1142 Maximal Clique 甲级xp_xht123

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

解题思路：模拟题，读懂题意最为重要

clique : 在集合中，任意两个不同的点，在图中都有边相连
maximal clique : 是clique ， 如果该clique不能通过加入某个新的顶点来扩展成一个更大的Clique

根据这两条性质，很容易的判断是哪种情况，首先先看联通性，其次再看除了集合中的点是否还跟集合中的点有边。

/*
clique : 在集合中，任意两个不同的点，在图中都有边相连
maximal clique : 是clique ， 如果该clique不能通过加入某个新的顶点来扩展成一个更大的Clique
*/
#include
#include
#include
#include
 
using namespace std;
const int N = 210;
int n , m;
bool g[N][N] , st[N];
vector<int>v;
 
bool check1()
{
    for(int i = 0;i < v.size();i ++)
        for(int j = 0;j < i;j ++)
            if(!g[v[i]][v[j]]) return false;
    return true;
}
 
bool check2()
{
    memset(st , false , sizeof st);
    for(int i = 0;i < v.size();i ++) st[v[i]] = true;//标记所有clique中的点
    
    for(int i = 1;i <= n;i ++)
    {
        if(!st[i]) //不是clique的点
        {
            bool flag = true;
            for(int j = 0;j < v.size();j ++)
            {
                if(!g[i][v[j]])
                {
                    flag = false;
                    break;
                }
            }
            if(flag) return false;
        }
    }
    return true;
}
 
int main()
{
    cin >> n >> m;
    while(m --)
    {
        int a , b;
        cin >> a >> b;
        g[a][b] = g[b][a] = true;
    }
    
    int k;
    cin >> k;
    while(k --)
    {
        int x;
        cin >> x;
        for(int i = 0;i < x;i ++)
        {
            int num;
            cin >> num;
            v.push_back(num);
        }
        
        //判断是否是clique
        if(check1())
        {
            if(check2()) puts("Yes");
            else puts("Not Maximal");
        }
        else puts("Not a Clique");
        v.clear();
    }
    return 0;
}