Sorting Algorithms/Circle Sort

From Rosetta Code
Sorting Algorithms/Circle 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.

Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.

For other sorting algorithms, see Category:Sorting Algorithms, or:
O(n logn) Sorts
Heapsort | Mergesort | Quicksort
O(n log2n) Sorts
Shell Sort
O(n2) Sorts
Bubble sort | Cocktail sort | Comb sort | Gnome sort | Insertion sort | Selection sort | Strand sort
Other Sorts
Bead sort | Bogosort | Counting sort | Pancake sort | Permutation sort | Radix sort | Sleep sort | Stooge sort | Sort three variables

Sort an array of integers (of any convenient size) into ascending order using Circlesort.

In short, compare the first element to the last element, then the second element to the second last element, etc.

Then split the array in two and recurse until there is only one single element in the array, like this:

Before:
6 7 8 9 2 5 3 4 1
After:
1 4 3 5 2 9 8 7 6

Repeat this procedure until quiescence (i.e. until there are no swaps).

Show both the initial, unsorted list and the final sorted list. (Intermediate steps during sorting are optional.)

Optimizations (like doing 0.5 log2(n) iterations and then continue with an Insertion sort) are optional.

Pseudo code:

 function circlesort (index lo, index hi, swaps)
 {
   if lo == hi return (swaps)
   high := hi
   low := lo
   mid := int((hi-lo)/2)
   while lo < hi {
     if  (value at lo) > (value at hi) {
        swap.values (lo,hi)
        swaps++
     }
     lo++
     hi--
   }
   if lo == hi
     if (value at lo) > (value at hi+1) {
         swap.values (lo,hi+1)
         swaps++
     }
   swaps := circlesort(low,low+mid,swaps)
   swaps := circlesort(low+mid+1,high,swaps)
   return(swaps)
 }
 while circlesort (0, sizeof(array)-1, 0)


See also
  • For more information on Circle sorting, see Sourceforge.



C[edit]

#include <stdio.h>
 
int circle_sort_inner(int *start, int *end)
{
int *p, *q, t, swapped;
 
if (start == end) return 0;
 
// funny "||" on next line is for the center element of odd-lengthed array
for (swapped = 0, p = start, q = end; p<q || (p==q && ++q); p++, q--)
if (*p > *q)
t = *p, *p = *q, *q = t, swapped = 1;
 
// q == p-1 at this point
return swapped | circle_sort_inner(start, q) | circle_sort_inner(p, end);
}
 
//helper function to show arrays before each call
void circle_sort(int *x, int n)
{
do {
int i;
for (i = 0; i < n; i++) printf("%d ", x[i]);
putchar('\n');
} while (circle_sort_inner(x, x + (n - 1)));
}
 
int main(void)
{
int x[] = {5, -1, 101, -4, 0, 1, 8, 6, 2, 3};
circle_sort(x, sizeof(x) / sizeof(*x));
 
return 0;
}
Output:
5 -1 101 -4 0 1 8 6 2 3 
-4 -1 0 3 6 1 2 8 5 101 
-4 -1 0 1 2 3 5 6 8 101

CoffeeScript[edit]

circlesort = (arr, lo, hi, swaps) ->
if lo == hi
return (swaps)
 
high = hi
low = lo
mid = Math.floor((hi-lo)/2)
 
while lo < hi
if arr[lo] > arr[hi]
t = arr[lo]
arr[lo] = arr[hi]
arr[hi] = t
swaps++
lo++
hi--
 
if lo == hi
if arr[lo] > arr[hi+1]
t = arr[lo]
arr[lo] = arr[hi+1]
arr[hi+1] = t
swaps++
 
swaps = circlesort(arr,low,low+mid,swaps)
swaps = circlesort(arr,low+mid+1,high,swaps)
 
return(swaps)
 
VA = [2,14,4,6,8,1,3,5,7,9,10,11,0,13,12,-1]
 
while circlesort(VA,0,VA.length-1,0)
console.log VA

Output:

console: -1,1,0,3,4,5,8,12,2,9,6,10,7,13,11,14
console: -1,0,1,3,2,5,4,8,6,7,9,12,10,11,13,14
console: -1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14

D[edit]

import std.stdio, std.algorithm, std.array, std.traits;
 
void circlesort(T)(T[] items) if (isMutable!T) {
uint inner(size_t lo, size_t hi, uint swaps) {
if (lo == hi)
return swaps;
auto high = hi;
auto low = lo;
immutable mid = (hi - lo) / 2;
 
while (lo < hi) {
if (items[lo] > items[hi]) {
swap(items[lo], items[hi]);
swaps++;
}
lo++;
hi--;
}
 
if (lo == hi && items[lo] > items[hi + 1]) {
swap(items[lo], items[hi + 1]);
swaps++;
}
swaps = inner(low, low + mid, swaps);
swaps = inner(low + mid + 1, high, swaps);
return swaps;
}
 
if (!items.empty)
while (inner(0, items.length - 1, 0)) {}
}
 
void main() {
import std.random, std.conv;
 
auto a = [5, -1, 101, -4, 0, 1, 8, 6, 2, 3];
a.circlesort;
a.writeln;
assert(a.isSorted);
 
// Fuzzy test.
int[30] items;
foreach (immutable _; 0 .. 100_000) {
auto data = items[0 .. uniform(0, items.length)];
foreach (ref x; data)
x = uniform(-items.length.signed * 3, items.length.signed * 3);
data.circlesort;
assert(data.isSorted);
}
}
Output:
[-4, -1, 0, 1, 2, 3, 5, 6, 8, 101]

