Understanding the map function

Question

map(function, iterable, ...)

Apply function to every item of iterable and return a list of the results. If additional iterable arguments are passed

Answer 1

Simplifying a bit, you can imagine map() doing something like this:

def mymap(func, lst):
    result = []
    for e in lst:
        result.append(func(e))
    return result

As you can see, it takes a function and a list, and returns a new list with the result of applying the function to each of the elements in the input list. I said "simplifying a bit" because in reality map() can process more than one iterable:

If additional iterable arguments are passed, function must take that many arguments and is applied to the items from all iterables in parallel. If one iterable is shorter than another it is assumed to be extended with None items.

For the second part in the question: What role does this play in making a Cartesian product? well, map() could be used for generating the cartesian product of a list like this:

lst = [1, 2, 3, 4, 5]

from operator import add
reduce(add, map(lambda i: map(lambda j: (i, j), lst), lst))

... But to tell the truth, using product() is a much simpler and natural way to solve the problem:

from itertools import product
list(product(lst, lst))

Either way, the result is the cartesian product of lst as defined above:

[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5),
 (2, 1), (2, 2), (2, 3), (2, 4), (2, 5),
 (3, 1), (3, 2), (3, 3), (3, 4), (3, 5),
 (4, 1), (4, 2), (4, 3), (4, 4), (4, 5),
 (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]