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 + 1, vector<int>(n + 1, 0));
    while (m--)
    {
        int a, b;
        cin >> a >> b;
        v[a][b] = v[b][a] = 1;
    }
    cin >> k;
    while (k--)
    {
        cin >> m;
        vector<int>temp(m);
        vector<bool>otherNum(n + 1, true);
        for (int i = 0; i < m; ++i)
        {
            cin >> temp[i];
            otherNum[temp[i]] = false;
        }
        bool flag = true, isMax = true;
        for (int i = 0; i < m && flag; ++i)//判断查询的点是不是两两相连
            for (int j = i + 1; j < m; ++j)
                if (v[temp[i]][temp[j]] == 0)
                    flag = false;
        if (flag == false)
            cout << "Not a Clique" << endl;
        else
        {
            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
            {
                if (otherNum[i] == false)continue;//在查询中的点不用判断
                int nums = 0;
                for (int j = 0; j < m; ++j)
                    if (v[i][temp[j]] == 1)
                        ++nums;
                if (nums == m)
                    isMax = false;
            }
            if (isMax)
                cout << "Yes" << endl;
            else
                cout << "Not Maximal" << endl;
        }
    }
    return 0;
}