POJ-2395: Out of Hay

最小生成树

Description

The cows have run out of hay, a horrible event that must be remedied immediately. Bessie intends to visit the other farms to survey their hay situation. There are N (2 <= N <= 2,000) farms (numbered 1..N); Bessie starts at Farm 1. She'll traverse some or all of the M (1 <= M <= 10,000) two-way roads whose length does not exceed 1,000,000,000 that connect the farms. Some farms may be multiply connected with different length roads. All farms are connected one way or another to Farm 1.

Bessie is trying to decide how large a waterskin she will need. She knows that she needs one ounce of water for each unit of length of a road. Since she can get more water at each farm, she's only concerned about the length of the longest road. Of course, she plans her route between farms such that she minimizes the amount of water she must carry.

Help Bessie know the largest amount of water she will ever have to carry: what is the length of longest road she'll have to travel between any two farms, presuming she chooses routes that minimize that number? This means, of course, that she might backtrack over a road in order to minimize the length of the longest road she'll have to traverse.

Input

• Line 1: Two space-separated integers, N and M.

• Lines 2..1+M: Line i+1 contains three space-separated integers, $A_i$, $B_i$, and $L_i$, describing a road from $A_i$ to $B_i$ of length $L_i$.
  Output

• Line 1: A single integer that is the length of the longest road required to be traversed.

Sample Input

3 3
1 2 23
2 3 1000
1 3 43

Sample Output

43

Hint

OUTPUT DETAILS: 
In order to reach farm 2, Bessie travels along a road of length 23. To reach farm 3, Bessie travels along a road of length 43. With capacity 43, she can travel along these roads provided that she refills her tank to maximum capacity before she starts down a road.

题意：输入n和m，代表有n个农场，下面有m行，有三个整数a，b，l，代表农场
a和b之间的距离为l，求从农场1出发到其他所有农场的最短路径中的最大值。【其实就是求最小生成树中的最大权值】

分析：每次的长度不用加起来，直接sum=max(sum,a[i].len)求得最大的权值。

• 完整代码：

#include<stdio.h>
#include<algorithm>
using namespace std;
int n,m,father[2222],sum;
struct node
{
    int st,en,len;
}a[11111];
int cmp(node a,node b)
{
    return a.len<b.len;
}
int findx(int x)
{
    if(x!=father[x])
        x=findx(father[x]);
    return father[x];
}
void kruskal()
{
    int i,x,y;
    sum=0;
    for(i=0;i<=n;i++)
        father[i]=i;
    for(i=0;i<m;i++)
    {
        x=findx(a[i].st);
        y=findx(a[i].en);
        if(x!=y)
        {
            sum=max(sum,a[i].len);
            father[x]=y;
        }
    }
    printf("%d\n",sum);
}
int main()
{
    int i;
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        for(i=0;i<m;i++)
            scanf("%d%d%d",&a[i].st,&a[i].en,&a[i].len);
        sort(a,a+m,cmp);
        kruskal();
    }
    return 0;
}