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.
Implement the Sattolo cycle for an integer array (or, if possible, an array of any type).
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.
| 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. |
C++
<lang cpp>
- include <ctime>
- include <string>
- include <iostream>
- 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
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>
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
version 1
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 /*obtain optional arguments from the CL*/ say 'original:' space(a) /*display the original list of items.*/ 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. */
/* [↑] build an array of given items. */
do i=n-1 by -1 to 1; j=random(0,i-1) /*get a random integer between 0 & I-1.*/
parse value @.i @.j with @.j @.i /*swap two array elements, J is random.*/
end /*i*/ /* [↑] shuffle @ via Sattolo algorithm*/
$= /* [↓] build a list of shuffled items.*/
do k=0 for n; $=$ @.k; end /*append the next element in the array.*/
say ' Sattolo:' space($) /*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 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 16output 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
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")