Smoothsort operating on an array which is mostly in order. The bars across the top show the tree structure.
Class
Sorting algorithm
Data structure
Array
Worst-case performance
O(n log n)
Best-case performance
O(n)
Average performance
O(n log n)
Worst-case space complexity
O(n) total, O(1) auxiliary
Optimal
When the data is already sorted
In computer science, smoothsort is a comparison-based sorting algorithm. A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981.[1] Like heapsort, smoothsort is an in-place algorithm with an upper bound of O(n log n) operations (see big O notation),[2] but it is not a stable sort.[3][self-published source?][4] The advantage of smoothsort is that it comes closer to O(n) time if the input is already sorted to some degree, whereas heapsort averages O(n log n) regardless of the initial sorted state.
^Dijkstra, Edsger W. 16 Aug 1981 (EWD-796a)(PDF). E.W. Dijkstra Archive. Center for American History, University of Texas at Austin. One can also raise the question why I have not chosen as available stretch lengths: ... 63 31 15 7 3 1 which seems attractive since each stretch can then be viewed as the postorder traversal of a balanced binary tree. In addition, the recurrence relation would be simpler. But I know why I chose the Leonardo numbers: (transcription)
^Cite error: The named reference hertel was invoked but never defined (see the help page).
^Eisenstat, David (13 September 2020). "Where is the smoothsort algorithm used?". Stack Overflow. Retrieved 2020-10-28. Smoothsort is not stable, and stability is often more desirable than in-place in practice
In computer science, smoothsort is a comparison-based sorting algorithm. A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981...
stack usage.) The smoothsort algorithm is a variation of heapsort developed by Edsger W. Dijkstra in 1981. Like heapsort, smoothsort's upper bound is O(n...
all less than a certain value; used in applications of number theory Smoothsort, a sorting algorithm "Analysis of the Jane Curve", an applied mathematics...
}}n>1\\\end{cases}}} Edsger W. Dijkstra used them as an integral part of his smoothsort algorithm, and also analyzed them in some detail. A Leonardo prime is...
{\displaystyle O(n)} in-place merge algorithm with a bottom-up merge sort. Smoothsort n n log n {\displaystyle n\log n} n log n {\displaystyle n\log n}...
{\displaystyle O(n\log n)} , merge sort, introsort, binary tree sort, smoothsort, patience sorting, etc. in the worst case Fast Fourier transforms, O (...
( n ) {\displaystyle n\log(n)} n log ( n ) {\displaystyle n\log(n)} Smoothsort Leonardo Heap n {\displaystyle n} n log ( n ) {\displaystyle n\log(n)}...
Smoothsort is a comparison-based sorting algorithm. It is a variation of heapsort developed by Edsger Dijkstra in 1981. Like heapsort, smoothsort's upper...
sort Odd–even sort Cocktail shaker sort Cycle sort Merge-insertion sort Smoothsort Timsort Block sort There are fundamental limits on the performance of...
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