Cycle Detection - 閉路検出
(Library/Graph/CycleDetection.hpp)

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Last update: 2026-02-13 15:23:31+09:00
Include: #include "Library/Graph/CycleDetection.hpp"

Cycle Detection - 閉路検出

頂点数 $V$ 辺数 $E$ の無向グラフに含まれる閉路を検出し、閉路を構成する辺のリストを返します。

vector<Edge<WeightType>> CycleDetection(Graph<WeightType> &G)

グラフ $G$ に含まれる閉路を1つ検出し、その閉路を構成する辺のリストを返します。
閉路が存在しない場合は空の配列を返します。
複数の閉路が存在する場合、そのうちの $1$ つを返します。

制約

$G$ は無向グラフ

計算量

$\textrm{O}(V + E)$

戻り値

閉路を構成する辺のリスト(閉路上の順序で格納)
閉路が存在しない場合は空の配列

Depends on

Verified with

Code

#pragma once

#include "Graph.hpp"

template<typename WeightType>
vector<Edge<WeightType>> CycleDetection(Graph<WeightType> &G){
    int V = G.VertexSize();
    vector<Edge<WeightType>> history;
    vector<int> state(V, 0);
    vector<Edge<WeightType>> ret;
    bool detected = false;
    auto dfs = [&](auto &self, int v, int pre) -> void {
        state[v] = 1;
        for(const Edge<WeightType> &e : G[v]){
            if(e.idx == pre) continue;
            if(state[e.to] == 2) continue;
            else if(state[e.to] == 1){
                ret.push_back(e);
                for(int i = history.size() - 1; i >= 0 && history[i].to != e.to; --i){
                    ret.push_back(history[i]);
                }
                detected = true;
            }
            else{
                history.push_back(e);
                self(self, e.to, e.idx);
                history.pop_back();
            }
            if(detected) return;
        }
        state[v] = 2;
    };
    for(int v = 0; v < V && !detected; ++v){
        if(state[v] == 0) dfs(dfs, v, -1);
    }
    reverse(ret.begin(), ret.end());
    return ret;
}

#line 2 "Library/Graph/CycleDetection.hpp"

#line 2 "Library/Graph/Graph.hpp"

#line 2 "Library/Common.hpp"

/**
 * @file Common.hpp
 */

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cstdint>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

using ll = int64_t;
using ull = uint64_t;

constexpr const ll INF = (1LL << 62) - (3LL << 30) - 1;
#line 4 "Library/Graph/Graph.hpp"

using Vertex = int;

template<typename WeightType = int32_t>
struct Edge{
    public:
    Edge() = default;

    Edge(Vertex from_, Vertex to_, WeightType weight_ = 1, int idx_ = -1) :
        from(from_), to(to_), cost(weight_), idx(idx_){}
    
    bool operator<(const Edge<WeightType> &e) const {return cost < e.cost;}

    operator int() const {return to;}

    Vertex from, to;
    WeightType cost;
    int idx;
};

template<typename WeightType = int32_t>
class Graph{
    public:
    Graph() = default;

    Graph(int V) : edge_size_(0), adjacent_list_(V){}
    
    inline void AddUndirectedEdge(Vertex u, Vertex v, WeightType w = 1){
        int idx = edge_size_++;
        adjacent_list_[u].push_back(Edge<WeightType>(u, v, w, idx));
        adjacent_list_[v].push_back(Edge<WeightType>(v, u, w, idx));
    }
    
    inline void AddDirectedEdge(Vertex u, Vertex v, WeightType w = 1){
        int idx = edge_size_++;
        adjacent_list_[u].push_back(Edge<WeightType>(u, v, w, idx));
    }

    inline size_t VertexSize() const {
        return adjacent_list_.size();
    }

    inline size_t EdgeSize() const {
        return edge_size_;
    }

    inline vector<Edge<WeightType>> &operator[](const Vertex v){
        return adjacent_list_[v];
    }

    inline const vector<Edge<WeightType>> &operator[](const Vertex v) const {
        return adjacent_list_[v];
    }
    
    private:
    size_t edge_size_;
    vector<vector<Edge<WeightType>>> adjacent_list_;
};

template<typename WeightType = int32_t>
Graph<WeightType> InputGraph(int N, int M, int padding = -1, bool weighted = false, bool directed = false){
    Graph<WeightType> G(N);
    for(int i = 0; i < M; ++i){
        Vertex u, v; WeightType w = 1;
        cin >> u >> v, u += padding, v += padding;
        if(weighted) cin >> w;
        if(directed) G.AddDirectedEdge(u, v, w);
        else G.AddUndirectedEdge(u, v, w);
    }
    return G;
}
#line 4 "Library/Graph/CycleDetection.hpp"

template<typename WeightType>
vector<Edge<WeightType>> CycleDetection(Graph<WeightType> &G){
    int V = G.VertexSize();
    vector<Edge<WeightType>> history;
    vector<int> state(V, 0);
    vector<Edge<WeightType>> ret;
    bool detected = false;
    auto dfs = [&](auto &self, int v, int pre) -> void {
        state[v] = 1;
        for(const Edge<WeightType> &e : G[v]){
            if(e.idx == pre) continue;
            if(state[e.to] == 2) continue;
            else if(state[e.to] == 1){
                ret.push_back(e);
                for(int i = history.size() - 1; i >= 0 && history[i].to != e.to; --i){
                    ret.push_back(history[i]);
                }
                detected = true;
            }
            else{
                history.push_back(e);
                self(self, e.to, e.idx);
                history.pop_back();
            }
            if(detected) return;
        }
        state[v] = 2;
    };
    for(int v = 0; v < V && !detected; ++v){
        if(state[v] == 0) dfs(dfs, v, -1);
    }
    reverse(ret.begin(), ret.end());
    return ret;
}

Cycle Detection - 閉路検出 (Library/Graph/CycleDetection.hpp)

Cycle Detection - 閉路検出

Depends on

Verified with

Code

Cycle Detection - 閉路検出
(Library/Graph/CycleDetection.hpp)