Sort stability

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Task
Sort stability
You are encouraged to solve this task according to the task description, using any language you may know.

When sorting records in a table by a particular column or field, a stable sort will always retain the relative order of records that have the same key.

For example, in this table of countries and cities, a stable sort on the second column, the cities, would keep the US Birmingham above the UK Birmingham. (Although an unstable sort might, in this case, place the US Birmingham above the UK Birmingham, a stable sort routine would guarantee it).

UK  London
US  New York
US  Birmingham
UK  Birmingham

Similarly, stable sorting on just the first column would generate “UK London” as the first item and “US Birmingham” as the last item (since the order of the elements having the same first word – “UK” or “US” – would be maintained).

  1. Examine the documentation on any in-built sort routines supplied by a language.
  2. Indicate if an in-built routine is supplied
  3. If supplied, indicate whether or not the in-built routine is stable.

(This Wikipedia table shows the stability of some common sort routines).

Contents

[edit] AutoHotkey

Autohotkey has got a build-in sorting method for tables, which is stable.

Table =
(
UK, London
US, New York
US, Birmingham
UK, Birmingham
)
 
Gui, Margin, 6
Gui, -MinimizeBox
Gui, Add, ListView, r5 w260 Grid, Orig.Position|Country|City
Loop, Parse, Table, `n, `r
{
StringSplit, out, A_LoopField, `,, %A_Space%
LV_Add("", A_Index, out1, out2)
}
LV_ModifyCol(1, "77 Center")
LV_ModifyCol(2, "100 Center")
LV_ModifyCol(3, 79)
Gui, Add, Button, w80, Restore Order
Gui, Add, Button, x+10 wp, Sort Countries
Gui, Add, Button, x+10 wp, Sort Cities
Gui, Show,, Sort stability
Return
 
GuiClose:
GuiEscape:
ExitApp
 
ButtonRestoreOrder:
LV_ModifyCol(1, "Sort")
Return
 
ButtonSortCountries:
LV_ModifyCol(2, "Sort")
Return
 
ButtonSortCities:
LV_ModifyCol(3, "Sort")
Return

[edit] AWK

 
# syntax: GAWK -f SORT_STABILITY.AWK [-v width=x] -v field=x SORT_STABILITY.TXT
#
# sort by country: GAWK -f SORT_STABILITY.AWK -v field=1 SORT_STABILITY.TXT
# sort by city: GAWK -f SORT_STABILITY.AWK -v field=2 SORT_STABILITY.TXT
#
# awk sort is not stable. Stability may be achieved by appending the
# record number, I.E. NR, to each key.
#
BEGIN {
FIELDWIDTHS = "4 20" # 2 fields: country city
PROCINFO["sorted_in"] = "@ind_str_asc"
if (width == "") {
width = 6
}
}
{ arr[$field sprintf("%0*d",width,NR)] = $0 }
END {
if (length(NR) > width) {
printf("error: sort may still be unstable; change width to %d\n",length(NR))
exit(1)
}
printf("after sorting on field %d:\n",field)
for (i in arr) {
printf("%s\n",arr[i])
}
exit(0)
}
 

input:

UK  London
US  New York
US  Birmingham
UK  Birmingham

output from: GAWK -f SORT_STABILITY.AWK -v field=1 SORT_STABILITY.TXT

after sorting on field 1:
UK  London
UK  Birmingham
US  New York
US  Birmingham

output from: GAWK -f SORT_STABILITY.AWK -v field=2 SORT_STABILITY.TXT

after sorting on field 2:
US  Birmingham
UK  Birmingham
UK  London
US  New York

[edit] BBC BASIC

The supplied SORTLIB library currently uses a Shell Sort, so it is not stable.

[edit] C

There is no built-in function in C language. stdlib which comes with any C implementation is required to provide a qsort() routine that can sort arbitrary datatypes. Although the sorting algorithm is not specified, most (all?) implementions use a combined quicksort/insertion sort method for efficiency. Quicksort is by nature unstable.

