洛谷 P2384 最短路 题解

题面

这道题需要用到一个神奇的知识点：log(n*m)=log(n)+log(m)；

所以对所有边权取个log，然后算log的最短路的同时维护乘积即可

#include <bits/stdc++.h>
#define int long long
using namespace std;
struct littlestar{
    int to;
    int nxt;
    long long w;
}star[];
int head[],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[];
double dis[];
long long dis2[];
void dijkstra(int s)
{
    for(int i=;i<=n;i++) dis[i]=99999999.999,dis2[i]=;
    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]=;
        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=;
    cin>>n>>m;
    for(register int i=;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();
    cout<<dis2[n]<<" ";
}
/*
3 3 1 3 5
1 2 2
2 3 4
1 3 11

*/