#include // clang-format off using namespace std; void print0(){}; template void print0(H h,T... t){cout<void print(H h,T... t){print0(h);if(sizeof...(T)>0)print0(" ");print(t...);} #define debug1(a) { cerr<<#a<<":"<; // clang-format on namespace marathon { mt19937 engine(0); clock_t start_time; double now() { return 1000.0 * (clock() - start_time) / CLOCKS_PER_SEC; } void marathon_init() { start_time = clock(); random_device seed_gen; engine.seed(seed_gen()); } int randint(int mn, int mx) { int rng = mx - mn + 1; return mn + (engine() % rng); } double uniform(double x, double y) { const int RND = 1e8; double mean = (x + y) / 2.0; double dif = y - mean; double p = double(engine() % RND) / RND; return mean + dif * (1.0 - 2.0 * p); } template T random_choice(vector &vec) { return vec[engine() % vec.size()]; } bool anneal_accept(double new_score, double old_score, double cur_time, double begin_time, double end_time, double begin_temp, double end_temp) { static int called = 0; static double temp = 0; if ((called & 127) == 0) { double ratio = (cur_time - begin_time) / (end_time - begin_time); ratio = min(ratio, 1.0); temp = pow(begin_temp, 1.0 - ratio) * pow(end_temp, ratio); } called++; const int ANNEAL_RND = 1e8; const double ANNEAL_EPS = 1e-6; return (exp((new_score - old_score) / temp) > double(engine() % ANNEAL_RND) / ANNEAL_RND + ANNEAL_EPS); } } // namespace marathon struct operation_t { int kind; int xyz; }; struct bomb_t { int cost; vector ranges; }; const int _U_ = 0; const int _R_ = 1; const int _D_ = 2; const int _L_ = 3; const int N = 50; const int M = 20; const int N2 = 2500; const int NNM = 50000; vector mvs = {{-1, 0}, {0, 1}, {1, 0}, {0, -1}}; using bsn2 = bitset; vector> mvtbl(N2); bsn2 break_bomb_bs[N][N][M]; char TBL_INIT[N][N]; bomb_t BOMBS[M]; int getmove(point src, point dest) { assert(abs(src.r - dest.r) + abs(src.c - dest.c) == 1); if (src.r < dest.r) { return _D_; } if (src.r > dest.r) { return _U_; } if (src.c < dest.c) { return _R_; } if (src.c > dest.c) { return _L_; } } bool ingrid(int i, int j) { return 0 <= i && i < N && 0 <= j && j < N; } bool ingrid(point p) { return ingrid(p.r, p.c); } int _p(int r, int c) { return r * N + c; } int _p(point p) { return _p(p.r, p.c); } void init_data() { for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { point u = {r, c}; for (auto mv : mvs) { auto v = mv + u; if (!ingrid(v)) continue; mvtbl[_p(u)].push_back(_p(v)); } } } for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { for (int bid = 0; bid < M; bid++) { break_bomb_bs[r][c][bid] = 0; point now = {r, c}; for (auto drc : BOMBS[bid].ranges) { point pt = now + drc; if (!ingrid(pt)) continue; break_bomb_bs[r][c][bid][_p(pt)] = 1; } } } } } vector> dij_cost(point ini, vector> &tbl) { // コスト上限が400くらいなのでpriority_queue不要 vector tbl_(N2); for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { tbl_[_p(r, c)] = tbl[r][c]; } } vector done(N2); vector costs(N2, inf); vector> cost_points(N * 4); cost_points[0].push_back(_p(ini)); costs[_p(ini)] = 0; for (int cost = 0; cost < N * 4; cost++) { for (auto u : cost_points[cost]) { if (done[u]) continue; done[u] = true; for (auto v : mvtbl[u]) { int nc = cost + 1; if (tbl_[v] != '.') { nc = cost + 2; } if (done[v]) continue; if (costs[v] <= nc) continue; costs[v] = nc; cost_points[nc].push_back(v); } } } vector> result(N, vector(N)); for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { result[r][c] = costs[_p(r, c)]; } } return result; } void dij_goto_ops(point &hulk, point dest, vector &ops, vector> &tbl) { priority_queue, vector>, greater>> pq; pq.push({0, hulk, {-1, -1}}); vector> costs(N, vector(N, inf)); vector> froms(N, vector(N, {-1, -1})); while (pq.size()) { int cost; point u, frm; tie(cost, u, frm) = pq.top(); pq.pop(); if (costs[u.r][u.c] <= cost) continue; costs[u.r][u.c] = cost; froms[u.r][u.c] = frm; if (u == dest) break; for (auto mv : mvs) { point v = mv + u; if (!ingrid(v)) continue; int nc = cost + 1; if (tbl[v.r][v.c] != '.') { nc = cost + 2; } pq.push({nc, v, u}); } } { point cur = dest; vector route; while (true) { route.push_back(cur); if (cur == hulk) break; cur = froms[cur.r][cur.c]; } reverse(route.begin(), route.end()); for (int i = 1; i < int(route.size()); i++) { point pre = route[i - 1]; point nxt = route[i]; int mvid = getmove(pre, nxt); ops.push_back({1, mvid}); } } hulk = dest; } pii evaluate_ops(vector &ops) { vector> tbl(N, vector(N)); for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { tbl[r][c] = TBL_INIT[r][c]; } } int move_cost = 0; int bomb_cost = 0; point hulk = {0, 0}; int bombs = 0; for (auto op : ops) { if (op.kind == 1) { hulk = hulk + mvs[op.xyz]; if (tbl[hulk.r][hulk.c] == '.') { move_cost += (1 + bombs) * (1 + bombs); } else { move_cost += 2 * (1 + bombs) * (1 + bombs); } } else if (op.kind == 2) { bombs++; int bombid = op.xyz; bomb_cost += BOMBS[bombid].cost; } else { bombs--; // WAにはならない前提 int bombid = op.xyz; for (auto drc : BOMBS[bombid].ranges) { point pt = hulk + drc; if (!ingrid(pt)) continue; tbl[pt.r][pt.c] = '.'; } } } return {move_cost, bomb_cost}; } int bomb_place_id(point p, int b) { return b * N * N + p.r * N + p.c; } int bpid2bombid(int bpid) { return bpid / N2; } point bpid2point(int bpid) { return point{(bpid / N) % N, bpid % N}; } vector hc_bomb_places(vector init_bomb_places, vector init_fillcnt, vector> bpid2walls, vector> wall2bpids) { // 破壊再構築系の山登り vector bpid2cost(NNM); for (int bpid = 0; bpid < NNM; bpid++) { bpid2cost[bpid] = BOMBS[bpid2bombid(bpid)].cost; } int old_score = 0; auto bomb_places = init_bomb_places; auto fillcnt = init_fillcnt; for (auto bpid : bomb_places) { old_score += -bpid2cost[bpid]; } double begin_time = marathon::now(); double end_time = begin_time + 1000; int hc_iter = 0; int hc_accept = 0; static uint16_t bpid_cnt[NNM]; while (marathon::now() < end_time) { hc_iter++; vector new_bomb_places = bomb_places; auto new_fillcnt = fillcnt; vector notfilled; int new_score = old_score; int rmnum = marathon::randint(4, 6); for (int r = 0; r < rmnum; r++) { int remove_bpid = marathon::random_choice(new_bomb_places); new_bomb_places.erase(std::remove(new_bomb_places.begin(), new_bomb_places.end(), remove_bpid), new_bomb_places.end()); new_score += bpid2cost[remove_bpid]; for (int pt : bpid2walls[remove_bpid]) { new_fillcnt[pt]--; if (new_fillcnt[pt] == 0) notfilled.push_back(pt); } } while (notfilled.size()) { // この中の処理が非常に重い for (int bpid = 0; bpid < NNM; bpid++) { bpid_cnt[bpid] = 0; } for (auto wall : notfilled) { for (auto bpid : wall2bpids[wall]) { bpid_cnt[bpid]++; } } int bestbpid = 0; int bestscore = -inf; for (int bpid = 0; bpid < NNM; bpid++) { if (bpid_cnt[bpid] > 0) { // int score = -1000 * marathon::uniform(1.0, 2.0) * bpid2cost[bpid] / bpid_cnt[bpid]; int score = -1000 * bpid2cost[bpid] / bpid_cnt[bpid]; if (bestscore < score) { bestscore = score; bestbpid = bpid; } } } for (auto wall : bpid2walls[bestbpid]) { new_fillcnt[wall]++; if (new_fillcnt[wall] == 1) { notfilled.erase(std::remove(notfilled.begin(), notfilled.end(), wall), notfilled.end()); } } new_score -= bpid2cost[bestbpid]; new_bomb_places.push_back(bestbpid); } if (new_score > old_score) { old_score = new_score; bomb_places = new_bomb_places; fillcnt = new_fillcnt; hc_accept++; } } debug2(hc_iter, hc_accept); return bomb_places; } vector make_bomb_places() { // 詰み防止のため建物がなくなるまで破壊してはいけない店舗を1個だけ決めておく vector is_hub_shop(N2); { point center = {12, 12}; pair minshop = {inf, {-1, -1}}; for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { if (TBL_INIT[r][c] == '@') { point now = {r, c}; int distance = abs(center.r - now.r) + abs(center.c - now.c); minshop = min(minshop, {distance, now}); } } } is_hub_shop[_p(minshop.second)] = true; } vector> wall2bpids(N2); // buildingと書くのがタイプ数多いのでwallとしておく