POJ 3268 - Silver Cow Party（dijkstra）

牛聚会最短路径

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本文介绍了一种利用Dijkstra算法解决有向图中各农场到指定聚会地点往返最短路径的问题，并通过实例演示了如何计算最长行走时间。

Silver Cow Party

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 10898		Accepted: 4836

Description

One cow from each of N farms (1 ≤ N ≤ 1000) conveniently numbered 1..N is going to attend the big cow party to be held at farm #X (1 ≤ X ≤ N). A total of M (1 ≤ M ≤ 100,000) unidirectional (one-way roads connects pairs of farms; road i requires T_i (1 ≤ T_i ≤ 100) units of time to traverse.

Each cow must walk to the party and, when the party is over, return to her farm. Each cow is lazy and thus picks an optimal route with the shortest time. A cow's return route might be different from her original route to the party since roads are one-way.

Of all the cows, what is the longest amount of time a cow must spend walking to the party and back?

Input

Line 1: Three space-separated integers, respectively: N, M, and X
Lines 2..M+1: Line i+1 describes road i with three space-separated integers: A_i, B_i, and T_i. The described road runs from farm A_i to farm B_i, requiring T_i time units to traverse.

Output

Line 1: One integer: the maximum of time any one cow must walk.

Sample Input

Sample Output

Hint

Cow 4 proceeds directly to the party (3 units) and returns via farms 1 and 3 (7 units), for a total of 10 time units.

=========================

有向图，求在不同点的牛到指定点来回的最短路之和的最大值是多少

由于dijkstra是求单源最短路，所以需要把矩阵逆置一次算两次最短路

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int maxn=111;
const int maxm=111111;
const int INF=0x3f3f3f;
int n,m,x,MAX=-1;
int map[1111][1111],dis1[1111],dis2[1111],vis[1111];

void dijkstra(int s,int dis[])
{
    for(int i=1; i<=n; i++){
        dis[i]=INF;
        vis[i]=false;
    }
    dis[s]=0;
    for(int rp=1;rp<=n;rp++)
    {
        int u=0,mn=INF;
        for (int i=1;i<=n;i++){
            if (!vis[i]&&dis[i]<mn){
                mn=dis[i];
                u=i;
            }
        }
        if(u==0) return;
        vis[u]=true;
        for(int i=1;i<=n;i++)
        {
            if(map[u][i]<INF&&dis[i]>dis[u]+map[u][i])
                dis[i]=dis[u]+map[u][i];
        }
    }
}

void change()
{
    for(int i=1;i<=n;i++)
        for(int j=i+1;j<=n;j++)
            swap(map[i][j],map[j][i]);
}

int main()
{
    scanf("%d%d%d",&n,&m,&x);
    memset(map,INF,sizeof(map));
    int u,v,w;
    for(int i=1;i<=n;i++)
        map[i][i]=0;
    for(int i=0;i<m;i++)
    {
        scanf("%d%d%d",&u,&v,&w);
        map[u][v]=w;
    }
    dijkstra(x,dis1);
    change();
    dijkstra(x,dis2);
    for(int i=1;i<=n;i++)
    {
        MAX=max(dis1[i]+dis2[i],MAX);
    }
    printf("%d\n",MAX);
    return 0;
}