Sorting algorithms/Comb sort
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The Comb Sort is a variant of the Bubble Sort. Like the Shell sort, the Comb Sort increases the gap used in comparisons and exchanges (dividing the gap by works best, but 1.3 may be more practical). Some implementations use the insertion sort once the gap is less than a certain amount. See the article on Wikipedia. Variants:
- Combsort11 makes sure the gap ends in (11, 8, 6, 4, 3, 2, 1), which is significantly faster than the other two possible endings
- Combsort with different endings changes to a more efficient sort when the data is almost sorted (when the gap is small). Comb sort with a low gap isn't much better than the Bubble Sort.
Pseudocode:
function combsort(array input) gap := input.size //initialize gap size loop until gap = 1 and swaps = 0 //update the gap value for a next comb. Below is an example gap := int(gap / 1.25) if gap < 1 //minimum gap is 1 gap := 1 end if i := 0 swaps := 0 //see Bubble Sort for an explanation //a single "comb" over the input list loop until i + gap >= input.size //see Shell sort for similar idea if input[i] > input[i+gap] swap(input[i], input[i+gap]) swaps := 1 // Flag a swap has occurred, so the // list is not guaranteed sorted end if i := i + 1 end loop end loop end function
ActionScript
<lang ActionScript>function combSort(input:Array) { var gap:uint = input.length; var swapped:Boolean = false; while(gap > 1 || swapped) { gap /= 1.25; swapped = false; for(var i:uint = 0; i + gap < input.length; i++) { if(input[i] > input[i+gap]) { var tmp = input[i]; input[i] = input[i+gap]; input[i+gap]=tmp; swapped = true; } } } return input; }</lang>
AutoHotkey
<lang autohotkey>List1 = 23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78 List2 = 88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70
List2Array(List1, "MyArray") CombSort("MyArray") MsgBox, % List1 "`n" Array2List("MyArray")
List2Array(List2, "MyArray") CombSort("MyArray") MsgBox, % List2 "`n" Array2List("MyArray")
- ---------------------------------------------------------------------------
CombSort(Array) { ; CombSort of Array %Array%, length = %Array%0
- ---------------------------------------------------------------------------
Gap := %Array%0 While Gap > 1 Or Swaps { If (Gap > 1) Gap := 4 * Gap // 5 i := Swaps := False While (j := ++i + Gap) <= %Array%0 { If (%Array%%i% > %Array%%j%) { Swaps := True %Array%%i% := (%Array%%j% "", %Array%%j% := %Array%%i%) } } }
}
- ---------------------------------------------------------------------------
List2Array(List, Array) { ; creates an array from a comma separated list
- ---------------------------------------------------------------------------
global StringSplit, %Array%, List, `,
}
- ---------------------------------------------------------------------------
Array2List(Array) { ; returns a comma separated list from an array
- ---------------------------------------------------------------------------
Loop, % %Array%0 List .= (A_Index = 1 ? "" : ",") %Array%%A_Index% Return, List
}</lang> Message (1) box shows:
23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78 12,14,23,24,24,31,35,38,46,51,57,57,58,76,78,89,92,95,97,99
