学步园

链接：http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=4141

题意：给出n个顶点，m条边，求一个生成树，使得最大边与最小边的差值最小。

思路：求一个生成树使最大边最小是瓶颈生成树。对于此题，我们枚举每一条边做最小边的情况，找对应的最小生成树的最大边，找出最大边与最小边差值最小的值即可。

#include<cstring>
#include<string>
#include<fstream>
#include<iostream>
#include<iomanip>
#include<cstdio>
#include<cctype>
#include<algorithm>
#include<queue>
#include<map>
#include<set>
#include<vector>
#include<stack>
#include<ctime>
#include<cstdlib>
#include<functional>
#include<cmath>
using namespace std;
#define PI acos(-1.0)
#define MAXN 50100
#define eps 1e-7
#define INF 0x7FFFFFFF
#define LLINF 0x7FFFFFFFFFFFFFFF
#define seed 131
#define MOD 1000000007
#define ll long long
#define ull unsigned ll
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1

struct node{
    int u,v,w;
}edge[MAXN];
int n,m,father[110],maxm;
bool cmp(node x,node y){
    return x.w<y.w;
}
int Find(int x){
    int t = x;
    while(t!=father[t])
        t = father[t];
    int k = x;
    while(k!=t){
        int temp = father[k];
        father[k] = t;
        k = temp;
    }
    return t;
}
bool kruskal(int x){
    int i,j;
    maxm = 0;
    for(i=0;i<=n;i++)    father[i] = i;
    int sum = 0;
    for(i=x;i<m;i++){
        int a = Find(edge[i].u);
        int b = Find(edge[i].v);
        if(a!=b){
            father[a] = b;
            sum++;
            maxm = max(maxm,edge[i].w);
            if(sum>=n-1)    return true;
        }
    }
    return false;
}
int main(){
    int i,j;
    while(scanf("%d%d",&n,&m),n||m){
        for(i=0;i<m;i++){
            scanf("%d%d%d",&edge[i].u,&edge[i].v,&edge[i].w);
        }
        sort(edge,edge+m,cmp);
        int ans = INF;
        for(i=0;i<m;i++){
            if(m-i<n-1) break;
            if(kruskal(i)){
                ans = min(ans,maxm-edge[i].w);
            }
        }
        if(ans==INF)    puts("-1");
        else        printf("%d\n",ans);
    }
    return 0;
}