【笨方法学PAT】1142 Maximal Clique （25 分）

一、题目

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

二、题目大意

给定一个图，之后判断所给的点是否全连接；能不能加入其他点，同样构成全连接。

三、考点

逻辑

四、注意

1、分别判断是否全连接，能不能加入其他点，注意flag的使用。

五、代码

#include<iostream>
#include<vector>
#define N 201
using namespace std;

bool v[N][N] = {0};

int main() {
	//read
	int m, n;
	cin >> n >> m;
	while (m--) {
		int a, b;
		cin >> a >> b;
		v[a][b] = v[b][a] = 1;
	}

	//every case
	cin >> m;
	while (m--) {
		int k;
		cin >> k;
		vector<int> vec(k);
		bool book[N] = { false };
		for (int i = 0; i < k; ++i) {
			cin >> vec[i];
			book[vec[i]] = true;
		}

		//judge clique
		bool flag_clique = true;
		for (int i = 0; i < k; ++i) {
			for (int j = 0; j < k; ++j) {
				if (i == j)
					continue;
				if (v[vec[i]][vec[j]] != 1) {
					flag_clique = false;
					break;
				}
			}
		}
		if (flag_clique == false) {
			cout << "Not a Clique" << endl;
			continue;
		}

		//judge max clique
		bool flag_max = true;
		for (int i = 1; i <= n; ++i) {
			//the node not in vec
			if (book[i] == false) {
				bool flag_adjacent = true;
				for (int j = 0; j < k; ++j) {
					if (v[i][vec[j]] == 0) {
						flag_adjacent = false;
						break;
					}
				}
				if (flag_adjacent == true) {
					flag_max = false;
					break;
				}
			}
		}
		if (flag_max == false) {
			cout << "Not Maximal" << endl;
			continue;
		}

		cout << "Yes" << endl;
	}

	system("pause");
	return 0;
}