Selection sort: Difference between revisions

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In [[computer science]], '''selection sort''' is an [[in-place algorithm|in-place]] [[comparison sort|comparison]] [[sorting algorithm]]. It has ana [[Big O notation|O]](''n''²) [[time complexity]], which makes it inefficient on large lists, and generally performs worse than the similar [[insertion sort]]. Selection sort is noted for its simplicity and has performance advantages over more complicated algorithms in certain situations, particularly where [[auxiliary memory]] is limited. Hello Mr. Rose

The algorithm divides the input list into two parts: a sorted sublist of items which is built up from left to right at the front (left) of the list and a sublist of the remaining unsorted items that occupy the rest of the list. Initially, the sorted sublist is empty and the unsorted sublist is the entire input list. The algorithm proceeds by finding the smallest (or largest, depending on sorting order) element in the unsorted sublist, exchanging (swapping) it with the leftmost unsorted element (putting it in sorted order), and moving the sublist boundaries one element to the right.

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== Implementations ==

{{unreferenced section|date=May 2019}}

Below is an implementation in [[C (programming language)|C]].

<syntaxhighlight lang="c" style="overflow:auto; width:auto;" line="1">

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if (jMin != i)

{

swap(&a[i], &a[jMin]);

}

}

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== Complexity ==

Selection sort is not difficult to analyze compared to other sorting algorithms, since none of the loops depend on the data in the array. Selecting the minimum requires scanning <math>n</math> elements (taking <math>n-1</math> comparisons) and then swapping it into the first position. Finding the next lowest element requires scanning the remaining <math>n-21</math> elements (taking <math>n-2</math> comparisons) and so on. Therefore, the total number of comparisons is

: <math>(n-1)+(n-2)+...\dots+1 =

\sum_{i=1}^{n-1}i</math>

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\frac{1}{2}(n^2-n)</math>

which is of complexity <math>O(n^2)</math> in terms of number of comparisons. Each of these scans requires one swap for <math>n-1</math> elements (the final element is already in place).

== Comparison to other sorting algorithms ==

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== Variants ==

[[Heapsort]] has been described as "nothing but an implementation of selection sort using the right [[data structure]]."<ref>{{cite book |first=Steven |last=Skiena |author-link=Steven Skiena |title=The Algorithm Design Manual |edition=3rd |publisher=Springer |year=2008 |page=116 |chapter=Searching and Sorting |isbn=978-3-030-54255-9 |quote=The name typically given to this algorithm, ''heapsort'', obscures the fact that the algorithm is nothing but an implementation of selection sort using the right data structure. |doi=10.1007/978-3-030-54256-6_4}}<!--DOI for chapter--></ref> It greatly improves the basic algorithm by using an [[implicit data structure|implicit]] [[heap (data structure)|heap]] [[data structure]] to speed up findingfind and removingremove the lowest datum. If implemented correctly, the heap will allow finding the nexteach lowest element in <math>\Theta(\log n)</math> time, instead of normal selection sort's <math>\Theta(n)</math> for the inner loop in normal selection sort, reducing the total running time to <math>\Theta(n\log n)</math>.

A bidirectional variant of selection sort (called '''double selection sort''' or sometimes '''cocktail sort''' due to its similarity to [[cocktail shaker sort]]) finds ''both'' the minimum and maximum values in the list in every pass. This requires three comparisons per two items (a pair of elements is compared, then the greater is compared to the maximum and the lesser is compared to the minimum) rather than regular selection sort's one comparison per item, but requires only half as many passes, a net 25% savings.

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last := length(A) - 1;

{ The first iteration is written to look very similar to
the subsequent ones, but without swaps. }

but without swaps. }

nextMax := A[last];

for i := last - 1 downto 0 do

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while last > 0 do begin

{ Each main loop searches for the new nextMax while

swapping items equal to prevMax into place. }

prevMax := nextMax;

nextMax := A[last];

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{{sorting}}

[[Category:Sorting algorithms]]

[[Category:Comparison sorts]]

[[Category:Articles with example C code]]