PAT 1134 Vertex Cover

Posted 2020-12-31 a-little-nut

A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. Now given a graph with several vertex sets, you are supposed to tell if each of them is a vertex cover or not.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers N and M (both no more than 10^4 ), being the total numbers of vertices and the edges, respectively. Then M lines follow, each describes an edge by giving the indices (from 0 to N?1) of the two ends of the edge.

After the graph, a positive integer K (≤ 100) is given, which is the number of queries. Then K lines of queries follow, each in the format:

N?v v[1] v[2]?v[Nv ]

where Nv is the number of vertices in the set, and v[i]‘s are the indices of the vertices.

Output Specification:

For each query, print in a line Yes if the set is a vertex cover, or No if not.

Sample Input:

10 11
8 7
6 8
4 5
8 4
8 1
1 2
1 4
9 8
9 1
1 0
2 4
5
4 0 3 8 4
6 6 1 7 5 4 9
3 1 8 4
2 2 8
7 9 8 7 6 5 4 2

Sample Output:

No
Yes
Yes
No
No

#include<iostream> //水题
#include<vector> 
using namespace std;
int main(){
  int n, m;
  cin>>n>>m;
  vector<int> edge(m, 0);
  for(int i=0; i<m; i++){
    int s, e;
    cin>>s>>e;
    edge[i]=s*10000+e;
  }
  int k;
  cin>>k;
  for(int i=0; i<k; i++){
    int nv, flag=0;
    cin>>nv;
    vector<int> visited(n+1, 0);
    for(int j=0; j<nv; j++){
      int t;
      cin>>t;
      visited[t]=1;
    }
    for(int j=0; j<m; j++){
      int s=edge[j]/10000;
      int e=edge[j]%10000;
      if(visited[s]==0&&visited[e]==0)
        flag=1;
    }
    flag==1?cout<<"No"<<endl:cout<<"Yes"<<endl;
  }
  return 0;
}