All Permutations: Difference between revisions
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(Created page with "{{DISPLAYTITLE:All Permutations (All Permutations)}} == Description == Generate all permuttaions of the characters/elements in a string/array. == Parameters == <pre>n: number of elements</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Steinhaus–Johnson–Trotter algorithm (All Permutations All Permutations)|Steinhaus–J...") |
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== Parameters == | == Parameters == | ||
$n$: number of elements | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Steinhaus–Johnson–Trotter algorithm (All Permutations All Permutations)|Steinhaus–Johnson–Trotter algorithm]] || 1963 || $O(n)$ on specific permutations || $O({1})$ | | [[Steinhaus–Johnson–Trotter algorithm (All Permutations All Permutations)|Steinhaus–Johnson–Trotter algorithm]] || 1963 || $O(n)$ on specific permutations || $O({1})$ || Exact || Deterministic || [https://www-ams-org.ezproxy.canberra.edu.au/journals/mcom/1963-17-083/S0025-5718-1963-0159764-2/home.html Time] | ||
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| [[Tompkins–Paige algorithm (All Permutations All Permutations)|Tompkins–Paige algorithm]] || 1956 || $O(n)$ on specific permutations || $O(n)$ | | [[Tompkins–Paige algorithm (All Permutations All Permutations)|Tompkins–Paige algorithm]] || 1956 || $O(n)$ on specific permutations || $O(n)$ || Exact || Deterministic || [https://mathscinet-ams-org.ezproxy.canberra.edu.au/mathscinet-getitem?mr=0080380 Time] | ||
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| [[Heap's algorithm (All Permutations All Permutations)|Heap's algorithm]] || 1963 || $O(n)$ per permutation || $O(n)$ | | [[Heap's algorithm (All Permutations All Permutations)|Heap's algorithm]] || 1963 || $O(n)$ per permutation || $O(n)$ || Exact || Deterministic || [https://academic-oup-com.ezproxy.canberra.edu.au/comjnl/article/6/3/293/360213 Time] | ||
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|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:All Permutations - Time.png|1000px]] | [[File:All Permutations - Time.png|1000px]] | ||
Latest revision as of 10:07, 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
