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Fibonacci search has an average- and worst-case complexity of O(log n) (see Big O notation). The Fibonacci sequence has the property that a number is the sum of its two predecessors. Therefore the sequence can be computed by repeated addition. The ratio of two consecutive numbers approaches the Golden ratio, 1.618... Binary search works by ...
Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted F n . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 [ 1 ] [ 2 ] and some (as did Fibonacci) from 1 and 2.
A Fibonacci sequence of order n is an integer sequence in which each sequence element is the sum of the previous elements (with the exception of the first elements in the sequence). The usual Fibonacci numbers are a Fibonacci sequence of order 2.
Pseudocode is commonly used in textbooks and scientific publications related to computer science and numerical computation to describe algorithms in a way that is accessible to programmers regardless of their familiarity with specific programming languages.
Multiple recursion can sometimes be converted to single recursion (and, if desired, thence to iteration). For example, while computing the Fibonacci sequence naively entails multiple iteration, as each value requires two previous values, it can be computed by single recursion by passing two successive values as parameters.
The Fibonacci code is closely related to the Zeckendorf representation, a positional numeral system that uses Zeckendorf's theorem and has the property that no number has a representation with consecutive 1s. The Fibonacci code word for a particular integer is exactly the integer's Zeckendorf representation with the order of its digits reversed ...
A Lagged Fibonacci generator (LFG or sometimes LFib) is an example of a pseudorandom number generator. This class of random number generator is aimed at being an improvement on the 'standard' linear congruential generator. These are based on a generalisation of the Fibonacci sequence. The Fibonacci sequence may be described by the recurrence ...
For example, consider the recursive formulation for generating the Fibonacci sequence: F i = F i−1 + F i−2, with base case F 1 = F 2 = 1. Then F 43 = F 42 + F 41, and F 42 = F 41 + F 40. Now F 41 is being solved in the recursive sub-trees of both F 43 as well as F 42. Even though the total number of sub-problems is actually small (only 43 ...