A1142 Maximal Clique (25 point(s))

强连通子图

1. 原文

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

2. 解析

连通子图判断：图内边连通 graph[ a ] [ b ] != Inf

强连通子图：子图外的结点不存在与子图内结点都相连的点

set记录子图内结点值，bool visit[]记录访问的子图结点

循环遍历visit为false的结点i，判断该结点是否有与set中的点graph[ i ] [ *j ] != Inf，存在则不是强连通子图

3. AC代码

#include<cstdio>
#include<algorithm>
#include<set>
using namespace std;
const int maxn=210;
const int Inf=312312312;
int graph[maxn][maxn];
bool visit[maxn]={false};
set<int> s;
int main()
{
	for (int i = 1; i < maxn; ++i)
	{
		for (int j = 1; j < maxn; ++j)
		{
			graph[i][j]=Inf;
		}
		graph[i][i]=1;
	}
	int nv,ne;
	scanf("%d%d",&nv,&ne);
	int a,b;
	for (int i = 0; i < ne; ++i)
	{
		scanf("%d%d",&a,&b);
		graph[a][b]=graph[b][a]=1;
	}
	int m;
	scanf("%d",&m);
	int k;
	while(m--)
	{
		bool clique=true; bool maxiaml=true;
		fill(visit,visit+maxn,false);
		s.clear();
		scanf("%d%d",&k,&a);
		visit[a]=true;
		s.insert(a);
		for (int i = 1; i < k; ++i)
		{
			scanf("%d",&b);
			s.insert(b);
			if (graph[a][b]==Inf)
			{
				clique=false;
			}
			visit[b]=true;
			a=b;
		}
		if (!clique)
		{
			printf("Not a Clique\n");
			continue;
		}
		int cnt=0;
		for (int i = 1; i <= nv; ++i)
		{
			if (visit[i]==false)
			{
				int flag=0;
				for (set<int>::iterator j = s.begin(); j != s.end(); ++j)
				{
					if (graph[i][*j]==Inf)
					{
						flag=1;
						break;
					}
				}
				if (flag==0)
				{
					cnt++;
				}
			}
		}
		if (cnt==0)
		{
			printf("Yes\n");
		}else{
			printf("Not Maximal\n");
		}
		
	}
	return 0;
}