Before we start with the dirty (and fun) job of improving program speed, I'd like to present a bit of computer science theory, namely the Big O notation.
You don't have to worry, I will not use pages of mathematical formulas and talk about infinitesimal asymptotics. Instead, I will just present the essence of the Big O notation, the parts that are important to every programmer.
In the literature and, of course, on the web, you will see expressions such as O(n), O(n^2), O(1) and similar. This fancy-looking notation hides a really simple story. It tells us how much slower the algorithm will become if we increase the data size by a factor of n.
The n^2 notation means "n to the power of two", or n2. This notation is frequently ...
