Strand sort: Difference between revisions

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{{Short description|Sorting algorithm}}

[[File:StrandSort.gif|thumb|220x220px|Strand Sort Animation]]

'''Strand sort''' is a [[Recursion (computer science)|recursive]] [[sorting algorithm]] that sorts items of a list into increasing order. It has {{math|1=[[Big O notation|''O'']](''n''²)}} worst-case [[time complexity]], which occurs when the input list is reverse sorted.<ref name=":0">{{Cite book|url=https://www.worldcat.org/oclc/641462443|title=IT enabled practices and emerging management paradigms|date=2008|publisher=Prestige Institute of Management and Research|others=Gupta, I. C. (Ishwar Chandra), 1946-, Jaroliya, Deepak., Prestige Institute of Management and Research.|isbn=9788174466761|edition=1st|___location=Indore|oclc=641462443}}</ref> It has a best -case [[time complexity]] of {{Math|''O''(''n'')}}, which occurs when the input is a list that is already sorted.<ref name=":1">{{CiteCitation webneeded|urlreason=https://xlinux.nist.gov/dads/HTML/strandSort.html|title=strandThe sort|website=xlinux.nist.gov|language=en-US|access-date=2018-11-06}}</ref>previously Strandgiven sortcitation isdoes not [[In-placemention algorithmperformance|in-place]] as it’s space complexity is O(n).<ref namedate=":0"May />2022}}

'''Strand sort''' is a very simple [[Recursion (computer science)|recursive]] [[sorting algorithm]] that sorts items of a list into increasing order.

The algorithm first moves the first element of a list into a sub-list.<ref name=":0" /> It then compares the last element in the sub-list to each subsequent element in the original list.<ref name=":0" /> Once there is an element in the original list that is greater than the last element in the sub-list, the element is removed from the original list and added to the sub-list.<ref name=":0" /> This process continues until the last element in the sub-list is compared to the remaining elements in the original list.<ref name=":0" /> The sub-list is then merged into a new list.<ref name=":0" /> Repeat this process and merge all sub-lists until all elements are sorted.<ref name=":0" /> This algorithm is called strand sort because there are strands of sorted elements within the unsorted elements that are removed one at a time.<ref name=":0" /> This algorithm is also used in [[J Sort]] for fewer than 40 elements.<ref>{{Cite book|url=https://www.worldcat.org/oclc/311311576|title=Data structures using C : 1000 problems and solutions|last=Sudipta.|first=Mukherjee,|date=2008|publisher=Tata McGraw-Hill|isbn=9780070667655|___location=New Delhi|oclc=311311576}}</ref>

It has [[Big O notation|O]](n²) worst time complexity which occurs when the input list is reverse sorted.<ref name=":0">{{Cite book|url=https://www.worldcat.org/oclc/641462443|title=IT enabled practices and emerging management paradigms|date=2008|publisher=Prestige Institute of Management and Research|others=Gupta, I. C. (Ishwar Chandra), 1946-, Jaroliya, Deepak., Prestige Institute of Management and Research.|isbn=9788174466761|edition=1st|___location=Indore|oclc=641462443}}</ref> It has a best case [[time complexity]] of O(n) which occurs when the input is a list that is already sorted.<ref name=":1">{{Cite web|url=https://xlinux.nist.gov/dads/HTML/strandSort.html|title=strand sort|website=xlinux.nist.gov|language=en-US|access-date=2018-11-06}}</ref> Strand sort is not [[In-place algorithm|in-place]] as it’s space complexity is O(n).<ref name=":0" />

The algorithm first moves the first element of a list into a sub-list.<ref name=":0" /> It then compares the last element in the sub-list to each subsequent element in the original list.<ref name=":0" /> Once there is an element in the original list that is greater than the last element in the sub-list, the element is removed from the original list and added to the sub-list.<ref name=":0" /> This process continues until the last element in the sub-list is compared to the remaining elements in the original list.<ref name=":0" /> The sub-list is then merged into a new list.<ref name=":0" /> Repeat this process and merge all sub-lists until all elements are sorted.<ref name=":0" /> This algorithm is called strand sort because there are strands of sorted elements within the unsorted elements that are removed one at a time.<ref name=":0" /> This algorithm is also used in [[J Sort]] for fewer than 40 elements.<ref>{{Cite book|url=https://www.worldcat.org/oclc/311311576|title=Data structures using C : 1000 problems and solutions|last=Sudipta.|first=Mukherjee,|date=2008|publisher=Tata McGraw-Hill|isbn=9780070667655|___location=New Delhi|oclc=311311576}}</ref>

== Example ==

BasedThis offexample ofis based on the description of the algorithm provided in the book, ''IT Enabled Practices and Emerging Management Paradigms''.<ref name=":0" />

'''Step 1:''' Start with a list of numbers: {5, 1, 4, 2, 0, 9, 6, 3, 8, 7 }.

'''Step 2:''' Next, move the first element of the list into a new sub-list:  sub-list contains {5}.

'''Step 3:''' Then, iterate through the original list and compare each number to 5 until there is a number greater than 5.

* 1 < 5, so 1 is not added to the sub-list.

* 04 < 45, so 04 is not added to the sub-list.

* 42 < 5, so 42 is not added to the sub-list.

* 0 < 5, so 0  is not added to the sub-list.

* 29 <> 5, so 29 is not added to the sub-list and removed from the original list.

* 0 < 5 so 0  is not added to the sub-list.

* 9 > 5 so 9 is added to the sub-list and removed from the original list.

'''Step 4:''' Now compare 9 with the remaining elements in the original list until there is a number greater than 9.  

* 6 < 9, so 6 is not added to the sub-list.

