test/verify/yosupo-maximum-independent-set.test.cpp

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• Last update: 2026-08-10 14:32:04+00:00
• Problem: https://judge.yosupo.jp/problem/maximum_independent_set

Depends on

• Maximum Independent Set(最大独立集合) (graph/others/maximum-independent-set.hpp)
• Matrix (行列) (math/matrix/matrix.hpp)

Code

// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/maximum_independent_set
// clang-format on

#include <iostream>

#include "../../graph/others/maximum-independent-set.hpp"
#include "../../math/matrix/matrix.hpp"

using namespace std;

int main() {
  int N, M;
  cin >> N >> M;
  Matrix<bool> mat(N);
  for (int i = 0; i < M; i++) {
    int a, b;
    cin >> a >> b;
    mat[a][b] = true;
    mat[b][a] = true;
  }
  auto ret = maximum_independent_set(mat);
  cout << ret.size() << endl;
  for (int i = 0; i < static_cast<int>(ret.size()); i++) {
    if (i > 0) cout << " ";
    cout << ret[i];
  }
  cout << endl;
}

#line 1 "test/verify/yosupo-maximum-independent-set.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/maximum_independent_set
// clang-format on

#include <iostream>

#line 2 "graph/others/maximum-independent-set.hpp"

#include <algorithm>
#include <cassert>
#include <chrono>
#include <cstdint>
#include <iterator>
#include <numeric>
#include <random>
#include <vector>

/**

 * @brief Maximum Independent Set(最大独立集合)
 */
template <typename Matrix>
std::vector<int> maximum_independent_set(const Matrix& g, int trial = 1000000) {
  int N = (int)g.size();
  std::vector<std::uint64_t> bit(N);
  assert(N <= 64);
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
      if (i != j) {
        assert(g[i][j] == g[j][i]);
        if (g[i][j]) bit[i] |= std::uint64_t(1) << j;
      }
    }
  }

  std::vector<int> ord(N);
  std::iota(std::begin(ord), std::end(ord), 0);
  std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count());
  int ret = 0;
  std::uint64_t ver = 0;
  for (int i = 0; i < trial; i++) {
    std::shuffle(std::begin(ord), std::end(ord), mt);
    std::uint64_t used = 0;
    int add = 0;
    for (int j : ord) {
      if (used & bit[j]) continue;
      used |= std::uint64_t(1) << j;
      ++add;
    }
    if (ret < add) {
      ret = add;
      ver = used;
    }
  }
  std::vector<int> ans;
  for (int i = 0; i < N; i++) {
    if ((ver >> i) & 1) ans.emplace_back(i);
  }
  return ans;
}
#line 2 "math/matrix/matrix.hpp"

#line 4 "math/matrix/matrix.hpp"
#include <cstddef>
#line 7 "math/matrix/matrix.hpp"

template <class T>
struct Matrix {
  std::vector<std::vector<T> > A;

  Matrix() {}

  Matrix(const std::vector<std::vector<T> >& A) : A(A) {}

  Matrix(std::size_t n, std::size_t m) : A(n, std::vector<T>(m, 0)) {}

  Matrix(std::size_t n) : A(n, std::vector<T>(n, 0)) {};

  std::size_t size() const {
    if (A.empty()) return 0;
    assert(A.size() == A[0].size());
    return A.size();
  }

  std::size_t height() const { return (A.size()); }

  std::size_t width() const { return (A[0].size()); }

  inline const std::vector<T>& operator[](int k) const { return (A.at(k)); }

  inline std::vector<T>& operator[](int k) { return (A.at(k)); }

  static Matrix I(std::size_t n) {
    Matrix mat(n);
    for (int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix& operator+=(const Matrix& B) {
    std::size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix& operator-=(const Matrix& B) {
    std::size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix& operator*=(const Matrix& B) {
    std::size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    std::vector<std::vector<T> > C(n, std::vector<T>(m, 0));
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        for (int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }

  Matrix& operator^=(long long k) {
    Matrix B = Matrix::I(height());
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

  Matrix operator+(const Matrix& B) const { return (Matrix(*this) += B); }

  Matrix operator-(const Matrix& B) const { return (Matrix(*this) -= B); }

  Matrix operator*(const Matrix& B) const { return (Matrix(*this) *= B); }

  Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }

  friend std::ostream& operator<<(std::ostream& os, Matrix& p) {
    std::size_t n = p.height(), m = p.width();
    for (int i = 0; i < n; i++) {
      os << "[";
      for (int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }

  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for (int i = 0; i < width(); i++) {
      int idx = -1;
      for (int j = i; j < width(); j++) {
        if (B[j][i] != 0) idx = j;
      }
      if (idx == -1) return (0);
      if (i != idx) {
        ret *= -1;
        std::swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for (int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for (int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for (int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};
#line 9 "test/verify/yosupo-maximum-independent-set.test.cpp"

using namespace std;

int main() {
  int N, M;
  cin >> N >> M;
  Matrix<bool> mat(N);
  for (int i = 0; i < M; i++) {
    int a, b;
    cin >> a >> b;
    mat[a][b] = true;
    mat[b][a] = true;
  }
  auto ret = maximum_independent_set(mat);
  cout << ret.size() << endl;
  for (int i = 0; i < static_cast<int>(ret.size()); i++) {
    if (i > 0) cout << " ";
    cout << ret[i];
  }
  cout << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	60 ms	3 MB
g++	example_01	AC	46 ms	4 MB
g++	hack0_00	AC	262 ms	4 MB
g++	handmade_00	AC	63 ms	4 MB
g++	many_maximals_00	AC	237 ms	4 MB
g++	max_random_00	AC	180 ms	3 MB
g++	max_random_01	AC	229 ms	4 MB
g++	max_random_02	AC	272 ms	4 MB
g++	max_random_03	AC	233 ms	4 MB
g++	max_random_04	AC	195 ms	4 MB
g++	one_two_00	AC	236 ms	4 MB
g++	random_00	AC	171 ms	4 MB
g++	random_01	AC	44 ms	4 MB
g++	random_02	AC	145 ms	4 MB
g++	random_03	AC	5 ms	4 MB
g++	random_04	AC	144 ms	4 MB
clang++	example_00	AC	40 ms	4 MB
clang++	example_01	AC	34 ms	4 MB
clang++	hack0_00	AC	181 ms	3 MB
clang++	handmade_00	AC	49 ms	4 MB
clang++	many_maximals_00	AC	181 ms	4 MB
clang++	max_random_00	AC	181 ms	4 MB
clang++	max_random_01	AC	181 ms	4 MB
clang++	max_random_02	AC	183 ms	4 MB
clang++	max_random_03	AC	181 ms	4 MB
clang++	max_random_04	AC	181 ms	4 MB
clang++	one_two_00	AC	181 ms	4 MB
clang++	random_00	AC	149 ms	4 MB
clang++	random_01	AC	31 ms	4 MB
clang++	random_02	AC	114 ms	4 MB
clang++	random_03	AC	6 ms	4 MB
clang++	random_04	AC	97 ms	4 MB

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