Submit Info #55668

Problem Lang User Status Time Memory
Assignment Problem cpp14 hitonanode AC 692 ms 18.57 MiB

ケース詳細
Name Status Time Memory
example_00 AC 1 ms 0.61 MiB
hand_minus_00 AC 533 ms 18.45 MiB
hand_plus_00 AC 508 ms 18.45 MiB
max_random_00 AC 692 ms 18.57 MiB
max_random_01 AC 682 ms 18.57 MiB
max_random_02 AC 679 ms 18.57 MiB
max_random_03 AC 674 ms 18.57 MiB
max_random_04 AC 684 ms 18.57 MiB
random_00 AC 51 ms 3.83 MiB
random_01 AC 64 ms 4.07 MiB
random_02 AC 9 ms 1.34 MiB
random_03 AC 60 ms 3.96 MiB
random_04 AC 1 ms 0.71 MiB

#line 2 "combinatorial_opt/mincostflow_nonegativeloop.hpp" #include <cassert> #include <limits> #include <queue> #include <vector> // CUT begin // Minimum cost flow WITH NO NEGATIVE CYCLE (just negative cost edge is allowed) // Verified: // - SRM 770 Div1 Medium https://community.topcoder.com/stat?c=problem_statement&pm=15702 // - CodeChef LTIME98 Ancient Magic https://www.codechef.com/problems/ANCT template <class Cap = long long, class Cost = long long, Cost INF_COST = std::numeric_limits<Cost>::max() / 2> struct MinCostFlow { struct _edge { int to, rev; Cap cap; Cost cost; template <class Ostream> friend Ostream &operator<<(Ostream &os, const _edge &e) { return os << '(' << e.to << ',' << e.rev << ',' << e.cap << ',' << e.cost << ')'; } }; bool _is_dual_infeasible; int V; std::vector<std::vector<_edge>> g; std::vector<Cost> dist; std::vector<int> prevv, preve; std::vector<Cost> dual; // dual[V]: potential std::vector<std::pair<int, int>> pos; bool _initialize_dual_dag() { std::vector<int> deg_in(V); for (int i = 0; i < V; i++) { for (const auto &e : g[i]) deg_in[e.to] += (e.cap > 0); } std::vector<int> st; st.reserve(V); for (int i = 0; i < V; i++) { if (!deg_in[i]) st.push_back(i); } for (int n = 0; n < V; n++) { if (int(st.size()) == n) return false; // Not DAG int now = st[n]; for (const auto &e : g[now]) { if (!e.cap) continue; deg_in[e.to]--; if (deg_in[e.to] == 0) st.push_back(e.to); if (dual[e.to] >= dual[now] + e.cost) dual[e.to] = dual[now] + e.cost; } } _is_dual_infeasible = false; return true; } bool _initialize_dual_spfa() { // Find feasible dual's when negative cost edges exist dual.assign(V, 0); std::queue<int> q; std::vector<int> in_queue(V); std::vector<int> nvis(V); for (int i = 0; i < V; i++) q.push(i), in_queue[i] = true; while (q.size()) { int now = q.front(); q.pop(), in_queue[now] = false; if (nvis[now] > V) return false; // Negative cycle exists nvis[now]++; for (const auto &e : g[now]) { if (!e.cap) continue; if (dual[e.to] > dual[now] + e.cost) { dual[e.to] = dual[now] + e.cost; if (!in_queue[e.to]) in_queue[e.to] = 1, q.push(e.to); } } } _is_dual_infeasible = false; return true; } bool initialize_dual() { return !_is_dual_infeasible or _initialize_dual_dag() or _initialize_dual_spfa(); } void _dinic_dijkstra(int s) { // O(ElogV) prevv.assign(V, -1); preve.assign(V, -1); dist.assign(V, INF_COST); dist[s] = 0; using P = std::pair<Cost, int>; std::priority_queue<P, std::vector<P>, std::greater<P>> q; q.emplace(0, s); while (!q.empty()) { P p = q.top(); q.pop(); int v = p.second; if (dist[v] < p.first) continue; for (int i = 0; i < (int)g[v].size(); i++) { _edge &e = g[v][i]; Cost c = dist[v] + e.cost + dual[v] - dual[e.to]; if (e.cap > 0 and dist[e.to] > c) { dist[e.to] = c, prevv[e.to] = v, preve[e.to] = i; q.emplace(dist[e.to], e.to); } } } } MinCostFlow(int