All Permutations: Difference between revisions

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[[File:All Permutations - Time.png|1000px]]
[[File:All Permutations - Time.png|1000px]]
== Space Complexity Graph ==
[[File:All Permutations - Space.png|1000px]]
== Time-Space Tradeoff ==
[[File:All Permutations - Pareto Frontier.png|1000px]]

Latest revision as of 09:07, 28 April 2023

Description

Generate all permuttaions of the characters/elements in a string/array.

Parameters

$n$: number of elements

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Steinhaus–Johnson–Trotter algorithm 1963 $O(n)$ on specific permutations $O({1})$ Exact Deterministic Time
Tompkins–Paige algorithm 1956 $O(n)$ on specific permutations $O(n)$ Exact Deterministic Time
Heap's algorithm 1963 $O(n)$ per permutation $O(n)$ Exact Deterministic Time

Time Complexity Graph

All Permutations - Time.png