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

• View this file on GitHub
• Last update: 2024-05-01 23:44:47+09:00
• 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)
• math/matrix/matrix.hpp
• template/template.hpp

Code

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

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

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

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;
  cout << ret << endl;
}

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

#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-maximum-independent-set.test.cpp"

#line 1 "math/matrix/matrix.hpp"
template <class T>
struct Matrix {
  vector<vector<T> > A;

  Matrix() {}

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

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

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

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

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

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

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

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

  Matrix &operator+=(const Matrix &B) {
    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) {
    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) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector<vector<T> > C(n, 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 ostream &operator<<(ostream &os, Matrix &p) {
    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;
        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 1 "graph/others/maximum-independent-set.hpp"
/**
 * @brief Maximum Independent Set(最大独立集合)
 */
template <typename Matrix>
vector<int> maximum_independent_set(const Matrix &g, int trial = 1000000) {
  int N = (int)g.size();
  vector<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] |= uint64_t(1) << j;
      }
    }
  }

  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
  int ret = 0;
  uint64_t ver = 0;
  for (int i = 0; i < trial; i++) {
    shuffle(begin(ord), end(ord), mt);
    uint64_t used = 0;
    int add = 0;
    for (int j : ord) {
      if (used & bit[j]) continue;
      used |= uint64_t(1) << j;
      ++add;
    }
    if (ret < add) {
      ret = add;
      ver = used;
    }
  }
  vector<int> ans;
  for (int i = 0; i < N; i++) {
    if ((ver >> i) & 1) ans.emplace_back(i);
  }
  return ans;
}
#line 7 "test/verify/yosupo-maximum-independent-set.test.cpp"

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;
  cout << ret << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	76 ms	4 MB
g++	example_01	AC	60 ms	4 MB
g++	hack0_00	AC	328 ms	4 MB
g++	handmade_00	AC	82 ms	4 MB
g++	many_maximals_00	AC	309 ms	4 MB
g++	max_random_00	AC	243 ms	4 MB
g++	max_random_01	AC	292 ms	4 MB
g++	max_random_02	AC	339 ms	4 MB
g++	max_random_03	AC	297 ms	4 MB
g++	max_random_04	AC	259 ms	4 MB
g++	one_two_00	AC	301 ms	4 MB
g++	random_00	AC	224 ms	4 MB
g++	random_01	AC	62 ms	4 MB
g++	random_02	AC	189 ms	4 MB
g++	random_03	AC	9 ms	4 MB
g++	random_04	AC	181 ms	4 MB
clang++	example_00	AC	45 ms	4 MB
clang++	example_01	AC	38 ms	4 MB
clang++	hack0_00	AC	187 ms	4 MB
clang++	handmade_00	AC	53 ms	4 MB
clang++	many_maximals_00	AC	188 ms	4 MB
clang++	max_random_00	AC	187 ms	4 MB
clang++	max_random_01	AC	186 ms	4 MB
clang++	max_random_02	AC	186 ms	4 MB
clang++	max_random_03	AC	187 ms	4 MB
clang++	max_random_04	AC	188 ms	4 MB
clang++	one_two_00	AC	190 ms	4 MB
clang++	random_00	AC	154 ms	4 MB
clang++	random_01	AC	35 ms	4 MB
clang++	random_02	AC	119 ms	4 MB
clang++	random_03	AC	10 ms	4 MB
clang++	random_04	AC	102 ms	4 MB

Back to top page