Python: Concatenate list of lists in the algebraic way

list, python, python-itertools

Solution

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)))

Problem

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?

Original source