Let’s say I have 4 distinguishable balls, and I want to distribute them into 3 cells (that’s 3^4 different ways of doing that) – how would you suggest me to demonstrate all those 81 different distributions using Python?
I want my program to return a list that contains 81 lists, each contain 3 lists representing the 3 cells, where in each sub-list there are numbers 1-4.
hope you understood what i meant.. it’s a bit complicated interpretation.
I’ll try to give an example of how my list should look like:
[ [ [1,2] , [3,4] , [] ] # cell #1 contains the balls 1,2 and cell #2 contains the balls 3,4 and cell #3 is empty [ [1,2] , [3] , [4] ] # cell #1 contains the balls 1,2 and cell #2 contains ball 3 and cell #3 contains ball 4 [ [1,2] , [] , [3,4] ] # cell #1 contains the balls 1,2, cell #2 is empty and cell #3 contains the balls 3,4 ... ]
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Answer
There is simple and bruteforce, but working, example:
import itertools import pprint balls = set('1234') splits = [] for i in range(0,len(balls)+1): # python ranges are upper-bound exclusive bucket_1_possibilities = (set(x) for x in itertools.combinations(balls,i)) for bucket1 in bucket_1_possibilities: for j in range(0,len(balls)-i+1): # in the second cell there may be up to len(balls)-i balls bucket_2_possibilities = list(set(x) for x in itertools.combinations(balls-bucket1,j)) for bucket_2 in bucket_2_possibilities: splits.append([list(bucket1), list(bucket_2),list(balls-bucket1-bucket_2)]) pprint.pprint(splits) print(len(splits))
Itertools.combinations (https://docs.python.org/3/library/itertools.html#itertools.combinations) allow you to get possible contents of first cell. From remaining balls you get possible contents of second cells, and so on.