Poj 1679 the unique MST (check whether the minimum spanning tree is unique)

The unique MST

Time limit:1000 ms		Memory limit:10000 K
Total submissions:20430		Accepted:7186

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

23 31 2 12 3 23 1 34 41 2 22 3 23 4 24 1 2

Sample output

3not unique!


Calculate the minimum spanning tree and then enumerate the edge. If the value of the minimum spanning tree removed from this edge is the same as that of the original one, it is not unique.

 1 #include <iostream> 2 #include <cstring> 3 #include <cstdio> 4 #include <string> 5 #include <iomanip> 6 #include <algorithm> 7 #include <queue> 8 #include <vector> 9 #include <map>10 using namespace std;11 struct Node{12     int u, v, w;13 }node[110*110/2];14 int t, n, m, sum1, sum2,  ans1, ans2;15 int pre[110], mark[110*110/2];16 int find(int x){17     if(pre[x] == x) return x;18     else return find(pre[x]);19 }20 bool cmp(Node x, Node y){21     return x.w < y.w;22 }23 24 int main(){25     scanf("%d", &t);26     while(t--){27         scanf("%d%d", &n, &m);28         for(int i = 1; i <= m; i++){29             scanf("%d%d%d", &node[i].u, &node[i].v, &node[i].w);30         }31         sort(node+1,node+1+m,cmp);32         sum1 = 0;33         ans1 = 0;34         for(int i = 1; i <= n; i++) pre[i] = i;35         for(int i = 1; i <= m; i++){36             if(ans1 == n-1) break;37             int aa = find(node[i].u);38             int bb = find(node[i].v);39             if(aa != bb){40                 sum1 += node[i].w;41                 pre[aa] = bb;42                 mark[++ans1] = i;43             //    ans++;44             }45         }46         bool flag = true;47         for(int k = 1; k <= ans1; k++){48             for(int i = 1; i <= n; i++) pre[i] = i;49             sum2 = 0; ans2 = 0;50             for(int i = 1; i <= m; i++){51                 if(i == mark[k]) continue;52                 if(ans2 == n-1) break;53                 int aa = find(node[i].u);54                 int bb = find(node[i].v);55                 if(aa != bb){56                     sum2 += node[i].w;57                     pre[aa] = bb;58                     ans2++;59                 }60             }61             if(ans2 == n-1 && sum2 == sum1){62                 flag = false; break;63             }64         }65         if(flag) printf("%d\n", sum1);66         else printf("Not Unique!\n");67         68         69 70     }71     72     return 0;73 }