God Of War

/*
    Task    : _example
    Author  : Phumipat C. [MAGCARI]
    Language: C++
    Created : 14 November 2022 [21:37]
*/
#include<bits/stdc++.h>
using namespace std;
struct A{
    int currentNode,sumDistance,usedTicket;
    bool operator < (const A&o) const{
        return sumDistance > o.sumDistance;
    }
};
priority_queue<A > heap;
struct B{
    int nextNode,edgeWeight;
};
vector<B > g[100010];
int dis[100010][2];
int main(){
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit);
    int n,m,s,t,sum = 0;
    cin >> n >> m >> s >> t;
    for(int i=1;i<=m;i++){
        int u,v,w;
        cin >> u >> v >> w;
        sum+=w;
        g[u].push_back({v,w});
        g[v].push_back({u,w});
    }
    for(int i=0;i<n;i++)
        dis[i][0] = dis[i][1] = 1e9;
    dis[s][0] = 0;
    heap.push({s,0,0});
    while(!heap.empty()){
        A now = heap.top();
        heap.pop();
        if(now.currentNode == t && now.usedTicket == 1){
            cout << sum-now.sumDistance << '\n';
            break;
        }
        for(auto x:g[now.currentNode]){
            //normal
            if(dis[x.nextNode][now.usedTicket] > now.sumDistance + x.edgeWeight){
                dis[x.nextNode][now.usedTicket] = now.sumDistance + x.edgeWeight;
                heap.push({x.nextNode,now.sumDistance + x.edgeWeight, now.usedTicket});
            }

            //special
            if(now.usedTicket == 0 && dis[x.nextNode][now.usedTicket+1] > now.sumDistance){
                dis[x.nextNode][now.usedTicket+1] > now.sumDistance;
                heap.push({x.nextNode,now.sumDistance,now.usedTicket+1});
            }
        }
    }
    return 0;
}