Question

For instance, suppose I have an algorithm that’s O(n) and an algorithm that’s an amortized O(n). Is it fair to say that in strictly big oh terms, the non-amortized algorithm will always be as fast or faster than the amortized algorithm? Or is there ever any reason to prefer the amortized version (ignoring things like code simplicity or ease of implementation)?

Answer 1

The main difference between a O(n) algorithm and an amortized O(n) algorithm is that you don’t know anything about the worst-case behavior of the amortized O(n) algorithm. In practice, that doesn’t matter very often: If your algorithm is being run many times, then you can count on the law of averages to balance out a few bad cases, and if your algorithm isn’t being run very many times, then it’s unlikely that you’ll ever hit the worst case at all.

The only cases where the word “amortized” should matter are cases where you can’t accept occasional bad performance for some reason. For example, in GUI applications, you would happily give up some average-case performance in return for a guarantee that you’ll never bog down and stop responding while the user is sitting there and getting bored. In such applications, you want to make sure that even the worst-case behavior is good for any code that could cause the GUI to stop responding.

Still, most of the time, you don’t need to worry about amortized O(n) versus O(n), and you can worry instead about what the constant factors are (as others have already said).