Twelve Simple Algorithms to Compute Fibonacci Numbers

Abstract

The Fibonacci numbers are a sequence of integers in which every number after the first two, 0 and 1, is the sum of the two preceding numbers. These numbers are well known and algorithms to compute them are so easy that they are often used in introductory algorithms courses. In this paper, we present twelve of these well-known algorithms and some of their properties. These algorithms, though very simple, illustrate multiple concepts from the algorithms field, so we highlight them. We also present the results of a small-scale experimental comparison of their runtimes on a personal laptop. Finally, we provide a list of homework questions for the students. We hope that this paper can serve as a useful resource for the students learning the basics of algorithms.