Sorting algorithms/Cycle sort

Sorting algorithms/Cycle sort is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

This page uses content from Wikipedia. The original article was at Cycle_sort. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

From the the Wikipedia entry on cycle sorting:

Cycle sort is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of writes to the original array, unlike any other in-place sorting algorithm.

It is based on the idea that the permutation to be sorted can be factored into cycles, which can individually be rotated to give a sorted result.

Unlike nearly every other sort, items are never written elsewhere in the array simply to push them out of the way of the action.

Each value is either written zero times, if it's already in its correct position, or written one time to its correct position.

This matches the minimal number of overwrites required for a completed in-place sort.

Minimizing the number of writes is useful when making writes to some huge data set is very expensive, such as with EEPROMs like Flash memory where each write reduces the lifespan of the memory.

See also

• Youtube Visualization and audibilization of Cycle Sort algorithm.

C

Translation of: NetRexx

<lang C>

1. include <stdio.h>
2. include <stdlib.h>

int cycleSort(int * list, size_t l_len); void show_array(int * array, size_t a_len);

/*

* Sort an array in place and return the number of writes.
*/

int cycleSort(int * list, size_t l_len) {

 int writes = 0;

 /* Loop through the array to find cycles to rotate. */
 for (int cycleStart = 0; cycleStart < l_len - 1; ++cycleStart)
 {
   int item = list[cycleStart];
   int swap_tmp;

   /* Find where to put the item. */
   int pos = cycleStart;
   for (int i = cycleStart + 1; i < l_len; ++i)
   {
     if (list[i] < item)
     {
       ++pos;
     }
   }

   /* If the item is already there, this is not a cycle. */
   if (pos == cycleStart)
   {
     continue;
   }

   /* Otherwise, put the item there or right after any duplicates. */
   while (item == list[pos])
   {
     ++pos;
   }
   swap_tmp = list[pos];
   list[pos] = item;
   item = swap_tmp;
   ++writes;

   /* Rotate the rest of the cycle. */
   while (pos != cycleStart)
   {
     /* Find where to put the item. */
     pos = cycleStart;
     for (int i = cycleStart + 1; i < l_len; ++i)
     {
       if (list[i] < item)
       {
         ++pos;
       }
     }

     /* Put the item there or right after any duplicates. */
     while (item == list[pos])
     {
       ++pos;
     }
     swap_tmp = list[pos];
     list[pos] = item;
     item = swap_tmp;
     ++writes;
   }
 }

 return writes;

}

int main(int argc, char ** argv) {

 int arr[] = { 0, 1, 2, 2, 2, 2, 1, 9, 3, 5, 5, 8, 4, 7, 0, 6, };
 int arr_k = sizeof(arr) / sizeof(arr[0]);
 int writes;

 show_array(arr, arr_k);
 writes = cycleSort(arr, arr_k);
 show_array(arr, arr_k);
 printf("writes: %d\n", writes);

 return 0;

}

void show_array(int * array, size_t a_len) {

 for (int ix = 0; ix < a_len; ++ix)
 {
   printf("%d ", array[ix]);
 }
 putchar('\n');
 
 return;

} </lang>

Output:

0 1 2 2 2 2 1 9 3 5 5 8 4 7 0 6 
0 0 1 1 2 2 2 2 3 4 5 5 6 7 8 9 
writes: 10

C++

Based on example code on Wikipedia <lang Cpp>

1. include <time.h>
2. include <iostream>
3. include <vector>

using namespace std;

class cSort { public:

   void doIt( vector<unsigned> s )
   {

sq = s; display(); c_sort(); cout << "writes: " << wr << endl; display();

   }

private:

   void display()
   {

copy( sq.begin(), sq.end(), ostream_iterator<unsigned>( std::cout, " " ) ); cout << endl;

   }
   void c_sort()
   {

wr = 0; unsigned it, p, vlen = static_cast<unsigned>( sq.size() ); for( unsigned c = 0; c < vlen - 1; c++ ) { it = sq[c]; p = c; for( unsigned d = c + 1; d < vlen; d++ ) if( sq[d] < it ) p++;

if( c == p ) continue;

doSwap( p, it );

while( c != p ) { p = c; for( unsigned e = c + 1; e < vlen; e++ ) if( sq[e] < it ) p++;

doSwap( p, it ); } }

   }
   void doSwap( unsigned& p, unsigned& it )
   {

while( sq[p] == it ) p++; swap( it, sq[p] ); wr++;

   }
   vector<unsigned> sq;
   unsigned wr;

};

int main(int argc, char ** argv) {

   srand( static_cast<unsigned>( time( NULL ) ) );
   vector<unsigned> s;
   for( int x = 0; x < 20; x++ )

s.push_back( rand() % 100 + 21 );

   cSort c; c.doIt( s );
   return 0;

} </lang>

Output:

38 119 38 33 33 28 24 101 108 120 99 59 69 24 117 22 90 94 78 75
writes: 19
22 24 24 28 33 33 38 38 59 69 75 78 90 94 99 101 108 117 119 120

D

This version doesn't use Phobos algorithms beside 'swap'. Algorithms can be used to find where to put the item1 and elsewhere.

