1142 Maximal Clique-PAT甲级

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

在一个无向图中，如果在给定的顶点集中任意两个不同的点之间都有一条边，那么我们称这样的点集为Clique。如果一个clique点集不可以再加入任何一个新的结点构成新的clique，我们称这样的Clique为maximal Clique。给定一个无向图和M个查询，问对于每一个查询中的点集是否是maximal Clique，如果不是，是否是Clique。
方法：对于每一组输入的测试样例，依次遍历两两结点之间是否存在路径，如果有一个不存在，则不是Clique；若是，则依次遍历未在该样例中的结点，若存在一个结点与样例中的结点之间都有路径，则不是maximal Clique,否则是

满分代码如下：

#include<bits/stdc++.h>
using namespace std;
const int N=205;
int e[N][N],nv,ne,m,k,vst[N];
int main(){
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			e[i][j]=0;
		}
	}
	scanf("%d%d",&nv,&ne);
	int u,v;
	for(int i=1;i<=ne;i++){
		scanf("%d%d",&u,&v);
		e[u][v]=e[v][u]=1;
	}
	scanf("%d",&m);
	for(int i=1;i<=m;i++){
		int clique=1,max_c=1;
		memset(vst,0,sizeof(vst));
		scanf("%d",&k);
		vector<int> ve(k);
		for(int j=0;j<k;j++){
			scanf("%d",&ve[j]);
			vst[ve[j]]=1;
		}
		for(int j=0;j<k;j++){
			for(int l=j+1;l<k;l++){
				if(e[ve[j]][ve[l]]==0){
					clique=0;
					break;
				}
			}
			if(clique==0) break;
		}
		for(int j=1;j<=nv;j++){
			if(vst[j]==0){
				for(int l=0;l<k;l++){
					if(e[j][ve[l]]==0)
						break;
					if(l==k-1){
						max_c=0;
						break;
					}
				}
			}
			if(max_c==0) break;
		}
		if(clique==0){
			printf("Not a Clique\n");
			continue;
		}
		if(max_c==0){
			printf("Not Maximal\n");
			continue;
		}
		printf("Yes\n");
	}
	return 0;
}