Cycle Detection(閉路検出) (graph/others/cycle-detection.hpp)

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• Last update: 2024-05-27 02:13:15+09:00
• Include: #include "graph/others/cycle-detection.hpp"

概要

有向グラフが与えられたとき, 辺素なサイクルを $1$ つみつける.

適当な頂点から DFS すると見つけられる.

使い方

• build(): 辺素なサイクルを $1$ つ見つけて返す. ただし, 見つからなかったとき空列を返す.

計算量

$O(E + V)$

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)

Verified with

• test/verify/yosupo-cycle-detection.test.cpp

Code

#pragma once

#include "../graph-template.hpp"

/**
 * @brief Cycle Detection(閉路検出)
 *
 */
template <typename T = int>
struct CycleDetection : Graph<T> {
  using Graph<T>::Graph;
  using Graph<T>::g;

  vector<int> used;
  Edges<T> pre, cycle;

  bool dfs(int idx) {
    used[idx] = 1;
    for (auto &e : g[idx]) {
      if (used[e] == 0) {
        pre[e] = e;
        if (dfs(e)) return true;
      } else if (used[e] == 1) {
        int cur = idx;
        while (cur != e) {
          cycle.emplace_back(pre[cur]);
          cur = pre[cur].from;
        }
        cycle.emplace_back(e);
        return true;
      }
    }

    used[idx] = 2;
    return false;
  }

  Edges<T> build() {
    used.assign(g.size(), 0);
    pre.resize(g.size());
    for (int i = 0; i < (int)g.size(); i++) {
      if (used[i] == 0 && dfs(i)) {
        reverse(begin(cycle), end(cycle));
        return cycle;
      }
    }
    return {};
  }
};

#line 2 "graph/others/cycle-detection.hpp"

#line 2 "graph/graph-template.hpp"

template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 4 "graph/others/cycle-detection.hpp"

/**
 * @brief Cycle Detection(閉路検出)
 *
 */
template <typename T = int>
struct CycleDetection : Graph<T> {
  using Graph<T>::Graph;
  using Graph<T>::g;

  vector<int> used;
  Edges<T> pre, cycle;

  bool dfs(int idx) {
    used[idx] = 1;
    for (auto &e : g[idx]) {
      if (used[e] == 0) {
        pre[e] = e;
        if (dfs(e)) return true;
      } else if (used[e] == 1) {
        int cur = idx;
        while (cur != e) {
          cycle.emplace_back(pre[cur]);
          cur = pre[cur].from;
        }
        cycle.emplace_back(e);
        return true;
      }
    }

    used[idx] = 2;
    return false;
  }

  Edges<T> build() {
    used.assign(g.size(), 0);
    pre.resize(g.size());
    for (int i = 0; i < (int)g.size(); i++) {
      if (used[i] == 0 && dfs(i)) {
        reverse(begin(cycle), end(cycle));
        return cycle;
      }
    }
    return {};
  }
};

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