Elixir[edit]

defmodule Sort do
def circle_sort(data) do
List.to_tuple(data)
|> circle_sort(0, length(data)-1)
|> Tuple.to_list
end
 
defp circle_sort(data, lo, hi) do
case circle_sort(data, lo, hi, 0) do
{result, 0} -> result
{result, _} -> circle_sort(result, lo, hi)
end
end
 
defp circle_sort(data, lo, lo, swaps), do: {data, swaps}
defp circle_sort(data, lo, hi, swaps) do
mid = div(lo + hi, 2)
{data, swaps} = do_circle_sort(data, lo, hi, swaps)
{data, swaps} = circle_sort(data, lo, mid, swaps)
circle_sort(data, mid+1, hi, swaps)
end
 
def do_circle_sort(data, lo, hi, swaps) when lo>=hi do
if lo==hi and elem(data, lo) > elem(data, hi+1),
do: {swap(data, lo, hi+1), swaps+1},
else: {data, swaps}
end
def do_circle_sort(data, lo, hi, swaps) do
if elem(data, lo) > elem(data, hi),
do: do_circle_sort(swap(data, lo, hi), lo+1, hi-1, swaps+1),
else: do_circle_sort(data, lo+1, hi-1, swaps)
end
 
defp swap(data, i, j) do
vi = elem(data, i)
vj = elem(data, j)
data |> put_elem(i, vj) |> put_elem(j, vi)
end
end
 
data = [6, 7, 8, 9, 2, 5, 3, 4, 1]
IO.puts "before sort: #{inspect data}"
IO.puts " after sort: #{inspect Sort.circle_sort(data)}"
Output:
before sort: [6, 7, 8, 9, 2, 5, 3, 4, 1]
 after sort: [1, 2, 3, 4, 5, 6, 7, 8, 9]

Forth[edit]

This one features the newest version of the algorithm on Sourceforge.

[UNDEFINED] cell- [IF] : cell- 1 cells - ; [THEN]
 
defer precedes ( addr addr -- flag )
variable (sorted?) \ is the array sorted?
 
: (compare) ( a1 a2 -- a1 a2)
over @ over @ precedes \ flag if swapped
if over over over @ over @ swap rot ! swap ! false (sorted?) ! then
;
 
: (circlesort) ( a1 a2 --)
over over = if drop drop exit then \ quit if indexes are equal
over over swap \ swap indexes (end begin)
begin
over over > \ as long as middle isn't passed
while
(compare) swap cell- swap cell+ \ check and swap opposite elements
repeat rot recurse recurse \ split array and recurse
;
 
: sort ( a n --)
1- cells over + \ calculate addresses
begin true (sorted?) ! over over (circlesort) (sorted?) @ until drop drop
;
 
:noname < ; is precedes
 
10 constant /sample
create sample 5 , -1 , 101 , -4 , 0 , 1 , 8 , 6 , 2 , 3 ,
 
: .sample sample /sample cells bounds do i ? 1 cells +loop ;
 
sample /sample sort .sample

Fortran[edit]

 
!
module circlesort
! I have commented the code that was here and also 'tightened up' various pieces such as how swap detection was done as well
! as fixing an error where the code would exceed array bounds for odd number sized arrays.
! Also, giving some some attribution to the author. - Pete
! This code is a Fortran adaptation of a Forth algorithm laid out by "thebeez" at this URL;
! https://sourceforge.net/p/forth-4th/wiki/Circle%20sort/
!
implicit none
logical, private :: csr
public :: circle_sort
 
contains
 
recursive logical function csr(a, left, right,n) result(swapped)
implicit none
integer, intent(in) :: left, right,n
integer, intent(inout) :: a(n)
integer :: lo, hi, mid
integer :: temp
logical :: lefthalf,righthalf
!
swapped = .FALSE.
if (right <= left) return
lo = left !Store the upper and lower bounds of list for
hi = right !Recursion later
!
do while (lo < hi)
! Swap the pair of elements if hi < lo
if (a(hi) < a(lo)) then
swapped = .TRUE.
temp = a(lo)
a(lo) = a(hi)
a(hi) = temp
endif
lo = lo + 1
hi = hi - 1
end do
! Special case if array is an odd size (not even)
if (lo == hi)then
if(a(hi+1) .lt. a(lo))then
swapped = .TRUE.
temp = a(hi+1)
a(hi+1) = a(lo)
a(lo) = temp
endif
endif
mid = (left + right) / 2 ! Bisection point
lefthalf = csr(a, left, mid,n)
righthalf = csr(a, mid + 1, right,n)
swapped = swapped .or. lefthalf .or. righthalf
end function csr
!
subroutine circle_sort(a, n)
use iso_c_binding, only: c_ptr, c_loc
implicit none
integer, intent(in) :: n
integer, target,intent(inout) :: a(n)
 
do while ( csr(a, 1, n,n))
! This is the canonical algorithm. However, if you want to
! speed it up, count the iterations and when you have approached
! 0.5*ln(n) iterations, perform a binary insertion sort then exit the loop.
end do
end subroutine circle_sort
 
end module circlesort
program sort
use circlesort
implicit none
integer :: a(9)
data a/6,7,8,9,2,5,3,4,1/
call circle_sort(a, size(a))
print *, a
end program sort
 
 

FreeBASIC[edit]

' version 21-10-2016
' compile with: fbc -s console
' for boundry checks on array's compile with: fbc -s console -exx
' converted pseudo code into FreeBASIC code
 
' shared variables need to be declared before first use
Dim Shared As Long cs(-7 To 7)
 
Function circlesort(lo As Long, hi As Long, swaps As ULong) As ULong
 
' array is declared shared
' sort from lower bound to the highter bound
' array's can have subscript range from -2147483648 to +2147483647
 
