PAT 1142 Maximal Clique

Posted 2021-01-06 a-little-nut

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

#include<iostream>
#include<vector>
using namespace std;
int main(){
    int nv, ne, k, n;
    cin>>nv>>ne;
    vector<vector<int>> G(205, vector<int>(205, 0));
    for(int i=0; i<ne; i++){
        int v1, v2;
        cin>>v1>>v2;
        G[v1][v2]=G[v2][v1]=1;
    } 
    cin>>k;
    for(int i=0; i<k; i++){
        bool full=true, clique=true;
        cin>>n;
        vector<int> vi(n, 0), a(nv+1, 0);
        for(int j=0; j<n; j++){
            cin>>vi[j];
            a[vi[j]]=1;
        }
        for(int j=0; j<n; j++){
            if(clique==false) break;
            for(int l=j+1; l<n; l++){
                if(G[vi[j]][vi[l]]!=1){
                    clique=false;
                    cout<<"Not a Clique"<<endl;
                    break;
                }       
            }   
        }
        if(clique==false) continue;
        for(int j=1; j<=200; j++){
            if(a[j]==0){
                for(int l=0; l<n; l++){
                    if(G[vi[l]][j]==0)  break;
                    if(l==n-1) full=false;
                }
            }
            if(!full){
                cout<<"Not Maximal"<<endl;
                break;
            }   
        }   
            if(full) cout<<"Yes"<<endl; 
    }
    return 0;
}