Sorting Algorithms/Circle Sort: Difference between revisions
SqrtNegInf (talk | contribs) (Added Perl example) |
|||
Line 960: | Line 960: | ||
end. |
end. |
||
</lang> |
</lang> |
||
=={{header|Perl}}== |
|||
Less flexible than the Perl 6 version, as written does only numeric comparisons. |
|||
{{trans|Perl 6}} |
|||
<lang perl>sub circlesort { |
|||
our @x; local *x = shift; |
|||
my($beg,$end) = @_; |
|||
my $swaps = 0; |
|||
if ($beg < $end) { |
|||
my $lo = $beg; |
|||
my $hi = $end; |
|||
while ($lo < $hi) { |
|||
if ($x[$lo] > $x[$hi]) { # 'gt' here for string comparison |
|||
@x[$lo,$hi] = @x[$hi,$lo]; |
|||
++$swaps; |
|||
} |
|||
++$hi if --$hi == ++$lo |
|||
} |
|||
$swaps += circlesort(\@x, $beg, $hi); |
|||
$swaps += circlesort(\@x, $lo, $end); |
|||
} |
|||
$swaps; |
|||
} |
|||
my @a = <16 35 -64 -29 46 36 -1 -99 20 100 59 26 76 -78 39 85 -7 -81 25 88>; |
|||
while (circlesort(\@a, 0, $#a)) { say join ' ', @a }</lang> |
|||
{{out}} |
|||
<pre>-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 |
|||
-99 -81 -78 -64 -29 -7 -1 16 20 25 26 35 36 39 46 59 76 85 88 100</pre> |
|||
=={{header|Perl 6}}== |
=={{header|Perl 6}}== |
Revision as of 00:17, 22 September 2018
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
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
<lang c>#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)
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; }</lang>
- 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
<lang>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</lang>
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
<lang d>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); }
}</lang>
- Output:
[-4, -1, 0, 1, 2, 3, 5, 6, 8, 101]
Elixir
<lang elixir>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)}"</lang>
- Output:
before sort: [6, 7, 8, 9, 2, 5, 3, 4, 1] after sort: [1, 2, 3, 4, 5, 6, 7, 8, 9]
Forth
This one features the newest version of the algorithm on Sourceforge. <lang>[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</lang>
Fortran
<lang fortran> ! 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
</lang>
FreeBASIC
<lang freebasic>' 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</lang>
- 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
<lang go>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) }
}</lang>
- 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
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.
<lang J> circle_sort =: post power_of_2_length@pre NB. the main sorting verb power_of_2_length =: even_length_iteration^:_ NB. repeat while the answer changes even_length_iteration =: (<./ (,&$: |.) >./)@(-:@# ({. ,: |.@}.) ])^:(1<#) pre =: , (-~ >.&.(2&^.))@# # >./ NB. extend data to next power of 2 length post =: ({.~ #)~ NB. remove the extra data </lang> Examples: <lang J>
show =: [ smoutput
8 ([: circle_sort&.>@show ;&(?~)) 13 NB. sort lists length 8 and 13
โโโโโโโโโโโโโโโโโฌโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ0 6 7 3 4 5 2 1โ3 10 1 4 7 8 5 6 2 0 9 11 12โ โโโโโโโโโโโโโโโโโดโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโโฌโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ0 1 2 3 4 5 6 7โ0 1 2 3 4 5 6 7 8 9 10 11 12โ โโโโโโโโโโโโโโโโโดโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
8 ([: circle_sort&.>@show ;&(1 }. 2 # ?~)) 13 NB. data has repetition
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโฌโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ2 3 3 5 5 1 1 7 7 6 6 4 4 0 0โ12 11 11 4 4 3 3 9 9 7 7 10 10 6 6 2 2 1 1 5 5 8 8 0 0โ โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโดโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโฌโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ0 0 1 1 2 3 3 4 4 5 5 6 6 7 7โ0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12โ โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโดโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ </lang>
Java
<lang java>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; }
}</lang>
[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
