God Of War

/*
    Task    : _example
    Author  : Phumipat C. [MAGCARI]
    Language: C++
    Created : 12 November 2022 [11:50]
*/
#include<bits/stdc++.h>
using namespace std;
struct A{
    int v,w;
};
vector<A > g[100010];
struct B{
    int v,d,k;
    bool operator < (const A&o) const{
        return d > o.d;
    }
};
priority_queue<B > heap;
int dis[100010][2];
int main(){
    int n,m,s,t,u,v,w,sumW = 0;
    scanf("%d %d %d %d",&n,&m,&s,&t);
    for(int i=1;i<=m;i++){
        scanf("%d %d %d",&u,&v,&w);
        g[u].push_back({v,w});
        g[v].push_back({u,w});
        sumW+=w;
    }
    for(int i=0;i<n;i++)
        dis[i][0] = dis[i][1] = 1e9;
    dis[s][1] = 0;
    heap.push({s,0,1});
    while(!heap.empty()){
        auto now = heap.top();
        heap.pop();
        if(now.v == t && now.k == 0){
            printf("%d\n",sumW-now.d);
            break;
        }
        for(auto x:g[now.v]){
            //special
            if(now.k && dis[x.v][0] > now.d){
                dis[x.v][0] = now.d;
                heap.push({x.v,now.d,0});
            }
            //normal
            if(dis[x.v][now.k] > now.d + x.w){
                dis[x.v][now.k] = now.d + x.w;
                heap.push({x.v,dis[x.v][now.k],now.k});
            }
        }
    }
    return 0;
}