hdu 1679 The Unique MST （克鲁斯卡尔）

最新推荐文章于 2021-04-07 14:51:36 发布

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最新推荐文章于 2021-04-07 14:51:36 发布

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探讨通过克鲁斯卡尔算法解决最小生成树是否唯一的问题，介绍如何判断图中是否存在等效边。

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The Unique MST

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 24152		Accepted: 8587

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

Sample Output

3
Not Unique!

题目链接：http://poj.org/problem?

id=1679

题目大意：n个点m条路。给出每条路以及边权。推断最小生成树是否是唯一的。

解题思路：克鲁斯卡尔，推断是否存在等效边。这题数据太弱了。我推断等效边的方法不太对，竟然过了= =

代码例如以下：

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
int fa[102];
struct EG
{
	int u,v,w;
}eg[5005];
void get_fa()
{
	for(int i=0;i<105;i++)
		fa[i]=i;
}
int find (int x)
{
	return x==fa[x]?x:fa[x]=find(fa[x]);
}
void Union(int a,int b)
{
	int a1=find(a);
	int b1=find(b);
	if(a1!=b1)
		fa[a1]=b1;
}
int cmp(EG a,EG b)
{
	return a.w<b.w;
}
int main(void)
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		int n,m,ans=0,p=0,cnt=0;
		get_fa();
		scanf("%d%d",&n,&m);
		for(int i=0;i<m;i++)
		{
			scanf("%d%d%d",&eg[i].u,&eg[i].v,&eg[i].w);
		}
		sort(eg,eg+m,cmp);
		for(int i=0;i<m;i++)
		{
			if(find(eg[i].u)!=find(eg[i].v))//假设当前边须要增加且下一条边也须要增加且它们权值相等即为等效边
			{
				if(i+1<m&&find(eg[i+1].u)!=find(eg[i+1].v)&&eg[i].w==eg[i+1].w)
				{
					p=1;
					break;
				}
				Union(eg[i].u,eg[i].v);
				ans+=eg[i].w;
				cnt++;
			}
			if(cnt>=n)
				break;
		}
		if(!p)
			printf("%d\n",ans );
		else
			printf("Not Unique!\n");
	}
}