* 83 < 9, so 83 is not added to the sub-list.

* 38 < 9, so 38 is not added to the sub-list.

* 7 < 9, so 7 is not added to the sub-list.

* 8 < 9 so 8 is not added to the sub-list.

* 7 < 9 so 7 is not added to the sub-list.

'''Step 5:''' Now there are no more elements to compare 9 to so merge the sub-list into a new list, called solution-list.

After step 5, the original list contains {1, 4, 2, 0, 6, 3, 8, 7}

'''Step 5:''' Now there are no more elements to compare 9 to, so merge the sub-list into a new list, called solution-list.

The sub-list is empty, and the solution list contains {5, 9}

After step 5, the original list contains {1, 4, 2, 0, 6, 3, 8, 7}.

'''Step 6:''' Move the first element of the original list into sub-list: sub-list contains {1}

The sub-list is empty, and the solution list contains {5, 9}.

'''Step 7:''' Iterate through the original list and compare each number to 1 until there is a number greater than 1.

'''Step 6:''' Move the first element of the original list into sub-list: sub-list contains {1}.

* 4 > 1 so 4 is added to the sub-list and 4 is removed from the original list.

'''Step 87:''' NowIterate comparethrough 4the withoriginal thelist remainingand elementscompare ineach thenumber originalto list1 until there is a number greater than 41.

* 24 <> 41, so 24 is not added to the sub-list. and 4 is removed from the original list.

'''Step 78:''' IterateNow throughcompare the4 originalwith listthe andremaining compareelements eachin numberthe tooriginal 1list until there is a number greater than 14.

* 0 < 4 so 0 is not added to the sub-list.

* 62 >< 4, so 62 is not added to the sub-list and is removed from the original list.

* 0 < 24, so 0 is not added to the sub-list.

* 96 > 54, so 96 is added to the sub-list and is removed from the original list.

'''Step 9:''' Now compare 6 with the remaining elements in the original list until there is a number greater than 6.  

* 3 < 6, so 3 is not added to the sub-list.

* 48 > 16, so 48 is added to the sub-list and 4 is removed from the original list.

*'''Step 810:''' >Now 6 socompare 8 iswith addedthe toremaining elements in the sub-original list anduntil there is removeda fromnumber thegreater originalthan list8.

* 7 < 8, so 7 is not added to the sub-list.

'''Step 10:''' Now compare 8 with the remaining elements in the original list until there is a number greater than 8.

'''Step 1511:''' Since there are no more elements in the original list to compare {78} to, the sub-list is merged with the solution list. TheNow the original list now contains {2, 0, 3, 7}, the sub-list is empty, and solutionthe solution-list contains: {1, 2, 3, 4, 5, 6, 7, 8, 9}.

* 7 < 8 so 7 is not added to the sub-list.

'''Step 1112:''' Since Move therethe arefirst noelement more elements inof the original list to compare {8} to, theinto sub-list is merged with the solution list. Now the original Sub-list contains {2, 0, 3, 7}, the sub-list is empty and the solution-list contains: {1, 4, 5, 6, 8, 9}.

'''Step 1213:'''  MoveIterate through the firstoriginal elementlist ofand thecompare originaleach listnumber intoto sub-list.2 Sub-listuntil containsthere is a number greater than {2}.

* 70 >< 32, so 70 is not added to the sub-list and is removed from the original list.

'''Step 13:''' Iterate through the original list and compare each number to 2 until there is a number greater than 2.

* 3 > 2, so 3 is added to the sub-list and is removed from the original list.

'''Step 1014:''' Now compare 83 with the remaining elements in the original list until there is a number greater than 83.

* 0 < 2 so 0 is not added to the sub-list.

* 37 > 23, so 37 is added to the sub-list and is removed from the original list.

'''Step 1415:''' NowSince there are no more elements in the original list to compare 3{7} withto, the remainingsub-list elementsis inmerged with the solution list. The original list untilnow therecontains {0}, the sub-list is aempty, numberand greatersolution thanlist contains {1, 2, 3., 4, 5, 6, 7, 8, 9}.

* 7 > 3 so 7 is added to the sub-list and is removed from the original list.

'''Step 15:''' Since there are no more elements in the original list to compare {7} to, the sub-list is merged with the solution list. The original list now contains {0}, the sub-list is empty, and solution list contains: {1, 2, 3, 4, 5, 6, 7, 8, 9}.

'''Step 16:'''  Move the first element of the original list into sub-list. Sub-list contains {0}.

'''Step 17:'''  Since the original list is now empty, the sub-list is merged with the solution list. The solution list now contains: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. There are now no more elements in the original list, and all of the elements in the solution list have successfully been sorted into increasing numerical order.

== Implementation ==

Since Strand Sort requires many insertions and deletions, it is best to use a linked list when implementing the algorithm.<ref name=":1">{{Cite web|url=https://xlinux.nist.gov/dads/HTML/strandSort.html|title=strand sort|website=xlinux.nist.gov|language=en-US|access-date=2018-11-06}}</ref> Linked lists require constant time for both insertions and removals of elements using iterators. The time to traverse through the linked list is directly related to the input size of the list.<ref>{{Cite web|url=https://www.cs.cmu.edu/~adamchik/15-121/lectures/Linked%20Lists/linked%20lists.html|title=LinkedLists|website=www.cs.cmu.edu|access-date=2018-11-06}}</ref> The following implementation is done in Java 8 and is based off ofon the description of the algorithm from the book, ''IT Enabled Practices and Emerging Management Paradigms''.<ref name=":0" /><syntaxhighlight lang="java" line="1">

package strandSort;

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[[Category:Sorting algorithms]]