test/verify/yosupo-bipartitematching.test.cpp

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• Last update: 2024-04-27 01:27:28+09:00
• Problem: https://judge.yosupo.jp/problem/bipartitematching

Depends on

• Bipartite Flow(二部グラフのフロー) (graph/flow/bipartite-flow.hpp)
• template/template.hpp

Code

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

#include "../../template/template.hpp"

#include "../../graph/flow/bipartite-flow.hpp"

int main() {
  int L, R, M;
  cin >> L >> R >> M;
  BipartiteFlow flow(L, R);
  for(int i = 0; i < M; i++) {
    int a, b;
    cin >> a >> b;
    flow.add_edge(a, b);
  }
  auto es = flow.max_matching();
  cout << es.size() << "\n";
  for(auto &p : es) cout << p.first << " " << p.second << "\n";
}

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

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-bipartitematching.test.cpp"

#line 1 "graph/flow/bipartite-flow.hpp"
/**
 * @brief Bipartite Flow(二部グラフのフロー)
 *
 */
struct BipartiteFlow {
  size_t n, m, time_stamp;
  vector<vector<int> > g, rg;
  vector<int> match_l, match_r, dist, used, alive;
  bool matched;

 public:
  explicit BipartiteFlow(size_t n, size_t m)
      : n(n),
        m(m),
        time_stamp(0),
        g(n),
        rg(m),
        match_l(n, -1),
        match_r(m, -1),
        used(n),
        alive(n, 1),
        matched(false) {}

  void add_edge(int u, int v) {
    g[u].push_back(v);
    rg[v].emplace_back(u);
  }

  vector<pair<int, int> > max_matching() {
    matched = true;
    for (;;) {
      build_augment_path();
      ++time_stamp;
      int flow = 0;
      for (int i = 0; i < (int)n; i++) {
        if (match_l[i] == -1) flow += find_min_dist_augment_path(i);
      }
      if (flow == 0) break;
    }
    vector<pair<int, int> > ret;
    for (int i = 0; i < (int)n; i++) {
      if (match_l[i] >= 0) ret.emplace_back(i, match_l[i]);
    }
    return ret;
  }

  /* http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3198 */
  void erase_edge(int a, int b) {
    if (match_l[a] == b) {
      match_l[a] = -1;
      match_r[b] = -1;
    }
    g[a].erase(find(begin(g[a]), end(g[a]), b));
    rg[b].erase(find(begin(rg[b]), end(rg[b]), a));
  }

  /* http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0334 */
  vector<pair<int, int> > lex_max_matching() {
    if (!matched) max_matching();
    for (auto &vs : g) sort(begin(vs), end(vs));
    vector<pair<int, int> > es;
    for (int i = 0; i < (int)n; i++) {
      if (match_l[i] == -1 || alive[i] == 0) {
        continue;
      }
      match_r[match_l[i]] = -1;
      match_l[i] = -1;
      ++time_stamp;
      find_augment_path(i);
      alive[i] = 0;
      es.emplace_back(i, match_l[i]);
    }
    return es;
  }

  vector<int> min_vertex_cover() {
    auto visited = find_residual_path();
    vector<int> ret;
    for (int i = 0; i < (int)(n + m); i++) {
      if (visited[i] ^ (i < (int)n)) {
        ret.emplace_back(i);
      }
    }
    return ret;
  }