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: <lang jq>def until(cond; next):
def _until: if cond then . else (next|_until) end; _until;</lang>
<lang jq>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 $swaps == 0 then . else circlesort end ;</lang>
Example: <lang jq>"The quick brown fox jumps over the lazy dog" | split(" ") | circlesort</lang>
- Output:
<lang sh>$ jq -n -c -f -M circleSort.jq ["The","brown","dog","fox","jumps","lazy","over","quick","the"]</lang>
Julia
<lang julia>function _ciclesort!(arr::Vector, lo::Int, hi::Int, swaps::Int)
lo == hi && return swaps high = hi low = lo mid = (hi - lo) รท 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))</lang>
- 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
<lang scala>// 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()}")
}</lang>
- 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
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. <lang Lua>-- 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, " "))</lang>
- Output:
1 2 3 4 5 6 7 8 9
Nim
<lang nim>proc innerCircleSort[T](a: var openArray[T], lo, hi, swaps: int): int =
var localSwaps: int = swaps var localHi: int = hi var localLo: int = lo if localLo == localHi: return swaps var `high` = localHi var `low` = localLo var mid = (localHi - localLo) div 2
while localLo < localHi: if a[localLo] > a[localHi]: swap a[localLo], a[localHi] inc localSwaps inc localLo dec localHi if localLo == localHi: if a[localLo] > a[localHi + 1]: swap a[localLo], a[localHi + 1] inc localSwaps
localswaps = a.innerCircleSort(`low`, `low` + mid, localSwaps) localSwaps = a.innerCircleSort(`low` + mid + 1, `high`, localSwaps) result = localSwaps
proc circleSort[T](a: var openArray[T]) =
while a.innerCircleSort(0, a.high, 0) != 0: discard
var arr = @[@[6, 7, 8, 9, 2, 5, 3, 4, 1],
@[2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1]]
for i in 0..arr.high:
echo "Original: ", $arr[i] arr[i].circleSort() echo "Sorted: ", $arr[i], if i != arr.high: "\n" else: ""</lang>
- 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]
Objeck
<lang 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; }
} </lang>
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
This follows the pseudocode pretty closely. <lang parigp>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));</lang>
- Output:
[6, 7, 8, 9, 2, 5, 3, 4, 1] [1, 2, 3, 4, 5, 6, 7, 8, 9]
Pascal
<lang pascal> {
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 && $a Free Pascal Compiler version 3.0.0+dfsg-8 [2016/09/03] for x86_64 Copyright (c) 1993-2015 by Florian Klaempfl and others Target OS: Linux for x86-64 Compiling ./p.p Linking p /usr/bin/ld.bfd: warning: link.res contains output sections; did you forget -T? 56 lines compiled, 0.0 sec 1 2 3 4 5 6 7 8 9
Compilation finished at Sat Mar 11 23:55:25
}
program sort;
var
a : array[0..999] of integer; i : integer;
procedure circle_sort(var a : array of integer; left : integer; right : integer); var swaps : integer;
procedure csinternal(var a : array of integer; left : integer; right : integer; var swaps : integer); var lo, hi, mid : integer; t : integer; begin if left < right then begin
lo := left; hi := right; while lo < hi do begin if a[hi] < a[lo] then begin t := a[lo]; a[lo] := a[hi]; a[hi] := t; swaps := swaps + 1; end; lo := lo + 1; hi := hi - 1; end; if (lo = hi) and (a[lo+1] < a[lo]) then begin t := a[lo]; a[lo] := a[lo+1]; a[lo+1] := t; swaps := swaps + 1; end; mid := trunc((hi + lo) / 2); csinternal(a, left, mid, swaps); csinternal(a, mid + 1, right, swaps)
end end;
begin;
swaps := 1; while (0 < swaps) do begin swaps := 0; csinternal(a, left, right, swaps); end
end;
begin
{ generating polynomial coefficients computed in j: 6 7 8 9 2 5 3 4 1x %. ^/~i.9x are 6 29999r280 _292519r1120 70219r288 _73271r640 10697r360 _4153r960 667r2016 _139r13440 } a[1]:=6;a[2]:=7;a[3]:=8;a[4]:=9;a[5]:=2;a[6]:=5;a[7]:=3;a[8]:=4;a[9]:=1; circle_sort(a,1,9); for i := 1 to 9 do write(a[i], ' '); writeln();
end. </lang>
Perl
Less flexible than the Perl 6 version, as written does only numeric comparisons.
