Sattolo cycle

The Sattolo cycle is an algorithm for randomly shuffling an array in such a way that each element ends up in a new position.

Task

Implement the Sattolo cycle for an integer array (or, if possible, an array of any type).

Specification

Sattolo's algorithm is defined as follows (pseudo-code):

let items = the input array

for each index i of items, from right to left, excluding the left-most one, do:
    let j = randomly chosen index below i
    swap items[i] with items[j]

This modifies the input array in-place. If that is unreasonable in your programming language, you may amend the algorithm to return the shuffled items as a new array instead.

Also note that the only difference between this and the Knuth shuffle, is that $j$ is chosen from the range $0\leq j<i$ , rather than $0\leq j\leq i$ . This is what ensures that every element ends up in a new position.

Related tasks

Knuth shuffle

C#

<lang csharp>private static readonly Random Rand = new Random();

void sattoloCycle<T>(IList<T> items) {

   for (var i = items.Count; i-- > 1;) {
       int j = Rand.Next(i);
       var tmp = items[i];
       items[i] = items[j];
       items[j] = tmp;
   }

}</lang>

J

This task currently needs a better description. That said, this achieves the result of the Sattolo cycle:

Java

<lang Java>private static final Random rng = new Random();

void sattoloCycle(Object[] items) {

   for (int i = items.length; i-- > 1;) {
       int j = rng.nextInt(i);
       Object tmp = items[i];
       items[i] = items[j];
       items[j] = tmp;
   }

}</lang>

JavaScript

<lang JavaScript>function sattoloCycle(items) {

   for (var i = items.length; i--> 1;) {
       var j = Math.floor(Math.random() * i);
       var tmp = items[i];
       items[i] = items[j];
       items[j] = tmp;
   }

}</lang>

Perl 6

This modifies the array passed as argument, in-place.

<lang perl6>sub sattolo-cycle (@array) {

   for reverse 1 .. @array.end -> $i {
       my $j = (^$i).pick;
       @array[$j, $i] = @array[$i, $j];
   }

}</lang>

Python

Copied from Wikipedia:

<lang python>from random import randrange

def sattoloCycle(items):

   i = len(items)
   while i > 1:
       i = i - 1
       j = randrange(i)  # 0 <= j <= i-1
       items[j], items[i] = items[i], items[j]
   return</lang>

REXX

This REXX example uses a zero-based array; the array elements can be of any type. <lang rexx>/*REXX program implements and displays a Sattolo shuffle for an array (of any type).*/ parse arg a; a=space(a) /*obtain optional arguments from the CL*/ if a= then a='-1 0 1 2 00 44 5 {6} 7 ~ 8 7.9 one two ¬¬ four +4 five six /\ [nine] Ace' say 'original:' a n=words(a) /*obtain the number of elements in list*/

          do j=0  for n;  @.j=word(a, j+1); end /*assign an element to the  @.  array. */

          do i=0  to  n-2;  j=random(i, n-1)    /*get a random integer between I & N-1.*/
          parse value  @.i  @.j  with  @.j  @.i /*swap two array elements, J is random.*/
          end   /*i*/

$=@.0 /*start with the first element in array*/

          do k=1  for n-1;  $=$  @.k;   end     /*append the next element in the array.*/

say ' Sattolo:' $ /*stick a fork in it, we're all done. */</lang>

output when using the default input:

original: -1 0 1 2 00 44 5 {6} 7 ~ 8 7.9 one two ¬¬ four +4 five six /\ [nine] Ace
 Sattolo: 7 ~ {6} +4 44 5 00 7.9 two [nine] four one 0 -1 /\ ¬¬ five 8 Ace 1 2 six

TypeScript

<lang TypeScript>function sattoloCycle<T>(items: Array<T>): void {

   for (let i = items.length; i--> 1;) {
       const j = Math.floor(Math.random() * i);
       const tmp = items[i];
       items[i] = items[j];
       items[j] = tmp;
   }

}</lang>

zkl

<lang zkl>fcn sattoloCycle(list){ // in place

  foreach i in ([list.len()-1 .. 1,-1]){
     list.swap(i,(0).random(i));  # 0 <= j < i
  }
  list

}</lang> <lang zkl>sattoloCycle([0..9].walk().copy()).println(); sattoloCycle("this is a test".split()).println();</lang>

Output:

L(6,3,8,2,5,7,1,0,9,4)
L("test","this","is","a")