test/verify/yosupo-chromatic-number.test.cpp

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

Depends on

• Chromatic Number (彩色数) (graph/others/chromatic-number.hpp)
• Square Matrix (正方行列) (math/matrix/square-matrix.hpp)

Code

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

#include <iostream>

#include "../../graph/others/chromatic-number.hpp"
#include "../../math/matrix/square-matrix.hpp"

using namespace std;

int main() {
  int N, M;
  cin >> N >> M;
  SquareMatrix<bool, 20> g;
  for (int i = 0; i < M; i++) {
    int u, v;
    cin >> u >> v;
    g[u][v] = g[v][u] = true;
  }
  cout << chromatic_number(g) << "\n";
}

#line 1 "test/verify/yosupo-chromatic-number.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/chromatic_number
// clang-format on

#include <iostream>

#line 2 "graph/others/chromatic-number.hpp"

#include <cstdint>
#include <utility>
#include <vector>

/**
 * @brief Chromatic Number(彩色数)
 *
 * @see https://www.slideshare.net/wata_orz/ss-12131479
 */
template <typename Matrix>
int chromatic_number(Matrix& g) {
  int N = (int)g.size();
  std::vector<int> es(N);
  for (int i = 0; i < (int)g.size(); i++) {
    for (int j = 0; j < (int)g.size(); j++) {
      if (g[i][j] != 0) es[i] |= 1 << j;
    }
  }
  std::vector<int> ind(1 << N);
  ind[0] = 1;
  for (int S = 1; S < (1 << N); S++) {
    int u = __builtin_ctz(S);
    ind[S] = ind[S ^ (1 << u)] + ind[(S ^ (1 << u)) & ~es[u]];
  }
  std::vector<int> cnt((1 << N) + 1);
  for (int i = 0; i < (1 << N); i++) {
    cnt[ind[i]] += __builtin_parity(i) ? -1 : 1;
  }
  std::vector<std::pair<unsigned, int> > hist;
  for (int i = 1; i <= (1 << N); i++) {
    if (cnt[i]) hist.emplace_back(i, cnt[i]);
  }
  constexpr int mods[] = {1000000007, 1000000011, 1000000021};
  int ret = N;
  for (int k = 0; k < 3; k++) {
    auto buf = hist;
    for (int c = 1; c < ret; c++) {
      std::int64_t sum = 0;
      for (auto& [i, x] : buf) {
        sum += (x = std::int64_t(x) * i % mods[k]);
      }
      if (sum % mods[k]) ret = c;
    }
  }
  return ret;
}
#line 2 "math/matrix/square-matrix.hpp"

#include <array>
#include <cstddef>
#line 7 "math/matrix/square-matrix.hpp"

/**
 * @brief Square-Matrix(正方行列)
 */
template <class T, std::size_t N>
struct SquareMatrix {
  std::array<std::array<T, N>, N> A;

  SquareMatrix() : A{{}} {}

  SquareMatrix(const std::array<std::array<T, N>, N>& A) : A(A) {}

  std::size_t size() const { return N; }

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

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

  static SquareMatrix add_identity() { return SquareMatrix(); }

  static SquareMatrix mul_identity() {
    SquareMatrix mat;
    for (std::size_t i = 0; i < N; i++) mat[i][i] = 1;
    return mat;
  }

  SquareMatrix& operator+=(const SquareMatrix& B) {
    for (std::size_t i = 0; i < N; i++) {
      for (std::size_t j = 0; j < N; j++) {
        (*this)[i][j] += B[i][j];
      }
    }
    return *this;
  }

  SquareMatrix& operator-=(const SquareMatrix& B) {
    for (std::size_t i = 0; i < N; i++) {
      for (std::size_t j = 0; j < N; j++) {
        (*this)[i][j] -= B[i][j];
      }
    }
    return *this;
  }

