I want to generate all unique crossword puzzle grids of a certain grid size (4x4 is a good size). All possible puzzles, including non-unique puzzles, are represented by a binary string with the length of the grid area (16 in the case of 4x4), so all possible 4x4 puzzles are represented by the binary forms of all numbers in the range 0 to 2^16.

Generating these is easy, but I'm curious if anyone has a good solution for how to programmatically eliminate invalid and duplicate cases. For example, all puzzles with a single column or single row are functionally identical, hence eliminating 7 of those 8 cases. Also, according to crossword puzzle conventions, all squares must be contiguous. I've had success removing all duplicate structures, but my solution took several minutes to execute and probably was not ideal. I'm at something of a loss for how to detect contiguity so if anyone has ideas on this it'd be much appreciated.

I'd prefer solutions in python but write in whichever language you prefer. If anyone wants, I can post my python code for generating all grids and removing duplicates, slow as it may be.