If lo = hi Then Return swaps
 
Dim As Long high = hi
Dim As Long low = lo
Dim As Long mid_ = (hi - lo) \ 2
 
While lo < hi
If cs(lo) > cs(hi) Then
Swap cs(lo), cs(hi)
swaps += 1
End If
lo += 1
hi -= 1
Wend
If lo = hi Then
If cs(lo) > cs(hi +1) Then
Swap cs(lo), cs(hi +1)
swaps += 1
End If
End If
swaps = circlesort(low , low + mid_, swaps)
swaps = circlesort(low + mid_ +1, high, swaps)
 
Return swaps
 
End Function
 
' ------=< MAIN >=------
 
Dim As Long i, a = LBound(cs), b = UBound(cs)
 
Randomize Timer
For i = a To b : cs(i) = i  : Next
For i = a To b ' little shuffle
Swap cs(i), cs(Int(Rnd * (b - a +1)) + a)
Next
 
Print "unsorted ";
For i = a To b : Print Using "####"; cs(i); : Next : Print
 
' sort the array, loop until sorted
While circlesort(a, b, 0) : Wend
 
Print " sorted ";
For i = a To b : Print Using "####"; cs(i); : Next : Print
 
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
Output:
unsorted   -4  -1   1   0   5  -7  -2   4  -6  -3   2   6   3   7  -5
  sorted   -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7

Go[edit]

package main
 
import "fmt"
 
func circleSort(a []int, lo, hi, swaps int) int {
if lo == hi {
return swaps
}
high, low := hi, lo
mid := (hi - lo) / 2
for lo < hi {
if a[lo] > a[hi] {
a[lo], a[hi] = a[hi], a[lo]
swaps++
}
lo++
hi--
}
if lo == hi {
if a[lo] > a[hi+1] {
a[lo], a[hi+1] = a[hi+1], a[lo]
swaps++
}
}
swaps = circleSort(a, low, low+mid, swaps)
swaps = circleSort(a, low+mid+1, high, swaps)
return swaps
}
 
func main() {
aa := [][]int{
{6, 7, 8, 9, 2, 5, 3, 4, 1},
{2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1},
}
for _, a := range aa {
fmt.Printf("Original: %v\n", a)
for circleSort(a, 0, len(a)-1, 0) != 0 {
// empty block
}
fmt.Printf("Sorted  : %v\n\n", a)
}
}
Output:
Original: [6 7 8 9 2 5 3 4 1]
Sorted  : [1 2 3 4 5 6 7 8 9]

Original: [2 14 4 6 8 1 3 5 7 11 0 13 12 -1]
Sorted  : [-1 0 1 2 3 4 5 6 7 8 11 12 13 14]

J[edit]

Of more parsing and atomic data, or less parsing with large data groups the latter produces faster J programs. Consequently each iteration laminates the original with its reverse. It joins the recursive call to the pairwise minima of the left block to the recursive call of the pairwise maxima of the right block, repeating the operations while the output changes. This is sufficient for power of 2 length data. The pre verb adjusts the data length. And post recovers the original data. This implementation discards the "in place" property described at the sourceforge link.

 
circle_sort =: post [email protected] NB. the main sorting verb
power_of_2_length =: even_length_iteration^:_ NB. repeat while the answer changes
even_length_iteration =: (<./ (,&$: |.) >./)@(-:@# ({. ,: |[email protected]}.) ])^:(1<#)
pre =: , (-~ >.&.(2&^.))@# # >./ NB. extend data to next power of 2 length
post =: ({.~ #)~ NB. remove the extra data
 

Examples:

 
show =: [ smoutput
 
8 ([: circle_sort&.>@show ;&(?~)) 13 NB. sort lists length 8 and 13
┌───────────────┬────────────────────────────┐
0 6 7 3 4 5 2 13 10 1 4 7 8 5 6 2 0 9 11 12
└───────────────┴────────────────────────────┘
┌───────────────┬────────────────────────────┐
0 1 2 3 4 5 6 70 1 2 3 4 5 6 7 8 9 10 11 12
└───────────────┴────────────────────────────┘
 
8 ([: circle_sort&.>@show ;&(1 }. 2 # ?~)) 13 NB. data has repetition
┌─────────────────────────────┬──────────────────────────────────────────────────────┐
2 3 3 5 5 1 1 7 7 6 6 4 4 0 012 11 11 4 4 3 3 9 9 7 7 10 10 6 6 2 2 1 1 5 5 8 8 0 0
└─────────────────────────────┴──────────────────────────────────────────────────────┘
┌─────────────────────────────┬──────────────────────────────────────────────────────┐
0 0 1 1 2 3 3 4 4 5 5 6 6 7 70 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12
└─────────────────────────────┴──────────────────────────────────────────────────────┘
 

Java[edit]

import java.util.Arrays;
 
public class CircleSort {
 
public static void main(String[] args) {
circleSort(new int[]{2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1});
}
 
public static void circleSort(int[] arr) {
if (arr.length > 0)
do {
System.out.println(Arrays.toString(arr));
} while (circleSortR(arr, 0, arr.length - 1, 0) != 0);
}
 
private static int circleSortR(int[] arr, int lo, int hi, int numSwaps) {
if (lo == hi)
return numSwaps;
 
int high = hi;
int low = lo;
int mid = (hi - lo) / 2;
 
while (lo < hi) {
if (arr[lo] > arr[hi]) {
swap(arr, lo, hi);
numSwaps++;
}
lo++;
hi--;
}
 
if (lo == hi && arr[lo] > arr[hi + 1]) {
swap(arr, lo, hi + 1);
numSwaps++;
}
 
numSwaps = circleSortR(arr, low, low + mid, numSwaps);
numSwaps = circleSortR(arr, low + mid + 1, high, numSwaps);
 
return numSwaps;
}
 
private static void swap(int[] arr, int idx1, int idx2) {
int tmp = arr[idx1];
arr[idx1] = arr[idx2];
arr[idx2] = tmp;
}
}
[2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]
[-1, 1, 0, 4, 3, 8, 12, 2, 7, 6, 11, 5, 13, 14]
[-1, 0, 1, 3, 2, 4, 7, 5, 6, 8, 12, 11, 13, 14]
[-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14]

jq[edit]

Works with: jq version 1.4

With kudos to #Perl 6.

