val = 0; // How valuable is the hub<->spoke route? int fwd_time = ft[hub][s]; int rev_time = ft[s][hub]; for (int ti = 0; ti < NT; ti++) { // hub -> spoke flight: dep, arr=dep+fwd_time // Check multiple possible arrival times for (int arr = tgt[ti]; arr >= TMIN + fwd_time; arr -= 30) { int dep = arr - fwd_time; if (dep >= TMIN && dep > ssq[hub][s][ti]) { val += (long long)cw[hub] * cw[s]; break; } } // spoke -> hub flight for (int arr = tgt[ti]; arr >= TMIN + rev_time; arr -= 30) { int dep = arr - rev_time; if (dep >= TMIN && dep > ssq[s][hub][ti]) { val += (long long)cw[s] * cw[hub]; break; } } } spokes.push_back({s, val}); } sort(spokes.begin(), spokes.end(), [](auto& a, auto& b){ return a.val > b.val; }); // Pick spoke for this plane (distribute among top spokes) int spoke = spokes[p % min((int)spokes.size(), 15)].city; // Build backward: hub <-> spoke shuttle from TMAX vector fs; int cur_city = hub; // end at hub (for transfer connectivity) int cur_deadline = TMAX; // Stagger start: offset the "end time" slightly per plane cur_deadline -= (p % 5) * 5; for (int step = 0; step < 20; step++) { int next_city = (cur_city == hub) ? spoke : hub; int flight_time = ft[next_city][cur_city]; int arr = (cur_deadline / 5) * 5; if (arr > TMAX) arr = TMAX; int dep = arr - flight_time; if (dep < TMIN) break; // Ensure 5-min alignment dep = (dep / 5) * 5; arr = dep + flight_time; if (arr > cur_deadline || arr > TMAX) break; fs.push_back({next_city, cur_city, dep, arr}); cur_city = next_city; cur_deadline = dep; } reverse(fs.begin(), fs.end()); planes[p].fs = fs; } } // ========================================================= // Phase-based SA evaluation // ========================================================= int phase_ti[3][NT]; int phase_nt[3]; double phase_scale[3]; void init_phases() { // Phase 0: every 3rd slot (7 slots) phase_nt[0] = 0; for (int i = 0; i < NT; i += 3) phase_ti[0][phase_nt[0]++] = i; phase_scale[0] = (double)NT / phase_nt[0]; // Phase 1: every 2nd slot (11 slots) phase_nt[1] = 0; for (int i = 0; i < NT; i += 2) phase_ti[1][phase_nt[1]++] = i; phase_scale[1] = (double)NT / phase_nt[1]; // Phase 2: all slots (21 slots) phase_nt[2] = NT; for (int i = 0; i < NT; i++) phase_ti[2][i] = i; phase_scale[2] = 1.0; } int main() { auto t0 = chrono::steady_clock::now(); auto el = [&]() { return chrono::duration(chrono::steady_clock::now()-t0).count(); }; int n, r; scanf("%d%d", &n, &r); for (int i = 0; i < N; i++) scanf("%d%d%d", &cx[i], &cy[i], &cw[i]); for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { if (i == j) { ft[i][j] = 0; vp[i][j] = false; continue; } double dx = cx[i]-cx[j], dy = cy[i]-cy[j]; double d = sqrt(dx*dx+dy*dy); ft[i][j] = cft(d); vp[i][j] = d >= 250.0; } int m; scanf("%d", &m); for (int i = 0; i < m; i++) { char s1[6], s2[6]; scanf("%d%5s%d%5s", &sqa_[i], s1, &sqb_[i], s2); sqa_[i]--; sqb_[i]--; sqs_[i] = parse_time(s1); sqt_[i] = parse_time(s2); } int k; scanf("%d", &k); for (int i = 0; i < NT; i++) tgt[i] = 660 + i*30; compute_sq(); init_phases(); long long tw = 0; for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (vp[i][j]) tw += (long long)cw[i]*cw[j]; tw *= NT; fprintf(stderr, "Precomp: %.3fs\n", el()); // ========================================================= // Initial solution: try both greedy and hub-spoke, pick better // ========================================================= vector planes(K); auto shuttle = [](int hub, int spoke, int start) -> vector { vector route; int cur = hub, ct = start; route.push_back(cur); while (true) { int next = (cur==hub)?spoke:hub; int d = ((ct+4)/5)*5; if (d < TMIN) d = TMIN; if (d+ft[cur][next] > TMAX) break; route.push_back(next); ct = d+ft[cur][next]; cur = next; } return build(route, start); }; // Option A: hub-spoke (original) vector planes_hs(K); { int asgn[][2] = { {0,1},{0,2},{0,3},{0,4},{0,5},{0,6},{0,7},{0,8}, {1,0},{1,2},{1,3},{1,4},{1,5},{1,6}, {2,0},{2,1},{2,3},{2,4},{2,5}, {0,9},{0,10},{0,11},{0,12},{0,13},{0,14} }; for (int i = 0; i < K; i++) planes_hs[i].fs = shuttle(asgn[i][0], asgn[i][1], TMIN + i*12); } long long score_hs = eval_full(planes_hs); fprintf(stderr, "Hub-spoke init: %lld share=%.4f (%.3fs)\n", score_hs, (double)score_hs/tw, el()); // Option B: greedy backward vector planes_gr(K); greedy_init(planes_gr); long long score_gr = eval_full(planes_gr); fprintf(stderr, "Greedy init: %lld share=%.4f (%.3fs)\n", score_gr, (double)score_gr/tw, el()); // Pick the better one if (score_gr > score_hs) { planes = planes_gr; fprintf(stderr, "Using greedy init\n"); } else { planes = planes_hs; fprintf(stderr, "Using hub-spoke init\n"); } long long cur = eval_full(planes); long long best = cur; vector best_p = planes; fprintf(stderr, "Init: %lld share=%.4f (%.3fs)\n", cur, (double)cur/tw, el()); // ========================================================= // SA with phased precision // ========================================================= const double phase_boundary[2] = {0.35, 0.70}; const double sa_lim = 0.90; int cur_phase = 0; // Compute partial score for current phase from cache long long cur_partial = 0; for (int k2 = 0; k2 < phase_nt[cur_phase]; k2++) { int ti = phase_ti[cur_phase][k2]; for (int j = 0; j < N; j++) cur_partial += spp[ti][j]; } double Ts_base = 3e13, Te_base = 1e9; int it = 0, ac = 0; int phase_its[3] = {0, 0, 0}; while (el() < sa_lim) { double t_now = el(); double prog = t_now / sa_lim; double sc = phase_scale[cur_phase]; double Ts_eff = Ts_base / sc, Te_eff = Te_base / sc; double T = Ts_eff * pow(Te_eff/Ts_eff, prog); // Phase transition int new_phase = (prog < phase_boundary[0]) ? 0 : (prog < phase_boundary[1]) ? 1 : 2; if (new_phase != cur_phase) { cur_phase = new_phase; eval_full(planes); cur_partial = 0; for (int k2 = 0; k2 < phase_nt[cur_phase]; k2++) { int ti = phase_ti[cur_phase][k2]; for (int j = 0; j < N; j++) cur_partial += spp[ti][j]; } long long full_now = 0; for (int ti = 0; ti < NT; ti++) for (int j = 0; j < N; j++) full_now += spp[ti][j]; if (full_now > best) { best = full_now; best_p = planes; } } it++; phase_its[cur_phase]++; int pi = rng() % K; Plane old = planes[pi]; int op = rng() % 100; if (op < 40) { int hub, spoke; int r2 = rng()%10; hub = (r2<5)?0:(r2<8)?1:2; spoke = rng()%N; if (spoke == hub) spoke = (hub+1+rng()%(N-1))%N; int start = TMIN + (rng()%72)*5; planes[pi].fs = shuttle(hub, spoke, start); } else if (op < 60) { int shift = ((int)(rng()%9)-4)*5; if (!shift) shift = 5; bool ok = true; for (auto& f : planes[pi].fs) { f.dep += shift; f.arr += shift; if (f.dep < TMIN || f.arr > TMAX) { ok = false; break; } } if (!ok) { planes[pi] = old; continue; } } else if (op < 80) { int sc2; int r2=rng()%10; sc2 = (r2<4)?rng()%3:(r2<7)?rng()%10:rng()%N; int start = TMIN + (rng()%72)*5; vector route = {sc2}; int c = sc2, ct = start; for (int t = 0; t < 15; t++) { int nx; int r3=rng()%10; nx = (r3<3)?rng()%3:(r3<6)?rng()%10:(r3<8)?rng()%20:rng()%N; if (nx == c) continue; int d = ((ct+4)/5)*5; if (d < TMIN) d = TMIN; if (d+ft[c][nx] > TMAX) continue; route.push_back(nx); ct = d+ft[c][nx]; c = nx; } planes[pi].fs = build(route, start); } else { auto& fs = planes[pi].fs; if (fs.size() < 2) { planes[pi] = old; continue; } int split = 1+rng()%((int)fs.size()-1); int c = fs[split-1].to, ct = fs[split-1].arr; vector nfs(fs.begin(), fs.begin()+split); for (int t = 0; t < 10; t++) { int nx; int r3=rng()%10; nx = (r3<3)?rng()%3:(r3<6)?rng()%10:rng()%N; if (nx == c) continue; int d = ((ct+4)/5)*5; if (d+ft[c][nx] > TMAX) break; nfs.push_back({c, nx, d, d+ft[c][nx]}); ct = d+ft[c][nx]; c = nx; } planes[pi].fs = nfs; } if (!valid(planes[pi])) { planes[pi] = old; continue; } long long ns = eval_incr_partial(planes, cur_partial, phase_ti[cur_phase], phase_nt[cur_phase]); long long delta = ns - cur_partial; if (delta > 0 || exp((double)delta/T) > (double)(rng()%1000000)/1e6) { cur_partial = ns; ac++; } else { planes[pi] = old; rollback(); } } // Final full evaluation { long long final_score = eval_full(planes); if (final_score > best) { best = final_score; best_p = planes; } } planes = best_p; fprintf(stderr, "SA: it=%d ac=%d best=%lld share=%.4f\n", it, ac, best, (double)best/tw); fprintf(stderr, "Phase iters: [%d, %d, %d]\n", phase_its[0], phase_its[1], phase_its[2]); long long verify = eval_full(planes); fprintf(stderr, "Verify: %lld (diff=%lld)\n", verify, verify - best); for (int p = 0; p < K; p++) { printf("%d\n", (int)planes[p].fs.size()); for (auto& f : planes[p].fs) { string sd = fmt(f.dep), sa2 = fmt(f.arr); printf("%d %s %d %s\n", f.from+1, sd.c_str(), f.to+1, sa2.c_str()); } } fprintf(stderr, "Score: %lld\nTotal: %.3fs\n", (long long)((double)best/tw*1e6), el()); return 0; }