Question

While watching lecture 1B of the Structure and Interpretation of Computer Programs, there’s a function that calculates Fibonacci numbers. The lecturer points out that the time complexity is O(fib n) – I’ve never seen that before. I’ve seen it rounded to constant, linear, n+m, quadratic, polynomial, or exponential complexity, but are there any other O(fib n) algorithms or other interesting big O notations that should be looked at or studied?

Answer 1

O(fib N) is nothing strange or special – it is exactly the same thing as exponential complexity – it is just that the lecturer did not take the time to spell it out. (You can easily* bound fib(N) with phi^n.)

You don’t have to believe me though – you would have a better explanation on Math.stackexchange.

*: I’ll clarify what I mean by “easily” – it means that the proof is readily available, for example in that wikipedia article (thanks to the previous answerer that originally gave the link to it).