[edit] C++

C++ standard library's std::sort() function is not guaranteed stable. The stable analog of it is the std::stable_sort() function. In addition, std::list's sort() method is guaranteed stable.

[edit] C#

The .NET library documentation for Array.Sort() says that it uses quicksort and is unstable.[1]

[edit] Clojure

Clojure's sort and sort-by functions are implemented using Java's java.utils.Array.sort methods, which are guaranteed stable.

[edit] Common Lisp

Common Lisp provides the two functions sort and stable-sort.

[edit] D

In the std.algorithm Phobos v.2 module there is SwapStrategy that defines the swapping strategy for algorithms like sort and partition.

Unstable, stable and semistable (in algorithms that partition ranges in two, semistable preserves stability on just the left of the partition point) are supported.

[edit] Déjà Vu

The included sorting algorithm, sort, is stable.

[edit] Erlang

The function lists:sort/1 is not documented as stable. The function lists:keysort/2 is documented as stable.

[edit] Factor

The sorting vocabulary implements a stable sort. sorting docs

[edit] F#

Array.sort is not stable. List.sort and Seq.sort are stable.

[edit] GAP

# According to section 21.18 of the reference manual, Sort is not stable (it's a Shell sort).
# However, SortingPerm is stable. We will see it on an example, showing indexes of elements after the sort.
 
n := 20;
L := List([1 .. n], i -> Random("AB"));
# "AABABBBABBABAABABBAB"
 
 
p := SortingPerm(L);
# (3,10,15,17,18,19,9,14,7,13,6,12,16,8,4)(5,11)
 
a := Permuted(L, p);;
b := Permuted([1 .. n], p);;
 
PrintArray(TransposedMat(List([1 .. n], i -> [a[i], b[i]])));
# [ [ 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B' ],
# [ 1, 2, 4, 8, 11, 13, 14, 16, 19, 3, 5, 6, 7, 9, 10, 12, 15, 17, 18, 20 ] ]

[edit] Go

New to Go 1.2 is the function Stable() in the sort package and is documented to be a stable sort. Other sort functions are documented to have no guarantee of stability.

[edit] Groovy

Groovy's Collection.sort(), Object[].sort(), Map.sort(), and their various and sundry overloads all use the same stable sort algorithm.

Example:

Translation of: Java
Works with: Groovy version 1.8.1
def cityList = ['UK  London', 'US  New York', 'US  Birmingham', 'UK  Birmingham',].asImmutable()
[
'Sort by city': { city -> city[4..-1] },
'Sort by country': { city -> city[0..3] },
].each{ String label, Closure orderBy ->
println "\n\nBefore ${label}"
cityList.each { println it }
println "\nAfter ${label}"
cityList.sort(false, orderBy).each{ println it }
}

Output:

Before Sort by city
UK  London
US  New York
US  Birmingham
UK  Birmingham

After Sort by city
US  Birmingham
UK  Birmingham
UK  London
US  New York


Before Sort by country
UK  London
US  New York
US  Birmingham
UK  Birmingham

After Sort by country
UK  London
UK  Birmingham
US  New York
US  Birmingham

[edit] Haskell

Haskell's sort and sortBy functions are guaranteed stable.[2]

[edit] Icon and Unicon

Icon and Unicon use Quick Sort internally. As described in The Implementation of Icon and Unicon: a Compendium] sorting is done by the standard C library routine qsort which is not guaranteed to be stable.

Note(1): The built-in sort handles lists of mixed types by sorting first by type and then value. No coercion of types is performed. The sort order of types is: &null, integer, real, string, cset, procedure, list, set, table, record.

[edit] J

J's grade primitive /:, and therefore its sort (such as /:~), are guaranteed stable.

From the dictionary page for /: : "Elements of /:y that select equal elements of y are in ascending order."

