グラフ/彩色数
(test/graph/chromatic_number.test.cpp)

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• Last update: 2023-02-25 01:48:23+09:00
• Problem: https://judge.yosupo.jp/problem/chromatic_number

Depends on

• 彩色数 (chromatic number) (include/emthrm/graph/chromatic_number.hpp)
• 辺 (include/emthrm/graph/edge.hpp)

Code

/*
 * @title グラフ/彩色数
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/chromatic_number
 */

#include <iostream>
#include <vector>

#include "emthrm/graph/chromatic_number.hpp"
#include "emthrm/graph/edge.hpp"

int main() {
  int n, m;
  std::cin >> n >> m;
  std::vector<std::vector<emthrm::Edge<bool>>> graph(n);
  while (m--) {
    int u, v;
    std::cin >> u >> v;
    graph[u].emplace_back(u, v);
    graph[v].emplace_back(v, u);
  }
  std::cout << emthrm::chromatic_number(graph) << '\n';
  return 0;
}

#line 1 "test/graph/chromatic_number.test.cpp"
/*
 * @title グラフ/彩色数
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/chromatic_number
 */

#include <iostream>
#include <vector>

#line 1 "include/emthrm/graph/chromatic_number.hpp"



#include <bit>
#include <numeric>
#include <ranges>
#line 8 "include/emthrm/graph/chromatic_number.hpp"

#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 10 "include/emthrm/graph/chromatic_number.hpp"

namespace emthrm {

template <typename CostType>
int chromatic_number(const std::vector<std::vector<Edge<CostType>>>& graph) {
  const int n = graph.size();
  std::vector<int> adj(n, 0);
  for (int i = 0; i < n; ++i) {
    for (const int e : graph[i] | std::views::transform(&Edge<CostType>::dst)) {
      adj[i] |= 1 << e;
    }
  }
  std::vector<int> indep(1 << n);
  indep[0] = 1;
  for (unsigned int i = 1; i < (1 << n); ++i) {
    const int v = std::countr_zero(i);
    indep[i] = indep[i ^ (1 << v)] + indep[(i ^ (1 << v)) & ~adj[v]];
  }
  int res = n;
  for (const int mod : std::vector<int>{1000000007, 1000000011}) {
    std::vector<long long> f(1 << n);
    for (unsigned int i = 0; i < (1 << n); ++i) {
      f[i] = ((n - std::popcount(i)) & 1 ? mod - 1 : 1);
    }
    for (int c = 1; c < res; ++c) {
      for (int i = 0; i < (1 << n); ++i) {
        f[i] = (f[i] * indep[i]) % mod;
      }
      if (std::reduce(f.begin(), f.end(), 0LL) % mod > 0) {
        res = c;
        break;
      }
    }
  }
  return res;
}

}  // namespace emthrm


#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 12 "test/graph/chromatic_number.test.cpp"

int main() {
  int n, m;
  std::cin >> n >> m;
  std::vector<std::vector<emthrm::Edge<bool>>> graph(n);
  while (m--) {
    int u, v;
    std::cin >> u >> v;
    graph[u].emplace_back(u, v);
    graph[v].emplace_back(v, u);
  }
  std::cout << emthrm::chromatic_number(graph) << '\n';
  return 0;
}

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