POJ 3615 Cow Hurdles（最短路径flyod）

Cow Hurdles

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 9337		Accepted: 4058

Description

Farmer John wants the cows to prepare for the county jumping competition, so Bessie and the gang are practicing jumping over hurdles. They are getting tired, though, so they want to be able to use as little energy as possible to jump over the hurdles.

Obviously, it is not very difficult for a cow to jump over several very short hurdles, but one tall hurdle can be very stressful. Thus, the cows are only concerned about the height of the tallest hurdle they have to jump over.

The cows' practice room has N (1 ≤ N ≤ 300) stations, conveniently labeled 1..N. A set of M (1 ≤ M ≤ 25,000) one-way paths connects pairs of stations; the paths are also conveniently labeled 1..M. Path i travels from station S_i to station E_i and contains exactly one hurdle of height H_i (1 ≤ H_i ≤ 1,000,000). Cows must jump hurdles in any path they traverse.

The cows have T (1 ≤ T ≤ 40,000) tasks to complete. Task i comprises two distinct numbers, A_i and B_i (1 ≤ A_i ≤ N; 1 ≤ B_i ≤ N), which connote that a cow has to travel from station A_i to station B_i (by traversing over one or more paths over some route). The cows want to take a path the minimizes the height of the tallest hurdle they jump over when traveling from A_i to B_i . Your job is to write a program that determines the path whose tallest hurdle is smallest and report that height.
　

Input

* Line 1: Three space-separated integers: N, M, and T
* Lines 2..M+1: Line i+1 contains three space-separated integers: S_i , E_i , and H_i 
* Lines M+2..M+T+1: Line i+M+1 contains two space-separated integers that describe task i: A_i and B_i

Output

* Lines 1..T: Line i contains the result for task i and tells the smallest possible maximum height necessary to travel between the stations. Output -1 if it is impossible to travel between the two stations.

Sample Input

5 6 3
1 2 12
3 2 8
1 3 5
2 5 3
3 4 4
2 4 8
3 4
1 2
5 1

Sample Output

4
8
-1

题意:
第一行输入n,m,t三个整数。
n表示有n个点，m表示有m条路线，t表示有t个奶牛需要经过的路线
接下来m行描述m条路线，每行表示由x到y需要跨过的高度为h
最后t行表示有t个奶牛，每个奶牛需要从起点s到终点t,问这个奶牛在s -> t过程中需要经过的最低高度是多少

//POJ3615
#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 123456789
int a[][];        //最大高度的最小值矩阵

int main()
{
    int n, m, t;
    int x, y, h;
    while (scanf("%d%d%d", &n, &m, &t) != EOF)
    {
        for (int i = ; i <= n; i++)                 //初始化
            for (int j = ; j <= n; j++)
                {
                    if(i==j)
                        a[i][j]=;
                    else
                        a[i][j]=INF;
                }
        for (int i = ; i <= m; i++)//读入高度差
        {
            scanf("%d%d%d", &x, &y, &h);
            a[x][y] = min(a[x][y], h);   //更新子问题高度差
        }

        for (int k = ; k <= n; k++)                 //Floyd
            for (int i = ; i <= n; i++)
                for (int j = ; j <= n; j++)
                {
                    a[i][j] = min(a[i][j], max(a[i][k], a[k][j]));//DP思想
                }
        for (int i = ; i <= t; i++)
        {
            scanf("%d%d", &x, &y);
            if (a[x][y] == INF) //输出，如果还是INF，那就代表不可达，两者时之间没有路径满足要求
                printf("-1\n");
            else
            printf("%d\n",a[x][y]);
        }
    }
    return ;
}