[edit] Java

Java's Collections.sort() and Arrays.sort() methods are guaranteed stable.

The following sample demonstrates Java's sort stability:

import java.util.Arrays;
import java.util.Comparator;
 
public class RJSortStability {
 
public static void main(String[] args) {
String[] cityList = { "UK London", "US New York", "US Birmingham", "UK Birmingham", };
 
String[] cn = cityList.clone();
System.out.println("\nBefore sort:");
for (String city : cn) {
System.out.println(city);
}
 
// sort by city
Arrays.sort(cn, new Comparator<String>() {
public int compare(String lft, String rgt) {
return lft.substring(4).compareTo(rgt.substring(4));
}
});
 
System.out.println("\nAfter sort on city:");
for (String city : cn) {
System.out.println(city);
}
 
cn = cityList.clone();
System.out.println("\nBefore sort:");
for (String city : cn) {
System.out.println(city);
}
 
// sort by country
Arrays.sort(cn, new Comparator<String>() {
public int compare(String lft, String rgt) {
return lft.substring(0, 2).compareTo(rgt.substring(0, 2));
}
});
 
System.out.println("\nAfter sort on country:");
for (String city : cn) {
System.out.println(city);
}
 
System.out.println();
}
}
Output
Before sort:
UK  London
US  New York
US  Birmingham
UK  Birmingham

After sort on city:
US  Birmingham
UK  Birmingham
UK  London
US  New York

Before sort:
UK  London
US  New York
US  Birmingham
UK  Birmingham

After sort on country:
UK  London
UK  Birmingham
US  New York
US  Birmingham

[edit] JavaScript

The ECMA standard does not specify what sorting algorithm to use, so it depends upon the implementation.

ary = [["UK", "London"], ["US", "New York"], ["US", "Birmingham"], ["UK", "Birmingham"]]
print(ary);
 
ary.sort(function(a,b){return (a[1]<b[1] ? -1 : (a[1]>b[1] ? 1 : 0))});
print(ary);
 
/* a stable sort will output ["US", "Birmingham"] before ["UK", "Birmingham"] */

Stable implementations:

Works with: SpiderMonkey version 1.8
Works with: Firefox version 3
Works with: Internet Explorer version 6
Works with: JScript version 5.7
Works with: OSSP js
UK,London,US,New York,US,Birmingham,UK,Birmingham
US,Birmingham,UK,Birmingham,UK,London,US,New York

Not stable:

Works with: Rhino version 1.7 rel 2
Works with: Google Chrome version 3.0
UK,London,US,New York,US,Birmingham,UK,Birmingham
UK,Birmingham,US,Birmingham,UK,London,US,New York

[edit] Julia

Julia's built-in sort function is documented to be stable by default (although non-stable sort algorithms can optionally be selected).

julia> A = [("UK", "London"), ("US", "New York"), ("US", "Birmingham"), ("UK", "Birmingham")];
julia> sort(A, by=x -> x[2])
4-element Array{(ASCIIString,ASCIIString),1}:
 ("US","Birmingham")
 ("UK","Birmingham")
 ("UK","London")    
 ("US","New York") 

[edit] Lasso

Arrays can be sorted in two “built in" ways in Lasso:

//Single param array:
array->sort
 
//An array of pairs, order by the right hand element of the pair:
with i in array order by #i->second do => { … }
 
//The array can also be ordered by multiple values:
with i in array order by #i->second, #i->first do => { … }

Sorting of arrays by either method uses “Qucksort” and is therefore unstable. A simulation of increasing sort stability would be introduced with additional params such as the example of ordering by the second then the first pair values in the example above - but would not be guaranteed stable.

  • Note this explanation of sorting does not cover ordering by properties of complex objects, which is also possible using query expressions.

