combinatorics as the whole is quite interesting. i've done an implementation that arranges different fixed-dimension flooring panels into rooms of different sizes.
it ended up starting out greedy, taking large panels first and adaptively backtracking when the current size could not be placed. if by the end of the iteration we did not reach a minimum coverage area, we would backtrack and remove the last significant size panel and fill it with smaller ones. it didnt get us the "optimal" solution but it was fast and more than sufficient.