PAT 甲级 刷题日记|A 1142 Maximal Clique (25 分)

单词积累

clique 派系 小圈子

undirected graph 无向图

adjacent 邻近的，毗邻的 相连的（说明两个点直接有连接）

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结尾无空行

Sample Output:

Yes
Yes
Yes
Yes
Not Maximal
Not a Clique结尾无空行

思路

按照题目的clique设定，暴力遍历即可。

代码

#include 
using namespace std;

const int maxn = 205;
int graph[maxn][maxn];

int main() {
    int N, M;
    cin>>N>>M;
    int num1, num2;
    for (int i = 0; i < M; i++) {
        cin>>num1>>num2;
        graph[num1][num2] = graph[num2][num1] = 1;
    }
    int cnt;
    cin>>cnt;
    while (cnt--) {
        int len;
        vector vec;
        cin>>len;
        int num;
        int flag1 = 0;
        int flag2 = 0;
        for (int i = 0; i < len; i++) {
            cin>>num;
            vec.push_back(num);
        }
        for (int i = 0; i < len; i++) {
            for (int j = i + 1; j < len; j++) {
                if (graph[vec[i]][vec[j]] != 1) {
                    flag1 = 1;
                    break;
                }
            }
        }
        if (flag1 == 0) {
            for (int i = 1; i <= N; i++) {
                int j;
                for (j = 0; j < len; j++) {
                    if (graph[i][vec[j]] != 1) {
                        break;
                    }
                }
                if (j == len) {
                    flag2 = 1;
                    break;
                }
            }
        }
        
        if (flag2 == 1) cout<<"Not Maximal"<