Sort by second value only:

local(a = array('UK'='London','US'='New York','US'='Birmingham','UK'='Birmingham'))
with i in #a order by #i->second do => {^ #i->first+' - '+#i->second+'\r' ^}
Output:
US - Birmingham
UK - Birmingham
UK - London
US - New York

Sort by second then by first:

local(a = array('UK'='London','US'='New York','US'='Birmingham','UK'='Birmingham'))
with i in #a order by #i->second, #i->first do => {^ #i->first+' - '+#i->second+'\r' ^}
Output:
UK - Birmingham
US - Birmingham
UK - London
US - New York

[edit] Lua

The built-in function table.sort is not guaranteed stable.

[edit] Mathematica

Sort is not always stable. Ordering, which gives a list of indices such as to put the elements of the list in order, is stable. An example would be to sort the list (of lists) {{1, 2, 3}, {4, 5, 6}, {5, 4, 3}, {9, 5, 1}}, and doing so by looking at the 2nd value of each list:

mylist = {{1, 2, 3}, {4, 5, 6}, {5, 4, 3}, {9, 5, 1}};
Sort[mylist, (#1[[2]] < #2[[2]]) &]
#[[Ordering[#[[All, 2]]]]] &[mylist]

gives:

{{1, 2, 3}, {5, 4, 3}, {9, 5, 1}, {4, 5, 6}}
{{1, 2, 3}, {5, 4, 3}, {4, 5, 6}, {9, 5, 1}}

Showing that Sort is unstable, and that by using input[[Ordering[input]]] Ordering provides a way to make a stable sort.

[edit] MATLAB

MathWorks' policy seems to be that their built-in sorting algorithm will always be a stable sort across all versions (reference). To check to see if your version of MATLAB provides a stable sort,check the output of command "help sort".

[edit] NetRexx

Java's Collections.sort() and Arrays.sort() methods are guaranteed stable. The following sample takes advantage of this to demonstrate sort stability.

/* NetRexx */
options replace format comments java crossref savelog symbols nobinary
 
class RCSortStability
 
method main(args = String[]) public constant
 
cityList = [String "UK London", "US New York", "US Birmingham", "UK Birmingham"]
 
cn = String[cityList.length]
 
say
say "Before sort:"
System.arraycopy(cityList, 0, cn, 0, cityList.length)
loop city = 0 to cn.length - 1
say cn[city]
end city
 
cCompNm = Comparator CityComparator()
Arrays.sort(cn, cCompNm)
 
say
say "After sort on city:"
loop city = 0 to cn.length - 1
say cn[city]
end city
 
say
say "Before sort:"
System.arraycopy(cityList, 0, cn, 0, cityList.length)
loop city = 0 to cn.length - 1
say cn[city]
end city
 
cCompCtry = Comparator CountryComparator()
Arrays.sort(cn, cCompCtry)
 
say
say "After sort on country:"
loop city = 0 to cn.length - 1
say cn[city]
end city
say
 
return
 
class RCSortStability.CityComparator implements Comparator
 
method compare(lft = Object, rgt = Object) public binary returns int
return (String lft).substring(4).compareTo((String rgt).substring(4))
 
class RCSortStability.CountryComparator implements Comparator
 
method compare(lft = Object, rgt = Object) public binary returns int
return (String lft).substring(0, 2).compareTo((String rgt).substring(0, 2))
 
Output
Before sort:
UK  London
US  New York
US  Birmingham
UK  Birmingham

After sort on city:
US  Birmingham
UK  Birmingham
UK  London
US  New York

Before sort:
UK  London
US  New York
US  Birmingham
UK  Birmingham

After sort on country:
UK  London
UK  Birmingham
US  New York
US  Birmingham

[edit] Nimrod

Default Nimrod sort in the algorithm module is stable.

[edit] OCaml

OCaml's List.sort and Array.sort functions are not guaranteed to be stable. The stable versions are List.stable_sort and Array.stable_sort, respectively.

