In maths, when you have two sets of words A={foo,bar} and B={x,y}, then the algebraic (or each-to-each) product is AB={foox,fooy,barx,bary}. I would like a similar thing in Python. Given two sets of words (= list of lists):
A = [ [0,1], [2,3] ]
B = [ [4,5], [6,7] ]
I would like to concatenate them each-to-each:
AB = [ [0,1,4,5], [0,1,6,7], [2,3,4,5], [2,3,6,7] ]
That itself is not so difficult, it can be done with product:
AB = [ a+b for (a,b) in itertools.product(A,B) ]
However, I have a list of "sets" (aka, list of lists of lists)
A = [ [0,1], [2,3] ]
B = [ [4,5], [6,7] ]
C = [ [4,5], [6,7] ]
SETS = [A,B,C]
Now I can do manually
ABC = [ a+b+c for (a,b,c) in itertools.product(A,B,C) ]
But I can't do that if I have 20 sets to concatenate. So, how to write a definition of ABC that would use only SETS and would accept any size of it?
ABC = [ sum(z, []) for z in itertools.product(*SETS) ]
product(*SETS) basically does product(A, B, C). The technical term is argument unpacking.
sum(z, []) basically does a + b + c + [].
EDIT:
As smart people said in the comments sum isn't a best way to join a list of lists. O(n^2) time complexity is pretty brutal.
To quote a documentation:
For some use cases, there are good alternatives to sum(). The preferred, fast way to concatenate a sequence of strings is by calling ''.join(sequence). To add floating point values with extended precision, see math.fsum(). To concatenate a series of iterables, consider using itertools.chain().
That's better:
from itertools import chain, product
ABC = [ list(chain(*z)) for z in product(*SETS) ]
or, if two argument unpackings is one argument unpacking too many:
ABC = [ list(chain.from_iterable(z)) for z in product(*SETS) ]
or, if you're into map:
ABC = map(list, map(chain.from_iterable, product(*SETS)))