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
题目大意：clique是一个点集，在一个无向图中，这个点集中任意两个不同的点之间都是相连的。maximal clique是一个clique，这个clique不可以再加入任何一个新的结点构成新的clique。点编号从1～nv，给出ne条边，以一对结点编号的方式给出。然后给出m条询问，每个询问是一个点集合，问这个点集合是否是maximal clique、是否是clique～
分析：先判断是否是clique，即判断是否任意两边都相连；之后判断是否是maximal，即遍历所有不在集合中的剩余的点，看是否存在一个点满足和集合中所有的结点相连，最后如果都满足，那就输出Yes表示是Maximal clique～
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#include <iostream> #include <vector> using namespace std; int e[210][210]; int main() { int nv, ne, m, ta, tb, k; scanf("%d %d", &nv, &ne); for (int i = 0; i < ne; i++) { scanf("%d %d", &ta, &tb); e[ta][tb] = e[tb][ta] = 1; } scanf("%d", &m); for (int i = 0; i < m; i++) { scanf("%d", &k); vector<int> v(k); int hash[210] = {0}, isclique = 1, isMaximal = 1; for (int j = 0; j < k; j++) { scanf("%d", &v[j]); hash[v[j]] = 1; } for (int j = 0; j < k; j++) { if (isclique == 0) break; for (int l = j + 1; l < k; l++) { if (e[v[j]][v[l]] == 0) { isclique = 0; printf("Not a Clique\n"); break; } } } if (isclique == 0) continue; for (int j = 1; j <= nv; j++) { if (hash[j] == 0) { for (int l = 0; l < k; l++) { if (e[v[l]][j] == 0) break; if (l == k - 1) isMaximal = 0; } } if (isMaximal == 0) { printf("Not Maximal\n"); break; } } if (isMaximal == 1) printf("Yes\n"); } return 0; } |
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