Graph Utilities - グラフユーティリティ
(Library/Graph/GraphMisc.hpp)

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

Graph Utilities - グラフユーティリティ

グラフ構造を変換・操作するためのユーティリティ関数群です。

Function

ConvertEdgeSet

template<typename CostType>
vector<Edge<CostType>> ConvertEdgeSet(const Graph<CostType> &G)

• グラフ $G$ の辺集合を配列として取得します。
• 無向グラフの場合、各辺は1回のみ含まれます（重複排除）。

制約

• $1 \le \lvert V \rvert \le 10^5$
• $0 \le \lvert E \rvert \le 10^5$

計算量

• $\textrm{O}(\lvert V \rvert + \lvert E \rvert)$

戻り値

• グラフの辺のリスト

---

ConvertDistanceMatrix

template<typename CostType>
vector<vector<CostType>> ConvertDistanceMatrix(const Graph<CostType> &G)

• グラフ $G$ を距離行列（隣接行列）に変換します。
• 辺が存在しない場合は INF が設定されます。
• 自己ループは距離 $0$ として設定されます。

制約

• $1 \le \lvert V \rvert \le 10^3$（メモリ制約に注意）

計算量

• $\textrm{O}(\lvert V \rvert^2)$

戻り値

• $\lvert V \rvert \times \lvert V \rvert$ の距離行列

---

ReverseGraph

template<typename CostType>
Graph<CostType> ReverseGraph(const Graph<CostType> &G)

• 有向グラフ $G$ のすべての辺の向きを反転したグラフを返します。
• 辺 $(u, v)$ は辺 $(v, u)$ になります。

制約

• $1 \le \lvert V \rvert \le 10^5$
• $0 \le \lvert E \rvert \le 10^5$

計算量

• $\textrm{O}(\lvert V \rvert + \lvert E \rvert)$

戻り値

• 辺を反転したグラフ

---

Depends on

• Library/Common.hpp
• Graph - グラフ構造 (Library/Graph/Graph.hpp)

Required by

• Bellman Ford - ベルマンフォード法 (Library/Graph/BellmanFord.hpp)
• Kruskal - クラスカル法 (Library/Graph/Kruskal.hpp)
• Strongly Connected Components - 強連結成分分解 (Library/Graph/StronglyConnectedComponents.hpp)
• Warshall Floyd - ワーシャルフロイド法 (Library/Graph/WarshallFloyd.hpp)

Verified with

• verify/AOJ-GRL-1-B.test.cpp
• verify/AOJ-GRL-1-C.test.cpp
• verify/AOJ-GRL-3-C.test.cpp
• verify/LC-MinimumSpanningTree.test.cpp
• verify/LC-StronglyConnectedComponents.test.cpp

Code

#pragma once

#include "Graph.hpp"

template<typename WeightType>
vector<Edge<WeightType>> ConvertEdgeSet(const Graph<WeightType> &G){
    vector<Edge<WeightType>> ret;
    vector<bool> check(G.EdgeSize(), false);
    int n = G.VertexSize();
    for(int u = 0; u < n; ++u){
        for(const Edge<WeightType> &e : G[u]){
            if(check[e.idx]) continue;
            check[e.idx] = true;
            ret.push_back(e);
        }
    }
    return ret;
}

template<typename WeightType>
vector<vector<WeightType>> ConvertDistanceMatrix(const Graph<WeightType> &G){
    int n = G.VertexSize();
    vector<vector<WeightType>> ret(n, vector<WeightType>(n, WeightType(INF)));
    for(int u = 0; u < n; ++u){
        ret[u][u] = WeightType(0);
        for(const Edge<WeightType> &e : G[u]){
            ret[u][e.to] = e.cost;
        }
    }
    return ret;
}

template<typename WeightType>
Graph<WeightType> ReverseGraph(const Graph<WeightType> &G){
    int n = G.VertexSize();
    Graph<WeightType> ret(n);
    for(int u = 0; u < n; ++u){
        for(const Edge<WeightType> &e : G[u]){
            ret.AddDirectedEdge(e.to, e.from, e.cost);
        }
    }
    return ret;
}

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

template<typename WeightType>
vector<Edge<WeightType>> ConvertEdgeSet(const Graph<WeightType> &G){
    vector<Edge<WeightType>> ret;
    vector<bool> check(G.EdgeSize(), false);
    int n = G.VertexSize();
    for(int u = 0; u < n; ++u){
        for(const Edge<WeightType> &e : G[u]){
            if(check[e.idx]) continue;
            check[e.idx] = true;
            ret.push_back(e);
        }
    }
    return ret;
}

template<typename WeightType>
vector<vector<WeightType>> ConvertDistanceMatrix(const Graph<WeightType> &G){
    int n = G.VertexSize();
    vector<vector<WeightType>> ret(n, vector<WeightType>(n, WeightType(INF)));
    for(int u = 0; u < n; ++u){
        ret[u][u] = WeightType(0);
        for(const Edge<WeightType> &e : G[u]){
            ret[u][e.to] = e.cost;
        }
    }
    return ret;
}

template<typename WeightType>
Graph<WeightType> ReverseGraph(const Graph<WeightType> &G){
    int n = G.VertexSize();
    Graph<WeightType> ret(n);
    for(int u = 0; u < n; ++u){
        for(const Edge<WeightType> &e : G[u]){
            ret.AddDirectedEdge(e.to, e.from, e.cost);
        }
    }
    return ret;
}

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