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

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Last update: 2022-09-11 00:53:50+09:00
Problem: https://judge.yosupo.jp/problem/chromatic_number

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/chromatic_number"

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

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

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"
#define PROBLEM "https://judge.yosupo.jp/problem/chromatic_number"

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

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-chromatic-number.test.cpp"

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

/**
 * @brief Chromatic Number(彩色数)
 * @docs docs/chromatic-number.md
 * @see https://www.slideshare.net/wata_orz/ss-12131479
 */
template< typename Matrix >
int chromatic_number(Matrix &g) {
  int N = (int) g.size();
  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;
    }
  }
  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]];
  }
  vector< int > cnt((1 << N) + 1);
  for(int i = 0; i < (1 << N); i++) {
    cnt[ind[i]] += __builtin_parity(i) ? -1 : 1;
  }
  vector< 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++) {
      int64_t sum = 0;
      for(auto&[i, x] : buf) {
        sum += (x = int64_t(x) * i % mods[k]);
      }
      if(sum % mods[k]) ret = c;
    }
  }
  return ret;
}
#line 1 "math/matrix/square-matrix.hpp"
/**
 * @brief Square-Matrix(正方行列)
 */
template< class T, size_t N >
struct SquareMatrix {
  array< array< T, N >, N > A;

  SquareMatrix() : A{{}} {}

  size_t size() const { return N; }

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

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

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

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

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

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

  SquareMatrix &operator*=(const SquareMatrix &B) {
    array< array< T, N >, N > C;
    for(size_t i = 0; i < N; i++) {
      for(size_t j = 0; j < N; j++) {
        for(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^=(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^(uint64_t k) const {
    return SquareMatrix(*this) ^= k;
  }

  friend ostream &operator<<(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 7 "test/verify/yosupo-chromatic-number.test.cpp"

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";
}