Kruskal模板题 Slim Span uva

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我是靠谱客的博主大胆画笔，最近开发中收集的这篇文章主要介绍Kruskal模板题 Slim Span uva，觉得挺不错的，现在分享给大家，希望可以做个参考。

概述

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

Submit Status

Description

Given an undirected weighted graph G , you should find one of spanning trees specified as follows.

The graph G is an ordered pair (V, E) , where V is a set of vertices {v₁, v₂,..., v_n} and E is a set of undirected edges {e₁, e₂,..., e_m} . Each edgeeE has its weight w(e) .

A spanning tree T is a tree (a connected subgraph without cycles) which connects all the n vertices with n - 1 edges. The slimness of a spanning tree T is defined as the difference between the largest weight and the smallest weight among the n - 1 edges of T .

For example, a graph G in Figure 5(a) has four vertices {v₁, v₂, v₃, v₄} and five undirected edges {e₁, e₂, e₃, e₄, e₅} . The weights of the edges are w(e₁) = 3 , w(e₂) = 5 , w(e₃) = 6 , w(e₄) = 6 , w(e₅) = 7 as shown in Figure 5(b).

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There are several spanning trees for G . Four of them are depicted in Figure 6(a)âˆ¼(d). The spanning tree T_a in Figure 6(a) has three edges whose weights are 3, 6 and 7. The largest weight is 7 and the smallest weight is 3 so that the slimness of the tree T_a is 4. The slimnesses of spanning trees T_b , T_c and T_d shown in Figure 6(b), (c) and (d) are 3, 2 and 1, respectively. You can easily see the slimness of any other spanning tree is greater than or equal to 1, thus the spanning tree T_d in Figure 6(d) is one of the slimmest spanning trees whose slimness is 1.

Your job is to write a program that computes the smallest slimness.

Input

The input consists of multiple datasets, followed by a line containing two zeros separated by a space. Each dataset has the following format.

nm
a₁b₁w₁

a_mb_mw_m

Every input item in a dataset is a non-negative integer. Items in a line are separated by a space.

n is the number of the vertices and m the number of the edges. You can assume 2n100 and 0mn(n - 1)/2 . a_k and b_k(k = 1,..., m) are positive integers less than or equal to n , which represent the two vertices v_{a_k} and v_{b_k} connected by the k -th edge e_k . w_k is a positive integer less than or equal to 10000, which indicates the weight of e_k . You can assume that the graph G = (V, E) is simple, that is, there are no self-loops (that connect the same vertex) nor parallel edges (that are two or more edges whose both ends are the same two vertices).

Output

For each dataset, if the graph has spanning trees, the smallest slimness among them should be printed. Otherwise, `-1' should be printed. An output should not contain extra characters.

Sample Input

Sample Output

<pre name="code" class="cpp">#include <stdio.h>
#include <string.h>
#include <math.h>
#include <algorithm>
#include <iostream>
using namespace std;
/*
这是一个最小生成树问题，我的Kruskal算法和并查集有部分模板
而且掌握的较好，所以用Kruskal；
从最小的边开始找最小生成树，然后去掉这个最小的边再找一个最小生成树
min1来储存最小的值，最后输出
*/
const int maxn=110;
struct aa
{
int x,y,l;
};
bool cmp(aa a,aa b)
{
return a.l<b.l;
};
aa a[maxn*55];
int fa[110],n;
int find(int a)
{
return fa[a]==a?a:find(fa[a]);
}
int haha(int i,int m)//处理
{
int rank=1,k=i,c,d;
for(; i<m; i++)
{
c=find(a[i].x);
d=find(a[i].y);
if(c!=d)
{
fa[c]=d;
rank++;
if(rank==n)return a[i].l-a[k].l;
}
}
return -1;
}
int main()
{
int m;
while(~scanf("%d%d",&n,&m))
{
if(m==0&&n==0)break;
memset(a,0,sizeof(a));
for(int i=0; i<n; i++)
fa[i]=i;
for(int i=0; i<m; i++)
{
scanf("%d%d%d",&a[i].x,&a[i].y,&a[i].l);
a[i].x--;
a[i].y--;
}
sort(a,a+m,cmp);
int min1=-1;
for(int i=0; i<m; i++)
{
int k=haha(i,m);
if(k!=-1)
{
if(min1==-1)min1=k;
else
min1=min(min1,k);
}
for(int i=0; i<n; i++)
fa[i]=i;
}
printf("%dn",min1);
}
return 0;
}