Message (2) box shows:
88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70 0,4,5,8,14,18,20,31,33,44,62,70,73,75,76,78,81,82,84,88
BBC BASIC
<lang BBC BASIC>DEF PROC_CombSort11(Size%)
gap%=Size% REPEAT
IF gap% > 1 THEN gap%=gap% / 1.3 IF gap%=9 OR gap%=10 gap%=11 ENDIF I% = 1 Finished%=TRUE REPEAT IF data%(I%) > data%(I%+gap%) THEN SWAP data%(I%),data%(I%+gap%) Finished% = FALSE ENDIF I%+=1 UNTIL I%+gap% > Size%
UNTIL gap%=1 AND Finished%
ENDPROC</lang>
C
Implementation of Combsort11. Its efficiency can be improved by just switching to Insertion sort when the gap size becomes less than 10. <lang c>void Combsort11(double a[], int nElements) {
int i, j, gap, swapped = 1; double temp;
gap = nElements; while (gap > 1 || swapped == 1) { gap = gap * 10 / 13; if (gap == 9 || gap == 10) gap = 11; if (gap < 1) gap = 1; swapped = 0; for (i = 0, j = gap; j < nElements; i++, j++) { if (a[i] > a[j]) { temp = a[i]; a[i] = a[j]; a[j] = temp; swapped = 1; } } }
}</lang>
C++
This is copied from the Wikipedia article. <lang cpp>template<class ForwardIterator> void combsort ( ForwardIterator first, ForwardIterator last ) {
static const double shrink_factor = 1.247330950103979; typedef typename std::iterator_traits<ForwardIterator>::difference_type difference_type; difference_type gap = std::distance(first, last); bool swaps = true; while ( (gap > 1) || (swaps == true) ){ if (gap > 1) gap = static_cast<difference_type>(gap/shrink_factor); swaps = false; ForwardIterator itLeft(first); ForwardIterator itRight(first); std::advance(itRight, gap); for ( ; itRight!=last; ++itLeft, ++itRight ){ if ( (*itRight) < (*itLeft) ){ std::iter_swap(itLeft, itRight); swaps = true; } } }
}</lang>
C#
<lang csharp>using System;
namespace CombSort {
class Program { static void Main(string[] args) { int[] unsorted = new int[] { 3, 5, 1, 9, 7, 6, 8, 2, 4 }; Console.WriteLine(string.Join(",", combSort(unsorted))); } public static int[] combSort(int[] input) { double gap = input.Length; bool swaps = true; while (gap > 1 || swaps) { gap /= 1.247330950103979; if (gap < 1) { gap = 1; } int i = 0; swaps = false; while (i + gap < input.Length) { int igap = i + (int)gap; if (input[i] > input[igap]) { int swap = input[i]; input[i] = input[igap]; input[igap] = swap; swaps = true; } i++; } } return input; } }
}</lang>
COBOL
This excerpt contains just enough of the procedure division to show the workings. See the example for the bubble sort for a more complete program. <lang COBOL> C-PROCESS SECTION.
C-000. DISPLAY "SORT STARTING".
MOVE WC-SIZE TO WC-GAP.
PERFORM E-COMB UNTIL WC-GAP = 1 AND FINISHED.
DISPLAY "SORT FINISHED".
C-999. EXIT.
E-COMB SECTION. E-000. IF WC-GAP > 1 DIVIDE WC-GAP BY 1.3 GIVING WC-GAP IF WC-GAP = 9 OR 10 MOVE 11 TO WC-GAP.
MOVE 1 TO WC-SUB-1. MOVE "Y" TO WF-FINISHED.
PERFORM F-SCAN UNTIL WC-SUB-1 + WC-GAP > WC-SIZE.
E-999. EXIT.
F-SCAN SECTION. F-000. ADD WC-SUB-1 WC-GAP GIVING WC-SUB-2. IF WB-ENTRY(WC-SUB-1) > WB-ENTRY(WC-SUB-2) MOVE WB-ENTRY(WC-SUB-1) TO WC-TEMP MOVE WB-ENTRY(WC-SUB-2) TO WB-ENTRY(WC-SUB-1) MOVE WC-TEMP TO WB-ENTRY(WC-SUB-2) MOVE "N" TO WF-FINISHED.
ADD 1 TO WC-SUB-1.
