Let be a number of buckets, containing each, a variable number of items. This function return all combinations possible of one item picked out of each bucket
example, with three buckets {ba, be, bi}, {ka, ko, ku, ke} and {to, ty}, the function enumerate as such:
0. ba-ka-to
1. ba-ka-ty
2. ba-ko-to
3. ba-ko-ty
4. ba-ku-to
5. ba-ku-ty
6. ba-ke-to
7. ba-ke-ty
8. be-ka-to
9. be-ka-ty
10. be-ko-to
11. be-ko-ty
12. be-ku-to
13. be-ku-ty
14. be-ke-to
15. be-ke-ty
16. bi-ka-to
17. bi-ka-ty
18. bi-ko-to
19. bi-ko-ty
20. bi-ku-to
21. bi-ku-ty
22. bi-ke-to
23. bi-ke-ty
Python, 16 lines
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | #!/usr/bin/env python3
def of_bucket(lst, depth=0) :
""" return all combinations of items in buckets """
#dbg print("of_bucket({0}, {1})".format(lst, depth))
for item in lst[0] :
if len(lst) > 1 :
for result in of_bucket(lst[1:], depth+1) :
yield [item,] + result
else :
yield [item,]
if __name__ == '__main__' :
bucket_lst = [["ba", "be", "bi"], ["ka", "ko", "ku", "ke"], ["to", "ty"]]
for n, combination in enumerate(of_bucket(bucket_lst)) :
print("{0:2d}. {1}".format(n, '-'.join(combination)))
|
Tags: combinatorics
