PAT_A1142#Maximal Clique

Source:

PAT A1142 Maximal Clique (25 分)

Description:

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

Keys:

• 图的存储和遍历

Attention:

• 想的有点多，数据规模不大，暴力求解就好了

Code:

 /*
 Data: 2019-08-06 20:50:04
 Problem: PAT_A1142#Maximal Clique
 AC: 30：25

 题目大意：
 判断所给子图是否是完全图（无向图）
 输入：
 第一行给出，顶点数Nv<=200，Ne边数
 接下来Ne行，v1,v2
 接下来一行，给出查询数M；
 接下来M行，给出顶点数K，和K个顶点；
 输出：
 YES，最大完全子图；
 Not Maximal，完全子图，非最大
 Not a Clique，完全图

 基本思路：
 先判断所给子图是否是完全图，
 再遍历图中其余顶点，加入该子图，判断是否为完全图
 */
 #include<cstdio>
 #include<algorithm>
 using namespace std;
 const int M=1e3,INF=1e9;
 int grap[M][M],v[M],vis[M];

 int main()
 {
 #ifdef ONLINE_JUDGE
 #else
     freopen("Test.txt", "r", stdin);
 #endif // ONLINE_JUDGE

     int n,m,k,v1,v2;
     scanf("%d%d", &n,&m);
     fill(grap[],grap[]+M*M,INF);
     for(int i=; i<m; i++)
     {
         scanf("%d%d", &v1,&v2);
         grap[v1][v2]=;
         grap[v2][v1]=;
     }
     scanf("%d", &m);
     while(m--)
     {
         scanf("%d", &k);
         fill(vis,vis+n+,);
         for(int i=; i<k; i++)
         {
             scanf("%d", &v[i]);
             vis[v[i]]=;
         }
         for(int i=; i<k-; i++)
         {
             v1 = v[i];
             for(int j=i+; j<k; j++)
             {
                 v2=v[j];
                 if(grap[v1][v2]==INF)
                 {
                     k=;
                     break;
                 }
                 v1=v2;
             }
         }
         if(k==)
         {
             printf("Not a Clique\n");
             continue;
         }
         for(int i=; i<=n; i++)
         {
             if(vis[i]==)
             {
                 for(int j=; j<k; j++)
                 {
                     if(grap[i][v[j]]==INF)
                     {
                         vis[i]=;
                         break;
                     }
                 }
                 if(vis[i]==)
                 {
                     printf("Not Maximal\n");
                     k=;break;
                 }
             }
         }
         if(k)
             printf("Yes\n");
     }

     return ;
 }