F-999. EXIT.</lang>
D
<lang d>import std.algorithm, std.stdio;
void combsort(T)(T[] input) {
int gap = input.length; bool swaps = true; while (gap > 1 || swaps) { gap = max(1, cast(int)(gap / 1.2473)); // minimum gap is 1 swaps = false; foreach (i; 0 .. input.length - gap) if (input[i] > input[i + gap]) { swap(input[i], input[i + gap]); swaps = true; } }
}
void main() {
auto a = [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70]; combsort(a); assert(a == a.dup.sort); writeln(a);
}</lang>
Forth
This is an implementation of Comb sort with a different ending. Here Gnome sort is used, since it is rather small. The dataset is rather large, because otherwise the Comb sort routine would never kick in, passing control to Gnome sort almost right away. Note Comb sort can be kept much simpler this way, because Combsort11 optimizations and swapped flags can be discarded. <lang forth>defer precedes defer exchange
- gnomesort ( a n)
swap >r 1 ( n c) begin ( n c) over over > ( n c f) while ( n c) dup if ( n c) dup dup 1- over over r@ precedes if r@ exchange 1- else drop drop 1+ then else 1+ then ( n c) repeat drop drop r> drop ( --)
- combsort ( a n --)
dup begin ( a n g) 10 13 */ tuck >r >r 0 ( a g 0) begin ( a g 0) over r@ < ( a g 0 f) while ( a g 0) rot >r over over r@ precedes ( g 0 f) if over over r@ exchange then ( g 0) r> rot 1+ rot 1+ ( a g 0) repeat drop drop r> r> ( a n g) dup 9 < ( a n g f) until drop gnomesort ( --)
create example
8 93 69 52 50 79 33 52 19 77 , , , , , , , , , , 72 85 11 61 64 80 64 76 47 65 , , , , , , , , , , 13 47 23 40 87 45 2 48 22 69 , , , , , , , , , , 1 53 33 60 57 14 76 32 59 12 , , , , , , , , , , 74 38 39 22 87 28 37 93 71 88 , , , , , , , , , , 56 35 48 99 21 35 26 28 58 85 , , , , , , , , , , 27 16 54 88 82 18 45 64 45 87 , , , , , , , , , , 98 97 60 77 43 1 64 0 32 89 , , , , , , , , , , 77 90 68 83 9 76 10 10 95 12 , , , , , , , , , , 99 23 74 58 54 25 50 9 94 1 , , , , , , , , , ,
- noname >r cells r@ + @ swap cells r> + @ swap < ; is precedes
- noname >r cells r@ + swap cells r> + over @ over @ swap rot ! swap ! ; is exchange
- .array 100 0 do example i cells + ? loop cr ;
.array example 100 combsort .array</lang>
Haskell
<lang haskell>import Data.List import Control.Arrow import Control.Monad
flgInsert x xs = ((x:xs==) &&& id)$ insert x xs
gapSwapping k = (and *** concat. transpose). unzip
. map (foldr (\x (b,xs) -> first (b &&)$ flgInsert x xs) (True,[])) . transpose. takeWhile (not.null). unfoldr (Just. splitAt k)
combSort xs = (snd. fst) $ until (\((b,_),g)-> b && g==1)
(\((_,xs),g) ->(gapSwapping g xs, fg g)) ((False,xs), fg $ length xs) where fg = max 1. truncate. (/1.25). fromIntegral</lang>
Example: <lang haskell>*Main> combSort [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78] [12,14,23,24,24,31,35,38,46,51,57,57,58,76,78,89,92,95,97,99]</lang>
Io
<lang io>List do(
combSortInPlace := method( gap := size swap := true
while(gap > 1 or swap, swap = false gap = (gap / 1.25) floor
for(i, 0, size - gap, if(at(i) > at(i + gap), swap = true swapIndices(i, i + gap) ) ) ) self)
)
lst := list(23, 76, 99, 58, 97, 57, 35, 89, 51, 38, 95, 92, 24, 46, 31, 24, 14, 12, 57, 78) lst combSortInPlace println # ==> list(12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99)</lang>
J
Large gap sizes allow some parallelism in comparisons and swaps. (If the gap size is G, then G pairs can be compared and swapped in parallel.) Beyond that, however, the data flow complexity of this algorithm requires a fair bit of micro-management.
