Last but not least, combinatoric generators. These are really fun, if you are into this kind of thing. Let's just see a simple example on permutations.
According to Wolfram Mathworld:
A permutation, also called an "arrangement number" or "order", is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself.
For example, there are six permutations of ABC: ABC, ACB, BAC, BCA, CAB, and CBA.
If a set has N elements, then the number of permutations of them is N! (N factorial). For the ABC string, the permutations are 3! = 3 * 2 * 1 = 6. Let's do it in Python:
# permutations.py
from itertools import permutations print(list(permutations('ABC')))
This very short snippet of code produces the following result:
$ python permutations.py
[('A', 'B', 'C'), ('A', 'C', 'B'), ('B', 'A', 'C'), ('B', 'C', 'A'), ('C', 'A', 'B'), ('C', 'B', 'A')]
Be very careful when you play with permutations. Their number grows at a rate that is proportional to the factorial of the number of the elements you're permuting, and that number can get really big, really fast.