グラフ/フロー/マッチング/二部グラフの重み付き最大マッチング
(test/graph/flow/matching/weighted_bipartite_matching.test.cpp)

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• Last update: 2023-02-25 16:35:06+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2429

Depends on

• 二部グラフの重み付き最大マッチング (include/emthrm/graph/flow/matching/weighted_bipartite_matching.hpp)
• 最小費用 $s$-$t$-フロー (minimum cost $s$-$t$-flow) 最短路反復法 (successive shortest path algorithm) 版 (include/emthrm/graph/flow/minimum_cost_flow/minimum_cost_s-t-flow.hpp)

Code

/*
 * @title グラフ/フロー/マッチング/二部グラフの重み付き最大マッチング
 *
 * verification-helper: IGNORE
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2429
 */

#include <iostream>
#include <string>
#include <vector>

#include "emthrm/graph/flow/matching/weighted_bipartite_matching.hpp"

int main() {
  int n;
  std::cin >> n;
  std::vector<std::vector<int>> w(n, std::vector<int>(n));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      std:: cin >> w[i][j];
    }
  }
  std::vector<std::vector<int>> e(n, std::vector<int>(n));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      std:: cin >> e[i][j];
    }
  }
  std::vector<std::string> f(n);
  long long ans = 0;
  for (int i = 0; i < n; ++i) {
    std::cin >> f[i];
    for (int j = 0; j < n; ++j) {
      if (f[i][j] == 'o') ans += e[i][j];
    }
  }
  emthrm::WeightedBipartiteMatching<long long>
      weighted_bipartite_matching(n, n);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      weighted_bipartite_matching.add_edge(i, j,
                                           f[i][j] == 'o' ? e[i][j] : -w[i][j]);
    }
  }
  std::cout << ans - weighted_bipartite_matching.solve() << '\n';
  std::vector<std::string> taro(n, std::string(n, '.'));
  const std::vector<int> matching = weighted_bipartite_matching.matching();
  for (int i = 0; i < n; ++i) {
    taro[i][matching[i]] = 'o';
  }
  std::vector<int> r, c;
  std::vector<std::string> operate;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (f[i][j] != taro[i][j]) {
        r.emplace_back(i);
        c.emplace_back(j);
        operate.emplace_back(f[i][j] == 'o' ? "erase" : "write");
      }
    }
  }
  const int cnt = r.size();
  std::cout << cnt << '\n';
  for (int i = 0; i < cnt; ++i) {
    std::cout << r[i] + 1 << ' ' << c[i] + 1 << ' ' << operate[i] << '\n';
  }
  return 0;
}

#line 1 "test/graph/flow/matching/weighted_bipartite_matching.test.cpp"
/*
 * @title グラフ/フロー/マッチング/二部グラフの重み付き最大マッチング
 *
 * verification-helper: IGNORE
 * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2429
 */

#include <iostream>
#include <string>
#include <vector>

#line 1 "include/emthrm/graph/flow/matching/weighted_bipartite_matching.hpp"



#include <cassert>
#line 6 "include/emthrm/graph/flow/matching/weighted_bipartite_matching.hpp"

#line 1 "include/emthrm/graph/flow/minimum_cost_flow/minimum_cost_s-t-flow.hpp"



#include <algorithm>
#line 6 "include/emthrm/graph/flow/minimum_cost_flow/minimum_cost_s-t-flow.hpp"
#include <functional>
#include <limits>
#include <queue>
#include <utility>
#line 11 "include/emthrm/graph/flow/minimum_cost_flow/minimum_cost_s-t-flow.hpp"

namespace emthrm {

template <typename T, typename U>
struct MinimumCostSTFlow {
  struct Edge {
    int dst, rev;
    T cap;
    U cost;
    explicit Edge(const int dst, const T cap, const U cost, const int rev)
        : dst(dst), rev(rev), cap(cap), cost(cost) {}
  };

  const U uinf;
  std::vector<std::vector<Edge>> graph;

  explicit MinimumCostSTFlow(const int n,
                             const U uinf = std::numeric_limits<U>::max())
      : uinf(uinf), graph(n), tinf(std::numeric_limits<T>::max()), n(n),
        has_negative_edge(false), prev_v(n, -1), prev_e(n, -1), dist(n),
        potential(n, 0) {}

  void add_edge(const int src, const int dst, const T cap, const U cost) {
    has_negative_edge |= cost < 0;
    graph[src].emplace_back(dst, cap, cost, graph[dst].size());
    graph[dst].emplace_back(src, 0, -cost, graph[src].size() - 1);
  }

  U solve(const int s, const int t, T flow) {
    if (flow == 0) [[unlikely]] return 0;
    U res = 0;
    has_negative_edge ? bellman_ford(s) : dijkstra(s);
    while (true) {
      if (dist[t] == uinf) return uinf;
      res += calc(s, t, &flow);
      if (flow == 0) break;
      dijkstra(s);
    }
    return res;
  }

