flow/bipartite_dense.hpp

• View this file on GitHub
• Last update: 2025-05-05 02:10:07+09:00
• Include: #include "flow/bipartite_dense.hpp"
• Link: https://codeforces.com/contest/1045/problem/A
• Link: https://codeforces.com/contest/786/problem/E
• Link: https://qoj.ac/problem/6308

Depends on

• ds/my_bitset.hpp

Verified with

• test/3_yukicoder/421.test.cpp
• test/3_yukicoder/421_2.test.cpp

Code

#include "ds/my_bitset.hpp"

// vc<bitset> で biadj matrix を渡す
// N_1^2N_2/w.
// (5000,5000) で 300ms 程度で動く場合がある
// https://qoj.ac/problem/6308
// (10000?, 5000) 655ms
// https://codeforces.com/contest/1045/problem/A
// (10000, 20000) で 3837ms
// https://codeforces.com/contest/786/problem/E
// (10000, 10000) 6500ms TLE. row, col とも shuffle で 3000ms AC.
// bitset の方が My_Bitset より高速？(2024/05/27)
template <typename BS>
struct BipartiteMatching_Dense {
  int N1, N2;
  vc<BS>& adj;
  vc<int> match_1, match_2;
  vc<int> que;
  vc<int> prev;
  BS vis;

  BipartiteMatching_Dense(vc<BS>& adj, int N1, int N2) : N1(N1), N2(N2), adj(adj), match_1(N1, -1), match_2(N2, -1) {
    if constexpr (is_same_v<BS, My_Bitset>) vis.resize(N2);
    FOR(s, N1) bfs(s);
  }

  void bfs(int s) {
    if (match_1[s] != -1) return;
    que.resize(N1), prev.resize(N1);
    int l = 0, r = 0;
    prev[s] = -1;
    vis.set();

    que[r++] = s;
    while (l < r) {
      int u = que[l++];
      BS cand = vis & adj[u];
      for (int v = cand._Find_first(); v < N2; v = cand._Find_next(v)) {
        vis[v] = 0;
        if (match_2[v] != -1) {
          que[r++] = match_2[v];
          prev[match_2[v]] = u;
          continue;
        }
        int a = u, b = v;
        while (a != -1) {
          int t = match_1[a];
          match_1[a] = b, match_2[b] = a, a = prev[a], b = t;
        }
        return;
      }
    }
    return;
  }

  vc<pair<int, int>> matching() {
    vc<pair<int, int>> res;
    FOR(v, N1) if (match_1[v] != -1) res.eb(v, match_1[v]);
    return res;
  }

  pair<vc<int>, vc<int>> vertex_cover() {
    vc<int> que(N1);
    int l = 0, r = 0;
    vis.set();
    vc<bool> done(N1);
    FOR(i, N1) {
      if (match_1[i] == -1) done[i] = 1, que[r++] = i;
    }
    while (l < r) {
      int a = que[l++];
      BS cand = adj[a] & vis;
      for (int b = cand._Find_first(); b < N2; b = cand._Find_next(b)) {
        vis[b] = 0;
        int to = match_2[b];
        assert(to != -1);
        if (!done[to]) done[to] = 1, que[r++] = to;
      }
    }
    vc<int> left, right;
    FOR(i, N1) if (!done[i]) left.eb(i);
    FOR(i, N2) if (!vis[i]) right.eb(i);
    return {left, right};
  }
};

#line 2 "ds/my_bitset.hpp"

// https://codeforces.com/contest/914/problem/F
// https://yukicoder.me/problems/no/142
// わずかに普通の bitset より遅いときもあるようだが，
// 固定長にしたくないときや slice 操作が必要なときに使う
struct My_Bitset {
  using T = My_Bitset;
  int N;
  vc<u64> dat;

  // x で埋める
  My_Bitset(int N = 0, int x = 0) : N(N) {
    assert(x == 0 || x == 1);
    u64 v = (x == 0 ? 0 : -1);
    dat.assign((N + 63) >> 6, v);
    if (N) dat.back() >>= (64 * len(dat) - N);
  }

  int size() { return N; }

  void resize(int size) {
    dat.resize((size + 63) >> 6);
    int remainingBits = size & 63;
    if (remainingBits != 0) {
      u64 mask = (u64(1) << remainingBits) - 1;
      dat.back() &= mask;
    }
    N = size;
  }

  void append(int idx, bool b) {
    assert(N == idx);
    resize(idx + 1), (*this)[idx] = b;
  }

  static T from_string(string &S) {
    int N = len(S);
    T ANS(N);
    FOR(i, N) ANS[i] = (S[i] == '1');
    return ANS;
  }

