Sattolo cycle

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Revision as of 15:21, 9 November 2017 by Aamrun (talk | contribs) (Added C implementation.)
Sattolo cycle 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.

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

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

Specification

Given an array items with indices ranging from 0 to last, the algorithm can be defined as follows (pseudo-code): 

for i from last downto 1 do:
    let j = random integer in range 0  j < i
    swap items[i] with items[j]

Notes:

  • It 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.
  • The algorithm can also be amended to iterate from left to right, if that is more convenient.
  • The only difference between this and the Knuth shuffle, is that is chosen from the range 0 j < i, rather than 0 j i. This is what ensures that every element ends up in a new position, as long as there are at least two elements.
Test cases
Input array Possible output arrays
[] []
[10] [10]
[10, 20] [20, 10]
[10, 20, 30] [20, 30, 10]
[30, 10, 20]
[11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22] 39,916,800 possibilities. You'll know you have a correct one if it has the same elements as the input array, but none in their original place.
Related tasks

C

This is generic to the extreme, although the function is technically being fed strings, it can handle any type, as shown in the outputs below :

Interactive and without hardcoded inputs

<lang C> /*Abhishek Ghosh, 9th November 2017*/

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

void sattoloCycle(void** arr,int count){ int i,j; void* temp;

if(count<2) return; for(i=count-1;i>=1;i--){ j = rand()%i; temp = arr[j]; arr[j] = arr[i]; arr[i] = temp; } }

int main(int argC,char* argV[]) { int i;

if(argC==1) printf("Usage : %s <array elements separated by a space each>",argV[0]); else{ 

               srand((unsigned)time(NULL));

sattoloCycle((void*)(argV + 1),argC-1);

for(i=1;i<argC;i++) printf("%s ",argV[i]); } return 0; } </lang> Output: 

C:\rosettaCode>sattoloCycle.exe ""

C:\rosettaCode>sattoloCycle.exe 10
10
C:\rosettaCode>sattoloCycle.exe 10 20
20 10
C:\rosettaCode>sattoloCycle.exe 10 20 30
30 10 20
C:\rosettaCode>sattoloCycle.exe 11 12 13 14 15 16 17 18 19 20 21 22
16 17 11 12 13 20 22 14 15 21 18 19
C:\rosettaCode>sattoloCycle.exe s a t t o l o C y c l e
l o s a t c e t o l C y
C:\rosettaCode>sattoloCycle.exe 1 2.3 4.2 1 3 e r q t 2 1 oo 2.1 eds
1 2.1 2.3 q r eds 1 e 3 t 1 2 oo 4.2
C:\rosettaCode>sattoloCycle.exe totally mixed up random string ( 1 2.3 2 ) which will get even more { a 2 q.1 } mixed up.
mixed q.1 a 1 up ) 2 even { will ( } 2 more totally random get which string up. 2.3 mixed

Non Interactive and with hardcoded inputs

Same code but with hardcoded integer arrays as in the task to show that the function can handle any type. <lang C> /*Abhishek Ghosh, 9th November 2017*/

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

void sattoloCycle(void** arr,int count){ int i,j; void* temp;

if(count<2) return; for(i=count-1;i>=1;i--){ j = rand()%i; temp = arr[j]; arr[j] = arr[i]; arr[i] = temp; } }

int main() { int i;

int a[] = {}; int b[] = {10}; int c[] = {10, 20}; int d[] = {10, 20, 30}; int e[] = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22};

srand((unsigned)time(NULL)); sattoloCycle((void*)a,0);

printf("\nShuffled a = "); for(i=0;i<0;i++) printf("%d ",a[i]);

sattoloCycle((void*)b,1);

printf("\nShuffled b = "); for(i=0;i<1;i++) printf("%d ",b[i]);

sattoloCycle((void*)c,2);

printf("\nShuffled c = "); for(i=0;i<2;i++) printf("%d ",c[i]);

sattoloCycle((void*)d,3);

printf("\nShuffled d = "); for(i=0;i<3;i++) printf("%d ",d[i]);

sattoloCycle((void*)e,12);

printf("\nShuffled e = "); for(i=0;i<12;i++) printf("%d ",e[i]);

return 0; } </lang> Output: 

