#line 1 "combinatorial_opt/test/mcf_costscaling.yuki1615.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/1615" #line 2 "data_structure/light_forward_list.hpp" #include // CUT begin // Simple forward_list for MLE-sensitive situations // Verify: template struct light_forward_list { static std::vector ptr; static std::vector val; unsigned head; light_forward_list() : head(0) {} void push_front(T x) { ptr.push_back(head), val.push_back(x); head = ptr.size() - 1; } struct iterator { unsigned p; iterator operator++() { return {p = ptr[p]}; } T &operator*() { return val[p]; } bool operator!=(const iterator &rhs) { return p != rhs.p; } }; iterator begin() { return {head}; } iterator end() { return {0}; } }; template std::vector light_forward_list::ptr = {0}; template std::vector light_forward_list::val = {T()}; #line 3 "combinatorial_opt/mcf_costscaling.hpp" #include #include #line 6 "combinatorial_opt/mcf_costscaling.hpp" // Cost scaling // https://people.orie.cornell.edu/dpw/orie633/ // Implementation idea: https://yukicoder.me/submissions/680169 template struct mcf_costscaling { mcf_costscaling() = default; mcf_costscaling(int n) : _n(n), to(n), b(n), p(n) {} int _n; std::vector cap; std::vector cost; std::vector opposite; std::vector> to; std::vector b; std::vector p; void add_edge(int from_, int to_, Cap cap_, Cost cost_) { assert(0 <= from_ && from_ < _n); assert(0 <= to_ && to_ < _n); assert(0 <= cap_); cost_ *= (_n + 1); int e = int(cap.size()); to[from_].push_front(e); cap.push_back(cap_); cost.push_back(cost_); opposite.push_back(to_); to[to_].push_front(e + 1); cap.push_back(0); cost.push_back(-cost_); opposite.push_back(from_); } void add_supply(int v, Cap supply) { b[v] += supply; } void add_demand(int v, Cap demand) { add_supply(v, -demand); } template RetCost solve() { Cost eps = 1; std::queue q; for (const auto c : cost) { while (eps <= -c) eps <<= SCALING; } for (; eps >>= SCALING;) { auto no_negative_loop = [&]() -> bool { std::vector dist = p; for (int iter = 0; iter < SKIP_REFINE_DEPTH; iter++) { bool flg = false; for (int e = 0; e < int(cap.size()); e++) { if (!cap[e]) continue; int i = opposite[e ^ 1], j = opposite[e]; if (dist[j] > dist[i] + cost[e] + eps) { dist[j] = dist[i] + cost[e] + eps; flg = true; } } if (!flg) { p = dist; return true; } } return false; }; if (no_negative_loop()) continue; for (int e = 0; e < int(cap.size()); e += 2) { const int i = opposite[e ^ 1], j = opposite[e]; const Cost cp_ij = cost[e] + p[i] - p[j]; if (cap[e] and cp_ij < 0) { b[i] -= cap[e], b[j] += cap[e], cap[e ^ 1] += cap[e], cap[e] = 0; } else if (cap[e ^ 1] and cp_ij > 0) { b[i] += cap[e ^ 1], b[j] -= cap[e ^ 1], cap[e] += cap[e ^ 1], cap[e ^ 1] = 0; } } for (int i = 0; i < _n; i++) { if (b[i] > 0) q.push(i); } while (q.size()) { const int i = q.front(); q.pop(); for (auto e : to[i]) { // Push if (!cap[e]) continue; int j = opposite[e]; Cost cp_ij = cost[e] + p[i] - p[j]; if (cp_ij >= 0) continue; Cap f = b[i] > cap[e] ? cap[e] : b[i]; if (b[j] <= 0 and b[j] + f > 0) q.push(j); b[i] -= f, b[j] += f, cap[e] -= f, cap[e ^ 1] += f; if (!b[i]) break; } if (b[i] > 0) { // Relabel bool flg = false; for (int e : to[i]) { if (!cap[e]) continue; Cost x = p[opposite[e]] - cost[e] - eps; if (!flg or x > p[i]) flg = true, p[i] = x; } q.push(i); } } } RetCost ret = 0; for (int e = 0; e < int(cap.size()); e += 2) ret += RetCost(cost[e]) * cap[e ^ 1]; return ret / (_n + 1); } std::vector potential() { std::vector ret = p; for (auto &x : ret) x /= (_n + 1); while (true) { bool flg = false; for (int i = 0; i < _n; i++) { for (auto e : to[i]) { if (!cap[e]) continue; int j = opposite[e]; auto y = ret[i] + cost[e] / (_n + 1); if (ret[j] > y) ret[j] = y, flg = true; } } if (!flg) break; } return ret; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int e) const { int m = cap.size() / 2; assert(e >= 0 and e < m); return {opposite[e * 2 + 1], opposite[e * 2], cap[e * 2] + cap[e * 2 + 1], cap[e * 2 + 1], cost[e * 2] / (_n + 1)}; } std::vector edges() const { int m = cap.size() / 2; std::vector result(m); for (int i = 0; i < m; i++) result[i] = get_edge(i); return result; } }; #line 3 "combinatorial_opt/test/mcf_costscaling.yuki1615.test.cpp" #include using namespace std; int main() { int N, M, K, L; cin >> N >> M >> K >> L; mcf_costscaling mcf(N + M + 2); for (int l = 0; l < L; l++) { int x, y, z; cin >> x >> y >> z; x--, y--; mcf.add_edge(x, y + N, 1, -(1LL << z)); } const int gs = N + M, gt = gs + 1; for (int i = 0; i < N; i++) mcf.add_edge(gs, i, 1, 0); for (int j = 0; j < M; j++) mcf.add_edge(N + j, gt, 1, 0); mcf.add_edge(gt, gs, N + M, 0); cout << -mcf.solve() << '\n'; }