"circlesort" as defined in this section can be used to sort any JSON array. In case your jq does not have "until" as a builtin, here is its definition:

def until(cond; next): 
def _until: if cond then . else (next|_until) end;
_until;
def circlesort:
 
def swap(i;j): .[i] as $t | .[i] = .[j] | .[j] = $t;
 
# state: [lo, hi, swaps, array]
def cs:
 
# increment lo, decrement hi, and if they are equal, increment hi again
# i.e. ++hi if --hi == $lo
def next: # [lo, hi]
.[0] += 1 | .[1] -= 1 | (if .[0] == .[1] then .[1] += 1 else . end) ;
 
.[0] as $start | .[1] as $stop
| if $start < $stop then
until(.[0] >= .[1];
.[0] as $lo | .[1] as $hi | .[3] as $array
| if $array[$lo] > $array[$hi] then
.[3] = ($array | swap($lo; $hi))
| .[2] += 1 # swaps++
else .
end
| next)
| .[0] as $lo | .[1] as $hi
| [$start, $hi, .[2], .[3]] | cs
| [$lo, $stop, .[2], .[3]] | cs
else .
end ;
 
[0, length-1, 0, .] | cs
| .[2] as $swaps
| .[3]
| if $swaps == 0 then .
else circlesort
end ;

Example:

"The quick brown fox jumps over the lazy dog" | split(" ") | circlesort
Output:
$ jq -n -c -f -M circleSort.jq
["The","brown","dog","fox","jumps","lazy","over","quick","the"]

Julia[edit]

Works with: Julia version 0.6
function _ciclesort!(arr::Vector, lo::Int, hi::Int, swaps::Int)
lo == hi && return swaps
high = hi
low = lo
mid = (hi - lo) ÷ 2
while lo < hi
if arr[lo] > arr[hi]
arr[lo], arr[hi] = arr[hi], arr[lo]
swaps += 1
end
lo += 1
hi -= 1
end
if lo == hi
if arr[lo] > arr[hi+1]
arr[lo], arr[hi+1] = arr[hi+1], arr[lo]
swaps += 1
end
end
swaps = _ciclesort!(arr, low, low + mid, swaps)
swaps = _ciclesort!(arr, low + mid + 1, high, swaps)
return swaps
end
 
function ciclesort!(arr::Vector)
while !iszero(_ciclesort!(arr, 1, endof(arr), 0)) end
return arr
end
 
v = rand(10)
println("# $v\n -> ", ciclesort!(v))
Output:
# [0.603704, 0.293639, 0.51395, 0.74624, 0.245282, 0.930508, 0.550865, 0.62253, 0.00608894, 0.270426]
 -> [0.00608894, 0.245282, 0.270426, 0.293639, 0.51395, 0.550865, 0.603704, 0.62253, 0.74624, 0.930508]

Kotlin[edit]

// version 1.1.0
 
fun<T: Comparable<T>> circleSort(array: Array<T>, lo: Int, hi: Int, nSwaps: Int): Int {
if (lo == hi) return nSwaps
 
fun swap(array: Array<T>, i: Int, j: Int) {
val temp = array[i]
array[i] = array[j]
array[j] = temp
}
 
var high = hi
var low = lo
val mid = (hi - lo) / 2
var swaps = nSwaps
while (low < high) {
if (array[low] > array[high]) {
swap(array, low, high)
swaps++
}
low++
high--
}
if (low == high)
if (array[low] > array[high + 1]) {
swap(array, low, high + 1)
swaps++
}
swaps = circleSort(array, lo, lo + mid, swaps)
swaps = circleSort(array, lo + mid + 1, hi, swaps)
return swaps
}
 
fun main(args: Array<String>) {
val array = arrayOf(6, 7, 8, 9, 2, 5, 3, 4, 1)
println("Original: ${array.asList()}")
while (circleSort(array, 0, array.size - 1, 0) != 0) ; // empty statement
println("Sorted  : ${array.asList()}")
println()
val array2 = arrayOf("the", "quick", "brown", "fox", "jumps", "over", "the", "lazy", "dog")
println("Original: ${array2.asList()}")
while (circleSort(array2, 0, array2.size - 1, 0) != 0) ;
println("Sorted  : ${array2.asList()}")
}
Output:
Original: [6, 7, 8, 9, 2, 5, 3, 4, 1]
Sorted  : [1, 2, 3, 4, 5, 6, 7, 8, 9]

Original: [the, quick, brown, fox, jumps, over, the, lazy, dog]
Sorted  : [brown, dog, fox, jumps, lazy, over, quick, the, the]

Lua[edit]

The first argument to the 'inner' function needs to be a reference to the table as Lua cannot use a pointer to the first element's memory address. Conversely the 'outer' function only needs one argument as the size of the table is innately knowable.

