Generate strings in lexicographical order in Python

Question

How can I write a Python generator that lazily generates all strings composed of lowercase English letters of up to a certain length¹?

I have written my own solution (posted below as an answer), but I would like to see if there are any more elegant/efficient/fun solutions out there.

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¹ An infinite iterator would be pretty useless because it would just generate strings composed of only the character a. This is because the lexicographical ordering of strings is not a well-order; it can be thought of as composed of an infinite sequence of infinitely nested sequences: (a, (aa, ...), (ab, ...), ...), (b, (ba, ...), (bb, ...), ...), ... The generator would never reach ab since it has an infinite amount of predecessors.

Answer 1

Here is my solution:

import string


def lexstrings(max_length: int, alphabet=string.ascii_lowercase):
    yield ""
    if max_length == 0: return
    for first in alphabet:
        for suffix in lexstrings(max_length - 1, alphabet=alphabet):
            yield first + suffix

Example:

>>> g = lexstrings(max_length=3, alphabet="ab")
>>> list(g)
['',
 'a',
 'aa',
 'aaa',
 'aab',
 'ab',
 'aba',
 'abb',
 'b',
 'ba',
 'baa',
 'bab',
 'bb',
 'bba',
 'bbb']

This might not be the best solution because it involves recursion and using the + operator m times to generate a string of length m, which isn't efficient because Python generates copies of the intermediate results (since strings are immutable).

This implementation also "supports" the infinite version:

>>> g = lexstrings(-1)
>>> next(g)
''
>>> next(g)
'a'
>>> next(g)
'aa'
>>> next(g)
'aaa'
...