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, …, vn} and E is a set of undirected edges {e1, e2, …, em}. Each edge e ∈ E 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<喎?http://www.Bkjia.com/kf/ware/vc/" target="_blank" class="keylink">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"http://www.2cto.com/uploadfile/Collfiles/20140815/20140815092125301.png" alt="\"> There are several spanning trees for G. Four of them are depicted in Figure 6(a)~(d). The spanning tree Ta 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 Ta is 4. The slimnesses of spanning trees Tb, Tc and Td 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 Td 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. 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 2 ≤ n ≤ 100 and 0 ≤ m ≤ n(n ?
1)/2. ak andbk (k = 1, …, m) are positive integers less than or equal to n, which represent the two vertices vak and vbk connected
by the kth edge ek. wk is a positive integer less than or equal to 10000, which indicates the weight ofek. 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 1 20 0 -1 -1 1 0 1686 50 題意及分析： 在一個無向圖裡有多棵生成樹，要求一棵特殊的生成樹。這棵樹最長的邊減去最短的邊得到的值最小。就是最苗條的一棵生成樹。 因為最苗條，所以最長的邊和最短的邊差值是最小的。那麼，我們將邊的從小到大權重排序，編號就是1~m了。然後從編號為1的邊開始枚舉。以這條邊作為樹的第一條邊，往後找，直至找到一棵生成樹。 接著以2號邊為生成樹的第一條邊，接著找生成樹。直至枚舉了所有情況。比較每次獲得的生成樹的slim值，取最小的那個。 AC代碼：
Figure 6: Examples of the spanning trees of G
4 5
1 2 3
1 3 5
1 4 6
2 4 6
3 4 7
4 6
1 2 10
1 3 100
1 4 90
2 3 20
2 4 80
3 4 40
2 1
1 2 1
3 0
3 1
1 2 1
3 3
1 2 2
2 3 5
1 3 6
5 10
1 2 110
1 3 120
1 4 130
1 5 120
2 3 110
2 4 120
2 5 130
3 4 120
3 5 110
4 5 120
5 10
1 2 9384
1 3 887
1 4 2778
1 5 6916
2 3 7794
2 4 8336
2 5 5387
3 4 493
3 5 6650
4 5 1422
5 8
1 2 1
2 3 100
3 4 100
4 5 100
1 5 50
2 5 50
3 5 50
4 1 150
0 0