-- Perform one iteration of a circle sort
function innerCircle (t, lo, hi, swaps)
if lo == hi then return swaps end
local high, low, mid = hi, lo, math.floor((hi - lo) / 2)
while lo < hi do
if t[lo] > t[hi] then
t[lo], t[hi] = t[hi], t[lo]
swaps = swaps + 1
end
lo = lo + 1
hi = hi - 1
end
if lo == hi then
if t[lo] > t[hi + 1] then
t[lo], t[hi + 1] = t[hi + 1], t[lo]
swaps = swaps + 1
end
end
swaps = innerCircle(t, low, low + mid, swaps)
swaps = innerCircle(t, low + mid + 1, high, swaps)
return swaps
end
 
-- Keep sorting the table until an iteration makes no swaps
function circleSort (t)
while innerCircle(t, 1, #t, 0) > 0 do end
end
 
-- Main procedure
local array = {6, 7, 8, 9, 2, 5, 3, 4, 1}
circleSort(array)
print(table.concat(array, " "))
Output:
1 2 3 4 5 6 7 8 9

Objeck[edit]

Translation of: Objeck
class CircleSort {
function : Main(args : String[]) ~ Nil {
circleSort([2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]);
}
 
function : circleSort(arr : Int[]) ~ Nil {
if(arr->Size() > 0) {
do {
arr->ToString()->PrintLine();
}
while(CircleSort(arr, 0, arr->Size() - 1, 0) <> 0);
};
}
 
function : CircleSort( arr : Int[], lo : Int, hi : Int, num_swaps : Int) ~ Int {
if(lo = hi) {
return num_swaps;
};
 
 
high := hi;
low := lo;
mid := (hi - lo) / 2;
 
while (lo < hi) {
if(arr[lo] > arr[hi]) {
Swap(arr, lo, hi);
num_swaps++;
};
lo++;
hi--;
};
 
if(lo = hi & arr[lo] > arr[hi + 1]) {
Swap(arr, lo, hi + 1);
num_swaps++;
};
 
num_swaps := CircleSort(arr, low, low + mid, num_swaps);
num_swaps := CircleSort(arr, low + mid + 1, high, num_swaps);
 
return num_swaps;
}
 
function : Swap(arr : Int[], idx1 : Int, idx2 : Int) ~ Nil {
tmp := arr[idx1];
arr[idx1] := arr[idx2];
arr[idx2] := tmp;
}
}
 

Output:

[2,14,4,6,8,1,3,5,7,11,0,13,12,-1]
[-1,1,0,4,3,8,12,2,7,6,11,5,13,14]
[-1,0,1,3,2,4,7,5,6,8,12,11,13,14]
[-1,0,1,2,3,4,5,6,7,8,11,12,13,14]

PARI/GP[edit]

This follows the pseudocode pretty closely.

circlesort(v)=
{
local(v=v); \\ share with cs
while (cs(1, #v),);
v;
}
cs(lo, hi)=
{
if (lo == hi, return (0));
my(high=hi,low=lo,mid=(hi-lo)\2,swaps);
while (lo < hi,
if (v[lo] > v[hi],
[v[lo],v[hi]]=[v[hi],v[lo]];
swaps++
);
lo++;
hi--
);
if (lo==hi && v[lo] > v[hi+1],
[v[lo],v[hi+1]]=[v[hi+1],v[lo]];
swaps++
);
swaps + cs(low,low+mid) + cs(low+mid+1,high);
}
print(example=[6,7,8,9,2,5,3,4,1]);
print(circlesort(example));
Output:
[6, 7, 8, 9, 2, 5, 3, 4, 1]
[1, 2, 3, 4, 5, 6, 7, 8, 9]

Pascal[edit]

 
{
source file name on linux is ./p.p
 
-*- mode: compilation; default-directory: "/tmp/" -*-
Compilation started at Sat Mar 11 23:55:25
 
a=./p && pc $a.p && $a
Free Pascal Compiler version 3.0.0+dfsg-8 [2016/09/03] for x86_64
Copyright (c) 1993-2015 by Florian Klaempfl and others
Target OS: Linux for x86-64
Compiling ./p.p
Linking p
/usr/bin/ld.bfd: warning: link.res contains output sections; did you forget -T?
56 lines compiled, 0.0 sec
1 2 3 4 5 6 7 8 9
 
Compilation finished at Sat Mar 11 23:55:25
}

 
program sort;
 
var
a : array[0..999] of integer;
i : integer;
 
procedure circle_sort(var a : array of integer; left : integer; right : integer);
var swaps : integer;
 
procedure csinternal(var a : array of integer; left : integer; right : integer; var swaps : integer);
var
lo, hi, mid : integer;
t : integer;
begin
if left < right then
begin
lo := left;
hi := right;
while lo < hi do
begin
if a[hi] < a[lo] then
begin
t := a[lo]; a[lo] := a[hi]; a[hi] := t;
swaps := swaps + 1;
end;
lo := lo + 1;
hi := hi - 1;
end;
if (lo = hi) and (a[lo+1] < a[lo]) then
begin
t := a[lo]; a[lo] := a[lo+1]; a[lo+1] := t;
swaps := swaps + 1;
end;
mid := trunc((hi + lo) / 2);
csinternal(a, left, mid, swaps);
csinternal(a, mid + 1, right, swaps)
end
end;
 
begin;
swaps := 1;
while (0 < swaps) do
begin
swaps := 0;
csinternal(a, left, right, swaps);
end
end;
 
begin
{
generating polynomial coefficients computed in j: 6 7 8 9 2 5 3 4 1x %. ^/~i.9x
are 6 29999r280 _292519r1120 70219r288 _73271r640 10697r360 _4153r960 667r2016 _139r13440
}

a[1]:=6;a[2]:=7;a[3]:=8;a[4]:=9;a[5]:=2;a[6]:=5;a[7]:=3;a[8]:=4;a[9]:=1;
circle_sort(a,1,9);
for i := 1 to 9 do write(a[i], ' ');
writeln();
end.
 