Shuffled a =
Shuffled b = 10
Shuffled c = 20 10
Shuffled d = 20 30 10
Shuffled e = 13 18 14 20 17 15 21 19 16 12 22 11

C++

<lang cpp>

  1. include <ctime>
  2. include <string>
  3. include <iostream>
  4. include <algorithm>

class cycle{ public: 

   template <class T>
   void cy( T* a, int len ) {
       int i, j;
       show( "original: ", a, len );
       std::srand( unsigned( time( 0 ) ) );

       for( int i = len - 1; i > 0; i-- ) {
           do {
               j = std::rand() % i;
           } while( j >= i );
           std::swap( a[i], a[j] );
       }

       show( "  cycled: ", a, len ); std::cout << "\n";
   }

private: 

   template <class T>
   void show( std::string s, T* a, int len ) {
       std::cout << s;
       for( int i = 0; i < len; i++ ) {
           std::cout << a[i] << " ";
       }
       std::cout << "\n";
   }

}; int main( int argc, char* argv[] ) { 

   std::string d0[] = { "" },
               d1[] = { "10" },
               d2[] = { "10", "20" };
   int         d3[] = { 10, 20, 30 },
               d4[] = { 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 };
   cycle c;
   c.cy( d0, sizeof( d0 ) / sizeof( d0[0] ) );
   c.cy( d1, sizeof( d1 ) / sizeof( d1[0] ) );
   c.cy( d2, sizeof( d2 ) / sizeof( d2[0] ) );
   c.cy( d3, sizeof( d3 ) / sizeof( d3[0] ) );
   c.cy( d4, sizeof( d4 ) / sizeof( d4[0] ) );

   return 0;

} </lang>

Output:
original:
  cycled:

original: 10
  cycled: 10

original: 10 20
  cycled: 20 10

original: 10 20 30
  cycled: 30 10 20

original: 11 12 13 14 15 16 17 18 19 20 21 22
  cycled: 13 17 14 22 11 18 20 12 21 19 15 16

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>

FreeBASIC

<lang freebasic>' version 22-10-2016 ' compile with: fbc -s console ' for boundry checks on array's compile with: fbc -s console -exx

' sort from lower bound to the highter bound ' array's can have subscript range from -2147483648 to +2147483647

Sub sattolo_cycle(a() As Long) 

   Dim As Long lb = LBound(a)
   Dim As ULong n = UBound(a) - lb +1
   Dim As ULong i, j

   Randomize Timer

   For i = n -1 To 1 Step -1
       j =Fix(Rnd * (i))       ' 0 <= j < i
       Swap a(lb + i), a(lb + j)
   Next

End Sub

' ------=< MAIN >=------

Dim As Long i, array(1 To 52)

For i = 1 To 52 : array(i) = i : Next

Print "Starting array from 1 to 52" For i = 1 To 52 

   Print Using " ###";array(i);

Next : Print : Print

sattolo_cycle(array())

Print "After Sattolo_Cycle" For i = 1 To 52 

   Print Using " ###";array(i);

Next : Print : Print


' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</lang>

Output:
Starting array from 1 to 52
   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52

After Sattolo_Cycle
  40  48   7  25  32  17  44   4   8  13  18  47   5  29  10  20  49  39  11  51   3  21  46   2  38  16  28  37  12  50   1   9  52  19  22  30  36  27  45  15  24  23  33  41  14  31  43  26  35  34  42   6

Haskell

<lang haskell>import Control.Monad ((>=>), (>>=), forM_) import Control.Monad.Primitive import qualified Data.Vector as V import qualified Data.Vector.Mutable as M import System.Random.MWC

type MutVec m a = M.MVector (PrimState m) a

-- Perform an in-place shuffle of the vector, making it a single random cyclic -- permutation of its initial value. The vector is also returned for -- convenience. cyclicPermM :: PrimMonad m => Gen (PrimState m) -> MutVec m a -> m (MutVec m a) cyclicPermM rand vec = forM_ [1..M.length vec-1] upd >> return vec 