  // thanks to chatgpt!
  class Proxy {
  public:
    Proxy(vc<u64> &d, int i) : dat(d), index(i) {}
    operator bool() const { return (dat[index >> 6] >> (index & 63)) & 1; }

    Proxy &operator=(u64 value) {
      dat[index >> 6] &= ~(u64(1) << (index & 63));
      dat[index >> 6] |= (value & 1) << (index & 63);
      return *this;
    }
    void flip() {
      dat[index >> 6] ^= (u64(1) << (index & 63)); // XOR to flip the bit
    }

  private:
    vc<u64> &dat;
    int index;
  };

  Proxy operator[](int i) { return Proxy(dat, i); }

  bool operator==(const T &p) {
    assert(N == p.N);
    FOR(i, len(dat)) if (dat[i] != p.dat[i]) return false;
    return true;
  }

  T &operator&=(const T &p) {
    assert(N == p.N);
    FOR(i, len(dat)) dat[i] &= p.dat[i];
    return *this;
  }
  T &operator|=(const T &p) {
    assert(N == p.N);
    FOR(i, len(dat)) dat[i] |= p.dat[i];
    return *this;
  }
  T &operator^=(const T &p) {
    assert(N == p.N);
    FOR(i, len(dat)) dat[i] ^= p.dat[i];
    return *this;
  }
  T operator&(const T &p) const { return T(*this) &= p; }
  T operator|(const T &p) const { return T(*this) |= p; }
  T operator^(const T &p) const { return T(*this) ^= p; }
  T operator~() const {
    T p = (*this);
    p.flip_range(0, N);
    return p;
  }

  void set_minus_inplace(T &other) {
    assert(N == other.N);
    FOR(i, len(dat)) dat[i] = dat[i] & (~other.dat[i]);
  }

  T set_minus(T other) {
    assert(N == other.N);
    FOR(i, len(dat)) other.dat[i] = dat[i] & (~other.dat[i]);
    return other;
  }

  int count() {
    int ans = 0;
    for (u64 val: dat) ans += popcnt(val);
    return ans;
  }

  int dot(T &p) {
    assert(N == p.N);
    int ans = 0;
    FOR(i, len(dat)) ans += popcnt(dat[i] & p.dat[i]);
    return ans;
  }

  int next(int i) {
    chmax(i, 0);
    if (i >= N) return N;
    int k = i >> 6;
    {
      u64 x = dat[k];
      int s = i & 63;
      x = (x >> s) << s;
      if (x) return (k << 6) | lowbit(x);
    }
    FOR(idx, k + 1, len(dat)) {
      if (dat[idx] == 0) continue;
      return (idx << 6) | lowbit(dat[idx]);
    }
    return N;
  }

  int prev(int i) {
    chmin(i, N - 1);
    if (i <= -1) return -1;
    int k = i >> 6;
    if ((i & 63) < 63) {
      u64 x = dat[k];
      x &= (u64(1) << ((i & 63) + 1)) - 1;
      if (x) return (k << 6) | topbit(x);
      --k;
    }
    FOR_R(idx, k + 1) {
      if (dat[idx] == 0) continue;
      return (idx << 6) | topbit(dat[idx]);
    }
    return -1;
  }

  My_Bitset range(int L, int R) {
    assert(L <= R);
    My_Bitset p(R - L);
    int rm = (R - L) & 63;
    FOR(rm) {
      p[R - L - 1] = bool((*this)[R - 1]);
      --R;
    }
    int n = (R - L) >> 6;
    int hi = L & 63;
    int lo = 64 - hi;
    int s = L >> 6;
    if (hi == 0) {
      FOR(i, n) { p.dat[i] ^= dat[s + i]; }
    } else {
      FOR(i, n) { p.dat[i] ^= (dat[s + i] >> hi) ^ (dat[s + i + 1] << lo); }
    }
    return p;
  }

  My_Bitset slice(int L, int R) { return range(L, R); }

  int count_range(int L, int R) {
    assert(L <= R);
    int cnt = 0;
    while ((L < R) && (L & 63)) cnt += (*this)[L++];
    while ((L < R) && (R & 63)) cnt += (*this)[--R];
    int l = L >> 6, r = R >> 6;
    FOR(i, l, r) cnt += popcnt(dat[i]);
    return cnt;
  }

  // [L,R) に p を代入
  void assign_to_range(int L, int R, My_Bitset &p) {
    assert(p.N == R - L);
    int a = 0, b = p.N;
    while (L < R && (L & 63)) { (*this)[L++] = bool(p[a++]); }
    while (L < R && (R & 63)) { (*this)[--R] = bool(p[--b]); }
    // p[a:b] を [L:R] に
    int l = L >> 6, r = R >> 6;
    int s = a >> 6, t = b >> t;
    int n = r - l;
    if (!(a & 63)) {
      FOR(i, n) dat[l + i] = p.dat[s + i];
    } else {
      int hi = a & 63;
      int lo = 64 - hi;
      FOR(i, n) dat[l + i] = (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo);
    }
  }

