跑一边最短路即可

#include<iostream>
#include<queue>
#include<cstring>
#include<algorithm>
#include<vector>
typedef long long LL;
#define _P(A) A=-~A
#define fione(i,a,b) for(register int i=a;i<=b;_P(i))
const int NUMBER1=2500,NUMBER2=6200;
struct EDGE{
	int to,w;
	EDGE *next;
	EDGE(){next=nullptr;}
}e[(NUMBER2<<1)+5],*head[NUMBER1+5];
int tot(0),n,m;
LL dis[NUMBER1+5];
bool visit[NUMBER1+5];
inline void add(const int &u,const int &v,const int &w){EDGE *p=&e[++tot];p->to=v,p->w=w,p->next=head[u];head[u]=p;}
inline void bfs(const int &begin){
	std::priority_queue<std::pair<LL,int>,std::vector<std::pair<LL,int> >,std::greater<std::pair<LL,int> > >q;
	memset(dis,0x7f7f7f,sizeof(dis));
	dis[begin]=0;q.push(std::make_pair(0LL,begin));
	while(!q.empty()){
		int u=q.top().second;q.pop();
		if(visit[u])continue;
		visit[u]=true;
		for(EDGE *i=head[u];i;i=i->next)if(dis[i->to]>dis[u]+i->w){
			dis[i->to]=dis[u]+i->w;
			if(!visit[i->to])q.push(std::make_pair(dis[i->to],i->to));
		}
	}
}
signed main(){
	int s,t;
	std::cin>>n>>m>>s>>t;
	for(register int a,b,c;m--;){
		std::cin>>a>>b>>c;
		add(a,b,c);add(b,a,c);
	}
	bfs(s);
	std::cout<<dis[t];
	return 0;
}