 where upd i = uniformR (0, i-1) rand >>= M.swap vec i

-- Return a vector that is a single random cyclic permutation of the argument. cyclicPerm :: PrimMonad m => Gen (PrimState m) -> V.Vector a -> m (V.Vector a) cyclicPerm rand = V.thaw >=> cyclicPermM rand >=> V.unsafeFreeze

test :: Show a => [a] -> IO () test xs = do 

 let orig = V.fromList xs
 cyc <- withSystemRandom . asGenIO $ \rand -> cyclicPerm rand orig
 putStrLn $ "original: " ++ show orig
 putStrLn $ "  cycled: " ++ show cyc

main :: IO () main = do 

 test ([] :: [()])
 test [10 :: Int]
 test [10, 20 :: Int]
 test [10, 20, 30 :: Int]
 test [11..22 :: Int]
 -- Also works for other types.
 test "abcdef"</lang>
Output:
$ ./sattolo 
original: []
  cycled: []
original: [10]
  cycled: [10]
original: [10,20]
  cycled: [20,10]
original: [10,20,30]
  cycled: [20,30,10]
original: [11,12,13,14,15,16,17,18,19,20,21,22]
  cycled: [13,14,16,11,17,20,18,21,22,15,19,12]
original: "abcdef"
  cycled: "cfeabd"

J

The key "feature" of this algorithm is that it cannot generate some legal random permutations. For example, given a two element list, it will always reverse that list.

Implementation:

<lang J>sattolo=:3 :0 

 for_i.}:i.-#y do.
   j=.?i
   y=. (<i,j) C. y
 end.
 y

) </lang>

Example use:

<lang J> sattolo 

  sattolo ,10

10 

  sattolo 10 20

20 10 

  sattolo 10 20 30

30 10 20 

  sattolo 11+i.12

19 18 15 21 12 17 22 16 20 13 11 14</lang>

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>

Julia

Works with: Julia version 0.6

<lang julia>function sattolocycle!(arr::Array, last::Int=length(arr)) 

   for i in last:-1:2
       j = rand(1:i-1)
       arr[i], arr[j] = arr[j], arr[i]
   end
   return arr

end

@show sattolocycle!([]) @show sattolocycle!([10]) @show sattolocycle!([10, 20, 30]) @show sattolocycle!([11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22])</lang>

Output:
sattolocycle!([]) = Any[]
sattolocycle!([10]) = [10]
sattolocycle!([10, 20, 30]) = [30, 10, 20]
sattolocycle!([11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]) = [19, 20, 15, 11, 17, 18, 21, 22, 13, 16, 12, 14]

Kotlin

<lang scala>// version 1.0.6

fun <T> sattolo(items: Array<T>) { 

   for (i in items.size - 1 downTo 1) {
       val j = (Math.random() * i).toInt()
       val t = items[i]
       items[i] = items[j]
       items[j] = t
   }

}

fun main(args: Array<String>) { 

   val items = arrayOf(11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22)
   println(items.joinToString())
   sattolo(items)
   println(items.joinToString())

}</lang> Sample output:

Output:
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22
22, 11, 19, 12, 21, 14, 18, 20, 17, 16, 13, 15

Lua

<lang Lua>function sattolo (items) 

   local j
   for i = #items, 2, -1 do
       j = math.random(i - 1)
       items[i], items[j] = items[j], items[i]
   end

end

math.randomseed(os.time()) local testCases = { 

   {},
   {10},
   {10, 20},
   {10, 20, 30},
   {11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22}

} for _, array in pairs(testCases) do 

   sattolo(array)
   print("[" .. table.concat(array, ", ") .. "]")

end</lang>

Output:
[]
[10]
[20, 10]
[30, 10, 20]
[15, 17, 22, 18, 16, 19, 21, 11, 12, 13, 20, 14]

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>

Phix

<lang Phix>sequence cards = tagset(52) puts(1,"Before: ") ?cards for i=52 to 2 by -1 do 

   integer r = rand(i-1)
   {cards[r],cards[i]} = {cards[i],cards[r]}

end for puts(1,"After: ") ?cards for i=1 to 52 do 

   if cards[i]=i then ?9/0 end if

end for if sort(cards)!=tagset(52) then ?9/0 end if puts(1,"Sorted: ") ?sort(cards)</lang> 

