Luzhiled's Library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub ei1333/library

:heavy_check_mark: test/verify/yosupo-bipartite-edge-coloring.test.cpp

Depends on

Code

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

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


#include "../../graph/others/bipartite-graph-edge-coloring.hpp"

int main() {
  int L, R, M;
  cin >> L >> R >> M;
  BipariteGraphEdgeColoring ecbg;
  for(int i = 0; i < M; i++) {
    int a, b;
    cin >> a >> b;
    ecbg.add_edge(a, b);
  }
  auto res = ecbg.build();
  cout << res.size() << "\n";
  vector< int > color(M);
  for(int i = 0; i < res.size(); i++) {
    for(auto &j : res[i]) color[j] = i;
  }
  for(auto &c : color) cout << c << "\n";
}

#line 1 "test/verify/yosupo-bipartite-edge-coloring.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/bipartite_edge_coloring

#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-bipartite-edge-coloring.test.cpp"


#line 2 "graph/others/bipartite-graph-edge-coloring.hpp"

#line 2 "structure/union-find/union-find.hpp"

struct UnionFind {
  vector<int> data;

  UnionFind() = default;

  explicit UnionFind(size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if (data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) { return -data[find(k)]; }

  bool same(int x, int y) { return find(x) == find(y); }

  vector<vector<int> > groups() {
    int n = (int)data.size();
    vector<vector<int> > ret(n);
    for (int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(remove_if(begin(ret), end(ret),
                        [&](const vector<int> &v) { return v.empty(); }),
              end(ret));
    return ret;
  }
};
#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 2 "graph/others/eulerian-trail.hpp"

#line 4 "graph/others/eulerian-trail.hpp"

/**
 * @brief Eulerian Trail(オイラー路)
 *
 */
template <bool directed>
struct EulerianTrail {
  vector<vector<pair<int, int> > > g;
  vector<pair<int, int> > es;
  int M;
  vector<int> used_vertex, used_edge, deg;

  explicit EulerianTrail(int V) : g(V), M(0), used_vertex(V), deg(V) {}

  void add_edge(int a, int b) {
    es.emplace_back(a, b);
    g[a].emplace_back(b, M);
    if (directed) {
      deg[a]++;
      deg[b]--;
    } else {
      g[b].emplace_back(a, M);
      deg[a]++;
      deg[b]++;
    }
    M++;
  }

  pair<int, int> get_edge(int idx) const { return es[idx]; }

  vector<vector<int> > enumerate_eulerian_trail() {
    if (directed) {
      for (auto &p : deg)
        if (p != 0) return {};
    } else {
      for (auto &p : deg)
        if (p & 1) return {};
    }
    used_edge.assign(M, 0);
    vector<vector<int> > ret;
    for (int i = 0; i < (int)g.size(); i++) {
      if (g[i].empty() || used_vertex[i]) continue;
      ret.emplace_back(go(i));
    }
    return ret;
  }

  vector<vector<int> > enumerate_semi_eulerian_trail() {
    UnionFind uf(g.size());
    for (auto &p : es) uf.unite(p.first, p.second);
    vector<vector<int> > group(g.size());
    for (int i = 0; i < (int)g.size(); i++) group[uf.find(i)].emplace_back(i);
    vector<vector<int> > ret;
    used_edge.assign(M, 0);
    for (auto &vs : group) {
      if (vs.empty()) continue;
      int latte = -1, malta = -1;
      if (directed) {
        for (auto &p : vs) {
          if (abs(deg[p]) > 1) {
            return {};
          } else if (deg[p] == 1) {
            if (latte >= 0) return {};
            latte = p;
          }
        }
      } else {
        for (auto &p : vs) {
          if (deg[p] & 1) {
            if (latte == -1)
              latte = p;
            else if (malta == -1)
              malta = p;
            else
              return {};
          }
        }
      }
      ret.emplace_back(go(latte == -1 ? vs.front() : latte));
      if (ret.back().empty()) ret.pop_back();
    }
    return ret;
  }

  vector<int> go(int s) {
    stack<pair<int, int> > st;
    vector<int> ord;
    st.emplace(s, -1);
    while (!st.empty()) {
      int idx = st.top().first;
      used_vertex[idx] = true;
      if (g[idx].empty()) {
        ord.emplace_back(st.top().second);
        st.pop();
      } else {
        auto e = g[idx].back();
        g[idx].pop_back();
        if (used_edge[e.second]) continue;
        used_edge[e.second] = true;
        st.emplace(e);
      }
    }
    ord.pop_back();
    reverse(ord.begin(), ord.end());
    return ord;
  }
};
#line 6 "graph/others/bipartite-graph-edge-coloring.hpp"

