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 (≤ 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 (≤ 100). Then M lines of query follow, each first gives a positive number K (≤ 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:

8 10
5 6
7 8
6 4
3 6
4 5
2 3
8 2
2 7
5 3
3 4
6
4 5 4 3 6
3 2 8 7
2 2 3
1 1
3 4 3 6
3 3 2 1

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
　　

 #include <iostream>
 #include <vector>
 using namespace std;
 int main()
 {
     int n, m, k;
     cin >> n >> m;
     vector<vector<int>>v(n + , vector<int>(n + , ));
     while (m--)
     {
         int a, b;
         cin >> a >> b;
         v[a][b] = v[b][a] = ;
     }
     cin >> k;
     while (k--)
     {
         cin >> m;
         vector<int>temp(m);
         vector<bool>otherNum(n + , true);
         for (int i = ; i < m; ++i)
         {
             cin >> temp[i];
             otherNum[temp[i]] = false;
         }
         bool flag = true, isMax = true;
         for (int i = ; i < m && flag; ++i)//判断查询的点是不是两两相连
             for (int j = i + ; j < m; ++j)
                 if (v[temp[i]][temp[j]] == )
                     flag = false;
         if (flag == false)
             cout << "Not a Clique" << endl;
         else
         {
             for (int i = ; 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
             {
                 if (otherNum[i] == false)continue;//在查询中的点不用判断
                 int nums = ;
                 for (int j = ; j < m; ++j)
                     if (v[i][temp[j]] == )
                         ++nums;
                 if (nums == m)
                     isMax = false;
             }
             if (isMax)
                 cout << "Yes" << endl;
             else
                 cout << "Not Maximal" << endl;
         }
     }
     return ;
 }