1134. Vertex Cover (25)-PAT甲级真题

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.

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

分析:用vector v[n]保存某结点属于的某条边的编号,比如a b两个结点构成的这条边的编号为0,则v[a].push_back(0),v[b].push_back(0)——表示a属于0号边,b也属于0号边。对于每一个集合做判断,遍历集合中的每一个元素,将当前元素能够属于的边的编号i对应的hash[i]标记为1,表示这条边是满足有一个结点出自集合S中的。最后判断hash数组中的每一个值是否都是1,如果有不是1的,说明这条边的两端结点没有一个出自集合S中,则输出No。否则输出Yes~

 

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