/**
 * @brief Bipartite Graph Edge Coloring(二部グラフの辺彩色)
 *
 * @see https://ei1333.hateblo.jp/entry/2020/08/25/015955
 */
struct BipariteGraphEdgeColoring {
 private:
  vector<vector<int> > ans;
  vector<int> A, B;
  int L, R;

  struct RegularGraph {
    int k{}, n{};
    vector<int> A, B;
  };
  RegularGraph g;

  static UnionFind contract(valarray<int> &deg, int k) {
    using pi = pair<int, int>;
    priority_queue<pi, vector<pi>, greater<> > que;
    for (int i = 0; i < (int)deg.size(); i++) {
      que.emplace(deg[i], i);
    }
    UnionFind uf(deg.size());
    while (que.size() > 1) {
      auto p = que.top();
      que.pop();
      auto q = que.top();
      que.pop();
      if (p.first + q.first > k) continue;
      p.first += q.first;
      uf.unite(p.second, q.second);
      que.emplace(p);
    }
    return uf;
  }

  RegularGraph build_k_regular_graph() {
    valarray<int> deg[2];
    deg[0] = valarray<int>(L);
    deg[1] = valarray<int>(R);
    for (auto &p : A) deg[0][p]++;
    for (auto &p : B) deg[1][p]++;

    int k = max(deg[0].max(), deg[1].max());

    /* step 1 */
    UnionFind uf[2];
    uf[0] = contract(deg[0], k);
    uf[1] = contract(deg[1], k);

    vector<int> id[2];
    int ptr[] = {0, 0};
    id[0] = vector<int>(L);
    id[1] = vector<int>(R);
    for (int i = 0; i < L; i++)
      if (uf[0].find(i) == i) id[0][i] = ptr[0]++;
    for (int i = 0; i < R; i++)
      if (uf[1].find(i) == i) id[1][i] = ptr[1]++;

    /* step 2 */
    int N = max(ptr[0], ptr[1]);
    deg[0] = valarray<int>(N);
    deg[1] = valarray<int>(N);

    /* step 3 */
    vector<int> C, D;
    C.reserve(N * k);
    D.reserve(N * k);
    for (int i = 0; i < (int)A.size(); i++) {
      int u = id[0][uf[0].find(A[i])];
      int v = id[1][uf[1].find(B[i])];
      C.emplace_back(u);
      D.emplace_back(v);
      deg[0][u]++;
      deg[1][v]++;
    }
    int j = 0;
    for (int i = 0; i < N; i++) {
      while (deg[0][i] < k) {
        while (deg[1][j] == k) ++j;
        C.emplace_back(i);
        D.emplace_back(j);
        ++deg[0][i];
        ++deg[1][j];
      }
    }

    return {k, N, C, D};
  }

  void rec(const vector<int> &ord, int k) {
    if (k == 0) {
      return;
    } else if (k == 1) {
      ans.emplace_back(ord);
      return;
    } else if ((k & 1) == 0) {
      EulerianTrail<false> et(g.n + g.n);
      for (auto &p : ord) et.add_edge(g.A[p], g.B[p] + g.n);
      auto paths = et.enumerate_eulerian_trail();
      vector<int> path;
      for (auto &ps : paths) {
        for (auto &e : ps) path.emplace_back(ord[e]);
      }
      vector<int> beet[2];
      for (int i = 0; i < (int)path.size(); i++) {
        beet[i & 1].emplace_back(path[i]);
      }
      rec(beet[0], k / 2);
      rec(beet[1], k / 2);
    } else {
      BipartiteFlow flow(g.n, g.n);
      for (auto &i : ord) flow.add_edge(g.A[i], g.B[i]);
      flow.max_matching();
      vector<int> beet;
      ans.emplace_back();
      for (auto &i : ord) {
        if (flow.match_l[g.A[i]] == g.B[i]) {
          flow.match_l[g.A[i]] = -1;
          ans.back().emplace_back(i);
        } else {
          beet.emplace_back(i);
        }
      }
      rec(beet, k - 1);
    }
  }

 public:
  explicit BipariteGraphEdgeColoring() : L(0), R(0) {}

  void add_edge(int a, int b) {
    A.emplace_back(a);
    B.emplace_back(b);
    L = max(L, a + 1);
    R = max(R, b + 1);
  }