Perl 6[edit]

The given algorithm can be simplified in several ways. There's no need to compute the midpoint, since the hi/lo will end up there. The extra swap conditional can be eliminated by incrementing hi at the correct moment inside the loop. There's no need to pass accumulated swaps down the call stack.

This does generic comparisons, so it works on any ordered type, including numbers or strings.

sub circlesort (@x, $beg, $end) {
my $swaps = 0;
if $beg < $end {
my ($lo, $hi) = $beg, $end;
repeat {
if @x[$lo] after @x[$hi] {
@x[$lo,$hi] .= reverse;
++$swaps;
}
++$hi if --$hi == ++$lo
} while $lo < $hi;
$swaps += circlesort(@x, $beg, $hi);
$swaps += circlesort(@x, $lo, $end);
}
$swaps;
}
 
say my @x = (-100..100).roll(20);
say @x while circlesort(@x, 0, @x.end);
 
say @x = <The quick brown fox jumps over the lazy dog.>;
say @x while circlesort(@x, 0, @x.end);
Output:
16 35 -64 -29 46 36 -1 -99 20 100 59 26 76 -78 39 85 -7 -81 25 88
-99 -78 16 20 36 -81 -29 46 25 59 -64 -7 39 26 88 -1 35 85 76 100
-99 -78 -29 -81 16 -64 -7 20 -1 39 25 26 36 46 59 35 76 88 85 100
-99 -81 -78 -64 -29 -7 -1 16 20 25 26 35 36 39 46 59 76 85 88 100
The quick brown fox jumps over the lazy dog.
The brown fox jumps lazy dog. quick over the
The brown dog. fox jumps lazy over quick the

Python[edit]

The doctest passes with odd and even length lists. As do the random tests. Please see circle_sort.__doc__ for example use and output.

 
#python3
#tests: expect no output.
#doctest with python3 -m doctest thisfile.py
#additional tests: python3 thisfile.py
 
def circle_sort_backend(A:list, L:int, R:int)->'sort A in place, returning the number of swaps':
'''
>>> L = [3, 2, 8, 28, 2,]
>>> circle_sort(L)
3
>>> print(L)
[2, 2, 3, 8, 28]
>>> L = [3, 2, 8, 28,]
>>> circle_sort(L)
1
>>> print(L)
[2, 3, 8, 28]
'''

n = R-L
if n < 2:
return 0
swaps = 0
m = n//2
for i in range(m):
if A[R-(i+1)] < A[L+i]:
(A[R-(i+1)], A[L+i],) = (A[L+i], A[R-(i+1)],)
swaps += 1
if (n & 1) and (A[L+m] < A[L+m-1]):
(A[L+m-1], A[L+m],) = (A[L+m], A[L+m-1],)
swaps += 1
return swaps + circle_sort_backend(A, L, L+m) + circle_sort_backend(A, L+m, R)
 
def circle_sort(L:list)->'sort A in place, returning the number of swaps':
swaps = 0
s = 1
while s:
s = circle_sort_backend(L, 0, len(L))
swaps += s
return swaps
 
# more tests!
if __name__ == '__main__':
from random import shuffle
for i in range(309):
L = list(range(i))
M = L[:]
shuffle(L)
N = L[:]
circle_sort(L)
if L != M:
print(len(L))
print(N)
print(L)
 

Racket[edit]

By default this sorts with the numeric < but any other (diadic) function can be used to compare... e.g. string<?.

#lang racket
(define (circle-sort v0 [<? <])
(define v (vector-copy v0))
 
(define (swap-if l r)
(define v.l (vector-ref v l))
(define v.r (vector-ref v r))
(and (<? v.r v.l)
(begin (vector-set! v l v.r) (vector-set! v r v.l) #t)))
 
(define (inr-cs! L R)
(cond
[(>= L (- R 1)) #f] ; covers 0 or 1 vectors
[else
(define M (quotient (+ L R) 2))
(define I-moved?
(for/or ([l (in-range L M)] [r (in-range (- R 1) L -1)])
(swap-if l r)))
(define M-moved? (and (odd? (- L R)) (> M 0) (swap-if (- M 1) M)))
(define L-moved? (inr-cs! L M))
(define R-moved? (inr-cs! M R))
(or I-moved? L-moved? R-moved? M-moved?)]))
 
(let loop () (when (inr-cs! 0 (vector-length v)) (loop)))
v)
 
(define (sort-random-vector)
(define v (build-vector (+ 2 (random 10)) (λ (i) (random 100))))
(define v< (circle-sort v <))
(define sorted? (apply <= (vector->list v<)))
(printf " ~.a\n-> ~.a [~a]\n\n" v v< sorted?))
 
(for ([_ 10]) (sort-random-vector))
 
(circle-sort '#("table" "chair" "cat" "sponge") string<?)
Output:
   #(36 94 63 51 33)
-> #(33 36 51 63 94) [#t]

   #(73 74 20 20 79)
-> #(20 20 73 74 79) [#t]

   #(83 42)
-> #(42 83) [#t]

   #(53 95 43 33 66 47 1 61 28 96)
-> #(1 28 33 43 47 53 61 66 95 96) [#t]

   #(71 85)
-> #(71 85) [#t]

   #(36 85 50 19 88 17 2 53 21)
-> #(2 17 19 21 36 50 53 85 88) [#t]

   #(5 97 62 21 99 73 17 16 37 28)
-> #(5 16 17 21 28 37 62 73 97 99) [#t]

   #(12 60 89 90 2 95 9 28)
-> #(2 9 12 28 60 89 90 95) [#t]

   #(50 32 30 47 63 74)
-> #(30 32 47 50 63 74) [#t]

   #(63 41)
-> #(41 63) [#t]

'#("cat" "chair" "sponge" "table")

REXX[edit]

This REXX version will work with any numbers that REXX supports, including negative and/or floating point numbers.