  // [L,R) に p を xor
  void xor_to_range(int L, int R, My_Bitset &p) {
    assert(p.N == R - L);
    int a = 0, b = p.N;
    while (L < R && (L & 63)) {
      dat[L >> 6] ^= u64(p[a]) << (L & 63);
      ++a, ++L;
    }
    while (L < R && (R & 63)) {
      --b, --R;
      dat[R >> 6] ^= u64(p[b]) << (R & 63);
    }
    // p[a:b] を [L:R] に
    int l = L >> 6, r = R >> 6;
    int s = a >> 6, t = b >> t;
    int n = r - l;
    if (!(a & 63)) {
      FOR(i, n) dat[l + i] ^= p.dat[s + i];
    } else {
      int hi = a & 63;
      int lo = 64 - hi;
      FOR(i, n) dat[l + i] ^= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo);
    }
  }

  // 行列基本変形で使うやつ
  // p は [i:N) にしかないとして p を xor する
  void xor_suffix(int i, My_Bitset &p) {
    assert(N == p.N && 0 <= i && i < N);
    FOR(k, i / 64, len(dat)) { dat[k] ^= p.dat[k]; }
  }

  // [L,R) に p を and
  void and_to_range(int L, int R, My_Bitset &p) {
    assert(p.N == R - L);
    int a = 0, b = p.N;
    while (L < R && (L & 63)) {
      if (!p[a]) (*this)[L] = 0;
      a++, L++;
    }
    while (L < R && (R & 63)) {
      --b, --R;
      if (!p[b]) (*this)[R] = 0;
    }
    // p[a:b] を [L:R] に
    int l = L >> 6, r = R >> 6;
    int s = a >> 6, t = b >> t;
    int n = r - l;
    if (!(a & 63)) {
      FOR(i, n) dat[l + i] &= p.dat[s + i];
    } else {
      int hi = a & 63;
      int lo = 64 - hi;
      FOR(i, n) dat[l + i] &= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo);
    }
  }

  // [L,R) に p を or
  void or_to_range(int L, int R, My_Bitset &p) {
    assert(p.N == R - L);
    int a = 0, b = p.N;
    while (L < R && (L & 63)) {
      dat[L >> 6] |= u64(p[a]) << (L & 63);
      ++a, ++L;
    }
    while (L < R && (R & 63)) {
      --b, --R;
      dat[R >> 6] |= u64(p[b]) << (R & 63);
    }
    // p[a:b] を [L:R] に
    int l = L >> 6, r = R >> 6;
    int s = a >> 6, t = b >> t;
    int n = r - l;
    if (!(a & 63)) {
      FOR(i, n) dat[l + i] |= p.dat[s + i];
    } else {
      int hi = a & 63;
      int lo = 64 - hi;
      FOR(i, n) dat[l + i] |= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo);
    }
  }
  // 行列基本変形で使うやつ
  // p は [i:N) にしかないとして p を or する
  void or_suffix(int i, My_Bitset &p) {
    assert(N == p.N && 0 <= i && i < N);
    FOR(k, i / 64, len(dat)) { dat[k] |= p.dat[k]; }
  }

  // [L,R) を 1 に変更
  void set_range(int L, int R) {
    while (L < R && (L & 63)) { set(L++); }
    while (L < R && (R & 63)) { set(--R); }
    FOR(i, L >> 6, R >> 6) dat[i] = u64(-1);
  }

  // [L,R) を 1 に変更
  void reset_range(int L, int R) {
    while (L < R && (L & 63)) { reset(L++); }
    while (L < R && (R & 63)) { reset(--R); }
    FOR(i, L >> 6, R >> 6) dat[i] = u64(0);
  }

  // [L,R) を flip
  void flip_range(int L, int R) {
    while (L < R && (L & 63)) { flip(L++); }
    while (L < R && (R & 63)) { flip(--R); }
    FOR(i, L >> 6, R >> 6) dat[i] ^= u64(-1);
  }

