Kruskal模板題 Slim Span uva
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 edgeeE has its weight w(e) .
A spanning tree T is a tree (a connected subgraph without cycles) which connects all the n
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
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 T
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
ambmwm
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 . ak and bk(k = 1,..., m) are positive integers less than or equal to n ,
which represent the two vertices vak and vbk connected by the k -th edge ek . wk is
a positive integer less than or equal to 10000, which indicates the weight of ek . 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).
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.
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
1 20 0 -1 -1 1 0 1686 50