POJ 1679 The Unique MST

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’.

【题目分析】

关于最小生成树是否唯一的问题。只需要计算一下删除任意一条原有的生成树的边，然后再跑一边最小生成树，然后比较一下是否相等就可以了。

【代码】

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
struct edge{
int a,b,w;
}c[20000];
int f[110],list[110];
inline int gf(int k)
{
if (f[k]==k) return k;
else return f[k]=gf(f[k]);
}
inline bool cmp(edge a,edge b)
{return a.w<b.w;}
inline void un(int a,int b)
{
int fa=gf(a),fb=gf(b);
if (fa==fb) return;
else f[fa]=fb;
return;
}
inline void kru()
{
int n,m,ans=0,ans2=0,k2,k=0;
scanf("%d%d",&n,&m);
memset(c,0,sizeof c);
memset(list,0,sizeof list);
for (int i=1;i<=m;++i) scanf("%d%d%d",&c[i].a,&c[i].b,&c[i].w);
for (int i=1;i<=n;++i) f[i]=i;
sort(c+1,c+m+1,cmp);
for (int i=1;i<=m&&k<n-1;++i)
{
int f1=gf(c[i].a),f2=gf(c[i].b);
if (f1!=f2)
{
un(f1,f2);
++k;
ans+=c[i].w;
list[k]=i;
}
}
for (int i=1;i<n;++i)
{
ans2=0,k2=0;
for (int j=1;j<=n;++j) f[j]=j;
for (int j=1;j<=m;++j)
{
if (j==list[i]) continue;
int f1=gf(c[j].a),f2=gf(c[j].b);
if (f1!=f2)
{
un(f1,f2);
k2++;
ans2+=c[j].w;
}
}
if (k2!=n-1) continue;
if (ans==ans2){
printf("Not Unique!\n");
return ;
}
}
printf("%d\n",ans);
}
int main()
{
int tt;
scanf("%d",&tt);
for (int z=1;z<=tt;++z)
{
kru();
}
}