Before: {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52}
After:  {51,47,8,9,20,5,43,21,12,2,7,19,4,32,10,23,30,29,31,38,13,44,41,26,42,15,34,46,27,33,40,18,24,17,28,48,3,45,11,22,39,1,35,49,36,14,6,25,50,16,52,37}
Sorted: {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52}

PHP

<lang PHP>function sattoloCycle($items) { 

  for ($i = 0; $i < count($items); $i++) {
       $j = floor((mt_rand() / mt_getrandmax()) * $i);
       $tmp = $items[$i];
       $items[$i] = $items[$j];
       $items[$j] = $tmp;
   } 
   return $items;

} </lang>

Python

<lang python> >>> from random import randrange >>> def sattoloCycle(items): for i in range(len(items) - 1, 0, -1): j = randrange(i) # 0 <= j <= i-1 items[j], items[i] = items[i], items[j]


>>> # Tests >>> for _ in range(10): lst = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] sattoloCycle(lst) print(lst)


[5, 8, 1, 2, 6, 4, 3, 9, 10, 7] [5, 9, 8, 10, 4, 3, 6, 2, 1, 7] [10, 5, 8, 3, 9, 1, 4, 2, 6, 7] [10, 5, 2, 6, 9, 7, 8, 3, 1, 4] [7, 4, 8, 5, 10, 3, 2, 9, 1, 6] [2, 3, 10, 9, 4, 5, 8, 1, 7, 6] [5, 7, 4, 6, 2, 9, 3, 10, 8, 1] [3, 10, 7, 2, 9, 5, 8, 4, 1, 6] [2, 6, 5, 3, 9, 8, 10, 7, 1, 4] [3, 6, 2, 5, 10, 4, 1, 9, 7, 8] >>> </lang>

Racket

<lang racket>#lang racket

although the shuffle is in-place, returning the shuffled vector makes
testing a little easier

(define (sattolo-shuffle v) 

 (for ((i (in-range (sub1 (vector-length v)) 0 -1)))
   (define j (random i))
   (define tmp (vector-ref v i))
   (vector-set! v i (vector-ref v j))
   (vector-set! v j tmp))
 v)

(define (derangement-of? A B #:strict? (strict? #t)) 

 (match* (A B)
   [('() '()) #t]
   [((list a) (list a)) #:when strict? #t]
   [((list a _ ...) (list a _ ...)) #f]
   [((list _ as ...) (list _ bs ...))
    (derangement-of? as bs #:strict? #t)]
   [((vector as ...) (vector bs ...))
    (derangement-of? as bs #:strict? strict?)]))

(module+ test 

 (require rackunit)

 (check-equal? (sattolo-shuffle (vector)) #())
 (check-equal? (sattolo-shuffle (vector 10)) #(10))
 (check-equal? (sattolo-shuffle (vector 'inky)) #(inky))

 (define v′ (sattolo-shuffle (vector 11 12 13 14 15 16 17 18 19 20 21)))

 v′
 
 (check-true (derangement-of? #(11 12 13 14 15 16 17 18 19 20 21) v′)))</lang>
Output:
'#(21 19 12 11 18 17 14 16 15 13 20)

REXX

version 1

This REXX example uses a zero-based array;   (to match the pseudo-code).

The array elements can be of any type (even mixed):   integer, floating point, characters, ···

The array elements are specified via the command line (C.L.). <lang rexx>/*REXX program implements and displays a Sattolo shuffle for an array (of any type).*/ parse arg a; say 'original:' space(a) /*obtain args from the CL; display 'em.*/ 

  do x=0 for words(a);  @.x=word(a, x+1);  end  /*assign all elements to the @. array. */
                                                /* [↑]  build an array of given items. */
      do #=x-1  by -1  to 1;  j=random(0, #-1)  /*get a random integer between 0 & I-1.*/
      parse value @.#  @.j    with    @.j  @.#  /*swap two array elements, J is random.*/
      end   /*j*/                               /* [↑]  shuffle @ via Sattolo algorithm*/