Translation of: Python

<lang d>import std.stdio, std.algorithm;

/// Sort an array in place and return the number of writes. uint cycleSort(T)(T[] data) pure nothrow @safe @nogc {

   typeof(return) nWrites = 0;

   // Loop through the data to find cycles to rotate.
   foreach (immutable cycleStart, item1; data) {
       // Find where to put the item1.
       size_t pos = cycleStart;
       foreach (item2; data[cycleStart + 1 .. $])
           if (item2 < item1)
               pos++;

       // If the item1 is already there, this is not a cycle.
       if (pos == cycleStart)
           continue;

       // Otherwise, put the item1 there or right after any duplicates.
       while (item1 == data[pos])
           pos++;
       data[pos].swap(item1);
       nWrites++;

       // Rotate the rest of the cycle.
       while (pos != cycleStart) {
           // Find where to put the item1.
           pos = cycleStart;
           foreach (item2; data[cycleStart + 1 .. $])
               if (item2 < item1)
                   pos++;

           // Put the item1 there or right after any duplicates.
           while (item1 == data[pos])
               pos++;
           data[pos].swap(item1);
           nWrites++;
       }
   }

   return nWrites;

}

void main() {

   immutable x = [0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6];
   auto xs = x.dup;
   immutable nWrites = xs.cycleSort;

   if (!xs.isSorted) {
       "Wrong order!".writeln;
   } else {
       writeln(x, "\nIs correctly sorted using cycleSort to:");
       writefln("%s\nusing %d writes.", xs, nWrites);
   }

}</lang>

Output:

[0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6]
Is correctly sorted using cycleSort to:
[0, 0, 1, 1, 2, 2, 2, 2, 3.5, 4, 5, 6, 7, 8, 9]
using 10 writes.

Go

This implementation was translated from the example code on Wikipedia.

<lang go>package main

import ( "fmt" "math/rand" "time" )

func cyclesort(ints []int) int { writes := 0

for cyclestart := 0; cyclestart < len(ints)-1; cyclestart++ { item := ints[cyclestart]

pos := cyclestart

for i := cyclestart + 1; i < len(ints); i++ { if ints[i] < item { pos++ } }

if pos == cyclestart { continue }

for item == ints[pos] { pos++ }

ints[pos], item = item, ints[pos]

writes++

for pos != cyclestart { pos = cyclestart for i := cyclestart + 1; i < len(ints); i++ { if ints[i] < item { pos++ } }

for item == ints[pos] { pos++ }

ints[pos], item = item, ints[pos] writes++ } }

return writes }

func main() { rand.Seed(time.Now().Unix())

ints := rand.Perm(10)

fmt.Println(ints) fmt.Printf("writes %d\n", cyclesort(ints)) fmt.Println(ints) }</lang>

Output:

[1 9 3 5 8 4 7 0 6 2]
writes 10
[0 1 2 3 4 5 6 7 8 9]

Note: output may be different due to the random numbers used.

J

J's sort is natively a single write sort, but it assigns the whole array at once. It would be trivial do the writes one at a time, and to avoid updating values which are not changed:

<lang J>noncyc=:3 :0

 writes=. 0
 for_item. /:~y do.
   if. item ~: item_index{y do.
     writes=. writes+1
     y=.item item_index} y
   end.
 end.
 smoutput (":writes),' writes'
 y 

)</lang>

Example use:

<lang J> noncyc 9 8 15 17 4 0 1 2 17 9 3 12 11 12 19 15 3 9 16 9 17 writes 0 1 2 3 3 4 8 9 9 9 9 11 12 12 15 15 16 17 17 19</lang>

Meanwhile, if we just wanted the "value at a time swapping" mechanism, an idiomatic approach might look something like this:

<lang j>cyc0=:3 :0

 c=. (#~ 1 < #@>)C./:/: y
 writes=. 0
 for_box. c do.
   inds=. >box
   v=. ({:inds) { y
   for_ind. inds do.
     writes=. writes+1
     t=. ind{ y
     y=. v ind} y
     v=. t
   end.
 end.
 smoutput (":writes),' writes'
 y

)</lang>

Example use:

<lang J> cyc0 9 8 15 17 4 0 1 2 17 9 3 12 11 12 19 15 3 9 16 9 18 writes 0 1 2 3 3 4 8 9 9 9 9 11 12 12 15 15 16 17 17 19</lang>

This gives us an extra write, because we're using a generic cycle abstraction.

