PAT甲级——A1141 PATRankingofInstitution【25】

A clique is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. A maximal clique is a clique that cannot be extended by including one more adjacent vertex. (Quoted from https://en.wikipedia.org/wiki/Clique_(graph_theory))

Now it is your job to judge if a given subset of vertices can form a maximal clique.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers Nv ( $\leq 200), the number of vertices in the graph, and Ne, the number of undirected edges. Then Ne lines follow, each gives a pair of vertices of an edge. The vertices are numbered from 1 to Nv.$

After the graph, there is another positive integer M ( $\leq 100). Then M lines of query follow, each first gives a positive number K (\leq Nv), then followed by a sequence of K distinct vertices. All the numbers in a line are separated by a space.$

Output Specification:

For each of the M queries, print in a line Yes if the given subset of vertices can form a maximal clique; or if it is a clique but not a maximal clique, print Not Maximal; or if it is not a clique at all, print Not a Clique.

Sample Input:

Sample Output:

Yes
Yes
Yes
Yes
Not Maximal
Not a Clique

Solution：
　　题意是，在给出的连通图中，判断查询的点是不是两两相连？如果是，那就是Clique,然后在判断这些查询点是是不是最大的集，即没有其他的点与查询的点是两两相连的
　　若存在，则不是最大集

 1 #include <iostream>
 2 #include <vector>
 3 using namespace std;
 4 int main()
 5 {
 6     int n, m, k;
 7     cin >> n >> m;
 8     vector<vector<int>>v(n + 1, vector<int>(n + 1, 0));
 9     while (m--)
10     {
11         int a, b;
12         cin >> a >> b;
13         v[a][b] = v[b][a] = 1;
14     }
15     cin >> k;
16     while (k--)
17     {
18         cin >> m;
19         vector<int>temp(m);
20         vector<bool>otherNum(n + 1, true);
21         for (int i = 0; i < m; ++i)
22         {
23             cin >> temp[i];
24             otherNum[temp[i]] = false;
25         }
26         bool flag = true, isMax = true;
27         for (int i = 0; i < m && flag; ++i)//判断查询的点是不是两两相连
28             for (int j = i + 1; j < m; ++j)
29                 if (v[temp[i]][temp[j]] == 0)
30                     flag = false;
31         if (flag == false)
32             cout << "Not a Clique" << endl;
33         else
34         {
35             for (int i = 1; i <= n && isMax; ++i)//判断查询之外的点与查询中的点是不是两两相连
36             {
37                 if (otherNum[i] == false)continue;//在查询中的点不用判断
38                 int nums = 0;
39                 for (int j = 0; j < m; ++j)
40                     if (v[i][temp[j]] == 1)
41                         ++nums;
42                 if (nums == m)
43                     isMax = false;
44             }
45             if (isMax)
46                 cout << "Yes" << endl;
47             else
48                 cout << "Not Maximal" << endl;
49         }
50     }
51     return 0;
52 }