[edit] ooRexx

Open Object Rexx provides sort methods (sort and sortWith(comparator)) for its collection classes. By default these sort methods are implemented via an unstable Quicksort algorithm but the language does provide stable sorting methods (stableSort and stableSortWith(comparator)) implemented via a stable Mergesort algorithm.

/* Rexx */
Do
cities = .array~of('UK London', 'US New York', 'US Birmingham', 'UK Birmingham',)
 
Say; Say 'Original table'
Call display cities
 
Say; Say 'Unstable sort on city'
sorted = cities~copy
sorted~sortWith(.ColumnComparator~new(4, 20))
Call display sorted
 
Say; Say 'Stable sort on city'
sorted = cities~copy
sorted~stableSortWith(.ColumnComparator~new(4, 20))
Call display sorted
 
Say; Say 'Unstable sort on country'
sorted = cities~copy
sorted~sortWith(.ColumnComparator~new(1, 2))
Call display sorted
 
Say; Say 'Stable sort on country'
sorted = cities~copy
sorted~stableSortWith(.ColumnComparator~new(1, 2))
Call display sorted
 
Return
End
Exit
 
display: Procedure
Do
Use arg CT
 
Say '-'~copies(80)
Loop c_ over CT
Say c_
End c_
 
Return
End
Exit
 
Output
Original table
--------------------------------------------------------------------------------
UK  London
US  New York
US  Birmingham
UK  Birmingham

Unstable sort on city
--------------------------------------------------------------------------------
UK  Birmingham
US  Birmingham
UK  London
US  New York

Stable sort on city
--------------------------------------------------------------------------------
US  Birmingham
UK  Birmingham
UK  London
US  New York

Unstable sort on country
--------------------------------------------------------------------------------
UK  London
UK  Birmingham
US  Birmingham
US  New York

Stable sort on country
--------------------------------------------------------------------------------
UK  London
UK  Birmingham
US  New York
US  Birmingham

[edit] OpenEdge/Progress

The results can be forced to stable by additionally sorting on the ROWID of the record. If you leave the additional sort out, the indexes on the temp-table can influence the result.

DEFINE TEMP-TABLE tt
FIELD country AS CHAR FORMAT 'x(2)'
FIELD city AS CHAR FORMAT 'x(16)'
.
 
DEFINE VARIABLE cc AS CHARACTER EXTENT 2.
 
CREATE tt. ASSIGN tt.country = 'UK' tt.city = 'London'.
CREATE tt. ASSIGN tt.country = 'US' tt.city = 'New York'.
CREATE tt. ASSIGN tt.country = 'US' tt.city = 'Birmingham'.
CREATE tt. ASSIGN tt.country = 'UK' tt.city = 'Birmingham'.
 
cc[1] = 'by country~n~n'.
FOR EACH tt BY tt.country BY ROWID( tt ):
cc[1] = cc[1] + tt.country + '~t' + tt.city + '~n'.
END.
 
cc[2] = 'by city~n~n'.
FOR EACH tt BY tt.city BY ROWID( tt ):
cc[2] = cc[2] + tt.country + '~t' + tt.city + '~n'.
END.
 
MESSAGE
cc[1] SKIP(1) cc[2]
VIEW-AS ALERT-BOX.

Output:

---------------------------
Message
---------------------------
by country

UK	London
UK	Birmingham
US	New York
US	Birmingham


by city

US	Birmingham
UK	Birmingham
UK	London
US	New York
---------------------------
OK   
---------------------------

[edit] Oz

Oz' Sort function is not guaranteed to be stable in the documentation.

However, internally it uses Merge sort and in practice is stable if a reflexive ordering is used, e.g. Value.'=<' or Value.'>='.

Example:

declare
Cities = ['UK'#'London'
'US'#'New York'
'US'#'Birmingham'
'UK'#'Birmingham']
in
%% sort by city; stable because '=<' is reflexiv
{Show {Sort Cities fun {$ A B} A.2 =< B.2 end}}
 
%% sort by country; NOT stable because '<' is not reflexiv
{Show {Sort Cities fun {$ A B} A.1 < B.1 end}}

[edit] PARI/GP

Pari's vecsort is stable, see 3.8.60 in the User's Guide. In particular, it uses a merge sort.

