graph/maximum_matching_size.hpp

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Last update: 2023-11-16 08:58:57+09:00
Include: #include "graph/maximum_matching_size.hpp"

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Code

#include "random/base.hpp"
#include "mod/modint61.hpp"
#include "linalg/matrix_rank.hpp"

template <typename GT>
int maximum_matching_size(GT& G) {
  static_assert(!GT::is_directed);
  using mint = modint61;
  int N = G.N;
  vv(mint, tutte, N, N);
  for (auto&& e: G.edges) {
    mint x = RNG(mint::get_mod());
    int i = e.frm, j = e.to;
    tutte[i][j] += x;
    tutte[j][i] -= x;
  }
  return matrix_rank(tutte, N, N) / 2;
}

#line 2 "random/base.hpp"

u64 RNG_64() {
  static uint64_t x_
      = uint64_t(chrono::duration_cast<chrono::nanoseconds>(
                     chrono::high_resolution_clock::now().time_since_epoch())
                     .count())
        * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "mod/modint61.hpp"

struct modint61 {
  static constexpr u64 mod = (1ULL << 61) - 1;
  u64 val;
  constexpr modint61() : val(0ULL) {}
  constexpr modint61(u32 x) : val(x) {}
  constexpr modint61(u64 x) : val(x % mod) {}
  constexpr modint61(int x) : val((x < 0) ? (x + static_cast<ll>(mod)) : x) {}
  constexpr modint61(ll x)
      : val(((x %= static_cast<ll>(mod)) < 0) ? (x + static_cast<ll>(mod))
                                              : x) {}
  static constexpr u64 get_mod() { return mod; }
  modint61 &operator+=(const modint61 &a) {
    val = ((val += a.val) >= mod) ? (val - mod) : val;
    return *this;
  }
  modint61 &operator-=(const modint61 &a) {
    val = ((val -= a.val) >= mod) ? (val + mod) : val;
    return *this;
  }
  modint61 &operator*=(const modint61 &a) {
    const unsigned __int128 y = static_cast<unsigned __int128>(val) * a.val;
    val = (y >> 61) + (y & mod);
    val = (val >= mod) ? (val - mod) : val;
    return *this;
  }
  modint61 &operator/=(const modint61 &a) { return (*this *= a.inverse()); }
  modint61 operator+(const modint61 &p) const { return modint61(*this) += p; }
  modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; }
  modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; }
  modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; }
  bool operator==(const modint61 &p) const { return val == p.val; }
  bool operator!=(const modint61 &p) const { return val != p.val; }
  modint61 inverse() const {
    ll a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint61(u);
  }
  modint61 pow(ll n) const {
    assert(n >= 0);
    modint61 ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul, n >>= 1;
    }
    return ret;
  }
};

#ifdef FASTIO
void rd(modint61 &x) {
  fastio::rd(x.val);
  assert(0 <= x.val && x.val < modint61::mod);
}

void wt(modint61 x) { fastio::wt(x.val); }
#endif
#line 1 "linalg/matrix_rank.hpp"
template <typename T>
int matrix_rank(vc<vc<T>> a, int n = -1, int m = -1) {
  if (n == 0) return 0;
  if (n == -1) { n = len(a), m = len(a[0]); }
  assert(n == len(a) && m == len(a[0]));
  int rk = 0;
  FOR(j, m) {
    if (rk == n) break;
    if (a[rk][j] == 0) {
      FOR3(i, rk + 1, n) if (a[i][j] != T(0)) {
        swap(a[rk], a[i]);
        break;
      }
    }
    if (a[rk][j] == 0) continue;
    T c = T(1) / a[rk][j];
    FOR(k, j, m) a[rk][k] *= c;
    FOR(i, rk + 1, n) {
      T c = a[i][j];
      FOR3(k, j, m) { a[i][k] -= a[rk][k] * c; }
    }
    ++rk;
  }
  return rk;
}
#line 4 "graph/maximum_matching_size.hpp"

template <typename GT>
int maximum_matching_size(GT& G) {
  static_assert(!GT::is_directed);
  using mint = modint61;
  int N = G.N;
  vv(mint, tutte, N, N);
  for (auto&& e: G.edges) {
    mint x = RNG(mint::get_mod());
    int i = e.frm, j = e.to;
    tutte[i][j] += x;
    tutte[j][i] -= x;
  }
  return matrix_rank(tutte, N, N) / 2;
}