Maximum Clique(最大クリーク) (graph/others/maximum-clique.hpp)

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• Last update: 2024-05-01 23:44:47+09:00
• Include: #include "graph/others/maximum-clique.hpp"

Verified with

• test/verify/yosupo-maximum-independent-set-2.test.cpp

Code

#pragma once

/**
 * @brief Maximum Clique(最大クリーク)
 */
template <int V>
struct MaximumClique {
  using B = bitset<V>;
  vector<B> g, col_buf;

  struct P {
    int idx, col, deg;

    P(int idx, int col, int deg) : idx(idx), col(col), deg(deg) {}
  };

  MaximumClique() = default;

  explicit MaximumClique(int N) : g(N), col_buf(N) {}

  void add_edge(int a, int b) {
    g[a].set(b);
    g[b].set(a);
  }

  vector<int> now, clique;

  void dfs(vector<P> &rem) {
    if (clique.size() < now.size()) clique = now;
    sort(begin(rem), end(rem),
         [](const P &a, const P &b) { return a.deg > b.deg; });
    int max_c = 1;
    for (auto &p : rem) {
      p.col = 0;
      while ((g[p.idx] & col_buf[p.col]).any()) ++p.col;
      max_c = max(max_c, p.idx + 1);
      col_buf[p.col].set(p.idx);
    }
    for (int i = 0; i < max_c; i++) col_buf[i].reset();
    sort(begin(rem), end(rem),
         [&](const P &a, const P &b) { return a.col < b.col; });
    for (; !rem.empty(); rem.pop_back()) {
      auto &p = rem.back();
      if (now.size() + p.col + 1 <= clique.size()) break;
      vector<P> nrem;
      B bs;
      for (auto &q : rem) {
        if (g[p.idx][q.idx]) {
          nrem.emplace_back(q.idx, -1, 0);
          bs.set(q.idx);
        }
      }
      for (auto &q : nrem) {
        q.deg = (bs & g[q.idx]).count();
      }
      now.emplace_back(p.idx);
      dfs(nrem);
      now.pop_back();
    }
  }

  vector<int> solve() {
    vector<P> remark;
    for (size_t i = 0; i < g.size(); i++) {
      remark.emplace_back(i, -1, (int)g[i].size());
    }
    dfs(remark);
    return clique;
  }
};

#line 2 "graph/others/maximum-clique.hpp"

/**
 * @brief Maximum Clique(最大クリーク)
 */
template <int V>
struct MaximumClique {
  using B = bitset<V>;
  vector<B> g, col_buf;

  struct P {
    int idx, col, deg;

    P(int idx, int col, int deg) : idx(idx), col(col), deg(deg) {}
  };

  MaximumClique() = default;

  explicit MaximumClique(int N) : g(N), col_buf(N) {}

  void add_edge(int a, int b) {
    g[a].set(b);
    g[b].set(a);
  }

  vector<int> now, clique;

  void dfs(vector<P> &rem) {
    if (clique.size() < now.size()) clique = now;
    sort(begin(rem), end(rem),
         [](const P &a, const P &b) { return a.deg > b.deg; });
    int max_c = 1;
    for (auto &p : rem) {
      p.col = 0;
      while ((g[p.idx] & col_buf[p.col]).any()) ++p.col;
      max_c = max(max_c, p.idx + 1);
      col_buf[p.col].set(p.idx);
    }
    for (int i = 0; i < max_c; i++) col_buf[i].reset();
    sort(begin(rem), end(rem),
         [&](const P &a, const P &b) { return a.col < b.col; });
    for (; !rem.empty(); rem.pop_back()) {
      auto &p = rem.back();
      if (now.size() + p.col + 1 <= clique.size()) break;
      vector<P> nrem;
      B bs;
      for (auto &q : rem) {
        if (g[p.idx][q.idx]) {
          nrem.emplace_back(q.idx, -1, 0);
          bs.set(q.idx);
        }
      }
      for (auto &q : nrem) {
        q.deg = (bs & g[q.idx]).count();
      }
      now.emplace_back(p.idx);
      dfs(nrem);
      now.pop_back();
    }
  }

  vector<int> solve() {
    vector<P> remark;
    for (size_t i = 0; i < g.size(); i++) {
      remark.emplace_back(i, -1, (int)g[i].size());
    }
    dfs(remark);
    return clique;
  }
};

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