  // bitset に仕様を合わせる
  void set(int i) { (*this)[i] = 1; }
  void reset(int i) { (*this)[i] = 0; }
  void flip(int i) { (*this)[i].flip(); }
  void set() {
    fill(all(dat), u64(-1));
    resize(N);
  }
  void reset() { fill(all(dat), 0); }
  void flip() {
    FOR(i, len(dat) - 1) { dat[i] = u64(-1) ^ dat[i]; }
    int i = len(dat) - 1;
    FOR(k, 64) {
      if (64 * i + k >= size()) break;
      flip(64 * i + k);
    }
  }
  bool any() {
    FOR(i, len(dat)) {
      if (dat[i]) return true;
    }
    return false;
  }

  bool ALL() {
    dat.resize((N + 63) >> 6);
    int r = N & 63;
    if (r != 0) {
      u64 mask = (u64(1) << r) - 1;
      if (dat.back() != mask) return 0;
    }
    for (int i = 0; i < N / 64; ++i)
      if (dat[i] != u64(-1)) return false;
    return true;
  }
  // bs[i]==true であるような i 全体
  vc<int> collect_idx() {
    vc<int> I;
    FOR(i, N) if ((*this)[i]) I.eb(i);
    return I;
  }

  bool is_subset(T &other) {
    assert(len(other) == N);
    FOR(i, len(dat)) {
      u64 a = dat[i], b = other.dat[i];
      if ((a & b) != a) return false;
    }
    return true;
  }

  int _Find_first() { return next(0); }
  int _Find_next(int p) { return next(p + 1); }

  template <typename F>
  void enumerate(int L, int R, F f) {
    if (L >= size()) return;
    int p = ((*this)[L] ? L : _Find_next(L));
    while (p < R) {
      f(p);
      p = _Find_next(p);
    }
  }

  static string TO_STR[256];
  string to_string() const {
    if (TO_STR[0].empty()) precompute();
    string S;
    for (auto &x: dat) { FOR(i, 8) S += TO_STR[(x >> (8 * i) & 255)]; }
    S.resize(N);
    return S;
  }

  static void precompute() {
    FOR(s, 256) {
      string x;
      FOR(i, 8) x += '0' + (s >> i & 1);
      TO_STR[s] = x;
    }
  }
};
string My_Bitset::TO_STR[256];
#line 2 "flow/bipartite_dense.hpp"

// vc<bitset> で biadj matrix を渡す
// N_1^2N_2/w.
// (5000,5000) で 300ms 程度で動く場合がある
// https://qoj.ac/problem/6308
// (10000?, 5000) 655ms
// https://codeforces.com/contest/1045/problem/A
// (10000, 20000) で 3837ms
// https://codeforces.com/contest/786/problem/E
// (10000, 10000) 6500ms TLE. row, col とも shuffle で 3000ms AC.
// bitset の方が My_Bitset より高速？(2024/05/27)
template <typename BS>
struct BipartiteMatching_Dense {
  int N1, N2;
  vc<BS>& adj;
  vc<int> match_1, match_2;
  vc<int> que;
  vc<int> prev;
  BS vis;

  BipartiteMatching_Dense(vc<BS>& adj, int N1, int N2) : N1(N1), N2(N2), adj(adj), match_1(N1, -1), match_2(N2, -1) {
    if constexpr (is_same_v<BS, My_Bitset>) vis.resize(N2);
    FOR(s, N1) bfs(s);
  }

  void bfs(int s) {
    if (match_1[s] != -1) return;
    que.resize(N1), prev.resize(N1);
    int l = 0, r = 0;
    prev[s] = -1;
    vis.set();

    que[r++] = s;
    while (l < r) {
      int u = que[l++];
      BS cand = vis & adj[u];
      for (int v = cand._Find_first(); v < N2; v = cand._Find_next(v)) {
        vis[v] = 0;
        if (match_2[v] != -1) {
          que[r++] = match_2[v];
          prev[match_2[v]] = u;
          continue;
        }
        int a = u, b = v;
        while (a != -1) {
          int t = match_1[a];
          match_1[a] = b, match_2[b] = a, a = prev[a], b = t;
        }
        return;
      }
    }
    return;
  }

  vc<pair<int, int>> matching() {
    vc<pair<int, int>> res;
    FOR(v, N1) if (match_1[v] != -1) res.eb(v, match_1[v]);
    return res;
  }

  pair<vc<int>, vc<int>> vertex_cover() {
    vc<int> que(N1);
    int l = 0, r = 0;
    vis.set();
    vc<bool> done(N1);
    FOR(i, N1) {
      if (match_1[i] == -1) done[i] = 1, que[r++] = i;
    }
    while (l < r) {
      int a = que[l++];
      BS cand = adj[a] & vis;
      for (int b = cand._Find_first(); b < N2; b = cand._Find_next(b)) {
        vis[b] = 0;
        int to = match_2[b];
        assert(to != -1);
        if (!done[to]) done[to] = 1, que[r++] = to;
      }
    }
    vc<int> left, right;
    FOR(i, N1) if (!done[i]) left.eb(i);
    FOR(i, N2) if (!vis[i]) right.eb(i);
    return {left, right};
  }
};

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