Greatest Common Divisor: Difference between revisions

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[[File:Greatest Common Divisor - Time.png|1000px]]
[[File:Greatest Common Divisor - Time.png|1000px]]
== Space Complexity Graph ==
[[File:Greatest Common Divisor - Space.png|1000px]]
== Time-Space Tradeoff ==
[[File:Greatest Common Divisor - Pareto Frontier.png|1000px]]

Latest revision as of 10:12, 28 April 2023

Description

Let $a_1, \ldots, a_m$ be given nonzero integers. Then $g$ is called the greatest common divisor (GCD) of $a_1, \ldots, a_m$ if and only if it is the largest integer that divides all $a_1, \ldots, a_m$.

Parameters

$n$: sum of number of bits among the integers

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Euclid's algorithm -300 $O(n^{2})$ $O(n)$ Exact Deterministic
Lehmer's GCD algorithm 1940 $O(n^{2})$ $O(n)$ Exact Deterministic
Binary GCD algorithm 1967 $O(n^{2})$ $O(n)$ Exact Deterministic Time
Sthele, Zimmermann 2006 $O(n \log^{2} n \log \log n)$ $O(n)$?? Exact Deterministic Time

Time Complexity Graph

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