In an undirected graph, a clique is a subset of vertices that are fully connected, i.e. there is an edge between all pairs of vertices in the subset. A maximal clique is one in which the subset of vertices is not part of a larger clique. So, for instance, a fully connected graph has many cliques, but only one maximal clique.
Given an NxN adjacency matrix (A) for an undirected graph with N vertices, return the number (num) of maximal cliques.
Example
Consider the graph shown below,
which has the following adjacency matrix:
A = [ 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 ]
The number of maximal cliques is 3. The maximal cliques are {1,2}, {2,3,4}, and {4,5}.
NOTE: You may assume the data type of the adjacency matrix is double.
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