/*REXX program uses a  circle sort algorithm  to sort an array (or list) of numbers.    */
parse arg x /*obtain optional arguments from the CL*/
if x='' | x="," then x= 6 7 8 9 2 5 3 4 1 /*Not specified? Then use the default.*/
call make_array 'before sort:' /*display the list and make an array. */
call circleSort # /*invoke the circle sort subroutine. */
call make_list ' after sort:' /*make a list and display it to console*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
circleSort: do while .circleSrt(1, arg(1), 0)\==0; end; return
make_array: #=words(x); do i=1 for #; @.i=word(x, i); end; say arg(1) x; return
make_list: [email protected].1; do j=2 for #-1; y=y @.j; end; say arg(1) y; return
.swap: parse arg a,b; parse value @.a @.b with @.b @.a; swaps=swaps+1; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
.circleSrt: procedure expose @.; parse arg LO,HI,swaps /*obtain LO & HI arguments.*/
if LO==HI then return swaps /*1 element? Done with sort.*/
high=HI; low=LO; mid=(HI-LO) % 2 /*assign some indices. */
/* [↓] sort a section of #'s*/
do while LO<HI /*sort within a section. */
if @.LO>@.HI then call .swap LO,HI /*are numbers out of order ? */
LO=LO+1; HI=HI-1 /*add to LO; shrink the HI. */
end /*while*/ /*just process one section. */
_=hi+1 /*point to HI plus one. */
if LO==HI & @.LO>@._ then call .swap LO, _ /*numbers still out of order?*/
swaps=.circleSrt(low, low+mid, swaps) /*sort the lower section. */
swaps=.circleSrt(low+mid+1, high, swaps) /* " " higher " */
return swaps /*the section sorting is done*/
output   when using the default input:
before sort:  6 7 8 9 2 5 3 4 1
 after sort:  1 2 3 4 5 6 7 8 9
output   when using the input of:   2 3 3 5 5 1 1 7 7 6 6 4 4 0 0
before sort: 2 3 3 5 5 1 1 7 7 6 6 4 4 0 0
 after sort: 0 0 1 1 2 3 3 4 4 5 5 6 6 7 7
output   when using the input of:   2 3 44 44 5.77 +1 -12345 -3 -3.9 1e7 9
before sort: 2 3 44 44 5.77 +1 -12345 -3 -3.9 1e7 0
 after sort: -12345 -3.9 -3 0 +1 2 3 5.77 44 44 1e7
output   when using the using the input of:   assinine donkey bovine cattle canine dog corvine crow equine horse feline cat hircine goat leporine hare lupine wolf murine rodent piscine fish porcine pig ursine bear vulpine fox
before sort: assinine donkey bovine cattle canine dog corvine crow equine horse feline cat hircine goat leporine hare lupine wolf murine rodent piscine fish porcine pig ursine bear vulpine fox
 after sort: assinine bear bovine canine cat cattle corvine crow dog donkey equine feline fish fox goat hare hircine horse leporine lupine murine pig piscine porcine rodent ursine vulpine wolf

Ring[edit]

 
# Project : Sorting Algorithms/Circle Sort
# Date  : 2017/10/23
# Author : Gal Zsolt (~ CalmoSoft ~)
# Email  : <[email protected]>
 
test = [-4, -1, 1, 0, 5, -7, -2, 4, -6, -3, 2, 6, 3, 7, -5]
while circlesort(1, len(test), 0) end
showarray(test)
 
func circlesort(lo, hi, swaps)
if lo = hi
return swaps
ok
high = hi
low = lo
mid = floor((hi-lo)/2)
while lo < hi
if test[lo] > test[hi]
temp = test[lo]
test[lo] = test[hi]
test[hi] = temp
swaps = swaps + 1
ok
lo = lo + 1
hi = hi - 1
end
if lo = hi
if test[lo] > test[hi+1]
temp = test[lo]
test[lo] = test[hi+1]
test[hi + 1] = temp
swaps = swaps + 1
ok
ok
swaps = circlesort(low, low+mid, swaps)
swaps = circlesort(low+mid+1 ,high, swaps)
return swaps
 
func showarray(vect)
see "["
svect = ""
for n = 1 to len(vect)
svect = svect + vect[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl
 

Output:

[-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7]

Ruby[edit]

class Array
def circle_sort!
while _circle_sort!(0, size-1) > 0
end
self
end
 
private
def _circle_sort!(lo, hi, swaps=0)
return swaps if lo == hi
low, high = lo, hi
mid = (lo + hi) / 2
while lo < hi
if self[lo] > self[hi]
self[lo], self[hi] = self[hi], self[lo]
swaps += 1
end
lo += 1
hi -= 1
end
if lo == hi && self[lo] > self[hi+1]
self[lo], self[hi+1] = self[hi+1], self[lo]
swaps += 1
end
swaps + _circle_sort!(low, mid) + _circle_sort!(mid+1, high)
end
end
 
ary = [6, 7, 8, 9, 2, 5, 3, 4, 1]
puts "before sort: #{ary}"
puts " after sort: #{ary.circle_sort!}"
Output:
before sort: [6, 7, 8, 9, 2, 5, 3, 4, 1]
 after sort: [1, 2, 3, 4, 5, 6, 7, 8, 9]

