tests/bipartite_matching.test.cpp

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• Last update: 2025-01-22 03:51:11+00:00
• Problem: https://judge.yosupo.jp/problem/bipartitematching

Depends on

• Matching on bipartite graph (tools/bipartite_matching.hpp)

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/bipartitematching

#include <iostream>
#include "tools/bipartite_matching.hpp"

using ll = long long;

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  ll L, R, M;
  std::cin >> L >> R >> M;
  tools::bipartite_matching graph(L, R);
  for (ll i = 0; i < M; ++i) {
    ll a, b;
    std::cin >> a >> b;
    graph.add_edge(a, b);
  }

  const auto edges = graph.query();
  std::cout << edges.size() << '\n';
  for (const auto k : edges) {
    std::cout << graph.get_edge(k).from << ' ' << graph.get_edge(k).to << '\n';
  }

  return 0;
}

#line 1 "tests/bipartite_matching.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/bipartitematching

#include <iostream>
#line 1 "tools/bipartite_matching.hpp"



#include <cstddef>
#include <vector>
#include <cassert>
#line 1 "lib/ac-library/atcoder/maxflow.hpp"



#include <algorithm>
#line 6 "lib/ac-library/atcoder/maxflow.hpp"
#include <limits>
#include <queue>
#line 9 "lib/ac-library/atcoder/maxflow.hpp"

#line 1 "lib/ac-library/atcoder/internal_queue.hpp"



#line 5 "lib/ac-library/atcoder/internal_queue.hpp"

namespace atcoder {

namespace internal {

template <class T> struct simple_queue {
    std::vector<T> payload;
    int pos = 0;
    void reserve(int n) { payload.reserve(n); }
    int size() const { return int(payload.size()) - pos; }
    bool empty() const { return pos == int(payload.size()); }
    void push(const T& t) { payload.push_back(t); }
    T& front() { return payload[pos]; }
    void clear() {
        payload.clear();
        pos = 0;
    }
    void pop() { pos++; }
};

}  // namespace internal

}  // namespace atcoder


#line 11 "lib/ac-library/atcoder/maxflow.hpp"

namespace atcoder {

template <class Cap> struct mf_graph {
  public:
    mf_graph() : _n(0) {}
    explicit mf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap});
        g[to].push_back(_edge{from, from_id, 0});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
    };

    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
    }
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result;
        for (int i = 0; i < m; i++) {
            result.push_back(get_edge(i));
        }
        return result;
    }
    void change_edge(int i, Cap new_cap, Cap new_flow) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        assert(0 <= new_flow && new_flow <= new_cap);
        auto& _e = g[pos[i].first][pos[i].second];
        auto& _re = g[_e.to][_e.rev];
        _e.cap = new_cap - new_flow;
        _re.cap = new_flow;
    }

    Cap flow(int s, int t) {
        return flow(s, t, std::numeric_limits<Cap>::max());
    }
    Cap flow(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        std::vector<int> level(_n), iter(_n);
        internal::simple_queue<int> que;

        auto bfs = [&]() {
            std::fill(level.begin(), level.end(), -1);
            level[s] = 0;
            que.clear();
            que.push(s);
            while (!que.empty()) {
                int v = que.front();
                que.pop();
                for (auto e : g[v]) {
                    if (e.cap == 0 || level[e.to] >= 0) continue;
                    level[e.to] = level[v] + 1;
                    if (e.to == t) return;
                    que.push(e.to);
                }
            }
        };
        auto dfs = [&](auto self, int v, Cap up) {
            if (v == s) return up;
            Cap res = 0;
            int level_v = level[v];
            for (int& i = iter[v]; i < int(g[v].size()); i++) {
                _edge& e = g[v][i];
                if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
                Cap d =
                    self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));
                if (d <= 0) continue;
                g[v][i].cap += d;
                g[e.to][e.rev].cap -= d;
                res += d;
                if (res == up) return res;
            }
            level[v] = _n;
            return res;
        };

        Cap flow = 0;
        while (flow < flow_limit) {
            bfs();
            if (level[t] == -1) break;
            std::fill(iter.begin(), iter.end(), 0);
            Cap f = dfs(dfs, t, flow_limit - flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }

    std::vector<bool> min_cut(int s) {
        std::vector<bool> visited(_n);
        internal::simple_queue<int> que;
        que.push(s);
        while (!que.empty()) {
            int p = que.front();
            que.pop();
            visited[p] = true;
            for (auto e : g[p]) {
                if (e.cap && !visited[e.to]) {
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return visited;
    }

  private:
    int _n;
    struct _edge {
        int to, rev;
        Cap cap;
    };
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};