  /* https://atcoder.jp/contests/utpc2013/tasks/utpc2013_11 */
  vector<int> lex_min_vertex_cover(const vector<int> &ord) {
    assert(ord.size() == n + m);
    auto res = build_risidual_graph();
    vector<vector<int> > r_res(n + m + 2);
    for (int i = 0; i < (int)(n + m + 2); i++) {
      for (auto &j : res[i]) r_res[j].emplace_back(i);
    }
    queue<int> que;
    vector<int> visited(n + m + 2, -1);
    auto expand_left = [&](int t) {
      if (visited[t] != -1) return;
      que.emplace(t);
      visited[t] = 1;
      while (!que.empty()) {
        int idx = que.front();
        que.pop();
        for (auto &to : r_res[idx]) {
          if (visited[to] != -1) continue;
          visited[to] = 1;
          que.emplace(to);
        }
      }
    };
    auto expand_right = [&](int t) {
      if (visited[t] != -1) return;
      que.emplace(t);
      visited[t] = 0;
      while (!que.empty()) {
        int idx = que.front();
        que.pop();
        for (auto &to : res[idx]) {
          if (visited[to] != -1) continue;
          visited[to] = 0;
          que.emplace(to);
        }
      }
    };
    expand_right(n + m);
    expand_left(n + m + 1);
    vector<int> ret;
    for (auto &t : ord) {
      if (t < (int)n) {
        expand_left(t);
        if (visited[t] & 1) ret.emplace_back(t);
      } else {
        expand_right(t);
        if (~visited[t] & 1) ret.emplace_back(t);
      }
    }
    return ret;
  }

  vector<int> max_independent_set() {
    auto visited = find_residual_path();
    vector<int> ret;
    for (int i = 0; i < (int)(n + m); i++) {
      if (visited[i] ^ (i >= (int)n)) {
        ret.emplace_back(i);
      }
    }
    return ret;
  }

  vector<pair<int, int> > min_edge_cover() {
    auto es = max_matching();
    for (int i = 0; i < (int)n; i++) {
      if (match_l[i] >= 0) {
        continue;
      }
      if (g[i].empty()) {
        return {};
      }
      es.emplace_back(i, g[i][0]);
    }
    for (int i = 0; i < (int)m; i++) {
      if (match_r[i] >= 0) {
        continue;
      }
      if (rg[i].empty()) {
        return {};
      }
      es.emplace_back(rg[i][0], i);
    }
    return es;
  }

  // left: [0,n), right: [n,n+m), S: n+m, T: n+m+1
  vector<vector<int> > build_risidual_graph() {
    if (!matched) max_matching();
    const size_t S = n + m;
    const size_t T = n + m + 1;
    vector<vector<int> > ris(n + m + 2);
    for (int i = 0; i < (int)n; i++) {
      if (match_l[i] == -1)
        ris[S].emplace_back(i);
      else
        ris[i].emplace_back(S);
    }
    for (int i = 0; i < (int)m; i++) {
      if (match_r[i] == -1)
        ris[i + n].emplace_back(T);
      else
        ris[T].emplace_back(i + n);
    }
    for (int i = 0; i < (int)n; i++) {
      for (auto &j : g[i]) {
        if (match_l[i] == j)
          ris[j + n].emplace_back(i);
        else
          ris[i].emplace_back(j + n);
      }
    }
    return ris;
  }

 private:
  vector<int> find_residual_path() {
    auto res = build_risidual_graph();
    queue<int> que;
    vector<int> visited(n + m + 2);
    que.emplace(n + m);
    visited[n + m] = true;
    while (!que.empty()) {
      int idx = que.front();
      que.pop();
      for (auto &to : res[idx]) {
        if (visited[to]) continue;
        visited[to] = true;
        que.emplace(to);
      }
    }
    return visited;
  }

  void build_augment_path() {
    queue<int> que;
    dist.assign(g.size(), -1);
    for (int i = 0; i < (int)n; i++) {
      if (match_l[i] == -1) {
        que.emplace(i);
        dist[i] = 0;
      }
    }
    while (!que.empty()) {
      int a = que.front();
      que.pop();
      for (auto &b : g[a]) {
        int c = match_r[b];
        if (c >= 0 && dist[c] == -1) {
          dist[c] = dist[a] + 1;
          que.emplace(c);
        }
      }
    }
  }

