Procon

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:heavy_check_mark: Warshall Floyd - ワーシャルフロイド法
(Library/Graph/WarshallFloyd.hpp)

Warshall Floyd - ワーシャルフロイド法

頂点数 $V$ 辺数 $E$ のグラフにおける全点対最短経路問題をワーシャルフロイド法を用いて解きます。

Function

Constructor

(1) WarshallFloyd(Graph<WeightType> &graph)
(2) WarshallFloyd(vector<vector<WeightType>> &A)

制約

計算量

Reachable

inline bool Reachable(const Vertex &s, const Vertex &t) const

制約

計算量

Distance

inline WeightType Distance(const Vertex &s, const Vertex &t) const

制約

計算量

NegativeCycle

inline bool NegativeCycle() const

計算量

operator[]

(1) vector<WeightType> &operator[](const Vertex &s)
(1) const vector<WeightType> &operator[](const Vertex &s) const

制約

計算量

Depends on

Verified with

Code

#include "Graph.hpp"
#include "GraphMisc.hpp"

template<typename WeightType>
class WarshallFloyd{
    public:
    WarshallFloyd(Graph<WeightType> &graph) :
        V(graph.VertexSize()), dist_(ConvertDistanceMatrix(graph)){
        Solve();
    }

    WarshallFloyd(vector<vector<WeightType>> &A) :
        V((int)A.size()), dist_(A){
        Solve();
    }

    inline bool Reachable(const Vertex &s, const Vertex &t) const {
        return dist_[s][t] != inf;
    }

    inline WeightType Distance(const Vertex &s, const Vertex &t) const {
        return dist_[s][t];
    }

    inline bool NegativeCycle() const {
        return negative_cycle_;
    }

    inline vector<WeightType> &operator[](const Vertex &s){
        return dist_[s];
    }

    inline const vector<WeightType> &operator[](const Vertex &s) const {
        return dist_[s];
    }

    private:
    int V;
    WeightType inf{WeightType(INF)};
    bool negative_cycle_{false};
    vector<vector<WeightType>> dist_;

    void Solve(){
        for(int i = 0; i < V; ++i) dist_[i][i] = min(dist_[i][i], WeightType(0));
        for(int k = 0; k < V; ++k){
            for(int i = 0; i < V; ++i){
                for(int j = 0; j < V; ++j){
                    if(dist_[i][k] == inf || dist_[k][j] == inf) continue;
                    dist_[i][j] = min(dist_[i][j], dist_[i][k] + dist_[k][j]);
                }
            }
        }
        for(int i = 0; i < V; ++i) negative_cycle_ |= dist_[i][i] < 0;
    }
};
#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 2 "Library/Graph/GraphMisc.hpp"

#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;
}
#line 3 "Library/Graph/WarshallFloyd.hpp"

template<typename WeightType>
class WarshallFloyd{
    public:
    WarshallFloyd(Graph<WeightType> &graph) :
        V(graph.VertexSize()), dist_(ConvertDistanceMatrix(graph)){
        Solve();
    }

    WarshallFloyd(vector<vector<WeightType>> &A) :
        V((int)A.size()), dist_(A){
        Solve();
    }

    inline bool Reachable(const Vertex &s, const Vertex &t) const {
        return dist_[s][t] != inf;
    }

    inline WeightType Distance(const Vertex &s, const Vertex &t) const {
        return dist_[s][t];
    }

    inline bool NegativeCycle() const {
        return negative_cycle_;
    }

    inline vector<WeightType> &operator[](const Vertex &s){
        return dist_[s];
    }

    inline const vector<WeightType> &operator[](const Vertex &s) const {
        return dist_[s];
    }

    private:
    int V;
    WeightType inf{WeightType(INF)};
    bool negative_cycle_{false};
    vector<vector<WeightType>> dist_;

    void Solve(){
        for(int i = 0; i < V; ++i) dist_[i][i] = min(dist_[i][i], WeightType(0));
        for(int k = 0; k < V; ++k){
            for(int i = 0; i < V; ++i){
                for(int j = 0; j < V; ++j){
                    if(dist_[i][k] == inf || dist_[k][j] == inf) continue;
                    dist_[i][j] = min(dist_[i][j], dist_[i][k] + dist_[k][j]);
                }
            }
        }
        for(int i = 0; i < V; ++i) negative_cycle_ |= dist_[i][i] < 0;
    }
};
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