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
作者: CHEN, Yue
单位: 浙江大学
时间限制: 400 ms
内存限制: 64 MB

给定一张图和几个查询，判断是一个最大集团、集团或者不是集团；

集团的定义，任意两个点之间都有一条边相连。
最大集团的定义，不能再插入一条边使它成为集团。

没想到什么好办法，直接暴力枚举了任意两个点直接是否存在边。如果有两个点之间没有存在边，那么肯定不是集团，否则从剩下的点中尝试插入一个点再判断能不能形成一个集团。

#include<bits/stdc++.h>
using namespace std;
bool f(vector<int>&num, vector<vector<int>>& edge){
	for (int i = 0; i < num.size(); i++)
		for (int j = i + 1; j < num.size(); j++)
			if (!edge[num[i]][num[j]])
				return false;
	return true;
}
int main()
{
	int n, m,a,b;
	cin >> n >> m;
	vector<vector<int>>edge(n +1, vector<int>(n + 1));
	for (int i = 0; i < m; i++){
		cin >> a >> b;
		edge[a][b] = 1;
		edge[b][a] = 1;
	}
	cin >> n;
	for (int i = 0; i < n; i++){
		cin >> m;
		vector<int>tmp(m);
		vector<bool>visited(edge.size());
		for (int j = 0; j < m; j++){
			cin >> tmp[j];
			visited[tmp[j]] = true;
		}
		if (f(tmp, edge)){
			bool flg = true;
			for (int j = 1; j <= edge.size(); j++){
				if (!visited[j]){
					tmp.push_back(j);
					if (f(tmp, edge)){
						cout << "Not Maximal"<<endl;
						flg = false;
						break;
					}
					tmp.pop_back();
				}
			}
			if(flg) cout << "Yes"<<endl;
		}
		else cout << "Not a Clique"<<endl;

	}
	return 0;
}