Understanding and simplifying this line

I found this example for finding all strings of an alphabet of a given length.

for i in range(length):
    result = [str(x)+str(y) for x in alphabet for y in result or ['']]

I'm trying to understand how this works and if this was implemented with for loops, how it would look - all my attempts at simplifying it become very messy and crash with infinite loops... while this one works every time.

Example:

def allstrings(alphabet, length):
    """Find the list of all strings of 'alphabet' of length 'length'"""

    alphabet = list(alphabet)

    result = []

    for i in range(length):
        result = [str(x)+str(y) for x in alphabet for y in result or ['']]

    return result

# will return ['aa', 'ab', 'ba', 'bb']
print(allstrings({'a', 'b'}, 2)))

# will return ['000', '001', '010', '011', '100', '101', '110', '111']
print(allstrings({'0', '1'}, 4)))

Code is modified from: http://code.activestate.com/recipes/425303-generating-all-strings-of-some-length-of-a-given-a/

Solution

In short this is equivalent of your code, since I haven't seen others provide you with it. I do recommend the use of itertools like Joran Beasley wrote because they're faster, and they also make a clear and simpler statement.

def permute(alphabet):
    result = []
    for x in alphabet:
        for y in alphabet:
            result.append(str(x)+str(y))
    return result

With ouptut in IDLE as:

>>> alphabet = ["a", "b", "c"]
>>> r = permute(alphabet)
>>> r
['aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc']

However this approach makes it harder to define the desired length. To achieve that effect you would have to do something like:

def permute(original, permutated):
    result = []
    for x in alphabet:
        for y in permutated or [""]:
            result.append(str(x)+str(y))
    return result

def helper(alphabet, length):
    res = []
    for i in range(length):
        res = permute(alphabet, res)
    return res

Output of which now looks like:

>>> h = helper(alphabet, 2)
>>> h
['aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc']
>>> h = helper(alphabet, 3)
>>> h
['aaa', 'aab', 'aac', 'aba', 'abb', 'abc', 'aca', 'acb', 'acc', 'baa', 'bab', 'bac', 'bba', 'bbb', 'bbc', 'bca', 'bcb', 'bcc', 'caa', 'cab', 'cac', 'cba', 'cbb', 'cbc', 'cca', 'ccb', 'ccc']

Can you make out what's happening? Or should I write up an explanation. (but please make an effort first).