POJ1679-The Unique MST(次小生成树)

45 阅读 0 评论 30 点赞

我是靠谱客的博主丰富秋天，最近开发中收集的这篇文章主要介绍POJ1679-The Unique MST(次小生成树)，觉得挺不错的，现在分享给大家，希望可以做个参考。

概述

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!

题意：是否存在唯一的MST，存在输出MST的权值，不存在输“Not Unique！”。

题解：通过Kruskal构建MST，存储权值t，并对组成MST的边进行标记，。枚举标记过的边将其删除，重新构建MST，存储新权值ans，如果新权值ans等于之前权值t，说明MST不唯一。

#include<iostream>
#include<algorithm>
using namespace std;
const int maxn = 110;
int n,m;
bool flag;
struct Edge{
int u,v,w;
bool del,use;
}edge[maxn*maxn];
int f[maxn];
void init()
{
for(int i=0;i<n;i++)
f[i]=i;
}
int Find(int x)
{
if(x==f[x]) return x;
return f[x]=Find(f[x]);
}
bool cmp(Edge p,Edge q) {return p.w<q.w;}
int Krusal()
{
int cnt=0,sum=0;
init();
for(int i=0;i<m;i++)
{
int xroot=Find(edge[i].u),yroot=Find(edge[i].v);
if(xroot!=yroot&&edge[i].del==false)
{
if(!flag) edge[i].use=true;
f[xroot]=yroot;
sum+=edge[i].w;
cnt++;
if(cnt==n-1)
{
return sum;
}
}
}
return -1;
}
int main()
{
int t;
cin>>t;
while(t--)
{
scanf("%d%d",&n,&m);
if(m==0){ printf("0n");continue;}
for (int i=0;i < m;i++)
{
scanf("%d%d%d",&edge[i].u,&edge[i].v,&edge[i].w);
edge[i].del = false;
edge[i].use = false;
}
sort(edge,edge+m,cmp);
flag=false;
int t=Krusal();
flag=true;
for(int i=0;i<m;i++)
{
if(edge[i].use==true)
{
edge[i].del=true;
int ans=Krusal();
if(t==ans)
{
t=-1;
break;
}
edge[i].del=false;
}
}
if(t==-1)
{
printf("Not Unique!n");
}
else{
printf("%dn",t);
}
}
}