Also that's still a bit different from the wikipedia algorithm. We might model the wikipedia algorithm like this:

<lang J>cyc1=:3 :0

 writes=. 0
 for_index. i.(#y)-1 do.
   item=. index{y
   adj=. item+/ .>(1+index)}.y
   if. 0<adj do.
     pos=. index+adj
     while. item=pos{y do. pos=.pos+1 end.
     writes=. writes+1
     t=. pos{y
     y=. item pos} y
     item=. t
     while. pos ~: index do.
       pos=. index+item+/ .>(1+index)}.y
       while. item=pos{y do. pos=.pos+1 end.
       writes=. writes+1
       t=. pos{y
       y=. item pos} y
       item=. t
     end.
   end.
 end.
 smoutput (":writes),' writes'
 y

)</lang>

Example use:

<lang J> cyc1 9 8 15 17 4 0 1 2 17 9 3 12 11 12 19 15 3 9 16 9 17 writes 0 1 2 3 3 4 8 9 9 9 9 11 12 12 15 15 16 17 17 19</lang>

Note that we've saved a write in this case, by following the wikipedia algorithm.

Java

<lang java>import java.util.Arrays;

public class CycleSort {

   public static void main(String[] args) {
       int[] arr = {5, 0, 1, 2, 2, 3, 5, 1, 1, 0, 5, 6, 9, 8, 0, 1};

       System.out.println(Arrays.toString(arr));

       int writes = cycleSort(arr);
       System.out.println(Arrays.toString(arr));
       System.out.println("writes: " + writes);
   }

   static int cycleSort(int[] a) {
       int writes = 0;

       for (int cycleStart = 0; cycleStart < a.length - 1; cycleStart++) {
           int val = a[cycleStart];

           // count the number of values that are smaller than val
           // since cycleStart
           int pos = cycleStart;
           for (int i = cycleStart + 1; i < a.length; i++)
               if (a[i] < val)
                   pos++;

           // there aren't any
           if (pos == cycleStart)
               continue;

           // skip duplicates
           while (val == a[pos])
               pos++;

           // put val into final position
           int tmp = a[pos];
           a[pos] = val;
           val = tmp;
           writes++;

           // repeat as long as we can find values to swap
           // otherwise start new cycle
           while (pos != cycleStart) {
               pos = cycleStart;
               for (int i = cycleStart + 1; i < a.length; i++)
                   if (a[i] < val)
                       pos++;

               while (val == a[pos])
                   pos++;

               tmp = a[pos];
               a[pos] = val;
               val = tmp;
               writes++;
           }
       }
       return writes;
   }

}</lang>

Output:

[5, 0, 1, 2, 2, 3, 5, 1, 1, 0, 5, 6, 9, 8, 0, 1]
[0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 5, 5, 5, 6, 8, 9]
writes: 14

NetRexx

Direct translation of the Wikipedia entry example <lang NetRexx>/* Rexx */ options replace format comments java crossref symbols nobinary

runSample(arg) return

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- Sort an array in place and return the number of writes. method cycleSort(array = Rexx[]) public static

 writes = 0

 -- Loop through the array to find cycles to rotate.
 loop cycleStart = 0 to array.length - 1 - 1
   item = array[cycleStart]

   -- Find where to put the item.
   pos = cycleStart
   loop i = cycleStart + 1 to array.length - 1
     if array[i] < item then
       pos = pos + 1
     end i

   -- If the item is already there, this is not a cycle.
   if pos == cycleStart then
     iterate

   -- Otherwise, put the item there or right after any duplicates.
   loop while item == array[pos]
     pos = pos + 1
     end
   swap_tmp = array[pos]
   array[pos] = item
   item = swap_tmp
   writes = writes + 1

   -- Rotate the rest of the cycle.
   loop while pos \= cycleStart

     -- Find where to put the item.
     pos = cycleStart
     loop i = cycleStart + 1 to array.length - 1
       if array[i] < item then
         pos = pos + 1
       end i

     -- Put the item there or right after any duplicates.
     loop while item == array[pos]
       pos = pos + 1
       end
     swap_tmp = array[pos]
     array[pos] = item
     item = swap_tmp
     writes = writes + 1

     end

   end cycleStart
 return writes

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method runSample(arg) public static

 samples = ArrayList()
 samples.add([1, 9, 3, 5, 8, 4, 7, 0, 6, 2])
 samples.add([0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6])
 samples.add(['Greygill Hole', 'Ogof Draenen', 'Ogof Ffynnon Ddu', 'Malham Tarn Pot'])
 samples.add([-3.14 ,3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4])
 samples.add(['George Washington: Virginia', 'John Adams: Massachusetts', 'Thomas Jefferson: Virginia', 'James Madison: Virginia', 'James Monroe: Virginia'])

 list = Rexx[]
 loop i_ = 0 to samples.size() - 1
   list = Rexx[] samples.get(i_)
   say 'Input list ' Arrays.asList(list)
   writes = cycleSort(list)
   say 'Sorted list' Arrays.asList(list)
   say 'Total number of writes:' writes
   say
   end i_
 return