<lang perl>sub circlesort {
our @x; local *x = shift; my($beg,$end) = @_;
my $swaps = 0; if ($beg < $end) { my $lo = $beg; my $hi = $end; while ($lo < $hi) { if ($x[$lo] > $x[$hi]) { # 'gt' here for string comparison @x[$lo,$hi] = @x[$hi,$lo]; ++$swaps; } ++$hi if --$hi == ++$lo } $swaps += circlesort(\@x, $beg, $hi); $swaps += circlesort(\@x, $lo, $end); } $swaps;
}
my @a = <16 35 -64 -29 46 36 -1 -99 20 100 59 26 76 -78 39 85 -7 -81 25 88>; while (circlesort(\@a, 0, $#a)) { say join ' ', @a }</lang>
- Output:
-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 -99 -81 -78 -64 -29 -7 -1 16 20 25 26 35 36 39 46 59 76 85 88 100
Perl 6
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. <lang perl6>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);</lang>
- 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
The doctest passes with odd and even length lists. As do the random tests. Please see circle_sort.__doc__ for example use and output. <lang python>
- 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)
</lang>
Racket
By default this sorts with the numeric <
but any other
(diadic) function can be used to compare... e.g. string<?
.
<lang racket>#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)) (ฮป (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<?)</lang>
- 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
This REXX version will work with any numbers that REXX supports, including negative and/or floating point numbers. <lang rexx>/*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. */ /*โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ*/ 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: y=@.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 /*โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ*/ .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. */ /* [โ] 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*/</lang>
- 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
<lang ring>
- Project : Sorting Algorithms/Circle Sort
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
</lang> Output:
[-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7]
Ruby
<lang ruby>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!}"</lang>
- Output:
before sort: [6, 7, 8, 9, 2, 5, 3, 4, 1] after sort: [1, 2, 3, 4, 5, 6, 7, 8, 9]
Scala
<lang Scala>object CircleSort extends App {
def sort(arr: Array[Int]): Array[Int] = { def circleSortR(arr: Array[Int], _lo: Int, _hi: Int, _numSwaps: Int): Int = { var lo = _lo var hi = _hi var numSwaps = _numSwaps
def swap(arr: Array[Int], idx1: Int, idx2: Int): Unit = { val tmp = arr(idx1) arr(idx1) = arr(idx2) arr(idx2) = tmp }
if (lo == hi) return numSwaps val (high, low) = (hi, lo) val mid = (hi - lo) / 2 while ( lo < hi) { if (arr(lo) > arr(hi)) { swap(arr, lo, hi) numSwaps += 1 } lo += 1 hi -= 1 } if (lo == hi && arr(lo) > arr(hi + 1)) { swap(arr, lo, hi + 1) numSwaps += 1 }
circleSortR(arr, low + mid + 1, high, circleSortR(arr, low, low + mid, numSwaps)) }
while (circleSortR(arr, 0, arr.length - 1, 0) != 0)() arr }
println(sort(Array[Int](2, 14, 4, 6, 8, 1, 3, 5, 7, 11, 0, 13, 12, -1)).mkString(", "))
}</lang>
Sidef
<lang ruby>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)</lang>
- 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
This one uses the optimized version featured at Sourceforge. <lang>PRINT "Circle sort:"
n = FUNC (_InitArray) PROC _ShowArray (n) PROC _Circlesort (n) PROC _ShowArray (n)
END
_InnerCircle PARAM (2)
LOCAL (3) c@ = a@ d@ = b@ e@ = 0
IF c@ = d@ THEN RETURN (0)
DO WHILE c@ < d@ IF @(c@) > @(d@) THEN PROC _Swap (c@, d@) : e@ = e@ + 1 c@ = c@ + 1 d@ = d@ - 1 LOOP
e@ = e@ + FUNC (_InnerCircle (a@, d@)) e@ = e@ + FUNC (_InnerCircle (c@, b@))
RETURN (e@)
_Circlesort PARAM(1) ' Circle sort
DO WHILE FUNC (_InnerCircle (0, a@-1)) LOOP
RETURN
_Swap PARAM(2) ' Swap two array elements
PUSH @(a@) @(a@) = @(b@) @(b@) = 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 a@-1 PRINT @(i), NEXT
RETURN</lang>
zkl
<lang zkl>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
}</lang> <lang zkl>circleSort(L(6,7,8,9,2,5,3,4,1)); circleSort(L(5,-1,101,-4,0,1,8,6,2,3));</lang>
- 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
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).
<lang zxbasic>
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
</lang>