1142. Maximal Click (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


Code:

#include <iostream>
#include <cstring>
#include <cstdio>
#include <map>
#define Max 100005
using namespace std;
int nv,ne,m,k;
char re[3][20] = {"Not a Clique","Not Maximal","Yes"};
int mp[201][201],vi[201],u[40001],v[40001],fir[40001],nex[40001],vis[201];
int check()
{
    for ( int i = 0 ;i < k;i ++ )///Determine whether any two points in the set are connected
    {
        for(int j = i + 1;j < k;j ++)
        {
            if (! mp [vi [i]] [vi [j]]) return  0 ;
        }
    } 
/// Satisfy clique
     for ( int i = 1 ;i <= nv;i ++ )///Determine whether there is a point outside the set that is connected to the point inside the set
    {
        if(!vis[i])
        {
            int kk = fir[i],c = 0;
            while(kk != -1)
            {
                if(vis[v[kk]])c ++;
                if(c >= k)return 1;
                kk = nex[kk];
            }
        }
    } 
/// Satisfy maximal
     return  2 ;
}
intmain ()
{
    scanf("%d%d",&nv,&ne);
    memset(fir,-1,sizeof(fir));
    for(int i = 0;i < ne;i ++)
    {
        scanf("%d%d",&u[i],&v[i]);
        if(u[i] == v[i])i --,ne --;
    }
    for(int i = 0;i < ne;i ++)
    {
        mp [u [i]] [v [i]] = mp [v [i]] [u [i]] = 1 ;
        u[i + ne] = v[i];
        v[i + ne] = u[i];
        nex[i] = fir[u[i]];
        fir [u [i]] = i;
        nex [i + ne] = fir [u [i + ne]];
        fir [u [i + ne]] = i + ne;
    }
    scanf("%d",&m);
    while(m --)
    {
        scanf("%d",&k);
        memset(vis,0,sizeof(vis));
        for(int i = 0;i < k;i ++)
        {
            scanf("%d",&vi[i]);
            show [vi [i]] = 1 ;
        }
        puts(re[check()]);
    }
}