This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// Judges with GCC >= 12 only needs Ofast
// #pragma GCC optimize("O3,no-stack-protector,fast-math,unroll-loops,tree-vectorize")
// MLE optimization
// #pragma GCC optimize("conserve-stack")
// Old judges
// #pragma GCC target("sse4.2,popcnt,lzcnt,abm,mmx,fma,bmi,bmi2")
// New judges. Test with assert(__builtin_cpu_supports("avx2"));
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma,tune=native")
// Atcoder
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma")
#include<bits/stdc++.h>
using namespace std;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
uniform_real_distribution<> pp(0.0,1.0);
#define int long long
#define pii pair<int,int>
const int inf=1e18;
const int mod=998244353;
const int maxn=100005;
const int maxl=20;
const int maxa=1000005;
int power(int a,int n){
int res=1;
while(n){
if(n&1) res=res*a%mod;
a=a*a%mod;n>>=1;
}
return res;
}
vector<pii> edge[maxn];
int n,m,du[maxn],dv[maxn],dist[maxn],dp[maxn][2][2];
void dijisktra(int st){
for(int i=1;i<=n;i++) du[i]=inf;
priority_queue<pii,vector<pii>,greater<pii>> pq;
du[st]=0;pq.push({0,st});
while(!pq.empty()){
int u=pq.top().second,d=pq.top().first;pq.pop();
if(du[u]!=d) continue;
for(pii v:edge[u]){
if(du[v.first]>d+v.second){
du[v.first]=d+v.second;
pq.push({d+v.second,v.first});
}
}
}
}
void solve(){
int u,v,s,t;cin >> n >> m >> s >> t >> u >> v;
for(int i=1;i<=m;i++){
int x,y,w;cin >> x >> y >> w;
edge[x].push_back({y,w});
edge[y].push_back({x,w});
}
dijisktra(v);
for(int i=1;i<=n;i++) dv[i]=du[i];
dijisktra(u);
for(int i=1;i<=n;i++){
dist[i]=inf;
for(int j=0;j<=1;j++){
for(int k=0;k<=1;k++) dp[i][j][k]=inf;
}
}
priority_queue<pii,vector<pii>,greater<pii>> pq;
dist[s]=0;pq.push({0,s});
dp[s][0][0]=0;dp[s][1][0]=du[s];dp[s][0][1]=dv[s];dp[s][1][1]=du[s]+dv[s];
while(!pq.empty()){
int u=pq.top().second,d=pq.top().first;pq.pop();
if(dist[u]!=d) continue;
//cout << u << ' ' << d << '\n';
for(pii v:edge[u]){
if(dist[v.first]>d+v.second){
dist[v.first]=d+v.second;
pq.push({d+v.second,v.first});
for(int i=0;i<=1;i++){
for(int j=0;j<=1;j++){
dp[v.first][i][j]=dp[u][i][j];
if(i) dp[v.first][i][j]=min(dp[v.first][i][j],dp[v.first][0][j]+du[v.first]);
if(j) dp[v.first][i][j]=min(dp[v.first][i][j],dp[v.first][i][0]+dv[v.first]);
if(i && j) dp[v.first][i][j]=min(dp[v.first][i][j],dp[v.first][0][0]+du[v.first]+dv[v.first]);
}
}
}
else if(dist[v.first]==d+v.second){
for(int i=0;i<=1;i++){
for(int j=0;j<=1;j++){
dp[v.first][i][j]=min(dp[u][i][j],dp[v.first][i][j]);
if(i) dp[v.first][i][j]=min(dp[v.first][i][j],dp[v.first][0][j]+du[v.first]);
if(j) dp[v.first][i][j]=min(dp[v.first][i][j],dp[v.first][i][0]+dv[v.first]);
if(i && j) dp[v.first][i][j]=min(dp[v.first][i][j],dp[v.first][0][0]+du[v.first]+dv[v.first]);
}
}
}
}
}
cout << min(dp[t][1][1],du[v]) << '\n';
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);cout.tie(NULL);
int t=1;//cin >> t;
while(t--) solve();
}
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