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:

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 ;

 }

巴特西

PAT_A1142#Maximal Clique

Source:

Description:

Input Specification:

Output Specification:

Sample Input:

Sample Output:

Keys:

Attention:

Code:

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