poj 1679 The Unique MST

原創

2020-02-20 21:36

http://acm.pku.edu.cn/JudgeOnline/problem?id=1679

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!

看到網上大家都是說求次小生成樹，對這個也不太熟，我的想法是利用MST的性質，邊數相同，MST邊中有相等邊的情況，簡單實現是先用Prim或者

kruskal算法求出一組解，並記錄所選擇的邊，爲驗證唯一直接採用刪邊法，逐條刪邊，出現相同的解則退出，得出唯一的結論則要訪問到最後一條邊

不過有個小優化是 只探查存在相同權值的邊，這樣開銷應該小很多，具體實現因爲時間的關係 現在就省了  留下某牛牛代碼以後參考：

#include<stdio.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef struct
{
int x;
int y;
int w;
}edge;
edge s[10010];
int top,t[10010];
bool cmp(edge s1,edge s2)
{
return s1.w<s2.w;
}
int kruscal(int n,int m,int x)
{
int i,j,a,b,tag[110],tem,sum,k;
for(i=0;i<n;i++)
{
   tag[i]=i;
}
k=1;j=0;sum=0;
while(k<n)
{
   a=s[j].x-1;
   b=s[j].y-1;
   if(j==x)
   {
    j++;
    continue;
   }
   if(tag[a]!=tag[b])
   {
    if(x==-1)
    {
     t[top]=j;
     top++;
    }
    tem=tag[b];
    k++;sum+=s[j].w;
    for(i=0;i<n;i++)
    {
     if(tag[i]==tem)
     {
      tag[i]=tag[a];
     }
    }
   }
   j++;
}
return sum;
}
int main()
{
freopen("in.txt","r",stdin);
int p,n,m,l,cmin,min,i,key;
while(scanf("%d",&p)!=EOF)
{
   while(p--)
   {
    scanf("%d%d",&n,&m);
    for(i=0;i<m;i++)
    {
     scanf("%d%d%d",&s[i].x,&s[i].y,&s[i].w);
    }
    sort(s,s+m,cmp);
    /*for(i=0;i<m;i++)
    {
     printf(" %d ",s[i].w);
    }
    printf("/n");*/
    top=0;
    min=kruscal(n,m,-1);
    key=top;
    for(l=0;l<key;l++)
    {
     cmin=kruscal(n,m,t[l]);
     if(cmin==min)
     {
      printf("Not Unique!/n");
      break;
     }
    }
    if(l==top&&cmin!=min)
    {
     printf("%d/n",min);
    }
   }
}
}