I was working on a little application that is similar to tinyurl.com (where any URL gets a unique random id that can be used to redirect with long clumsy URL strings) and came up with this little algorithm that I wanted to share with the world for some feedback.

There are two loops, one nested inside one big loop that goes on for infinity. The inner loop creates a list of possible combinations from a sample of letters and numbers eg (abc, acb, bac, bca, cab, cba). For each such found combinations it does a check to see if this has been saved before and if not it exists the loop like this:

if not hasattr(self, combination):
    return combination

What's important is the sample to use. This algorithm starts with 1 letter and 1 number, then when it's exhausted all the combinations using that samplespace, it increments the number of letters by 1 and the next time the samplespace is exhausted the number of digits is increased by 1.

A clever thing about this little algorithm is that its inner loop is done of the combinations and not its permutations. The number of combinations of AAA is 1 and ABC is 3! but the number of permutations of AAA is 3! and ABC is also 3!. This efficiency is accomplished with these lines:

unique = Set(genid_bits)
possible_combinations = factorial(len(unique))

This means that if genid_bits is (A, A, B) you get possible_combinations = 2! = 2, not 3! which it would be had we not taken the unique set.

The whole algorithm looks like this in python code:

import random
from sets import Set
class Container:
   def __init__(self):
       self.minlength_alpha=1
       self.minlength_numeric=1
       self.upper_and_lower=False

   def _generateID(self):
       """ generate a new ID that hasn't been instanciated in this
       self before """
       assert self.minlength_alpha >= 1
       assert self.minlength_numeric >= 1
       letters = "abcdefghijklmnopqrstuvwxyz"
       if self.upper_and_lower:
           letters += letters.upper()
       numbers = "0123456789"
       while 1:
           try:
               genid_bits = random.sample(letters, self.minlength_alpha) + \
                            random.sample(numbers, self.minlength_numeric)
           except:
               letters += letters
               numbers += numbers
               continue
           unique = Set(genid_bits)
           possible_combinations = factorial(len(unique))
           combinations = []

           while len(combinations) < possible_combinations:
               random.shuffle(genid_bits)
               combination = ''.join(genid_bits)
               if combination not in combinations:
                   if not hasattr(self, combination):
                       return combination
                   combinations.append(combination)

           if self.minlength_numeric < self.minlength_alpha:
               self.minlength_numeric += 1
           else:
               self.minlength_alpha += 1

If you want to run it, download idgeneratordummy.py and run it's profile() function and you'll see that it's damn fast. What do you think?

So far, this actually has little to do with Zope but it will. I can now write my little competing system to tinyurl.com. I think I'll also drop certain characters that might cause confusion such as 0 and o.



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