  SquareMatrix& operator*=(const SquareMatrix& B) {
    std::array<std::array<T, N>, N> C;
    for (std::size_t i = 0; i < N; i++) {
      for (std::size_t j = 0; j < N; j++) {
        for (std::size_t k = 0; k < N; k++) {
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
        }
      }
    }
    A.swap(C);
    return (*this);
  }

  SquareMatrix& operator^=(std::uint64_t k) {
    SquareMatrix B = SquareMatrix::mul_identity();
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return *this;
  }

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

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

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

  SquareMatrix operator^(std::uint64_t k) const {
    return SquareMatrix(*this) ^= k;
  }

  friend std::ostream& operator<<(std::ostream& os, SquareMatrix& p) {
    for (int i = 0; i < N; i++) {
      os << "[";
      for (int j = 0; j < N; j++) {
        os << p[i][j] << (j + 1 == N ? "]\n" : ",");
      }
    }
    return os;
  }
};
#line 9 "test/verify/yosupo-chromatic-number.test.cpp"

using namespace std;

int main() {
  int N, M;
  cin >> N >> M;
  SquareMatrix<bool, 20> g;
  for (int i = 0; i < M; i++) {
    int u, v;
    cin >> u >> v;
    g[u][v] = g[v][u] = true;
  }
  cout << chromatic_number(g) << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	big_00	AC	7 ms	12 MB
g++	big_01	AC	6 ms	12 MB
g++	big_02	AC	7 ms	12 MB
g++	big_03	AC	5 ms	12 MB
g++	big_04	AC	6 ms	12 MB
g++	big_05	AC	5 ms	12 MB
g++	big_06	AC	6 ms	12 MB
g++	big_07	AC	5 ms	11 MB
g++	big_08	AC	6 ms	12 MB
g++	big_09	AC	5 ms	12 MB
g++	clique_cycle_00	AC	6 ms	12 MB
g++	clique_cycle_01	AC	6 ms	12 MB
g++	clique_cycle_02	AC	6 ms	12 MB
g++	clique_cycle_03	AC	6 ms	12 MB
g++	example_00	AC	6 ms	12 MB
g++	example_01	AC	6 ms	12 MB
g++	random_00	AC	5 ms	12 MB
g++	random_01	AC	6 ms	12 MB
g++	random_02	AC	6 ms	12 MB
g++	random_03	AC	6 ms	11 MB
g++	random_04	AC	6 ms	12 MB
g++	random_05	AC	6 ms	12 MB
g++	random_06	AC	6 ms	11 MB
g++	random_07	AC	6 ms	12 MB
g++	random_08	AC	5 ms	12 MB
g++	random_09	AC	5 ms	11 MB
clang++	big_00	AC	7 ms	12 MB
clang++	big_01	AC	5 ms	12 MB
clang++	big_02	AC	6 ms	12 MB
clang++	big_03	AC	6 ms	12 MB
clang++	big_04	AC	6 ms	12 MB
clang++	big_05	AC	5 ms	12 MB
clang++	big_06	AC	6 ms	12 MB
clang++	big_07	AC	6 ms	12 MB
clang++	big_08	AC	6 ms	12 MB
clang++	big_09	AC	6 ms	12 MB
clang++	clique_cycle_00	AC	5 ms	12 MB
clang++	clique_cycle_01	AC	6 ms	12 MB
clang++	clique_cycle_02	AC	5 ms	12 MB
clang++	clique_cycle_03	AC	5 ms	12 MB
clang++	example_00	AC	5 ms	11 MB
clang++	example_01	AC	6 ms	12 MB
clang++	random_00	AC	6 ms	12 MB
clang++	random_01	AC	6 ms	11 MB
clang++	random_02	AC	6 ms	12 MB
clang++	random_03	AC	6 ms	12 MB
clang++	random_04	AC	6 ms	12 MB
clang++	random_05	AC	6 ms	12 MB
clang++	random_06	AC	5 ms	11 MB
clang++	random_07	AC	5 ms	12 MB
clang++	random_08	AC	6 ms	12 MB
clang++	random_09	AC	6 ms	12 MB

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