  vector<vector<int> > build() {
    g = build_k_regular_graph();
    vector<int> ord(g.A.size());
    iota(ord.begin(), ord.end(), 0);
    rec(ord, g.k);
    vector<vector<int> > res;
    for (int i = 0; i < (int)ans.size(); i++) {
      res.emplace_back();
      for (auto &j : ans[i])
        if (j < (int)A.size()) res.back().emplace_back(j);
    }
    return res;
  }
};
#line 7 "test/verify/yosupo-bipartite-edge-coloring.test.cpp"

int main() {
  int L, R, M;
  cin >> L >> R >> M;
  BipariteGraphEdgeColoring ecbg;
  for(int i = 0; i < M; i++) {
    int a, b;
    cin >> a >> b;
    ecbg.add_edge(a, b);
  }
  auto res = ecbg.build();
  cout << res.size() << "\n";
  vector< int > color(M);
  for(int i = 0; i < res.size(); i++) {
    for(auto &j : res[i]) color[j] = i;
  }
  for(auto &c : color) cout << c << "\n";
}

Test cases

Env Name Status Elapsed Memory
g++ example_00 :heavy_check_mark: AC 6 ms 4 MB
g++ line_00 :heavy_check_mark: AC 39 ms 15 MB
g++ line_01 :heavy_check_mark: AC 39 ms 14 MB
g++ many_smalls_00 :heavy_check_mark: AC 115 ms 23 MB
g++ many_smalls_01 :heavy_check_mark: AC 115 ms 23 MB
g++ max_random_00 :heavy_check_mark: AC 114 ms 18 MB
g++ max_random_01 :heavy_check_mark: AC 114 ms 18 MB
g++ max_random_02 :heavy_check_mark: AC 149 ms 28 MB
g++ random_00 :heavy_check_mark: AC 30 ms 6 MB
g++ random_01 :heavy_check_mark: AC 36 ms 8 MB
g++ random_02 :heavy_check_mark: AC 117 ms 21 MB
g++ random_03 :heavy_check_mark: AC 106 ms 21 MB
g++ random_04 :heavy_check_mark: AC 44 ms 8 MB
g++ random_05 :heavy_check_mark: AC 112 ms 21 MB
g++ random_06 :heavy_check_mark: AC 39 ms 8 MB
g++ random_07 :heavy_check_mark: AC 53 ms 10 MB
g++ random_08 :heavy_check_mark: AC 82 ms 15 MB
g++ random_09 :heavy_check_mark: AC 34 ms 8 MB
g++ worst_00 :heavy_check_mark: AC 209 ms 23 MB
g++ worst_01 :heavy_check_mark: AC 210 ms 23 MB
g++ worst_02 :heavy_check_mark: AC 210 ms 23 MB
clang++ example_00 :heavy_check_mark: AC 6 ms 4 MB
clang++ line_00 :heavy_check_mark: AC 39 ms 14 MB
clang++ line_01 :heavy_check_mark: AC 40 ms 15 MB
clang++ many_smalls_00 :heavy_check_mark: AC 113 ms 23 MB
clang++ many_smalls_01 :heavy_check_mark: AC 112 ms 23 MB
clang++ max_random_00 :heavy_check_mark: AC 113 ms 18 MB
clang++ max_random_01 :heavy_check_mark: AC 113 ms 18 MB
clang++ max_random_02 :heavy_check_mark: AC 147 ms 28 MB
clang++ random_00 :heavy_check_mark: AC 29 ms 6 MB
clang++ random_01 :heavy_check_mark: AC 36 ms 9 MB
clang++ random_02 :heavy_check_mark: AC 116 ms 21 MB
clang++ random_03 :heavy_check_mark: AC 108 ms 21 MB
clang++ random_04 :heavy_check_mark: AC 43 ms 8 MB
clang++ random_05 :heavy_check_mark: AC 111 ms 21 MB
clang++ random_06 :heavy_check_mark: AC 40 ms 8 MB
clang++ random_07 :heavy_check_mark: AC 52 ms 10 MB
clang++ random_08 :heavy_check_mark: AC 80 ms 15 MB
clang++ random_09 :heavy_check_mark: AC 34 ms 8 MB
clang++ worst_00 :heavy_check_mark: AC 199 ms 23 MB
clang++ worst_01 :heavy_check_mark: AC 203 ms 23 MB
clang++ worst_02 :heavy_check_mark: AC 198 ms 23 MB
Back to top page