POJ-1679 kruskal算法最小生成树唯一？

最新推荐文章于 2024-05-06 20:12:28 发布

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最新推荐文章于 2024-05-06 20:12:28 发布 · 587 阅读

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该博客探讨了如何确定无向图的最小生成树是否唯一。通过给出连通无向图的定义，以及最小生成树的概念，博主提出了一种解决方法：运行两次Kruskal算法。如果在第二次运行中发现未标记的边，则说明最小生成树不唯一。博主提供了样例输入和输出，并给出了解题思路。

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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:

V’ = V.
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!
解题思路：
跑一遍kruskal，标记用过的边，排个序放到后面，再跑一遍kruskal，
如果出现没标记的边，就不唯一
代码：

#include<iostream>
#include<vector>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#define maxn 105
using namespace std;
inline int read(){
   
   
    	int x=0,f=0;char ch=getchar()