1142 Maximal Clique (25 分)

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

判断最大团问题，可以用个标记数组差不多就能解决了。

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 int n,m,k,p;
 4 vector<int> v[250];
 5 int an[205], vis[205],val[205];
 6 int main(){
 7     cin >> n >> m;
 8     int x,y;
 9     for(int i = 0 ; i < m; ++i){
10         cin >> x >> y;
11         v[x].push_back(y);
12         v[y].push_back(x);
13     }
14     cin >> k;
15     while(k--){
16         cin >> p;
17         memset(vis,0,sizeof(vis));
18         for(int i = 0; i < p; i++){
19             cin >> an[i];
20             for(int j = 0; j < v[an[i]].size(); ++j){
21                 vis[v[an[i]][j]]++;
22             }
23         }
24         bool flag = true;
25         for(int i = 0; i < p; i++){
26             if(vis[an[i]] != p-1){
27                 flag = false;
28                 break;
29             }
30         }
31         if(!flag){
32             printf("Not a Clique\n");
33             continue;
34         }
35         bool prime = true;
36         for(int i = 1; i <= n; i++){
37             if(vis[i] == p){
38                 prime = false;
39                 break;
40             }
41         }
42         if(prime)
43             printf("Yes\n");
44         else
45             printf("Not Maximal\n");
46     }
47     return 0;
48 }