$= /* [↓] build a list of shuffled items.*/ 

      do k=0  for x;   $=$  @.k;    end  /*k*/  /*append the next element in the array.*/

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

output   when using the input of:   [a null]
original: 
 Sattolo:
output   when using the input of:   10 
original: 10
 Sattolo: 10
output   when using the input of:   10 20 
original: 10 20 
 Sattolo: 20 10
output   when using the input of:   10 20 30 
original: 10 20 30
 Sattolo: 20 30 10
output   when using the input of:   11 12 13 14 15 16 17 18 19 20 21 22 
original: 11 12 13 14 15 16 17 18 19 20 21 22
 Sattolo: 15 14 17 19 18 12 22 13 20 21 11 16
output   when using the input of:   -1 0 00 oNe 2.7 /\ [] +6e1 ~~~ 
original: -1 0 00 one 2.7 /\ [] +6e1 ~~~
 Sattolo: /\ 00 +6e1 0 ~~~ oNe -1 2.7 []

version 2

<lang rexx>n=25 Do i=0 To n 

 a.i=i
 b.i=i
 End

Call show ' pre' Do i=n to 1 By -1 

 j=random(0,i-1)
 Parse Value a.i a.j With a.j a.i
 End

Call show 'post' Do i=0 To n 

 If a.i=b.i Then
   Say i a.i '=' b.i
 End

Exit Show: ol=arg(1) Do i=0 To n 

 ol=ol right(a.i,2)
 End

Say ol Return</lang>

Output:
 pre  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
post  3  4  8 18 14 21 20 13 10  1 25  7  2 24 12 23  5 11  6 22 16 19  9  0 15 17

Ring

<lang ring>

  1. Project : Sattolo cycle
  2. Date  : 2017/11/02
  3. Author : Gal Zsolt (~ CalmoSoft ~)
  4. Email  : <calmosoft@gmail.com>

a = "123456789abcdefghijklmnopqrstuvwxyz" n = len(a) sit = list(n)

for i = 1 to n 

   sit[i] = substr(a, i, 1)

next showsit() for i = n to 1 step -1 

   j = floor(i * random(9)/10) + 1
   h = sit[i]
   sit[i] = sit[j]
   sit[j] = h

next showsit()

func showsit 

    for i = 1 to n
        see sit[i] + " "
    next 
    see nl

</lang> Output: 

1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z 
i v 3 c 7 x 6 5 4 n a b r t e f g 2 8 u m o p w q l j h 9 s d y k z 1

Run BASIC

<lang Runbasic>a$ = "123456789abcdefghijklmnopqrstuvwxyz" n = len(a$) dim sit$(n) ' hold area to string global n

for i = 1 to n ' put string in array 

   sit$(i) = mid$(a$,i,1)

next i

call shoSit ' show before change

for i = n to 1 step -1 

   j		= int(i * rnd(1)) + 1
   h$		= sit$(i)
   sit$(i)	= sit$(j)
   sit$(j)	= h$

next i

call shoSit ' show after change end

sub shoSit 

   for i = 1 to n
      print sit$(i);" ";
   next i
   print

end sub

</lang>

Output:
1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z
d c 5 e v 3 n 7 8 h r p 2 y j l s x q 6 f 9 o a u i w 4 1 m g z t k b

SequenceL

<lang sequenceL> import <Utilities/Random.sl>; import <Utilities/Sequence.sl>;

sattolo(x(1), seed) := shuffle(x, seedRandom(seed), size(x));

shuffle(x(1), RG, n) := let next := getRandom(RG); in x when n <= 1 else shuffle(swap(x, n, next.Value mod (n - 1) + 1), next.Generator, n - 1);

swap(list(1), i(0), j(0)) := swapHelper(list, i, j, list[i], list[j]); swapHelper(list(1), i(0), j(0), vali(0), valj(0)) := setElementAt(setElementAt(list, i, valj), j, vali);

</lang>

Sidef

Modifies the array in-place: <lang ruby>func sattolo_cycle(arr) { 

   for i in (arr.len ^.. 1) {
       arr.swap(i, i.irand)
   }

}</lang>

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")
Retrieved from "https://rosettacode.org/wiki/Sattolo_cycle?oldid=269931"