4 python scripts which all do the same. namely generating all possible partitions of a set. e.g.: if you have a set "a", "b", "c", "d" then all possible partitions are:
[1, 1, 1, 1] [1, 1, 1, 2] [1, 1, 2, 1] [1, 1, 2, 2] [1, 1, 2, 3] [1, 2, 1, 1] [1, 2, 1, 2] [1, 2, 1, 3] [1, 2, 2, 1] [1, 2, 2, 2] [1, 2, 2, 3] [1, 2, 3, 1] [1, 2, 3, 2] [1, 2, 3, 3] [1, 2, 3, 4]
This approach is based on "a fast iterative algorithm for generating set partitions", The Computer Journal, Vol. 32, No. 3, 1989.
So such a partition called "codeword" from above like [1, 2, 1, 3] means:
a b c d
[1, 2, 1, 3]
a is in partition 1
b is in partition 2
c is in partition 1
d is in partition 3
There are some py files: All implement different algorithms from the net (papers, repos, ...) some are not working because of incompleteness and errors they provided. The main files for this project are partitions.counting.recursive.py and partitions.counting.iterative.py. They implement a new algorithm: in the first the implementation is recursive in the latter one its iterative. Sure, the iterative one is faster. Further with this algorithm it is possible to define the maximum amount of partitions.