1142 Maximal Clique

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

 

题意：

　　给出一个无向图，然后再给出这个图里的几个结点判断这几个结点是不是Maximal Clique（最大团）。

思路：

　　暴力穷举。

 

Code：

#include <iostream>
#include <set>
#include <vector>

using namespace std;

bool isClique(vector<int>& v, vector<vector<int> >& grap) {
    for (int i = 0; i < v.size(); ++i) {
        for (int j = i + 1; j < v.size(); ++j) {
            if (grap[v[i]][v[j]] == -1) return false;
        }
    }
    return true;
}

bool isMaxClique(vector<int>& v, vector<vector<int> >& grap) {
    set<int> s(v.begin(), v.end());
    for (int i = 1; i < grap.size(); ++i) {
        bool isMax = false;
        if (s.find(i) == s.end()) {
            for (int j = 0; j < v.size(); ++j) {
                if (grap[i][v[j]] == -1) {
                    isMax = true;
                    break;
                }
            }
            if (!isMax) return false;
        }
    }
    return true;
}

int main() {
    int Nv, Ne;
    cin >> Nv >> Ne;

    int v1, v2;
    vector<vector<int> > grap(Nv + 1, vector<int>(Nv + 1, -1));
    for (int i = 0; i < Ne; ++i) {
        cin >> v1 >> v2;
        grap[v1][v2] = grap[v2][v1] = 1;
    }
    int n, k, t;
    cin >> n;
    for (int i = 0; i < n; ++i) {
        cin >> k;
        vector<int> v(k, 0);
        for (int j = 0; j < k; ++j) {
            cin >> v[j];
        }if (isClique(v, grap)) {
            if (isMaxClique(v, grap)) {
                cout << "Yes" << endl;
            } else {
                cout << "Not Maximal" << endl;
            }
        } else {
            cout << "Not a Clique" << endl;
        }
    }

    return 0;
}