1142 Maximal Clique (25分)

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

最大点集，已知点集的定义：每两个点之间都必定有一条边。如果有其他点与这个集合的每个点都有公用边，则不是最大点集

#include <iostream>
using namespace std;
int N, M, K, G[300][300] = {0}, a, b, sz, *arr;
int main() {
    scanf("%d%d", &N, &M);
    while(M--) {
        scanf("%d%d", &a, &b);
        G[a][b] = G[b][a] = 1;
    }
    scanf("%d", &K);
    while(K--) {
        int m[300] = {0};
        bool notClique = false, notMaximal = false;
        scanf("%d", &sz);
        arr = new int(sz);
        for(int i = 0; i < sz; i++) {
            scanf("%d", &arr[i]);
            m[arr[i]] = 1;
        }
        for(int i = 0; i < sz - 1; i++) 
            for(int j = i + 1; j < sz; j++) 
                if(G[arr[i]][arr[j]] == 0) notClique = true;
        if(notClique) printf("Not a Clique
");
        else {
            // check maximal
            for(int i = 1; i <= N; i++) {
                if(m[i] == 0) {
                    int judge = 0;
                    for(int j = 0; j < sz; j++) 
                        if(i != arr[j] && G[i][arr[j]] == 1) 
                            judge++;
                    if(judge == sz) {
                        notMaximal = true;
                        break;
                    }
                }
            }
            if(notMaximal) printf("Not Maximal
");
            else printf("Yes
");
        }
    }
    return 0;
}