POJ 1679 The Unique MST （最小生成树）

The Unique MST

题目链接：

http://acm.hust.edu.cn/vjudge/contest/124434#problem/J

Description

Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undirected graph G = (V, E). A spanning tree of G is a subgraph of G, say T = (V', E'), with the following properties: 1. V' = V. 2. T is connected and acyclic. Definition 2 (Minimum Spanning Tree): Consider an edge-weighted, connected, undirected graph G = (V, E). The minimum spanning tree T = (V, E') of G is the spanning tree that has the smallest total cost. The total cost of T means the sum of the weights on all the edges in E'.

Input

The first line contains a single integer t (1 <= t <= 20), the number of test cases. Each case represents a graph. It begins with a line containing two integers n and m (1 <= n <= 100), the number of nodes and edges. Each of the following m lines contains a triple (xi, yi, wi), indicating that xi and yi are connected by an edge with weight = wi. For any two nodes, there is at most one edge connecting them.

Output

For each input, if the MST is unique, print the total cost of it, or otherwise print the string 'Not Unique!'.

Sample Input

2 3 3 1 2 1 2 3 2 3 1 3 4 4 1 2 2 2 3 2 3 4 2 4 1 2

Sample Output

3 Not Unique!
##题意： 求最小生成树并判断是否唯一.
##题解： 做法一： 先求一次最小生成树并记录MST中的边，枚举删除MST中的边，判断删除后的结果是否与删除前相同. 这样做一定要注意：删边后可能最小生成树不存在(求得的结果不联通). 很遗憾做了久都没过. 挖坑待填.
做法二： 考虑MST中每条边的作用： kruskal在枚举边时，当一条边连接了并查集中不同的两个集合时，便把它加到结果中. 那么MST中边的作用是连接不同的两个集合. 如果存在多个MST，那么一定有一条或多条边可以起到相同的作用，即： 长度相等 且 连接集合的作用也相同. 基于以上理论，在kruskal过程中对长度相同的边作特判即可.
做法三： 直接求次小生成树.
##代码： ``` cpp #include #include #include #include #include #include #include