Subgraphs

You are given an int k that is between 2 and 23, inclusive. Your task is to construct an undirected graph with some properties (listed below) and to locate some special subsets of nodes in the graph.

More precisely, your graph must satisfy the following:

• The number n of nodes must be between 1 and 46, inclusive.
• The nodes must be labeled from 0 to n-1.
• The graph must be a simple undirected graph. (I.e., there cannot be any self-loops or multiple edges.)
• For every number x between 0 and k*(k-1)/2, inclusive, there must be a way to choose exactly k nodes so that there will be exactly x edges between them.

Return a String[] with n + k*(k-1)/2 + 1 elements. The return value should look as follows:

• The first n elements of the return value should contain the adjacency matrix of your graph. Character j of element i of the return value should be '1' of nodes i and j are connected by an edge and '0' if they aren't. Note that the main diagonal of the adjacency matrix must contain only '0's.
• The remaining k*(k-1)/2 + 1 elements of the return value should describe the subsets of nodes that correspond to the last constraint the graph should satisfy. More precisely, the i-th of these Strings (0-based index) describes one set of k nodes such that the subgraph induced by these nodes contains exactly i edges. Encode the subset as a String of length n: character j of this string should be 'Y' if node j belongs into the subset and 'N' otherwise.

You may assume that there is always a graph with the desired properties. If there are multiple correct answers, you may return any of them.