</lang>

Output:

Input list  [1, 9, 3, 5, 8, 4, 7, 0, 6, 2]
Sorted list [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Total number of writes: 10

Input list  [0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6]
Sorted list [0, 0, 1, 1, 2, 2, 2, 2, 3.5, 4, 5, 6, 7, 8, 9]
Total number of writes: 10

Input list  [Greygill Hole, Ogof Draenen, Ogof Ffynnon Ddu, Malham Tarn Pot]
Sorted list [Greygill Hole, Malham Tarn Pot, Ogof Draenen, Ogof Ffynnon Ddu]
Total number of writes: 3

Input list  [-3.14, 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4]
Sorted list [-3.14, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9]
Total number of writes: 34

Input list  [George Washington: Virginia, John Adams: Massachusetts, Thomas Jefferson: Virginia, James Madison: Virginia, James Monroe: Virginia]
Sorted list [George Washington: Virginia, James Madison: Virginia, James Monroe: Virginia, John Adams: Massachusetts, Thomas Jefferson: Virginia]
Total number of writes: 4

ooRexx

<lang oorexx>/*REXX program demonstrates a cycle sort on a list of numbers**********

• 13.06.2014 Walter Pachl
• Modified from Rexx Version 2
• ooRexx allows to pass a stemmed variable by reference
• swapping variables uses a temporary instead of the parse.
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

 a.1='George Washington  Virginia'
 a.2='John Adams  Massachusetts'
 a.3='Thomas Jefferson  Virginia'
 a.4='James Madison  Virginia'
 a.5='James Monroe  Virginia'
 n=5
 Call show 'Unsorted list: '
 w=sortcycle(a.,n)
 Say 'sorted'
 Call show 'Sorted list'
 Say ' '
 Say 'This took' w 'writes.'
 Exit

sortcycle: Procedure

 Use Arg a.,n
 writes=0
 Do c=1 For n
   x=a.c
   p=c
   x=a.c
   Do j=c+1 To n
     If a.j<x Then
       p=p+1
     End
   If p==c Then
     Iterate
   Do While x==a.p
     p=p+1
     End
   t=x
   x=a.p
   a.p=t
   writes=writes+1
   Do While p\==c
     p=c
     Do k=c+1 To n
       If a.k<x Then
         p=p+1
       End
     Do While x==a.p
       p=p+1
       End
     t=x
     x=a.p
     a.p=t
     writes=writes+1
     End
   End
 Return writes

show:

 Parse Arg hdr
 Say ' '
 Say hdr
 Do i=1 To n
   Say format(i,2) a.i
   End
 Return</lang>

Output:

Unsorted list:
 1 George Washington  Virginia
 2 John Adams  Massachusetts
 3 Thomas Jefferson  Virginia
 4 James Madison  Virginia
 5 James Monroe  Virginia
sorted

Sorted list
 1 George Washington  Virginia
 2 James Madison  Virginia
 3 James Monroe  Virginia
 4 John Adams  Massachusetts
 5 Thomas Jefferson  Virginia

This took 4 writes.

Perl

This is based on the Wikipedia pseudocode. <lang perl>use strict; use warnings;

sub cycleSort(@) { my ($array) = @_; my $writes = 0;

my @alreadysorted;

# For each index except the last: for my $start ( 0 .. $#$array - 1 ) { next if $alreadysorted[$start]; my $item = $array->[$start]; # If there are N items less than $item, then we # must move $item N items rightward. my $pos = $start + grep $array->[$_] lt $item, $start + 1 .. $#$array; # If the item is where it should be, continue. next if $pos == $start; # If $item is one of several repetitions, move it to the right # of the last repeat. ++$pos while $item eq $array->[ $pos ]; # Store $item at $pos, where it belongs, and fetch the # value that had been at $pos, and put it in $item. ($array->[ $pos ], $item) = ($item, $array->[ $pos ]); ++$writes;