  bool find_min_dist_augment_path(int a) {
    used[a] = time_stamp;
    for (auto &b : g[a]) {
      int c = match_r[b];
      if (c < 0 || (used[c] != (int)time_stamp && dist[c] == dist[a] + 1 &&
                    find_min_dist_augment_path(c))) {
        match_r[b] = a;
        match_l[a] = b;
        return true;
      }
    }
    return false;
  }

  bool find_augment_path(int a) {
    used[a] = time_stamp;
    for (auto &b : g[a]) {
      int c = match_r[b];
      if (c < 0 || (alive[c] == 1 && used[c] != (int)time_stamp &&
                    find_augment_path(c))) {
        match_r[b] = a;
        match_l[a] = b;
        return true;
      }
    }
    return false;
  }
};
#line 6 "test/verify/yosupo-bipartitematching.test.cpp"

int main() {
  int L, R, M;
  cin >> L >> R >> M;
  BipartiteFlow flow(L, R);
  for(int i = 0; i < M; i++) {
    int a, b;
    cin >> a >> b;
    flow.add_edge(a, b);
  }
  auto es = flow.max_matching();
  cout << es.size() << "\n";
  for(auto &p : es) cout << p.first << " " << p.second << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	cycle_00	AC	108 ms	20 MB
g++	cycle_01	AC	109 ms	21 MB
g++	example_00	AC	7 ms	4 MB
g++	kuhn_killer_00	AC	54 ms	17 MB
g++	line_00	AC	58 ms	17 MB
g++	line_01	AC	58 ms	17 MB
g++	line_random_00	AC	96 ms	18 MB
g++	line_random_01	AC	94 ms	18 MB
g++	many_paths_00	AC	160 ms	15 MB
g++	many_paths_01	AC	124 ms	15 MB
g++	many_paths_02	AC	139 ms	15 MB
g++	many_smalls_00	AC	59 ms	12 MB
g++	many_smalls_01	AC	58 ms	12 MB
g++	max_random_00	AC	76 ms	17 MB
g++	max_random_01	AC	75 ms	17 MB
g++	max_random_02	AC	75 ms	17 MB
g++	random_00	AC	12 ms	7 MB
g++	random_01	AC	43 ms	10 MB
g++	random_02	AC	36 ms	11 MB
g++	random_03	AC	42 ms	8 MB
g++	random_04	AC	14 ms	8 MB
g++	random_05	AC	23 ms	8 MB
g++	random_06	AC	65 ms	12 MB
g++	random_07	AC	20 ms	9 MB
g++	random_08	AC	35 ms	8 MB
g++	random_09	AC	45 ms	10 MB
clang++	cycle_00	AC	108 ms	20 MB
clang++	cycle_01	AC	109 ms	21 MB
clang++	example_00	AC	7 ms	4 MB
clang++	kuhn_killer_00	AC	54 ms	17 MB
clang++	line_00	AC	59 ms	17 MB
clang++	line_01	AC	60 ms	17 MB
clang++	line_random_00	AC	115 ms	18 MB
clang++	line_random_01	AC	94 ms	18 MB
clang++	many_paths_00	AC	155 ms	15 MB
clang++	many_paths_01	AC	120 ms	15 MB
clang++	many_paths_02	AC	135 ms	15 MB
clang++	many_smalls_00	AC	61 ms	12 MB
clang++	many_smalls_01	AC	57 ms	12 MB
clang++	max_random_00	AC	73 ms	17 MB
clang++	max_random_01	AC	74 ms	17 MB
clang++	max_random_02	AC	75 ms	17 MB
clang++	random_00	AC	12 ms	7 MB
clang++	random_01	AC	43 ms	10 MB
clang++	random_02	AC	36 ms	11 MB
clang++	random_03	AC	42 ms	8 MB
clang++	random_04	AC	13 ms	8 MB
clang++	random_05	AC	23 ms	8 MB
clang++	random_06	AC	59 ms	12 MB
clang++	random_07	AC	20 ms	9 MB
clang++	random_08	AC	35 ms	8 MB
clang++	random_09	AC	44 ms	10 MB

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