# 描述

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.

# 指定输入

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.

# 指定输出

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.

# 输入样例

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


# 输出样例

Yes
Yes
Yes
Yes
Not Maximal
Not a Clique


# 分析

#include <iostream>
#include <vector>
using namespace std;
int e[210][210]; // 图
int main() {
// nv:顶点数
// ne:边数
// m:要判断的顶点序列数
// ta,tb:两个顶点
// k要判断的顶点数
int nv, ne, m, ta, tb, k;
scanf("%d %d", &nv, &ne);
// 建立一个用数组表示的图
for (int i = 0; i < ne; i++) {
scanf("%d %d", &ta, &tb);
e[ta][tb] = e[tb][ta] = 1;
}
scanf("%d", &m);
for (int i = 0; i < m; i++) {
scanf("%d", &k);
// 存放顶点序列
vector<int> v(k);
// 映射,主要是为了在遍历所有顶点时判断顶点是否在这个序列中,这是一种很好的空间
// 换时间的一种做法,值得学习🤔🤔
int hash[210] = {0}, isclique = 1, isMaximal = 1;
for (int j = 0; j < k; j++) {
scanf("%d", &v[j]);
hash[v[j]] = 1;
}
// 根据团的定义判断是否是一个团,比较暴力,只有顶点两两邻接才算是一个团
for (int j = 0; j < k; j++) {
if (isclique == 0) break;
for (int l = j + 1; l < k; l++) {
if (e[v[j]][v[l]] == 0) {
isclique = 0;
printf("Not a Clique\n");
break;
}
}
}
if (isclique == 0) continue;
for (int j = 1; j <= nv; j++) {
// 判断是否在顶点判断序列里,如果在的话就被置1了
if (hash[j] == 0) {
// 判断不在顶点序列的顶点是否和所有在顶点序列的顶点相邻接
// 如果有这么一个点,说明其不是最大的团
for (int l = 0; l < k; l++) {
if (e[v[l]][j] == 0) break;
if (l == k - 1) isMaximal = 0;
}
}
if (isMaximal == 0) {
printf("Not Maximal\n");
break;
}
}
if (isMaximal == 1) printf("Yes\n");
}
return 0;
}

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