<lang J>combSort=:3 :0
gap=. #y whilst.1 < gap+swaps do. swaps=. 0 i=. i.2,gap=. 1 >. <.gap%1.25 while.{:$i=.i #"1~ ({: i) < #y do. swaps=.swaps+#{:k=.i #"1~b=. >/ i{y i=. i+gap y=.((|.k){y) k} y end. end. y
)</lang>
Example use:
combSort 23 76 99 58 97 57 35 89 51 38 95 92 24 46 31 24 14 12 57 78 12 14 23 24 24 31 35 38 46 51 57 57 58 76 78 89 92 95 97 99 combSort 88 18 31 44 4 0 8 81 14 78 20 76 84 33 73 75 82 5 62 70 0 4 5 8 14 18 20 31 33 44 62 70 73 75 76 78 81 82 84 88
Java
This is copied from the Wikipedia article. <lang java>public static <E extends Comparable<? super E>> void sort(E[] input) {
int gap = input.length; boolean swapped = true; while (gap > 1 || swapped) { if (gap > 1) { gap = (int) (gap / 1.3); } swapped = false; for (int i = 0; i + gap < input.length; i++) { if (input[i].compareTo(input[i + gap]) > 0) { E t = input[i]; input[i] = input[i + gap]; input[i + gap] = t; swapped = true; } } }
}</lang>
Lua
<lang lua>function combsort(t)
local gapd, gap, swaps = 1.2473, #t, 0 while gap + swaps > 1 do local k = 0 swaps = 0 if gap > 1 then gap = math.floor(gap / gapd) end for k = 1, #t - gap do if t[k] > t[k + gap] then t[k], t[k + gap], swaps = t[k + gap], t[k], swaps + 1 end end end return t
end
print(unpack(combsort{3,5,1,2,7,4,8,3,6,4,1}))</lang>
MATLAB
<lang MATLAB>function list = combSort(list)
listSize = numel(list); gap = int32(listSize); %Coerce gap to an int so we can use the idivide function swaps = true; %Swap flag while not((gap <= 1) && (swaps == false)) gap = idivide(gap,1.25,'floor'); %Int divide, floor the resulting operation if gap < 1 gap = 1; end i = 1; %i equals 1 because all arrays are 1 based in MATLAB swaps = false; %i + gap must be subtracted by 1 because the pseudo-code was writen %for 0 based arrays while not((i + gap - 1) >= listSize) if (list(i) > list(i+gap)) list([i i+gap]) = list([i+gap i]); %swap swaps = true; end i = i + 1; end %while end %while
end %combSort</lang>
Sample Output: <lang MATLAB>>> combSort([4 3 1 5 6 2])
ans =
1 2 3 4 5 6</lang>
OCaml
<lang ocaml>let comb_sort ~input =
let input_length = Array.length input in let gap = ref(input_length) in let swapped = ref true in while (!gap > 1 || !swapped) do if (!gap > 1) then gap := int_of_float (float !gap /. 1.3);
let i = ref 0 in swapped := false; while (!i + !gap < input_length) do if input.(!i) > input.(!i + !gap) then begin let tmp = input.(!i) in input.(!i) <- input.(!i + !gap); input.(!i + !gap) <- tmp; swapped := true; end; incr i; done done
- </lang>
Oz
<lang oz>declare
proc {CombSort Arr} Low = {Array.low Arr} High = {Array.high Arr} Size = High - Low + 1 Gap = {NewCell Size} Swapped = {NewCell true} proc {Swap I J} Arr.J := (Arr.I := Arr.J) end in for while:@Gap>1 orelse @Swapped do if @Gap > 1 then Gap := {Float.toInt {Floor {Int.toFloat @Gap} / 1.3}} end Swapped := false for I in Low..High-@Gap do if Arr.I > Arr.(I+@Gap) then {Swap I I+@Gap} Swapped := true end end end end Arr = {Tuple.toArray unit(3 1 4 1 5 9 2 6 5)}
in
{CombSort Arr} {Show {Array.toRecord unit Arr}}</lang>
PHP
<lang php>function combSort($arr){ $gap = count($arr); while ($gap > 1 || $swap){ if($gap > 1) $gap /= 1.25;
$swap = false; $i = 0; while($i+$gap < count($arr)){ if($arr[$i] > $arr[$i+$gap]){ list($arr[$i], $arr[$i+$gap]) = array($arr[$i+$gap],$arr[$i]); $swap = true; } $i++; } } return $arr; }</lang>
PL/I
<lang PL/I> /* From the pseudocode. */ comb_sort: procedure (A);
declare A(*) fixed; declare t fixed; declare (i, gap) fixed binary (31); declare swaps bit (1) aligned;