# Whatever $item is now, it certainly doesn't belong at $pos; do { # Find the correct $pos, $pos = $start + grep $array->[$_] lt $item, $start+1 .. $#$array; ++$pos while $item eq $array->[ $pos ]; # Swap the value there with $item, ($array->[ $pos ] , $item ) = ($item, $array->[ $pos ]); # And mark $pos as having the correct value in it.. $alreadysorted[ $pos ] = 1; ++$writes; # The loop ends after we have just written an item to $start } while $pos != $start; } $writes; }

use List::Util 'shuffle'; my @test = shuffle( ('a'..'z') x 2 ); print "Before sorting: @test\n"; print "There were ", cycleSort( \@test ), " writes\n"; print "After sorting: @test\n"; </lang>

Output:

Before sorting: a t d b f g y l t p w c r r x i y j k i z q e v a f o q j u x k m h s u v z g m b o l e n h p n c s w d
There were 50 writes
After  sorting: a a b b c c d d e e f f g g h h i i j j k k l l m m n n o o p p q q r r s s t t u u v v w w x x y y z z

Perl 6

<lang perl6>sub cycle_sort ( @nums is rw ) {

   my $writes = 0;

   # Loop through the array to find cycles to rotate.
   for @nums.kv -> $cycle_start, $item is copy {

       # Find where to put the item.
       my $pos = $cycle_start
               + @nums[ $cycle_start ^.. * ].grep: * < $item;

       # If the item is already there, this is not a cycle.
       next if $pos == $cycle_start;

       # Otherwise, put the item there or right after any duplicates.
       $pos++ while $item == @nums[$pos];
       ( @nums[$pos], $item ) .= reverse;
       $writes++;

       # Rotate the rest of the cycle.
       while $pos != $cycle_start {

           # Find where to put the item.
           $pos = $cycle_start
                + @nums[ $cycle_start ^.. * ].grep: * < $item;

           # Put the item there or right after any duplicates.
           $pos++ while $item == @nums[$pos];
           ( @nums[$pos], $item ) .= reverse;
           $writes++;
       }
   }

   return $writes;

}

my @a = <0 1 2 2 2 2 1 9 3.5 5 8 4 7 0 6>;

say @a; say 'writes ', cycle_sort(@a); say @a; </lang>

Output:

0 1 2 2 2 2 1 9 3.5 5 8 4 7 0 6
writes 10
0 0 1 1 2 2 2 2 3.5 4 5 6 7 8 9

Python

The Wikipedia algorithm pseudocode is very nearly Python. The main changes needed were to change the name array to vector to stop it obscuring a built-in name, and iterating over an enumerated collection rather than using explicit indices.

<lang python>def cycleSort(vector):

   "Sort a vector in place and return the number of writes."
   writes = 0

   # Loop through the vector to find cycles to rotate.
   for cycleStart, item in enumerate(vector):

       # Find where to put the item.
       pos = cycleStart
       for item2 in vector[cycleStart + 1:]:
           if item2 < item:
               pos += 1

       # If the item is already there, this is not a cycle.
       if pos == cycleStart:
           continue

       # Otherwise, put the item there or right after any duplicates.
       while item == vector[pos]:
           pos += 1
       vector[pos], item = item, vector[pos]
       writes += 1

       # Rotate the rest of the cycle.
       while pos != cycleStart:

           # Find where to put the item.
           pos = cycleStart
           for item2 in vector[cycleStart + 1:]:
               if item2 < item:
                   pos += 1

           # Put the item there or right after any duplicates.
           while item == vector[pos]:
               pos += 1
           vector[pos], item = item, vector[pos]
           writes += 1

   return writes

if __name__ == '__main__':

   x = [0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6]
   xcopy = x[::]
   writes = cycleSort(xcopy)
   if xcopy != sorted(x):
       print('Wrong order!')
   else:
       print('%r\nIs correctly sorted using cycleSort to'
             '\n%r\nUsing %i writes.' % (x, xcopy, writes))</lang>

Output:

[0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6]
Is correctly sorted using cycleSort to
[0, 0, 1, 1, 2, 2, 2, 2, 3.5, 4, 5, 6, 7, 8, 9]
Using 10 writes.

Racket

<lang racket>#lang racket/base (require racket/match)

Sort an array in place and return the number of writes.

(define (cycle-sort! v < =?)

 (define v-len (vector-length v))
 (for/sum ; Loop through the array to find cycles to rotate.
   ((cycle-start (in-range 0 (sub1 v-len))))
   (define item (vector-ref v cycle-start))
   (define (find-insertion-point) ; Find where to put the item.    
     (+ cycle-start
        (for/sum 
          ((i (in-range (add1 cycle-start) v-len))
           #:when (< (vector-ref v i) item)) 1)))
   ;; Put the item there or right after any duplicates
   (define (insert-after-duplicates pos)
     (match (vector-ref v pos)
       [(== item =?) (insert-after-duplicates (add1 pos))]
       [tmp (vector-set! v pos item) ; / swap
            (set! item tmp)          ; \ [this is my only write point]
            pos]))
   
   (define i-p (find-insertion-point))
   (if (= i-p cycle-start)
       0 ; If the item is already there, this is not a cycle.
       (let loop ; Rotate the rest of the cycle.        
         ((e-p (insert-after-duplicates i-p))
          (W 1 #| we've already written once |#))
         (if (= e-p cycle-start)
             W
             (loop (insert-after-duplicates (find-insertion-point))
                   (add1 W))))))) ; we've written again!