[edit] Pascal

Standard Pascal has no built-in routine for sorting. The RTL of FreePascal uses Quicksort for TList, TFPList and TStringList in the Classes unit.

[edit] Perl

The stability of Perl's in-built sort function is version-dependent. If you want to guarantee a stable sort from it, you should use the following sort pragma:

use sort 'stable';

[edit] Perl 6

The sort built-in (available as sub and method) is stable.

Short demonstration for sorting only on the second item of each array:

use v6;
my @cities =
['UK', 'London'],
['US', 'New York'],
['US', 'Birmingham'],
['UK', 'Birmingham'],
;
 
.say for @cities.sort: { .[1] };

[edit] PHP

PHP uses QuickSort for most of its sort functions so it is unstable. [3]

[edit] PicoLisp

The sort function is unstable

[edit] PureBasic

PureBasic's includes two built-in sort functions for arrays, SortArray() and SortStructuredArray(), and two built-in sort functions for linked lists, SortList() and SortStructuredList(). Sorting of linked lists is stable and uses a merge-sort, while sorting for arrays is unstable and uses a quicksort.

[edit] Python

Python's in-built sorted function as well as the sort method of lists are guaranteed stable (since version 2.3). (For even more information on the underlying routine, wp:timsort, see this).

[edit] R

R uses shell sort (stable) or quick sort (unstable). An easy way to show the difference is names to vector entries, then check if names are still ordered after sorting.

 
# First, define a bernoulli sample, of length 26.
x <- sample(c(0, 1), 26, replace=T)
 
x
# [1] 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 0
 
# Give names to the entries. "letters" is a builtin value
names(x) <- letters
 
x
# a b c d e f g h i j k l m n o p q r s t u v w x y z
# 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 0
 
# The unstable one, see how "a" appears after "l" now
sort(x, method="quick")
# z h s u e q x n j r t v w y p o m l a i g f d c b k
# 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
# The stable sort, letters are ordered in each section
sort(x, method="shell")
# e h j n q s u x z a b c d f g i k l m o p r t v w y
# 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 

[edit] Racket

Racket comes with a standard sort function, which is documented [here]. It is documented as stable.

 
#lang racket
 
(sort '(("UK" "London")
("US" "New York")
("US" "Birmingham")
("UK" "Birmingham"))
string<? #:key first)
;; -> (("UK" "London") ("UK" "Birmingham")
;; ("US" "New York") ("US" "Birmingham"))
 
(sort '(("UK" "London")
("US" "New York")
("US" "Birmingham")
("UK" "Birmingham"))
string<? #:key second)
;; -> '(("US" "Birmingham") ("UK" "Birmingham")
;; ("UK" "London") ("US" "New York"))
 

[edit] REBOL

; REBOL's sort function is not stable by default. You need to use a custom comparator to make it so.
 
blk: [
[UK London]
[US New-York]
[US Birmingham]
[UK Birmingham]
]
sort/compare blk func [a b] [either a/2 < b/2 [-1] [either a/2 > b/2 [1] [0]]]
 
; Note that you can also do a stable sort without nested blocks.
blk: [
UK London
US New-York
US Birmingham
UK Birmingham
]
sort/skip/compare blk 2 func [a b] [either a < b [-1] [either a > b [1] [0]]]

[edit] REXX

A Rexx implementation of this task can be found here in the ooRexx solution.

[edit] Ruby

Ruby's built-in sort methods (Array#sort, Array#sort!, Array#sort_by!, Enumerable#sort and Enumerable#sort_by) are not stable. MRI uses quicksort, which is not stable (1). It seems that stable sorting is not worth the performance trade-off; MRI rejected a proposal to switch to a stable sort (2).

