1142. Maximal Clique (25)

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本文介绍了一种算法，用于判断给定子图是否为原图中的最大完全图。该算法首先检查子图是否为完全图，然后判断是否可以扩展以形成更大的完全图。

1142. Maximal Clique (25)

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

题意：给一个子图，看其在原图中是否是最大的完全图。

#include<bits/stdc++.h>
using namespace std;
int n,m,nv,a,b,flag,k,len,cnt;
int mp[250][250];
int main(){
    scanf("%d%d",&n,&nv);
    for(int i=0;i<=n;i++)for(int j=0;j<=n;j++)mp[i][j]=-1,mp[i][i]=1;
    for(int i=0;i<nv;i++){
        scanf("%d%d",&a,&b);
        mp[a][b]=mp[b][a]=1;
    }
    scanf("%d",&m);
    while(m--){
        flag=1;
        scanf("%d",&k);
        vector<int>q;
        q.resize(k+1);
        for(int i=0;i<k;i++)scanf("%d",&q[i]);

        ///Not a Clique
        for(int i=0;i<k;i++){
            for(int j=0;j<k;j++){
                a=q[i];b=q[j];
                if(mp[a][b]!=1){flag=-1;break;}
            }
            if(flag==-1)break;
        }
        if(flag==-1){cout<<"Not a Clique"<<endl;continue;}

        ///Not Maximal
        for(int i=1;i<=n;i++){
            cnt=0;
            for(int j=0;j<k;j++){
                a=i;
                b=q[j];
                if(a!=b&&mp[a][b]==1)cnt++;
            }
            if(cnt==k){flag=-2;break;}
        }
        if(flag==-2){cout<<"Not Maximal"<<endl;continue;}
        else cout<<"Yes"<<endl;
    }
    return 0;
}