POJ 1679 The Unique MST
The Unique MST
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 15153 | Accepted: 5241 |
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'.
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
2 3 3 1 2 1 2 3 2 3 1 3 4 4 1 2 2 2 3 2 3 4 2 4 1 2
Sample Output
3 Not Unique!
Source
//这么久没刷题了、回到学校了、第一次写次小生成树,开心的是1A,不过写代码速度下降了
//I am back
#include <iostream> #include <stdio.h> #include <string.h> #include <algorithm> #include <queue> #define N 102 using namespace std; struct node { int a,b,w; bool visit; bool operator <(const node &t)const { return w<t.w; } }; struct Link { int to; int next; }; Link link[N]; int len[N][N]; int fa[N]; node Ed[5055]; int n,m,Min; int Find(int x) { if(x!=fa[x]) { return fa[x]=Find(fa[x]); } return x; } bool merge(int x,int y,int i) { x=Find(x); y=Find(y); if(x!=y) { int u,v; for(u=link[x].to;;u=link[u].next) { for(v=link[y].to;;v=link[v].next) { len[u][v]=len[v][u]=Ed[i].w; if(link[v].next==-1) break; } if(link[u].next==-1) break; } Ed[i].visit=1; link[u].next=y; fa[y]=x; return true; } return false; } void Kruskal() { int i; for(Min=i=0;i<m;i++) if(merge(Ed[i].a,Ed[i].b,i)) Min+=Ed[i].w; } int main() { int t,i; scanf("%d",&t); while(t--) { scanf("%d %d",&n,&m); for(i=1;i<=n;i++) fa[i]=i,link[i].to=i,link[i].next=-1; for(i=0;i<m;i++) { scanf("%d %d %d",&Ed[i].a,&Ed[i].b,&Ed[i].w); Ed[i].visit=0; } sort(Ed,Ed+m); Kruskal(); int Mi=-1,tp; for(i=0;i<m;i++) if(!Ed[i].visit) { tp=Min+Ed[i].w-len[Ed[i].a][Ed[i].b]; if(tp>Min) Mi=tp; else { Mi=tp;break; } } if(Min==Mi) printf("Not Unique!\n"); else printf("%d\n",Min); } return 0; }