(module+ main

 ;; This will be random with duplicates
 (define A (list->vector (build-list 30 (λ (i) (random 20)))))
 A
 (cycle-sort! A < =)
 A
 (define B #(1 1 1 1 1 1))
 B
 (cycle-sort! B < =))</lang>

Output:

'#(7 17 5 16 14 9 18 10 1 4 10 1 9 3 3 0 1 18 16 12 9 14 14 12 19 2 12 15 16 8)
28
'#(0 1 1 1 2 3 3 4 5 7 8 9 9 9 10 10 12 12 12 14 14 14 15 16 16 16 17 18 18 19)
'#(1 1 1 1 1 1)
0

REXX

version 1

<lang rexx>/* REXX ***************************************************************

• 12.06.2014 Walter Pachl translated from Wikipedia's code
• 20.06.2014 WP corrected (courtesy Alan Sampson)
  • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • /

list='1 9 3 5 8 4 7 0 6 2' n=words(list) Do i=0 To n-1

 array.i=word(list,i+1)
 End

Say list writes=cyclesort() Say 'writes='writes ol= Do i=0 To n-1

 ol=ol array.i
 End

Say strip(ol) Exit

cycleSort: procedure expose array. n

 writes = 0
 -- Loop through the array to find cycles to rotate.
 do cycleStart=0 to n-2
   item = array.cycleStart

   -- Find where to put the item.
   pos = cycleStart
   Do i=cycleStart+1 to n-1
     if array.i < item Then
       pos += 1
     End

   -- If the item is already there, this is not a cycle.
   if pos == cycleStart Then
     Iterate

   -- Otherwise, put the item there or right after any duplicates.
   Do while item == array.pos
     pos += 1
     End
   Parse Value array.pos item With item array.pos
   writes += 1

   -- Rotate the rest of the cycle.
   Do while pos <> cycleStart

     -- Find where to put the item.
     pos = cycleStart
     Do i=cycleStart + 1 to n-1
       if array.i < item Then
         pos += 1
       End

     -- Put the item there or right after any duplicates.
     Do while item == array.pos
       pos += 1
       End
     Parse Value array.pos item With item array.pos
     writes += 1
     End
   End
 return writes</lang>

Output:

1 9 3 5 8 4 7 0 6 2
writes=10
0 1 2 3 4 5 6 7 8 9

version 2

This REXX version demonstrates the use of negative numbers and non-integer values in the list.

As a default, the program uses (for the input list) some digits of pi, which for practical purposes, appear random. <lang rexx>/*REXX program demonstrates a cycle sort on a list of items. */ parse arg z /* [↓] not specified? Use π digs*/ if z= then z=-3.14 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 say 'unsorted list: ' z /*show the original unsorted #s. */ w=sortCycle(z) /*W: the # of writes done in sort*/ say 'and took' w 'writes.' /*show # of writes done in sort. */ exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────SORTCYCLE subroutine────────────────*/ sortCycle: procedure expose @.; parse arg y; #=words(y); writes=0

       do i=1  for #; @.i=word(y,i); end  /*i*/     /*put items ───► @.*/
                                      /* [↓]  find cycles to rotate.   */
 do c=1  for #;    x=@.c;         p=c /*X  is the  item  being sorted. */
       do j=c+1  to #; if @.j<x  then p=p+1; end      /*where to put X.*/
 if p==c then  iterate                /*Is it there? This ain't a cycle*/
       do  while x==@.p;  p=p+1;  end /*put X right after any duplicate*/
 parse value @.p x with x @.p         /*swap the two values: @.p and X.*/
 writes=writes+1                      /*bump counter for  #  of writes.*/
     do while p\==c;     p=c          /*rotate the rest of the cycle.  */
       do k=c+1  to #;   if @.k<x  then p=p+1;  end  /*k*/
       do while x==@.p;  p=p+1;  end  /*put X here or right after dups.*/
     parse value @.p x with x @.p     /*swap the two values: @.p and X.*/
     writes=writes+1                  /*bump counter for  #  of writes.*/
     end   /*while p\==c*/
 end       /*c*/
                                      /* [↓]  display the sorted list. */

_=@.1; do j=2 to #; _=_ @.j; end; say ' sorted list: ' _ return writes</lang>

Output:

using the default input

unsorted list:  -3.14 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4
  sorted list:  -3.14 0 1 1 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 7 7 8 8 8 8 8 9 9 9 9
and took 34 writes.