V = 0) : _is_dual_infeasible(false), V(V), g(V), dual(V, 0) { static_assert(INF_COST > 0, "INF_COST must be positive"); } int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from and from < V); assert(0 <= to and to < V); assert(cap >= 0); if (cost < 0) _is_dual_infeasible = true; pos.emplace_back(from, g[from].size()); g[from].push_back({to, (int)g[to].size() + (from == to), cap, cost}); g[to].push_back({from, (int)g[from].size() - 1, (Cap)0, -cost}); return int(pos.size()) - 1; } // Flush flow f from s to t. Graph must not have negative cycle. std::pair<Cap, Cost> flow(int s, int t, const Cap &flow_limit) { if (!initialize_dual()) throw; // Fail to find feasible dual Cost cost = 0; Cap flow_rem = flow_limit; while (flow_rem > 0) { _dinic_dijkstra(s); if (dist[t] == INF_COST) break; for (int v = 0; v < V; v++) dual[v] = std::min(dual[v] + dist[v], INF_COST); Cap d = flow_rem; for (int v = t; v != s; v = prevv[v]) d = std::min(d, g[prevv[v]][preve[v]].cap); flow_rem -= d; cost += d * dual[t]; for (int v = t; v != s; v = prevv[v]) { _edge &e = g[prevv[v]][preve[v]]; e.cap -= d; g[v][e.rev].cap += d; } } return std::make_pair(flow_limit - flow_rem, cost); } struct edge { int from, to; Cap cap, flow; Cost cost; template <class Ostream> friend Ostream &operator<<(Ostream &os, const edge &e) { return os << '(' << e.from << "->" << e.to << ',' << e.flow << '/' << e.cap << ",$" << e.cost << ')'; } }; edge get_edge(int edge_id) const { int m = int(pos.size()); assert(0 <= edge_id and edge_id < m); auto _e = g[pos[edge_id].first][pos[edge_id].second]; auto _re = g[_e.to][_e.rev]; return {pos[edge_id].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost}; } std::vector<edge> edges() const { std::vector<edge> ret(pos.size()); for (int i = 0; i < int(pos.size()); i++) ret[i] = get_edge(i); return ret; } template <class Ostream> friend Ostream &operator<<(Ostream &os, const MinCostFlow &mcf) { os << "[MinCostFlow]V=" << mcf.V << ":"; for (int i = 0; i < mcf.V; i++) { for (auto &e : mcf.g[i]) os << "\n" << i << "->" << e.to << ":cap" << e.cap << ",$" << e.cost; } return os; } }; #line 2 "combinatorial_opt/test/assignment_problem.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/assignment" #include <algorithm> #include <iostream> template <typename TC> std::pair<TC, std::vector<int>> AssignmentProblem(std::vector<std::vector<TC>> cost) { int N = cost.size(); MinCostFlow<int, TC> mcf(N * 2 + 2); int S = N * 2, T = N * 2 + 1; TC bias_total_cost = 0; for (int i = 0; i < N; i++) { TC lo = *min_element(cost[i].begin(), cost[i].end()); bias_total_cost += lo; mcf.add_edge(S, i, 1, 0); mcf.add_edge(N + i, T, 1, 0); for (int j = 0; j < N; j++) mcf.add_edge(i, N + j, 1, cost[i][j] - lo); } auto total_cost = mcf.flow(S, T, N).second + bias_total_cost; std::vector<int> ret; for (int i = 0; i < N; i++) { for (const auto &g : mcf.g[i]) { if (g.to != S and !g.cap) { ret.emplace_back(g.to - N); break; } } } return std::make_pair(total_cost, ret); } int main() { int N; std::cin >> N; std::vector<std::vector<long long>> A(N, std::vector<long long>(N)); for (auto &vec : A) { for (auto &x : vec) { std::cin >> x; } } auto ret = AssignmentProblem(A); std::cout << ret.first << '\n'; for (auto x : ret.second) std::cout << x << ' '; std::cout << '\n'; }