图论--最短路--dijkstra（含路径输出）模板

#include<iostream>
#include<stack>
#include<queue>
#include<cstring>
#include<cstdio>
using namespace std;
typedef long long ll;
typedef pair<int,int> PII;
struct Node
{
    int var,next,val;
} edge[100000005];
int head[100005],tot,dis[100005],N,M;
int pre[100005]; //松弛数组
bool vis[100005]; //唯一定理
priority_queue<PII> Q; //大根堆优化
void add(int a, int b, int c)
{
    edge[++tot].var = b;
    edge[tot].val = c;
    edge[tot].next = head[a];
    head[a] = tot;
}
void init()//多组输入调用
{
    tot=0;
    memset(head,0,sizeof(head));
}
void dijkstra(int s)
{
    memset(dis,0x3f,sizeof(dis));
    memset(vis,0,sizeof(vis));
    memset(pre,-1,sizeof(pre));
    while(Q.size()) Q.pop();
    dis[s] = 0;
    Q.push(make_pair(0,s));
    while(!Q.empty())
    {
        int x=Q.top().second;
        Q.pop();
        if(vis[x])continue;
        vis[x]=1;
        for(int i=head[x]; i; i=edge[i].next)
        {
            int y=edge[i].var;
            if(dis[x]+edge[i].val<dis[y]) //图论三角不等式
            {
                dis[y]=dis[x]+edge[i].val;
                if(!vis[y])
                Q.push(make_pair(-dis[y],y));
                pre[y]=x;
            }
        }

    }
}
int main()
{
    int S,E;
    init();
   cin>>N>>M>>S>>E;
    while(M--)
    {
        int x,y,z;
        cin>>x>>y>>z;
        add(x+1,y+1,z);
    }
    dijkstra(S+1);
    if(dis[E+1]>0x3f000000)
    {
        cout<<"no answer"<<endl;
        return 0;
    }
    cout<<dis[E+1]<<endl;
    stack<int> ans;
    for(int i=E+1;i!=-1;i=pre[i])
    {
        ans.push(i-1);
        //cout<<i-1<<endl;
    }
    while(ans.size())
    {
        cout<<'v';
        cout<<ans.top()<<" ";
        ans.pop();
    }
    puts("");
}