Second Max path (LOJ 1088. Not the best)

/******************
Find Second Maximum path (LOJ 1088)
******************/
#include <cstdio>
#include <vector>
#include <queue>
using namespace std;
struct R{int n,w;};
int main(){
    int t,n,m,i,u,v,w,w1,mn1,mn2,cs=1;
    scanf("%d",&t);
    while (t--){
        scanf("%d %d",&n,&m);
        vector<R> g[n+2];
        for (i=0; i<m; i++){
            scanf("%d %d %d",&u,&v,&w);
            g[u].push_back({v,w});
            g[v].push_back({u,w});
        }
        queue<R> q;
        q.push({1,0});
        mn1=mn2=1e9;
        while (q.size()){
            u=q.front().n, w=q.front().w, q.pop();
            for (i=0; i<g[u].size(); i++){
                v=g[u][i].n, w1=w+g[u][i].w;
                if (w1<mn1 || w1<mn2){
                    q.push({v,w1});
                    if (v==n){
                        if (w1<mn1) mn2=mn1, mn1=w1;
                        else if (w1!=mn1) mn2=w1;
                    }
                }
            }
        }
        printf("Case %d: %d\n",cs++,mn2);
    } return 0;
}