Southern Bread Blog

I mentioned in the last post that I’ve been doing a programming project for a few months.  One of the things that we found necessary was url shortening.  You know, that’s where you take a web address that looks like this: 

http://www.slate.com/articles/sports/fivering_circus/2012/07/london_olympics_viewers_guide_slate_s_day_by_day_cheat_sheet_for_the_2012_games_.html

and turns it into something that looks like: 

http://sobr.org/aF

This is beneficial for services like Twitter, that have limited content space. You start with “/0″, then go to “/1″, “/2″ and so on until you get to “/Z”. Then you flip to “/00″, “/01″, “/02″ and so on. When you get to “/ZZ”, you flip to “/000″. You get the idea.

Anyway, I started thinking about it today and wondering how many possible url’s we will be able to shorten with that scheme.

We use this character set:  0-9, a-z, A-Z, for a total of 62 possible characters. So, the math is 62 ^ x, where x is the number of character spaces in the shortened url.

Here’s the result:

1 chars: 62
2 chars: 3844
3 chars: 238328
4 chars: 14776336
5 chars: 916132832
6 chars: 56800235584
7 chars: 3521614606208
8 chars: 2.183401055849E+14
9 chars: 1.3537086546264E+16

So, by the time we get through 6 characters (http://sobr.org/ZZZZZZ), we would have shortened a total of 57,731,387,490. I’d say 57 billion url’s is probably gonna last me the rest of my life.

Here’s the php script that runs the calculation:

  $charset = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ';
  $charcnt = strlen($charset);

  for( $i = 1; $i < 10 ; $i++ ) {
    echo "$i chars: ".pow($charcnt, $i)".\n";
  }