Luogu P2384 Shortest Problem Solving

topic

This question requires a magical knowledge point: log(n*m)=log(n)+log(m);

So take a log for all edge weights, and then calculate the shortest path of the log while maintaining the product.

#include <bits/stdc++.h>
#define int long long
using namespace std;
struct littlestar{
    int to;
    int nxt;
    long long w;
}star[1000010];
int head[1000010],cnt;
long long n,m,s,t,p;
inline void add(int u,int v,long long w)
{
    star[++cnt].to=v;
    star[cnt].w=w;
    star[cnt].nxt=head[u];
    head[u]=cnt;
}
bool cmp(littlestar x,littlestar y)
{
    return x.w<y.w;
}
priority_queue<pair<double,int> > q;
int vis[100010];
double dis[100010];
long long dis2[100010];
void dijkstra(int s)
{
    for(int i=1;i<=n;i++) dis[i]=99999999.999,dis2[i]=1;
    q.push(make_pair(0.00000,s));
    dis[s]=0.0000;
    while(q.size()){
        int u=q.top().second;
        q.pop();
        if(vis[u]) continue;
        vis[u]=1;
        for(int i=head[u];i;i=star[i].nxt){
            int v=star[i].to;       
            if(dis[v]>dis[u]+(double)log(star[i].w)){
                dis[v]=dis[u]+(double)log(star[i].w);
                dis2[v]=(star[i].w%p*dis2[u])%p;
                q.push(make_pair(-dis[v],v));
            }
        }
    }
}
signed main()
{
    p=9987;
    cin>>n>>m;
    for(register int i=1;i<=m;i++){
        int u,v;
        long long w;
        scanf("%lld%lld",&u,&v);
        cin>>w;
        add(u,v,w);
        add(v,u,w);
    }
    dijkstra(1);
    cout<<dis2[n]<<" ";
}
/*
3 3 1 3 5
1 2 2
2 3 4
1 3 11
 
*/

 

Reprinted in: https://www.cnblogs.com/kamimxr/p/11557818.html