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

浅析

判断是否是 clique：给定顶点集合是否顶点两两之间都有边
判断是否是 maximal clique：剩下的定点是否与给定的顶点集合中所有顶点相连

Code

#include 
#include 
using namespace std;
bool G[209][209] = {false};

int main(){
    int n, m;
    cin >> n >> m;
    while(m--){
        int a1, a2;
        cin >> a1 >> a2;
        G[a1][a2] = G[a2][a1] = true;
    }

    int k;
    cin >> k;
    while(k--){
        int ns;
        cin >> ns;
        vector<int> v(ns);
        bool in[209] = {false};
        for (int i = 0; i < ns;i++){
            cin >> v[i];
            in[v[i]]=true;
        }
        bool flag_c = false, flag_m = false;

        for (int i = 0; i < ns;i++)
            for (int j = i + 1; j < ns;j++)
                if(G[v[i]][v[j]]==false)
                    flag_c = true;
        if(flag_c){
            printf("Not a Clique\n");
            continue;
        }

        for (int i = 1; i < n+1;i++)
            if(in[i]==false){
                int count = 0;
                for (int j = 0; j < ns;j++)
                    if(G[i][v[j]])
                        count++;
                if(count == ns){
                    flag_m = true;
                    break;
                }
            }
        if(!flag_m)
            printf("Yes\n");
        else
            printf("Not Maximal\n");
    }
    return 0;
}