Sidef[edit]

func circlesort(arr, beg=0, end=arr.end) {
var swaps = 0
if (beg < end) {
var (lo, hi) = (beg, end)
do {
if (arr[lo] > arr[hi]) {
arr.swap(lo, hi)
++swaps
}
++hi if (--hi == ++lo)
} while (lo < hi)
swaps += circlesort(arr, beg, hi)
swaps += circlesort(arr, lo, end)
}
return swaps
}
 
var numbers = %n(2 3 3 5 5 1 1 7 7 6 6 4 4 0 0)
do { say numbers } while circlesort(numbers)
 
var strs = ["John", "Kate", "Zerg", "Alice", "Joe", "Jane", "Alice"]
do { say strs } while circlesort(strs)
Output:
[2, 3, 3, 5, 5, 1, 1, 7, 7, 6, 6, 4, 4, 0, 0]
[0, 0, 1, 4, 1, 5, 3, 7, 2, 3, 4, 5, 6, 6, 7]
[0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 5, 7, 6, 6, 7]
[0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7]
["John", "Kate", "Zerg", "Alice", "Joe", "Jane", "Alice"]
["Alice", "Jane", "Alice", "Joe", "John", "Kate", "Zerg"]
["Alice", "Alice", "Jane", "Joe", "John", "Kate", "Zerg"]

uBasic/4tH[edit]

This one uses the optimized version featured at Sourceforge.

PRINT "Circle sort:"
n = FUNC (_InitArray)
PROC _ShowArray (n)
PROC _Circlesort (n)
PROC _ShowArray (n)
PRINT
 
END
 
_InnerCircle PARAM (2)
LOCAL (3)
[email protected] = [email protected]
[email protected] = [email protected]
[email protected] = 0
 
IF [email protected] = [email protected] THEN RETURN (0)
 
DO WHILE [email protected] < [email protected]
IF @([email protected]) > @([email protected]) THEN PROC _Swap ([email protected], [email protected]) : [email protected] = [email protected] + 1
[email protected] = [email protected] + 1
[email protected] = [email protected] - 1
LOOP
 
[email protected] = [email protected] + FUNC (_InnerCircle ([email protected], [email protected]))
[email protected] = [email protected] + FUNC (_InnerCircle ([email protected], [email protected]))
RETURN ([email protected])
 
 
_Circlesort PARAM(1) ' Circle sort
DO WHILE FUNC (_InnerCircle (0, [email protected]))
LOOP
RETURN
 
 
_Swap PARAM(2) ' Swap two array elements
PUSH @([email protected])
@([email protected]) = @([email protected])
@([email protected]) = POP()
RETURN
 
 
_InitArray ' Init example array
PUSH 4, 65, 2, -31, 0, 99, 2, 83, 782, 1
 
FOR i = 0 TO 9
@(i) = POP()
NEXT
 
RETURN (i)
 
 
_ShowArray PARAM (1) ' Show array subroutine
FOR i = 0 TO [email protected]
PRINT @(i),
NEXT
 
PRINT
RETURN

zkl[edit]

fcn circleSort(list){
csort:=fcn(list,lo,hi,swaps){
if(lo==hi) return(swaps);
high,low,mid:=hi,lo,(hi-lo)/2;
while(lo<hi){
if(list[lo]>list[hi]){
list.swap(lo,hi);
swaps+=1;
}
lo+=1; hi-=1;
}
if(lo==hi)
if (list[lo]>list[hi+1]){
list.swap(lo,hi+1);
swaps+=1;
}
swaps=self.fcn(list,low,low + mid,swaps);
swaps=self.fcn(list,low + mid + 1,high,swaps);
return(swaps);
};
list.println();
while(csort(list,0,list.len()-1,0)){ list.println() }
list
}
circleSort(L(6,7,8,9,2,5,3,4,1));
circleSort(L(5,-1,101,-4,0,1,8,6,2,3));
Output:
L(6,7,8,9,2,5,3,4,1)
L(1,3,4,2,5,6,7,8,9)
L(1,2,3,4,5,6,7,8,9)
L(5,-1,101,-4,0,1,8,6,2,3)
L(-4,-1,0,3,6,1,2,8,5,101)
L(-4,-1,0,1,2,3,5,6,8,101)

ZX Spectrum Basic[edit]

A language like ZX BASIC is not the most obvious choice for a routine which depends on local variables and recursion. This program proves that it can be implemented quite efficiently using arrays and global variables. The b and e variables are set up in such a way that they can be used for the first recursive call. The variables for the next recursion are saved in array s() which serves as a stack together with stack pointer p.

The size of the stack is determined by the amount of memory on the ZX Spectrum, which is 64KB (or 216 bytes). Each call requires two array elements. Note the size of a ZX Spectrum floating point number is 5 bytes, so this stack is slightly oversized. The somewhat strange indexing between both recursions is due to an stack pointer adjustment which was optimized away.

This version of Circle sort was based on the optimized version on Sourceforge. It will also show a few asterisks while running, because it will take some time to finish (about two minutes).

 
10 DIM a(100): DIM s(32): RANDOMIZE : LET p=1: GO SUB 3000: GO SUB 2000: GO SUB 4000
20 STOP
1000 IF b=e THEN RETURN
1010 LET s(p)=b: LET s(p+1)=e
1020 IF a(s(p))>a(e) THEN LET t=a(s(p)): LET a(s(p))=a(e): LET a(e)=t: LET c=1
1030 LET s(p)=s(p)+1: LET e=e-1: IF s(p)<e THEN GO TO 1020
1040 LET p=p+2: GO SUB 1000: LET b=s(p-2): LET e=s(p-1): GO SUB 1000: LET p=p-2: RETURN
2000 PRINT "*";: LET b=1: LET e=100: LET c=0: GO SUB 1000: IF c>0 THEN GO TO 2000
2010 CLS : RETURN
3000 FOR x=1 TO 100: LET a(x)=RND: NEXT x: RETURN
4000 FOR x=1 TO 100: PRINT x,a(x): NEXT x: RETURN