Output:

using the input of

  FM Stereo has been around since 1961.

unsorted list:  FM Stereo has been around since 1961.
  sorted list:  1961. FM Stereo around been has since
and took 7 writes.

Note (for the above output).   This REXX program was executed on an ASCII machine.
On an   ASCII   machine, the order of sorting is numbers, uppercase letters, lowercase letters.
On an EBCDIC machine, the order of sorting is lowercase letters, uppercase letters, numbers.
Other (special) characters are also in a different order.

version 3

This version uses a faster (but a more cryptic) version of incrementing   1   (one) to   P   within two do loops. <lang rexx>/*REXX program demonstrates a cycle sort on a list of items. */ parse arg z /* [↓] not specified? Use π digs*/ if z= then z=-3.14 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 say 'unsorted list: ' z /*show the original unsorted #s. */ w=sortCycle(z) /*W: the # of writes done in sort*/ say 'and took' w 'writes.' /*show # of writes done in sort. */ exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────SORTCYCLE subroutine────────────────*/ sortCycle: procedure expose @.; parse arg y; #=words(y); writes=0

       do i=1  for #; @.i=word(y,i); end  /*i*/     /*put items ───► @.*/
                                      /* [↓]  find cycles to rotate.   */
   do c=1  for #;     x=@.c;      p=c /*X  is the  item  being sorted. */
         do j=c+1  to #; if @.j<x  then p=p+1; end    /*where to put X.*/
   if p==c then  iterate              /*Is it there? This ain't a cycle*/
         do p=p  while x==@.p;  end   /*put X right after any duplicate*/
 parse  value  @.p x  with  x @.p     /*swap the two values: @.p and X.*/
 writes=writes+1                      /*bump counter for  #  of writes. */
     do while p\==c;     p=c          /*rotate the rest of the cycle.  */
       do k=c+1  to #;   if @.k<x  then p=p+1;  end  /*k*/
       do p=p  while x==@.p;  end     /*put X here or right after dups.*/
     parse  value  @.p x  with  x @.p /*swap the two values: @.p and X.*/
     writes=writes+1                  /*bump counter for  #  of writes.*/
     end   /*while p\==c*/
 end       /*c*/
                                      /* [↓]  display the sorted list. */

_=@.1; do j=2 to #; _=_ @.j; end; say ' sorted list: ' _ return writes</lang> output is identical to the 2^nd version.

version 4

This version uses a subroutine to perform the task of handling an (sorted) item placement (possibly after duplicates). <lang rexx>/*REXX program demonstrates a cycle sort on a list of items. */ parse arg z /* [↓] not specified? Use π digs*/ if z= then z=-3.14 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 say 'unsorted list: ' z /*show the original unsorted #s. */ w=sortCycle(z) /*W: the # of writes done in sort*/ say 'and took' w 'writes.' /*show # of writes done in sort. */ exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────SORTCYCLE subroutine────────────────*/ sortCycle: procedure expose @.; parse arg y; #=words(y); w=0

         do i=1  for #; @.i=word(y,i); end  /*i*/     /*put items───►@.*/

 do c=1  for #;     x=@.c;      p=c   /*X  is the  item  being sorted. */
     do j=c+1  to #; if @.j<x  then p=p+1; end  /*j*/  /*where to put X*/
 if p==c  then  iterate               /*Is it there? This ain't a cycle*/
 call .swap                           /*put X here or right after dups.*/
     do while p\==c;     p=c          /*rotate the rest of the cycle.  */
       do k=c+1  to #;   if @.k<x  then p=p+1;  end  /*k*/
     call .swap                       /*put X here or right after dups.*/
     end   /*while p\==c*/
 end       /*c*/
                                      /* [↓]  display the sorted list. */

_=@.1; do j=2 to #; _=_ @.j; end; say ' sorted list: ' _ return w /* [↓] find where to put X into @*/ .swap: do p=p while x==@.p; end; parse value @.p x with x @.p;w=w+1;return</lang> output is identical to the 2^nd version.

