分数 25

全屏浏览题目

切换布局

作者 CHEN, Yue

单位 浙江大学

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

代码长度限制

16 KB

时间限制

400 ms

内存限制

64 MB

#include<bits/stdc++.h>
using namespace std;
const int N=209,INF=0x3f3f3f3f;
int nv,ne;
int g[N][N];
bool st[N];
int main(){
    cin>>nv>>ne;
    for(int i=0;i<ne;i++){
        int a,b;
        cin>>a>>b;
        g[a][b]=g[b][a]=1;
    }
    int m;
    cin>>m;
    for(int i=0;i<m;i++){//m个query 
        int k;
        cin>>k;
        vector<int>v; 
        memset(st,0,sizeof st);
        while(k--){//insert序列 
            int node;
            cin>>node;
            v.push_back(node);
            st[node]=true;
        }
        int flag=1;//1表示Maximal，0表示Not a Clique
        for(int i=0;i<v.size()-1;i++)//若相邻结点没有边则flag置为0 
            for(int j=i+1;j<v.size();j++)
                if(!g[v[i]][v[j]])flag=0;
        if(flag){//若相邻结点两两有边 
            for(int i=1;i<=nv;i++){//将任意一个结点加入看看是否能成新的clique 
                if(!st[i]){//将没访问过的结点加入 
                    int cnt=0;
                    for(int j=0;j<v.size();j++){//若新加入的结点与序列有边 
                        if(g[i][v[j]])cnt++;//边数+1 
                    }
                    if(cnt==v.size()){//若都有边 
                        flag=0;//此时的flag为0表示Not Maximal 
                        break;
                    }
                }
            }
            if(flag)printf("Yes\n");//若此时flag仍为1 
            else printf("Not Maximal\n");//若此时flag为0 
        }
        else printf("Not a Clique\n");//若相邻结点不是两两有边 
    }
    return 0;
}