  U solve(const int s, const int t) {
    U res = 0;
    T flow = tinf;
    bellman_ford(s);
    while (potential[t] < 0 && dist[t] != uinf) {
      res += calc(s, t, &flow);
      dijkstra(s);
    }
    return res;
  }

  std::pair<T, U> minimum_cost_maximum_flow(const int s, const int t,
                                            const T flow) {
    if (flow == 0) [[unlikely]] return {0, 0};
    T f = flow;
    U cost = 0;
    has_negative_edge ? bellman_ford(s) : dijkstra(s);
    while (dist[t] != uinf) {
      cost += calc(s, t, &f);
      if (f == 0) break;
      dijkstra(s);
    }
    return {flow - f, cost};
  }

 private:
  const T tinf;
  const int n;
  bool has_negative_edge;
  std::vector<int> prev_v, prev_e;
  std::vector<U> dist, potential;
  std::priority_queue<std::pair<U, int>, std::vector<std::pair<U, int>>,
                      std::greater<std::pair<U, int>>> que;

  void bellman_ford(const int s) {
    std::fill(dist.begin(), dist.end(), uinf);
    dist[s] = 0;
    bool is_updated = true;
    for (int step = 0; step < n && is_updated; ++step) {
      is_updated = false;
      for (int i = 0; i < n; ++i) {
        if (dist[i] == uinf) continue;
        for (int j = 0; std::cmp_less(j, graph[i].size()); ++j) {
          const Edge& e = graph[i][j];
          if (e.cap > 0 && dist[e.dst] > dist[i] + e.cost) {
            dist[e.dst] = dist[i] + e.cost;
            prev_v[e.dst] = i;
            prev_e[e.dst] = j;
            is_updated = true;
          }
        }
      }
    }
    assert(!is_updated);
    for (int i = 0; i < n; ++i) {
      if (dist[i] != uinf) potential[i] += dist[i];
    }
  }

  void dijkstra(const int s) {
    std::fill(dist.begin(), dist.end(), uinf);
    dist[s] = 0;
    que.emplace(0, s);
    while (!que.empty()) {
      const auto [d, ver] = que.top();
      que.pop();
      if (dist[ver] < d) continue;
      for (int i = 0; std::cmp_less(i, graph[ver].size()); ++i) {
        const Edge& e = graph[ver][i];
        const U nxt = dist[ver] + e.cost + potential[ver] - potential[e.dst];
        if (e.cap > 0 && dist[e.dst] > nxt) {
          dist[e.dst] = nxt;
          prev_v[e.dst] = ver;
          prev_e[e.dst] = i;
          que.emplace(dist[e.dst], e.dst);
        }
      }
    }
    for (int i = 0; i < n; ++i) {
      if (dist[i] != uinf) potential[i] += dist[i];
    }
  }

  U calc(const int s, const int t, T* flow) {
    T f = *flow;
    for (int v = t; v != s; v = prev_v[v]) {
      f = std::min(f, graph[prev_v[v]][prev_e[v]].cap);
    }
    *flow -= f;
    for (int v = t; v != s; v = prev_v[v]) {
      Edge& e = graph[prev_v[v]][prev_e[v]];
      e.cap -= f;
      graph[v][e.rev].cap += f;
    }
    return potential[t] * f;
  }
};

}  // namespace emthrm


#line 8 "include/emthrm/graph/flow/matching/weighted_bipartite_matching.hpp"

namespace emthrm {

template <typename T>
struct WeightedBipartiteMatching {
  explicit WeightedBipartiteMatching(const int left, const int right)
      : is_built(false), left(left), right(right), mcf(left + right + 2) {}

  void add_edge(const int src, const int dst, const T cost) {
    mcf.add_edge(src, left + dst, 1, -cost);
  }

  T solve() {
    assert(!is_built);
    is_built = true;
    const int s = left + right, t = left + right + 1;
    for (int i = 0; i < left; ++i) {
      mcf.add_edge(s, i, 1, 0);
    }
    for (int i = 0; i < right; ++i) {
      mcf.add_edge(left + i, t, 1, 0);
    }
    return -mcf.minimum_cost_maximum_flow(s, t, left).second;
  }

  std::vector<int> matching() const {
    assert(is_built);
    std::vector<int> res(left, -1);
    for (int i = 0; i < left; ++i) {
      for (const auto& e : mcf.graph[i]) {
        if (e.cap == 0 && left <= e.dst && e.dst < left + right) {
          res[i] = e.dst - left;
          break;
        }
      }
    }
    return res;
  }

 private:
  bool is_built;
  const int left, right;
  MinimumCostSTFlow<int, T> mcf;
};

}  // namespace emthrm


#line 13 "test/graph/flow/matching/weighted_bipartite_matching.test.cpp"

int main() {
  int n;
  std::cin >> n;
  std::vector<std::vector<int>> w(n, std::vector<int>(n));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      std:: cin >> w[i][j];
    }
  }
  std::vector<std::vector<int>> e(n, std::vector<int>(n));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      std:: cin >> e[i][j];
    }
  }
  std::vector<std::string> f(n);
  long long ans = 0;
  for (int i = 0; i < n; ++i) {
    std::cin >> f[i];
    for (int j = 0; j < n; ++j) {
      if (f[i][j] == 'o') ans += e[i][j];
    }
  }
  emthrm::WeightedBipartiteMatching<long long>
      weighted_bipartite_matching(n, n);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      weighted_bipartite_matching.add_edge(i, j,
                                           f[i][j] == 'o' ? e[i][j] : -w[i][j]);
    }
  }
  std::cout << ans - weighted_bipartite_matching.solve() << '\n';
  std::vector<std::string> taro(n, std::string(n, '.'));
  const std::vector<int> matching = weighted_bipartite_matching.matching();
  for (int i = 0; i < n; ++i) {
    taro[i][matching[i]] = 'o';
  }
  std::vector<int> r, c;
  std::vector<std::string> operate;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (f[i][j] != taro[i][j]) {
        r.emplace_back(i);
        c.emplace_back(j);
        operate.emplace_back(f[i][j] == 'o' ? "erase" : "write");
      }
    }
  }
  const int cnt = r.size();
  std::cout << cnt << '\n';
  for (int i = 0; i < cnt; ++i) {
    std::cout << r[i] + 1 << ' ' << c[i] + 1 << ' ' << operate[i] << '\n';
  }
  return 0;
}

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