Ruby

Direct translation of the pseudocode on the Wikipedia. <lang ruby>def cycleSort!(array)

 writes = 0
 
 # Loop through the array to find cycles to rotate.
 for cycleStart in 0 .. array.size-2
   item = array[cycleStart]
   
   # Find where to put the item.
   pos = cycleStart
   for i in cycleStart+1 ... array.size
     pos += 1  if array[i] < item
   end
   
   # If the item is already there, this is not a cycle.
   next  if pos == cycleStart
   
   # Otherwise, put the item there or right after any duplicates.
   pos += 1  while item == array[pos]
   array[pos], item = item, array[pos]
   writes += 1
   
   # Rotate the rest of the cycle.
   while pos != cycleStart
     
     # Find where to put the item.
     pos = cycleStart
     for i in cycleStart+1 ... array.size
       pos += 1  if array[i] < item
     end
     
     # Put the item there or right after any duplicates.
     pos += 1  while item == array[pos]
     array[pos], item = item, array[pos]
     writes += 1
   end
 end
 writes

end

p a = [0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6] puts "writes : #{cycleSort!(a)}" p a</lang>

Output:

[0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6]
writes : 10
[0, 0, 1, 1, 2, 2, 2, 2, 3.5, 4, 5, 6, 7, 8, 9]

Scala

Translation of Java version <lang scala>

 def cycleSort(a: Array[Int]): (Array[Int], Int) = {
   var writes = 0

   for (cycleStart <- 0 until a.length - 1) {
     var value = a(cycleStart)

     // count the number of values that are smaller than value since cycleStart
     var pos = cycleStart
     
     for (i <- cycleStart + 1 until a.length)
       if (a(i) < value) pos += 1

     // skip if there aren't any
     if (pos != cycleStart) {
       
       // skip duplicates
       while (a(pos) == value) pos += 1

       // put val into final position
       val tmp = a(pos)
       a(pos) = value
       value = tmp
       writes += 1

       // repeat as long as we can find values to swap
       // otherwise start new cycle
       while (pos != cycleStart) {
         pos = cycleStart
         for (i <- cycleStart + 1 until a.length)
           if (a(i) < value) pos += 1

         while (a(pos) == value) pos += 1

         val tmp = a(pos)
         a(pos) = value
         value = tmp
         writes += 1
       }
     }
   }
   (a, writes)
 }

</lang>

Sidef

<lang ruby>func cycle_sort (array) {

   var (writes=0, pos=0)

   func f(i, Ref item, bool=false) {
       pos = (i + array.ft(i+1).count{ _ < *item })
       return(false) if (bool && pos==i)
       while (*item == array[pos]) { ++pos }
       (array[pos], *item) = (*item, array[pos])
       ++writes
       return true
   }

   array.each_kv { |i, item|
       f(i, \item, true) || next
       while (pos != i) {
           f(i, \item)
       }
   }

   return writes

}

var a = %n(0 1 2 2 2 2 1 9 3.5 5 8 4 7 0 6)

say a.join(' ') say ('writes ', cycle_sort(a)) say a.join(' ')</lang>

Output:

0 1 2 2 2 2 1 9 3.5 5 8 4 7 0 6
writes 10
0 0 1 1 2 2 2 2 3.5 4 5 6 7 8 9

Tcl

Direct translation of the pseudocode on the Wikipedia page <lang tcl>proc cycleSort {listVar} {

   upvar 1 $listVar array
   set writes 0

   # Loop through the array to find cycles to rotate.
   for {set cycleStart 0} {$cycleStart < [llength $array]} {incr cycleStart} {

set item [lindex $array $cycleStart]

# Find where to put the item. set pos $cycleStart for {set i [expr {$pos + 1}]} {$i < [llength $array]} {incr i} { incr pos [expr {[lindex $array $i] < $item}] }

# If the item is already there, this is not a cycle. if {$pos == $cycleStart} continue

# Otherwise, put the item there or right after any duplicates. while {$item == [lindex $array $pos]} { incr pos } set tmp [lindex $array $pos] lset array $pos $item set item $tmp incr writes

# Rotate the rest of the cycle. while {$pos != $cycleStart} { # Find where to put the item. set pos $cycleStart

for {set i [expr {$cycleStart + 1}]} {$i < [llength $array]} {incr i} { incr pos [expr {[lindex $array $i] < $item}] }

# Put the item there or right after any duplicates. while {$item == [lindex $array $pos]} { incr pos } set tmp [lindex $array $pos] lset array $pos $item set item $tmp incr writes }

   }

   return $writes

}</lang> Demonstrating: <lang tcl>set example {0 1 2 2 2 2 1 9 3.5 5 8 4 7 0 6} puts "Data was: $example" set writes [cycleSort example] puts "Data is now: $example" if {$example eq [lsort -real $example]} {

   puts "\twhich is correctly sorted"

} else {

   puts "\twhich is the wrong order!"

} puts "Writes required: $writes"</lang>

Output:

Data was: 0 1 2 2 2 2 1 9 3.5 5 8 4 7 0 6
Data is now: 0 0 1 1 2 2 2 2 3.5 4 5 6 7 8 9
	which is correctly sorted
Writes required: 10