题目来源:https://pintia.cn/problem-sets/994805342720868352/problems/994805346428633088
备考汇总贴:2020年6月PAT甲级满分必备刷题技巧
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:
Nv 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
题目大意
给n个结点m条边,再给k个集合。对这k个集合逐个进行判断。每个集合S里面的数字都是结点编号,求问整个图是否符合顶点覆盖的定义(即所有的m条边两端的结点,是否至少一个结点出自集合S中)。如果是,输出Yes否则输出No。
题目分析
用vector和结构体存边,然后遍历每条边,如果存在一条边,它的两个顶点都不在查询的集合里,那就输出No,否则输出Yes。
满分代码
#include<iostream>
#include<vector>
using namespace std;
struct edge{
int a,b;
};
int main(){
int n,m,k,e,x;
scanf("%d %d",&n,&m);
vector<edge> g(m);
for(int i=0;i<m;i++){
scanf("%d %d",&g[i].a,&g[i].b);
}
cin>>k;
while(k--){
cin>>e;
set<int> s;
for(int j=0;j<e;j++){
scanf("%d",&x);
s.insert(x);
}
bool f=true;
for(int i=0;i<m;i++){
if(s.find(g[i].a)==s.end()&&s.find(g[i].b)==s.end()){
cout<<"No"<<endl;
f=false;
break;
}
}
if(f)cout<<"Yes"<<endl;
}
}