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
最大团问题:团的概念,在由点和线组成的图中,如果有一堆点(也就是点的集合,这么说可能有点不严谨但是会好理解一些),它们之间两两相邻,那么他们就是一个团(clique),如果这堆点不仅能两两相邻,而且它们不能通过新加入一个点进而形成一个更大的团,那么这个团就叫做最大团。
#include <iostream>
#include<cstdlib>
#include<cstdio>
#include <algorithm>
#include <string>
using namespace std;
int e[210][210];
int judge(int a[],int k)
{
for(int i=0; i<k; i++)
{
for(int j=0; j<k; j++)
{
if(e[a[i]][a[j]]==0)
return 0;
}
}
return 1;
}
int main()
{
int nv,ne,c,d;
scanf("%d%d",&nv,&ne);
for(int i=0; i<210; i++)
for(int j=0; j<210; j++)
{
e[i][j]=0;
if(i==j)
e[i][j]=1;
}
for(int i=0; i<ne; i++)
{
scanf("%d%d",&c,&d);
e[c][d]=1;
e[d][c]=1;
}
int m;
scanf("%d",&m);
int k,a[210];
for(int i=0; i<m; i++)
{
scanf("%d",&k);
for(int j=0; j<k; j++)
{
scanf("%d",&a[j]);
}
if(judge(a,k)==0)
{
printf("Not a Clique\n");
}
else
{
int g=0;
for(int i=1;i<=nv;i++)
{
int flag=0;
for(int j=0;j<k;j++)
{
if(a[j]==i)
{
flag=1;
break;
}
}
if(flag==0)
{
a[k]=i;
if(judge(a,k+1)==1)
{
g=1;
printf("Not Maximal\n");
break;
}
}
}
if(g==0)
printf("Yes\n");
}
}
return 0;
}