8/4 dijkstra

最短路径（迪科斯特算法模板）

#include<bits/stdc++.h>
using namespace std;

int n,m,s;
bool vis[10005];
int INF=0x3f3f3f3f;
int d[10005];

struct node{
    int v,w;
}; 
vector<node> G[1005];

struct hn{
    int u,dist;
    hn(int _u,int _dist){
        u=_u;
        dist=_dist;
    }
};

struct cmp{
    bool operator()(hn a,hn b){
        return a.dist>b.dist;
    }
};

priority_queue<hn,vector<hn>,cmp>q;


void dijkstra(){
    memset(vis,false,sizeof(vis));
    memset(d,INF,sizeof(d));
    d[s]=0;
    q.push(hn(s,0));
    while(q.size()){
        int x=q.top().u;
        q.pop();
        vis[x]=true;
        
        for(int i=0; i<G[x].size(); i++){
            int y=G[x][i].v;
            int z=G[x][i].w;
            if(!vis[y] && d[x]+z<d[y]){
                d[y]=d[x]+z;
                q.push(hn(y,d[y]));
            }
        }
    }
}

int main(){
    cin>>n>>m>>s;
    for(int i=1; i<=m; i++){
        int xx,yy,zz;
        cin>>xx>>yy>>zz;
        G[xx].push_back({yy,zz});
        G[yy].push_back({xx,zz});
    }
    dijkstra();
    for(int i=1; i<=n; i++){
        cout<<d[i]<<" ";
    }
    cout<<endl;
    return 0;
}

单源最短路

#include<bits/stdc++.h>
using namespace std;

int n,m,s,t;
bool vis[100005];
int INF=0x3f3f3f3f;
int d[100005];

struct node{
    int v,w;
}; 
vector<node> G[10005];

struct hn{
    int u,dist;
    hn(int _u,int _dist){
        u=_u;
        dist=_dist;
    }
};

struct cmp{
    bool operator()(hn a,hn b){
        return a.dist>b.dist;
    }
};

priority_queue<hn,vector<hn>,cmp>q;


void dijkstra(){
    memset(vis,false,sizeof(vis));
    memset(d,INF,sizeof(d));
    d[s]=0;
    q.push(hn(s,0));
    while(q.size()){
        int x=q.top().u;
        q.pop();
        vis[x]=true;
        
        for(int i=0; i<G[x].size(); i++){
            int y=G[x][i].v;
            int z=G[x][i].w;
            if(!vis[y] && d[x]+z<d[y]){
                d[y]=d[x]+z;
                q.push(hn(y,d[y]));
            }
        }
    }
}

int main(){
    cin>>n>>m>>s>>t;
    for(int i=1; i<=m; i++){
        int xx,yy,zz;
        cin>>xx>>yy>>zz;
        G[xx].push_back({yy,zz});
        G[yy].push_back({xx,zz});
    }
    dijkstra();
    cout<<d[t]<<endl;
    return 0;
}

信使

#include<bits/stdc++.h>
using namespace std;

int n,m,s;
bool vis[10005];
int INF=0x3f3f3f3f;
int d[10005];

struct node{
    int v,w;
}; 
vector<node> G[1005];

struct hn{
    int u,dist;
    hn(int _u,int _dist){
        u=_u;
        dist=_dist;
    }
};

struct cmp{
    bool operator()(hn a,hn b){
        return a.dist>b.dist;
    }
};

priority_queue<hn,vector<hn>,cmp>q;


void dijkstra(){
    memset(vis,false,sizeof(vis));
    memset(d,INF,sizeof(d));
    d[1]=0;
    q.push(hn(1,0));
    while(q.size()){
        int x=q.top().u;
        q.pop();
        vis[x]=true;
        
        for(int i=0; i<G[x].size(); i++){
            int y=G[x][i].v;
            int z=G[x][i].w;
            if(!vis[y] && d[x]+z<d[y]){
                d[y]=d[x]+z;
                q.push(hn(y,d[y]));
            }
        }
    }
}

int main(){
    cin>>n>>m;
    for(int i=1; i<=m; i++){
        int xx,yy,zz;
        cin>>xx>>yy>>zz;
        G[xx].push_back({yy,zz});
        G[yy].push_back({xx,zz});
    }
    int ans=INT_MIN;
    dijkstra();
    for(int i=1; i<=n; i++){
        ans=max(ans,d[i]);
    }
    cout<<ans<<endl;
    return 0;
}