poj 3268 Silver Cow Party(最短路dijkstra）

描述：

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

4 8 2
1 2 4
1 3 2
1 4 7
2 1 1
2 3 5
3 1 2
3 4 4
4 2 3

Sample Output

10

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.

 

题解：

　　要求的其实就是1-n的每个点到x以及从x回来的最短路之和的最大值。就可以用两次dijkstra算法求解，一次算从i到x，一次算从x到i，最后求得相加的最大值即可。

代码：

#include <iostream>
#include <stdio.h>

using namespace std;
#define inf 1<<29
int n,m,x;
bool vis[1010];
int map[1010][1010];
int go[1010],dback[1010];  //go是从i—>x  back是从x—>i

int dijkstra()
{
    int i,j,f,v;
    for(i=1;i<=n;i++)
    {
        vis[i]=0;
        go[i]=map[i][x];
        dback[i]=map[x][i];
    }

    for(i=1;i<=n;i++)
    {
        f=inf;
        for(j=1;j<=n;j++)
        {
            if(!vis[j]&&dback[j]<f)
            {
                v=j;
                f=dback[j];
            }
        }
        vis[v]=1;
        for(j=1;j<=n;j++)
            if(!vis[j]&&map[v][j]+dback[v]<dback[j])
                dback[j]=map[v][j]+dback[v];
    }

    for(i=1;i<=n;i++) vis[i]=0;

    for(i=1;i<=n;i++)
    {
        f=inf;
        for(j=1;j<=n;j++)
        {
            if(!vis[j]&&go[j]<f)
            {
                v=j;
                f=go[j];
            }
        }
        vis[v]=1;
        for(j=1;j<=n;j++)
        {
            if(!vis[j]&&map[j][v]+go[v]<go[j])
                go[j]=map[j][v]+go[v];
        }
    }

    f=-1;
    for(i=1;i<=n;i++)
    {
        if(go[i]+dback[i]>f)
            f=go[i]+dback[i];
    }
    return f;
}

int main()
{
    int a,b,c;
    while(~scanf("%d%d%d",&n,&m,&x)){
        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++)
            {
                if(i!=j) map[i][j]=inf;
                else map[i][j]=0;
            }
        for(int i=0;i<m;i++)
        {
            scanf("%d%d%d",&a,&b,&c);
            map[a][b]=c;
        }
        printf("%d
",dijkstra());
    }
    return 0;
}