[PAT] 1142 Maximal Clique（25 分）

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

题意：
clique是一个无向图的点的子集，clique里每两个不同的点都是相连的。最大clique是不能扩展更多相连点的clique。
判断给定的点的子集是否为一个最大的clique。

思路：
将输入存在一个二维数组（矩阵）内，对于每一个查询，先判断是否为clique（每两个点对应的二维数组为1），再判断是否为max clique（遍历给定点之外的点是否和给定的点都有连线）。

题解：

 #include<cstdlib>
 #include<cstdio>
 #include<vector>
 using namespace std;
 ][];

 int main() {
     int nv, ne, m;
     scanf("%d %d", &nv, &ne);
     ; i < ne; i++) {
         int a, b;
         scanf("%d %d", &a, &b);
         vertex[a][b] = vertex[b][a] = ;
     }
     scanf("%d", &m);
     ; i < m; i++) {
         int k;
         scanf("%d", &k);
         vector<);
         vector<int> verts;
         ; j < k; j++) {
             int t;
             scanf("%d", &t);
             verts.push_back(t);
             v[t] = true;
         }
         //判断是否为clique
         //只要给定查询中的每两个点对应矩阵上的值为0，说明它不是clique
         bool isClique = true;
         ; j < verts.size(); j++) {
             ; r < verts.size(); r++) {
                 ) {
                     printf("Not a Clique\n");
                     isClique = false;
                     break;
                 }
             }
             if (!isClique) break;
         }

         if (!isClique) continue;

         //如果是clique，
         //并且还存在给定之外的点与给定的所有点对应矩阵的值为1
         //说明其不是max clique
         bool notMaximal = false;
         ; j <= nv; j++) {
             if (v[j] == true) continue;
             bool isMaxClique = false;
             ; r < verts.size(); r++) {
                 ) {
                     isMaxClique = true;
                     break;
                 }
             }
             if (!isMaxClique) {
                 printf("Not Maximal\n");
                 notMaximal = true;
                 break;
             }
         }
         if (!notMaximal) printf("Yes\n");
     }
     ;
 }