POJ 1679 The Unique MST 推断最小生成树是否唯一
2017-05-12 10:45
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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'.
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
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 22715 | Accepted: 8055 |
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
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!
#include <iostream> #include <stdio.h> #include <string> #include <cstring> #include <cmath> #include <algorithm> #define N 10090 using namespace std; struct Node { int a,b,c; bool same,used,del; }f ; int n,m; int fa ; int findfa(int x) { if(x!=fa[x]) fa[x]=findfa(fa[x]); return fa[x]; } void init() { for(int i=0;i<200;i++) fa[i]=i; } int cmp(Node a,Node b) { return a.c<b.c; } bool first; void make_same(int m) { for(int i=1;i<m;i++) if(f[i].c==f[i-1].c) f[i-1].same=true; } int kruscal(int m) { int ans=0; for(int i=0;i<m;i++) { if(f[i].del)continue; int x=findfa(f[i].a); int y=findfa(f[i].b); if(x==y) continue; else { fa[x]=y; ans+=f[i].c; if(first) f[i].used=true; } } return ans; } int main() { int ca=1; scanf("%d",&ca); while(ca--) { scanf("%d %d",&n,&m); for(int i=0;i<m;i++) { scanf("%d %d %d",&f[i].a,&f[i].b,&f[i].c); f[i].del=false;f[i].same=false;f[i].used=false; } sort(f,f+m,cmp); first=true; init(); int ans1=kruscal(m); first=false; make_same(m); int flag=0; for(int i=0;i<m;i++) { if(f[i].used && f[i].same)//used表示在第一次求出的最小生成树中加入过的边 {//same表示在存在和已加入边权值同样的边,此时标记删除该边在推断是否ans相等 f[i].del=true; init(); int ans2=kruscal(m); //cout<<"ans2="<<ans2<<endl; if(ans1==ans2) { puts("Not Unique!"); flag=1; break; } f[i].del=false; } } if(flag==0) printf("%d\n",ans1); } return 0; }
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