vector> bpid2walls(NNM); for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { for (int b = 0; b < M; b++) { point place = point{r, c}; int bpid = bomb_place_id(place, b); // ハブ店を破壊する爆弾配置は除外する bool valid = true; for (auto drc : BOMBS[b].ranges) { point pt = place + drc; if (!ingrid(pt)) continue; if (is_hub_shop[_p(pt)]) valid = false; } if (!valid) continue; for (auto drc : BOMBS[b].ranges) { point pt = place + drc; if (!ingrid(pt)) continue; if (TBL_INIT[pt.r][pt.c] != '#') continue; bpid2walls[bpid].push_back(_p(pt)); wall2bpids[_p(pt)].push_back(bpid); } } } } // 初期解を作る // 破壊できる確率が低い建物を破壊できたときのスコアを高く見積もる vector wall_score(N2); for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { int u = _p(r, c); if (wall2bpids[u].size()) { wall_score[u] = 1e9 / wall2bpids[u].size(); } } } vector bomb_places; vector fillcnt(N2); { while (true) { pair bestbpid = {-inf, -inf}; for (int bpid = 0; bpid < NNM; bpid++) { long long ws = 0; for (auto wall : bpid2walls[bpid]) { if (fillcnt[wall] == 0) { ws += wall_score[wall]; } } if (ws > 0) { double score = -1.0 * BOMBS[bpid2bombid(bpid)].cost / ws; bestbpid = max(bestbpid, {score, bpid}); } } if (bestbpid.second == -inf) break; bomb_places.push_back(bestbpid.second); for (auto wall : bpid2walls[bestbpid.second]) { fillcnt[wall]++; } } } return hc_bomb_places(bomb_places, fillcnt, bpid2walls, wall2bpids); } double calc_tsp_cost(vector &route, vector &bomb_places) { point hulk = {0, 0}; vector> tbl(N, vector(N)); for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { tbl[r][c] = TBL_INIT[r][c]; } } int cost = 0; int m = route.size(); for (int r = 1; r < int(route.size()) - 1; r++) { int bpid = bomb_places[route[r]]; point bombpt = bpid2point(bpid); auto cost_hulk = dij_cost(hulk, tbl); auto cost_bomb = dij_cost(bombpt, tbl); int now_mincost = inf; for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { if (tbl[r][c] == '@') { now_mincost = min(now_mincost, cost_hulk[r][c] + cost_bomb[r][c] * 4); } } } for (auto drc : BOMBS[bpid2bombid(bpid)].ranges) { point pt = bombpt + drc; if (!ingrid(pt)) continue; tbl[pt.r][pt.c] = '.'; } cost += now_mincost; hulk = bombpt; } return cost; } vector bomb_places_tsp(vector bomb_places) { int m = bomb_places.size() + 2; int start = m - 2; int goal = m - 1; vector best_route; double best_score = -1e18; int route_search_iter = 0; while (marathon::now() < 2400) { route_search_iter++; // コスト固定のTSP vector route; route.push_back(start); { vector perm(m - 2); iota(perm.begin(), perm.end(), 0); shuffle(perm.begin(), perm.end(), marathon::engine); for (auto r : perm) { route.push_back(r); } } route.push_back(goal); point ini = {0, 0}; vector> costtbl(m, vector(m)); for (int i = 0; i < m - 1; i++) { for (int j = 0; j < m - 1; j++) { point src = i == start ? ini : bpid2point(bomb_places[i]); point dest = i == start ? ini : bpid2point(bomb_places[j]); costtbl[i][j] = abs(src.r - dest.r) + abs(src.c - dest.c); } } double begin_temp = 5; double end_temp = 0.5; double old_score = 0; for (int r = 1; r < int(route.size()); r++) { old_score -= costtbl[route[r - 1]][route[r]]; } int anneal_accepted = 0; int anneal_iter = 0; while (anneal_iter < 50000) { anneal_iter++; vector new_route = route; int x = 0; int y = 0; while (x == y) { x = 1 + marathon::engine() % (int(new_route.size()) - 2); y = 1 + marathon::engine() % (int(new_route.size()) - 2); } if (x > y) { swap(x, y); } for (int i = x + 1; i <= y - 1; i++) { int j = y - 1 - (i - (x + 1)); if (i > j) break; swap(new_route[i], new_route[j]); } double new_score = 0; for (int r = 1; r < int(new_route.size()); r++) { new_score -= costtbl[new_route[r - 1]][new_route[r]]; } if (marathon::anneal_accept(new_score, old_score, anneal_iter, 0, 50000, begin_temp, end_temp)) { route = new_route; old_score = new_score; anneal_accepted++; } } // 正しいコストで評価 double now_score = -calc_tsp_cost(route, bomb_places); if (best_score < now_score) { best_route = route; best_score = now_score; debug1(best_score); } } debug2(route_search_iter, best_score); vector result; for (int r = 1; r < int(best_route.size()) - 1; r++) { result.push_back(bomb_places[best_route[r]]); } return result; } void solve() { // 爆弾位置と爆弾IDからなる「爆弾配置」 の集合を山登りにより作る。 // 爆弾配置は N*N*M 種類存在し、そこから全ての建物を破壊しつつ爆弾コストが小さい集合を選ぶ。 vector bomb_places = make_bomb_places(); vector ops; { point hulk = {0, 0}; vector> tbl(N, vector(N)); for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { tbl[r][c] = TBL_INIT[r][c]; } } { // 爆弾配置が決まったら、コストが動的に変化するTSP的な問題を解く。  bomb_places = bomb_places_tsp(bomb_places); for (auto bpid : bomb_places) { point midshop = {-1, -1}; { // TODO 2個同時に運ぶのをDP的にやるとよい可能性がある auto hulk_cost = dij_cost(hulk, tbl); auto bp_cost = dij_cost(bpid2point(bpid), tbl); pair bestmidshop = {inf, {inf, inf}}; for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { if (tbl[r][c] == '@') { int cost = hulk_cost[r][c] + bp_cost[r][c] * 4; pair now = {cost, {r, c}}; bestmidshop = min(now, bestmidshop); } } } midshop = bestmidshop.second; } int bombid = bpid2bombid(bpid); point bombpt = bpid2point(bpid); dij_goto_ops(hulk, midshop, ops, tbl); ops.push_back({2, bombid}); dij_goto_ops(hulk, bombpt, ops, tbl); ops.push_back({3, bombid}); for (auto drc : BOMBS[bombid].ranges) { point pt = hulk + drc; if (!ingrid(pt)) continue; tbl[pt.r][pt.c] = '.'; } } } // 残った店を貪欲に破壊 while (true) { vector shops; for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { if (tbl[r][c] == '@') shops.push_back({r, c}); } } if (shops.size() == 0) break; pair bestop = {1e18, -1}; auto hulk_cost = dij_cost(hulk, tbl); vector> midshop(N, vector(N, {-1, -1})); vector> move_cost(N, vector(N, inf)); for (auto shop : shops) { auto shop_cost = dij_cost(shop, tbl); for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { int cost = shop_cost[r][c] * 4 + hulk_cost[shop.r][shop.c]; if (move_cost[r][c] > cost) { move_cost[r][c] = cost; midshop[r][c] = shop; } } } } for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { point place = {r, c}; for (int bid = 0; bid < M; bid++) { int break_shop = 0; int break_hub_shop = 0; for (auto drc : BOMBS[bid].ranges) { point pt = place + drc; if (!ingrid(pt)) continue; if (tbl[pt.r][pt.c] == '@') break_shop++; } // (移動コスト+爆弾コスト)/破壊する店数 が最小の爆弾配置を選ぶ double score = 1.0 * (move_cost[r][c] + BOMBS[bid].cost) / break_shop; bestop = min(bestop, {score, bomb_place_id(place, bid)}); } } } { int bpid = bestop.second; int bombid = bpid / N2; point bombpt = bpid2point(bpid); dij_goto_ops(hulk, midshop[bombpt.r][bombpt.c], ops, tbl); ops.push_back({2, bombid}); dij_goto_ops(hulk, bombpt, ops, tbl); ops.push_back({3, bombid}); for (auto drc : BOMBS[bombid].ranges) { point pt = hulk + drc; if (!ingrid(pt)) continue; tbl[pt.r][pt.c] = '.'; } } } } { cout << ops.size() << endl; for (auto op : ops) { if (op.kind == 1) { char d = '.'; if (op.xyz == _L_) d = 'L'; if (op.xyz == _R_) d = 'R'; if (op.xyz == _U_) d = 'U'; if (op.xyz == _D_) d = 'D'; cout << op.kind << " " << d << endl; } else { cout << op.kind << " " << op.xyz + 1 << endl; } } } { int move_cost, bomb_cost; tie(move_cost, bomb_cost) = evaluate_ops(ops); int totalcost = move_cost + bomb_cost; int score = 1e12 / (1e4 + totalcost); cerr << "score==" << score << " move_cost==" << move_cost << " bomb_cost==" << bomb_cost << " time==" << marathon::now() << endl; } } int main() { marathon::marathon_init(); int n, m; cin >> n >> m; for (int r = 0; r < N; r++) { for (int c = 0; c < N; c++) { cin >> TBL_INIT[r][c]; } } for (int b = 0; b < M; b++) { int c, l; cin >> c >> l; bomb_t bomb; bomb.cost = c; for (int i = 0; i < l; i++) { int dr, dc; cin >> dr >> dc; bomb.ranges.push_back({dr, dc}); } BOMBS[b] = bomb; } init_data(); solve(); }