Works with: MRI version 1.8.7, 1.9.2
ary = [["UK", "London"],
["US", "New York"],
["US", "Birmingham"],
["UK", "Birmingham"]]
p ary.sort {|a,b| a[1] <=> b[1]}
# MRI reverses the Birminghams:
# => [["UK", "Birmingham"], ["US", "Birmingham"], ["UK", "London"], ["US", "New York"]]

Other implementations of Ruby might differ. Old versions of JRuby used java.util.Arrays.sort, which was a stable sort, but was slower than MRI. To increase performance, JRuby switched to quicksort, which is not stable. (3)

[edit] Stable sort in Ruby

To code a stable sort, without implementing another sorting algorithm (such as merge sort), use a Schwartzian transform.

class Array
def stable_sort
n = -1
if block_given?
collect {|x| n += 1; [x, n]
}.sort! {|a, b|
c = yield a[0], b[0]
if c.nonzero? then c else a[1] <=> b[1] end
}.collect! {|x| x[0]}
else
sort_by {|x| n += 1; [x, n]}
end
end
 
def stable_sort_by
block_given? or return enum_for(:stable_sort_by)
n = -1
sort_by {|x| n += 1; [(yield x), n]}
end
end
ary = [["UK", "London"],
["US", "New York"],
["US", "Birmingham"],
["UK", "Birmingham"]]
p ary.stable_sort {|a, b| a[1] <=> b[1]}
# => [["US", "Birmingham"], ["UK", "Birmingham"], ["UK", "London"], ["US", "New York"]]
p ary.stable_sort_by {|x| x[1]}
# => [["US", "Birmingham"], ["UK", "Birmingham"], ["UK", "London"], ["US", "New York"]]

[edit] Scala

Works with: Scala version 2.8

There are two sort methods defined on Seq, which is the base collection trait for all sequences. The methods are sortWith and sortBy, and differ only on the argument used. The first expects a function that will implement the "less than" method for the type of the sequence. The second expects a function from the type of the sequence into any type for which there is an Ordering, plus an implicit Ordering of the proper type.

The sort is stable.

Examples:

scala> val list = List((1, 'c'), (1, 'b'), (2, 'a'))
list: List[(Int, Char)] = List((1,c), (1,b), (2,a))
 
scala> val srt1 = list.sortWith(_._2 < _._2)
srt1: List[(Int, Char)] = List((2,a), (1,b), (1,c))
 
scala> val srt2 = srt1.sortBy(_._1) // Ordering[Int] is implicitly defined
srt2: List[(Int, Char)] = List((1,b), (1,c), (2,a))
 
scala> val cities = """
| |UK London
| |US New York
| |US Birmingham
| |UK Birmingham
| |"
"".stripMargin.lines.filterNot(_ isEmpty).toSeq
cities: Seq[String] = ArrayBuffer(UK London, US New York, US Birmingham, UK Birmingham)
 
scala> cities.sortBy(_ substring 4)
res47: Seq[String] = ArrayBuffer(US Birmingham, UK Birmingham, UK London, US New York)

Besides that, there is the object scala.util.Sorting, which provides quickSort<tt> and <tt>stableSort. The former is only provided on Array, but the latter is provided over both Array and Seq. These sorts operate in-place, with the one over Seq returning a sorted Array. Here is one example:

scala> val cityArray = cities.toArray
cityArray: Array[String] = Array(UK London, US New York, US Birmingham, UK Birmingham)
 
scala> scala.util.Sorting.stableSort(cityArray, (_: String).substring(4) < (_: String).substring(4))
 
scala> cityArray
res56: Array[String] = Array(US Birmingham, UK Birmingham, UK London, US New York)

[edit] Tcl

Tcl's built-in lsort command implements a stable sort. It has been guaranteed to be stable since Tcl 8.0. Internally, it uses the mergesort algorithm.

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