1142 Maximal Clique （25 分）

最新推荐文章于 2020-05-09 19:33:15 发布

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最新推荐文章于 2020-05-09 19:33:15 发布

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本文深入探讨了图论中的最大团问题，介绍了团和最大团的概念，并提供了一个判断给定顶点子集是否能构成最大团的算法实现。通过具体实例展示了输入输出规范，帮助读者理解和应用最大团问题。

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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:

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;
}