}  // namespace atcoder


#line 8 "tools/bipartite_matching.hpp"

namespace tools {

  class bipartite_matching {
  public:
    struct edge {
      ::std::size_t id;
      ::std::size_t from;
      ::std::size_t to;
    };

  private:
    ::std::size_t m_size1;
    ::std::size_t m_size2;
    ::atcoder::mf_graph<int> m_graph;
    ::std::vector<edge> m_edges;

  public:
    bipartite_matching() = default;
    bipartite_matching(const ::tools::bipartite_matching&) = default;
    bipartite_matching(::tools::bipartite_matching&&) = default;
    ~bipartite_matching() = default;
    ::tools::bipartite_matching& operator=(const ::tools::bipartite_matching&) = default;
    ::tools::bipartite_matching& operator=(::tools::bipartite_matching&&) = default;

    bipartite_matching(const ::std::size_t size1, const ::std::size_t size2) :
      m_size1(size1), m_size2(size2), m_graph(size1 + size2 + 2) {
      for (::std::size_t i = 0; i < size1; ++i) {
        this->m_graph.add_edge(size1 + size2, i, 1);
      }
      for (::std::size_t i = 0; i < size2; ++i) {
        this->m_graph.add_edge(size1 + i, size1 + size2 + 1, 1);
      }
    }

    ::std::size_t size1() const {
      return this->m_size1;
    }

    ::std::size_t size2() const {
      return this->m_size2;
    }

    ::std::size_t add_edge(const ::std::size_t i, const ::std::size_t j) {
      assert(i < this->size1());
      assert(j < this->size2());
      this->m_graph.add_edge(i, this->m_size1 + j, 1);
      this->m_edges.emplace_back(edge({this->m_edges.size(), i, j}));
      return this->m_edges.size() - 1;
    }

    const edge& get_edge(const ::std::size_t k) const {
      assert(k < this->m_edges.size());
      return this->m_edges[k];
    }

    const ::std::vector<edge>& edges() const {
      return this->m_edges;
    }

    ::std::vector<::std::size_t> query() {
      ::std::vector<::std::size_t> edges;

      this->m_graph.flow(this->m_size1 + this->m_size2, this->m_size1 + this->m_size2 + 1);
      for (::std::size_t i = 0; i < this->m_edges.size(); ++i) {
        if (this->m_graph.get_edge(this->m_size1 + this->m_size2 + i).flow == 1) {
          edges.push_back(i);
        }
      }

      return edges;
    }
  };
}


#line 5 "tests/bipartite_matching.test.cpp"

using ll = long long;

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  ll L, R, M;
  std::cin >> L >> R >> M;
  tools::bipartite_matching graph(L, R);
  for (ll i = 0; i < M; ++i) {
    ll a, b;
    std::cin >> a >> b;
    graph.add_edge(a, b);
  }

  const auto edges = graph.query();
  std::cout << edges.size() << '\n';
  for (const auto k : edges) {
    std::cout << graph.get_edge(k).from << ' ' << graph.get_edge(k).to << '\n';
  }

  return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	cycle_00	AC	572 ms	45 MB
g++	cycle_01	AC	583 ms	49 MB
g++	example_00	AC	5 ms	4 MB
g++	issue1068_00	AC	4 ms	4 MB
g++	issue1068_large_00	AC	61 ms	30 MB
g++	issue1068_large_01	AC	60 ms	28 MB
g++	issue1068_large_02	AC	84 ms	29 MB
g++	issue1068_large_03	AC	65 ms	35 MB
g++	issue1068_large_04	AC	61 ms	30 MB
g++	issue1068_large_05	AC	90 ms	36 MB
g++	issue1124_00	AC	95 ms	25 MB
g++	issue1124_01	AC	52 ms	24 MB
g++	issue1124_02	AC	47 ms	24 MB
g++	kuhn_killer_00	AC	76 ms	33 MB
g++	line_00	AC	144 ms	64 MB
g++	line_01	AC	143 ms	64 MB
g++	line_random_00	AC	635 ms	62 MB
g++	line_random_01	AC	607 ms	43 MB
g++	many_paths_00	AC	521 ms	37 MB
g++	many_paths_01	AC	382 ms	36 MB
g++	many_paths_02	AC	445 ms	37 MB
g++	many_smalls_00	AC	95 ms	29 MB
g++	many_smalls_01	AC	94 ms	29 MB
g++	max_random_00	AC	143 ms	34 MB
g++	max_random_01	AC	149 ms	35 MB
g++	max_random_02	AC	149 ms	35 MB
g++	random_00	AC	19 ms	12 MB
g++	random_01	AC	55 ms	22 MB
g++	random_02	AC	65 ms	20 MB
g++	random_03	AC	57 ms	18 MB
g++	random_04	AC	26 ms	15 MB
g++	random_05	AC	28 ms	13 MB
g++	random_06	AC	127 ms	27 MB
g++	random_07	AC	28 ms	15 MB
g++	random_08	AC	54 ms	22 MB
g++	random_09	AC	59 ms	22 MB

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