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The Fibonacci number or sequence is:

$0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\;$

Each number is the sum of the previous two numbers. In mathematical terms:

$F_n = F_{n-1} + F_{n-2}$


$F_1 = 1,\; F_2 = 1$

Recursive algorithm

The recursive algorithm to calculate a fibonacci number is very simple and is a direct translation from the mathematical definition. Unfortunately it is very slow. It uses $O(\phi^n)$ time, where $\phi=\frac{\sqrt{5}+1}{2}$ (the golden ratio).

λ fibonacci-recursive

Fast doubling algorithm

fibonacci.1360517562.txt.gz · Last modified: 2015/02/02 08:24 (external edit)