1134. Vertex Cover (25)

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 104), 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.

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

No
Yes
Yes
No
No

思路

判断一个集合的点是否覆盖了所有的边。

1.用vector保存所有的边（包含起止点）

2.将需要查询的点插入set容器中。

3.对于每一条边，检查它的起止点是否有至少一个点在集合中。如果有Yes，如果没有No。

代码

#include<iostream>
#include<vector>
#include<set>
using namespace std;

class edge
{
public:
int a;
int b;
};

int main()
{
int N,M;
while(cin >> N >> M)
{
vector<edge> edges(M);
for(int i = 0; i < M; i++)
{
cin >> edges[i].a >>edges[i].b;
}
int K;
cin >> K;
for(int i = 0; i < K; i++)
{
int Nv;
cin >> Nv;
set<int> nodes;
for(int j = 0; j < Nv; j++)
{
int node;
cin >> node;
nodes.insert(node);
}
bool isCovered = true;
for(int v = 0; v < M; v++)
{
if(nodes.find(edges[v].a) == nodes.end() && nodes.find(edges[v].b) == nodes.end())
{
isCovered = false;
break;
}
}
if(isCovered)
cout << "Yes" << endl;
else
cout << "No" << endl;
}
}
}