gap = hbound(A,1) - lbound(A,1); /* initialize the gap size. */ do until (gap <= 1 & swaps); /* update the gap value for a next comb. */ put skip data (gap); gap = gap / 1.25e0; put skip data (gap); swaps = '1'b; /* a single "comb" over the array. */ do i = lbound(A,1) by 1 until (i + gap >= hbound(A,1)); if A(i) > A(i+gap) then do; t = A(i); A(i) = A(i+gap); A(i+gap) = t; swaps = '0'b; /* Flag a swap has occurred, so */ /* the list is not guaranteed sorted. */ end; end; end;
end comb_sort; </lang>
PureBasic
Implementation of CombSort11. <lang PureBasic>;sorts an array of integers Procedure combSort11(Array a(1))
Protected i, gap, swaps = 1 Protected nElements = ArraySize(a()) gap = nElements While (gap > 1) Or (swapped = 1) gap * 10 / 13 If gap = 9 Or gap = 10: gap = 11: EndIf If gap < 1: gap = 1: EndIf i = 0 swaps = 0 While (i + gap) <= nElements If a(i) > a(i + gap) Swap a(i), a(i + gap) swaps = 1 EndIf i + 1 Wend Wend
EndProcedure</lang> Implementation of CombSort. <lang PureBasic>;sorts an array of integers Procedure combSort(Array a(1))
Protected i, gap, swaps = 1 Protected nElements = ArraySize(a()) gap = nElements While (gap > 1) Or (swaps = 1) gap = Int(gap / 1.25) i = 0 swaps = 0 While (i + gap) <= nElements If a(i) > a(i + gap) Swap a(i), a(i + gap) swaps = 1 EndIf i + 1 Wend Wend
EndProcedure</lang>
Python
<lang python>>>> def combsort(input):
gap = len(input) swaps = True while gap > 1 or swaps: gap = max(1, int(gap / 1.25)) # minimum gap is 1 swaps = False for i in range(len(input) - gap): j = i+gap if input[i] > input[j]: input[i], input[j] = input[j], input[i] swaps = True
>>> y = [88, 18, 31, 44, 4, 0, 8, 81, 14, 78, 20, 76, 84, 33, 73, 75, 82, 5, 62, 70]
>>> combsort(y)
>>> assert y == sorted(y)
>>> y
[0, 4, 5, 8, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
>>> </lang>
Ruby
<lang ruby>class Array
def combsort! gap = size swaps = true until gap <= 1 and swaps gap = (gap / 1.25).to_int swaps = false 0.upto(size - gap - 1) do |i| if self[i] > self[i+gap] self[i], self[i+gap] = self[i+gap], self[i] swaps = true end end end self end
end
p [23, 76, 99, 58, 97, 57, 35, 89, 51, 38, 95, 92, 24, 46, 31, 24, 14, 12, 57, 78].combsort!</lang> results in
[12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
Sather
<lang sather>class SORT{T < $IS_LT{T}} is
private swap(inout a, inout b:T) is temp ::= a; a := b; b := temp; end;
-- ---------------------------------------------------------------------------------
comb_sort(inout a:ARRAY{T}) is gap ::= a.size; swapped ::= true; loop until!(gap <= 1 and ~swapped); if gap > 1 then gap := (gap.flt / 1.25).int; end; i ::= 0; swapped := false; loop until! ( (i + gap) >= a.size ); if (a[i] > a[i+gap]) then
swap(inout a[i], inout a[i+gap]); swapped := true; end;
i := i + 1; end; end; end;
end;
class MAIN is
main is a:ARRAY{INT} := |88, 18, 31, 44, 4, 0, 8, 81, 14, 78, 20, 76, 84, 33, 73, 75, 82, 5, 62, 70|; b ::= a.copy; SORT{INT}::comb_sort(inout b); #OUT + b + "\n"; end;
end;</lang>
Tcl
<lang tcl>proc combsort {input} {
set gap [llength $input] while 1 {
set gap [expr {int(floor($gap / 1.3))}] set swaps 0 for {set i 0} {$i+$gap < [llength $input]} {incr i} { set j [expr {$i+$gap}] if {[lindex $input $i] > [lindex $input $j]} { set tmp [lindex $input $i] lset input $i [lindex $input $j] lset input $j $tmp incr swaps } } if {$gap <= 1 && !$swaps} break
} return $input
}
set data {23 76 99 58 97 57 35 89 51 38 95 92 24 46 31 24 14 12 57 78} puts [combsort $data]</lang> Produces this output:
12 14 23 24 24 31 35 38 46 51 57 57 58 76 78 89 92 95 97 99
TI-83 BASIC
Requires prgmSORTINS. Gap division of 1.3. Switches to Insertion sort when gap is less than 5.
:L1→L2 :dim(L2)→A :While A>5 and B=0 :int(A/1.3)→A :1→C :0→B :While (C+A)≥dim(L2) :If L2(C)>L2(C+A) :Then :L2(C)→D :L2(C+A)→L2(C) :D→L2(C+A) :1→B :End :C+1→C :End :DelVar A :DelVar B :DelVar C :DelVar D :L1→L3 :L2→L1 :prgmSORTINS :L3→L1 :DelVar L3 :Return