poj 2395 Out of Hay(最小生成树，水)

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.

Source

USACO 2005 March Silver

 

求干草：奶牛没草吃了，要去附近的农场找，求最短遍历路径上最长的那条路。

水最小生成树，kruskal找出最大边即可。

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<math.h>
#include<algorithm>
#include<queue>
#include<set>
#include<bitset>
#include<map>
#include<vector>
#include<stdlib.h>
#include <stack>
using namespace std;
#define PI acos(-1.0)
#define max(a,b) (a) > (b) ? (a) : (b)  
#define min(a,b) (a) < (b) ? (a) : (b)
#define ll long long
#define eps 1e-10
#define MOD 1000000007
#define N 2006
#define M 20006
#define inf 1e12
struct Node{
    int x,y;
    int cost;
}edge[M];
int n,m;
int fa[N];
void init(){
    for(int i=0;i<N;i++){
        fa[i]=i;
    }
}
int find(int x){
    return fa[x]==x?x:fa[x]=find(fa[x]);
}
bool cmp(Node a,Node b){
    return a.cost<b.cost;
}
int main()
{
    while(scanf("%d%d",&n,&m)==2){
        init();
        for(int i=0;i<m;i++){
            int a,b,c;
            scanf("%d%d%d",&edge[i].x,&edge[i].y,&edge[i].cost);
        }
        sort(edge,edge+m,cmp);
        int ans=0;
        //int num=n-1;
        for(int i=0;i<m;i++){
            int root1=find(edge[i].x);
            int root2=find(edge[i].y);
            if(root1!=root2){
                //ans+=edge[i].cost;
                ans=max(ans,edge[i].cost);
                fa[root1]=root2;
                //num--;
            }
        }
        
            printf("%d
",ans);
        
    }
    return 0;
}