counting using variable length string as base

[Dan Bishop]

On Mar 27, 1:15 am, Grimsqueaker <Grimsqueake... at gmail.com> wrote:
> Hi, I'm fairly new to Python and to this list. I have a problem that
> is driving me insane, sorry if it seems simple to everyone, I've been
> fighting with it for a while. :))
>
> I want to take a variable length string and use it as a base for
> counting, eg. given the string 'abc' the  sequence would be:
>
> a
> b
> c
> aa
> ba
> ca
> ab
> bb
> cb
> ...
> ccc
>
> Basically I want to find every possible order of every combination.
> Its easy if you know how many characters there will be in your string
> (use nested for loops), but I am stuck with the variable length
> string. I think I have to use a generator but I'm not sure exactly
> how.
>
> Can anyone give me a pointer in the right direction?

def cartesian_product(*args):
    """Iterates over the Cartesian product of args[0], args[1], ..."""
    if not args:
        return
    elif len(args) == 1:
        for item in args[0]:
            yield (item,)
    else:
        for item in args[0]:
            for item2 in cartesian_product(*args[1:]):
                yield (item,) + item2

def string_cartesian_product(*args):
    return (''.join(combo) for combo in cartesian_product(*args))