python unique string creation

Question

I've looked at several other SO questions (and google'd tons) that are 'similar'-ish to this, but none of them seem to fit my question right.

I am trying to make a non fixed length, unique text string, only containing characters in a string I specify. E.g. made up of capital and lower case a-zA-Z characters. (for this example I use only a, b, and c lower case)

Something like this (broken code below)

def next(index, validCharacters = 'abc'):
    return uniqueShortAsPossibleString

The index argument would be an index (integer) that relate to a text string, for instance:

next(1)  == 'a'
next(2)  == 'b'
next(3)  == 'c'

next(4)  == 'aa'
next(5)  == 'ab'
next(6)  == 'ac'

next(7)  == 'ba'
next(8)  == 'bb'
next(9)  == 'bc'

next(10) == 'ca'
next(11) == 'cb'
next(12) == 'cc'

And so forth. The string:

1. Must be unique, I'll be using it as an identifier, and it can only be a-zA-Z chars
2. As short as possible, with lower index numbers being shortest (see above examples)
3. Contain only the characters specified in the given argument string validCharacters

In conclusion, how could I write the next() function to relate an integer index value to an unique short string with the characters specified?

P.S. I'm new to SO, this site has helped me tons throughout the years, and while I've never made an account or asked a question (till now), I really hope I've done an okay job explaining what I'm trying to accomplish with this.

Answer 1

What you are trying to do is write the parameter of the next function in another base.

Let's suppose validCharacters contains k characters: then the job of the next function will be to transform parameter p into base k by using the characters in validCharacters.

In your example, you can write the numbers in base 3 and then associate each digit with one letter:

next(1) -> 1 -> 'a'
next(2) -> 2 -> 'b'

next(4) -> 11 -> 'aa'
next(7) -> 21 -> 'ba'

And so forth.

With this method, you can call next(x) without knowing or computing any next(x-i), which you can't do with iterative methods.