C++ Library for Competitive Programming
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/* * @title グラフ/フロー/最大流/submodular quadratic pseudo-Boolean optimisation * * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2903 */ #include <iostream> #include <string> #include <vector> #include "emthrm/graph/flow/maximum_flow/dinic.hpp" #include "emthrm/graph/flow/maximum_flow/submodular_quadratic_pseudo-boolean_optimisation.hpp" int main() { int r, c; std::cin >> r >> c; std::vector<std::string> s(r); for (int i = 0; i < r; ++i) { std::cin >> s[i]; } std::vector<std::vector<int>> id(r, std::vector<int>(c, -1)); int n = 0; for (int i = 0; i < r; ++i) { for (int j = 0; j < c; ++j) { if (s[i][j] == '#') id[i][j] = n++; } } emthrm::SubmodularQPBO<emthrm::Dinic, int> submodular_qpbo(n); for (int i = 0; i < r; ++i) { for (int j = 0; j < c; ++j) { if (id[i][j] == -1) continue; if (i + 1 < r && id[i + 1][j] != -1) { submodular_qpbo.add_eq(id[i][j], id[i + 1][j], 0, -1); } if (j + 1 < c && id[i][j + 1] != -1) { submodular_qpbo.add_eq(id[i][j], id[i][j + 1], 1, -1); } } } std::cout << n + submodular_qpbo.solve() << '\n'; return 0; }
#line 1 "test/graph/flow/maximum_flow/submodular_quadratic_pseudo-boolean_optimisation.test.cpp" /* * @title グラフ/フロー/最大流/submodular quadratic pseudo-Boolean optimisation * * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2903 */ #include <iostream> #include <string> #include <vector> #line 1 "include/emthrm/graph/flow/maximum_flow/dinic.hpp" #include <algorithm> #include <limits> #include <queue> #include <utility> #line 9 "include/emthrm/graph/flow/maximum_flow/dinic.hpp" namespace emthrm { template <typename T> struct Dinic { struct Edge { int dst, rev; T cap; explicit Edge(const int dst, const T cap, const int rev) : dst(dst), rev(rev), cap(cap) {} }; std::vector<std::vector<Edge>> graph; explicit Dinic(const int n) : graph(n), level(n), itr(n) {} void add_edge(const int src, const int dst, const T cap) { graph[src].emplace_back(dst, cap, graph[dst].size()); graph[dst].emplace_back(src, 0, graph[src].size() - 1); } T maximum_flow(const int s, const int t, T limit = std::numeric_limits<T>::max()) { T res = 0; while (limit > 0) { std::fill(level.begin(), level.end(), -1); level[s] = 0; std::queue<int> que; que.emplace(s); while (!que.empty()) { const int ver = que.front(); que.pop(); for (const Edge& e : graph[ver]) { if (level[e.dst] == -1 && e.cap > 0) { level[e.dst] = level[ver] + 1; que.emplace(e.dst); } } } if (level[t] == -1) break; std::fill(itr.begin(), itr.end(), 0); while (limit > 0) { const T f = dfs(s, t, limit); if (f == 0) break; limit -= f; res += f; } } return res; } private: std::vector<int> level, itr; T dfs(const int ver, const int t, const T flow) { if (ver == t) return flow; for (; std::cmp_less(itr[ver], graph[ver].size()); ++itr[ver]) { Edge& e = graph[ver][itr[ver]]; if (level[ver] < level[e.dst] && e.cap > 0) { const T tmp = dfs(e.dst, t, std::min(flow, e.cap)); if (tmp > 0) { e.cap -= tmp; graph[e.dst][e.rev].cap += tmp; return tmp; } } } return 0; } }; } // namespace emthrm #line 1 "include/emthrm/graph/flow/maximum_flow/submodular_quadratic_pseudo-boolean_optimisation.hpp" #include <cassert> #line 7 "include/emthrm/graph/flow/maximum_flow/submodular_quadratic_pseudo-boolean_optimisation.hpp" #line 1 "include/emthrm/graph/flow/maximum_flow/maximum_flow.hpp" /** * @title 最大流コンセプト */ #ifndef EMTHRM_GRAPH_FLOW_MAXIMUM_FLOW_MAXIMUM_FLOW_HPP_ #define EMTHRM_GRAPH_FLOW_MAXIMUM_FLOW_MAXIMUM_FLOW_HPP_ #include <concepts> #line 10 "include/emthrm/graph/flow/maximum_flow/maximum_flow.hpp" namespace emthrm { template <template <typename> class C, typename T> concept MaximumFlow = requires (C<T> mf) { {mf.add_edge(std::declval<int>(), std::declval<int>(), std::declval<T>())} -> std::same_as<void>; {mf.maximum_flow(std::declval<int>(), std::declval<int>())} -> std::same_as<T>; }; } // namespace emthrm #endif // EMTHRM_GRAPH_FLOW_MAXIMUM_FLOW_MAXIMUM_FLOW_HPP_ #line 9 "include/emthrm/graph/flow/maximum_flow/submodular_quadratic_pseudo-boolean_optimisation.hpp" namespace emthrm { template <template <typename> class C, typename T> requires MaximumFlow<C, T> struct SubmodularQPBO { explicit SubmodularQPBO(const int n) : inf(std::numeric_limits<T>::max()), n(n), res(0) {} void add_neq(const int u, const int v, const T cost) { assert(cost >= 0); us.emplace_back(u); vs.emplace_back(v); costs.emplace_back(cost); } void add(const int v, bool group, T cost) { if (cost < 0) { cost = -cost; res += cost; group = !group; } if (group) { add_neq(-2, v, cost); // -2 represents S. } else { add_neq(v, -1, cost); // -1 represents T. } } void add_or(const std::vector<int>& v, const bool group, const T cost) { assert(cost >= 0); add(n, group, cost); if (group) { for (const int e : v) add_neq(n, e, inf); } else { for (const int e : v) add_neq(e, n, inf); } ++n; } void add_or(const int u, const int v, const bool group, const T cost) { add_or({u, v}, group, cost); } void add_eq(const std::vector<int>& v, const bool group, T cost) { assert(cost <= 0); cost = -cost; res += cost; add_or(v, !group, cost); } void add_eq(const int u, const int v, const bool group, const T cost) { add_eq({u, v}, group, cost); } T solve() { C<T> mf(n + 2); const int neq_size = costs.size(); for (int i = 0; i < neq_size; ++i) { mf.add_edge(us[i] < 0 ? us[i] + n + 2 : us[i], vs[i] < 0 ? vs[i] + n + 2 : vs[i], costs[i]); } return mf.maximum_flow(n, n + 1, inf) - res; } private: const T inf; int n; T res; std::vector<int> us, vs; std::vector<T> costs; }; } // namespace emthrm #line 13 "test/graph/flow/maximum_flow/submodular_quadratic_pseudo-boolean_optimisation.test.cpp" int main() { int r, c; std::cin >> r >> c; std::vector<std::string> s(r); for (int i = 0; i < r; ++i) { std::cin >> s[i]; } std::vector<std::vector<int>> id(r, std::vector<int>(c, -1)); int n = 0; for (int i = 0; i < r; ++i) { for (int j = 0; j < c; ++j) { if (s[i][j] == '#') id[i][j] = n++; } } emthrm::SubmodularQPBO<emthrm::Dinic, int> submodular_qpbo(n); for (int i = 0; i < r; ++i) { for (int j = 0; j < c; ++j) { if (id[i][j] == -1) continue; if (i + 1 < r && id[i + 1][j] != -1) { submodular_qpbo.add_eq(id[i][j], id[i + 1][j], 0, -1); } if (j + 1 < c && id[i][j + 1] != -1) { submodular_qpbo.add_eq(id[i][j], id[i][j + 1], 1, -1); } } } std::cout << n + submodular_qpbo.solve() << '\n'; return 0; }