Dijkstra
(Graph2/Dijkstra.hpp)

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• Last update: 2023-07-17 18:02:31+09:00
• Include: #include "Graph2/Dijkstra.hpp"

概要

Dijkstra法
O((E+V)logV)

仕様

• build(st) 始点をstとして構築
• get_path(gl) st-glのパス上の頂点が入ったvectorを返す

あ

これ書いてて思ったのですが，get_path, 辺のvectorを返す方が情報量多くていいかもしれないのでいつかそうするかもしれない

Depends on

• Graph2/GraphTemplate.hpp

Verified with

• test/AOJ_GRL_1_A.test.cpp

Code

#include "./GraphTemplate.hpp"

template<typename T>
struct Dijkstra{
    const T inf;
    Graph<T> g;
    vector<T> d;
    vector<int> prev,eid;
    
    Dijkstra(Graph<T> g):inf(numeric_limits<T>::max()/4),g(g){}

    vector<T> build(int st){
        d.assign(g.V,inf);
        prev.assign(g.V,-1);
        eid.assign(g.V,-1);
        d[st]=0;
        priority_queue<pair<T,int>,vector<pair<T,int>>,greater<pair<T,int>>> que;
        que.emplace(d[st],st);
        while(!que.empty()){
            auto p=que.top();que.pop();
            int cur=p.second;
            if(d[cur]<p.first) continue;
            for(auto &e:g[cur]){
                if(d[e]>d[cur]+e.w){
                    d[e]=d[cur]+e.w;
                    prev[e]=cur;
                    que.emplace(d[e],e);
                }
            }
        }
        return d;
    }

    // vertex = false :-> edge idx
    vector<int> get_path(int gl,bool vertex=true){
        vector<int> ret;
        if(d[gl]==inf) return ret;
        for(;gl!=-1;gl=prev[gl]){
            ret.push_back(vertex?gl:eid[gl]);
        }
        reverse(ret.begin(),ret.end());
        return ret;
    }
};

#line 1 "Graph2/GraphTemplate.hpp"



// graph template
// ref : https://ei1333.github.io/library/graph/graph-template.hpp
template<typename T=int>
struct Edge{
    int from,to;
    T w;
    int idx;
    Edge()=default;
    Edge(int from,int to,T w=1,int idx=-1):from(from),to(to),w(w),idx(idx){}
    operator int() const{return to;}
};

template<typename T=int>
struct Graph{
    vector<vector<Edge<T>>> g;
    int V,E;
    Graph()=default;
    Graph(int n):g(n),V(n),E(0){}

    int size(){
        return (int)g.size();
    }
    void resize(int k){
        g.resize(k);
        V=k;
    }
    inline const vector<Edge<T>> &operator[](int k)const{
        return (g.at(k));
    }
    inline vector<Edge<T>> &operator[](int k){
        return (g.at(k));
    }
    void add_directed_edge(int from,int to,T cost=1){
        g[from].emplace_back(from,to,cost,E++);
    }
    void add_edge(int from,int to,T cost=1){
        g[from].emplace_back(from,to,cost,E);
        g[to].emplace_back(to,from,cost,E++);
    }
    void read(int m,int pad=-1,bool weighted=false,bool directed=false){
        for(int i=0;i<m;i++){
            int u,v;cin>>u>>v;
            u+=pad,v+=pad;
            T w=T(1);
            if(weighted) cin>>w;
            if(directed) add_directed_edge(u,v,w);
            else         add_edge(u,v,w);
        }
    }
};


#line 2 "Graph2/Dijkstra.hpp"

template<typename T>
struct Dijkstra{
    const T inf;
    Graph<T> g;
    vector<T> d;
    vector<int> prev,eid;
    
    Dijkstra(Graph<T> g):inf(numeric_limits<T>::max()/4),g(g){}

    vector<T> build(int st){
        d.assign(g.V,inf);
        prev.assign(g.V,-1);
        eid.assign(g.V,-1);
        d[st]=0;
        priority_queue<pair<T,int>,vector<pair<T,int>>,greater<pair<T,int>>> que;
        que.emplace(d[st],st);
        while(!que.empty()){
            auto p=que.top();que.pop();
            int cur=p.second;
            if(d[cur]<p.first) continue;
            for(auto &e:g[cur]){
                if(d[e]>d[cur]+e.w){
                    d[e]=d[cur]+e.w;
                    prev[e]=cur;
                    que.emplace(d[e],e);
                }
            }
        }
        return d;
    }

    // vertex = false :-> edge idx
    vector<int> get_path(int gl,bool vertex=true){
        vector<int> ret;
        if(d[gl]==inf) return ret;
        for(;gl!=-1;gl=prev[gl]){
            ret.push_back(vertex?gl:eid[gl]);
        }
        reverse(ret.begin(),ret.end());
        return ret;
    }
};

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