C++ Library for Competitive Programming
/*
* @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;
}