NAME

Algorithms::Numerical::Shuffle - Shuffle a list.

SYNOPSIS

use Algorithms::Numerical::Shuffle qw /shuffle/;

@shuffled = shuffle (1, 2, 3, 4, 5, 6, 7);

$in_situ = [qw /one two three four five six/];
shuffle $in_situ;

DESCRIPTION

shuffle performs a one pass, fair shuffle on a list. If the list is passed as a reference to an array, the shuffle is done in situ.

The subroutine returns the list in list context, and a reference to the list in scalar context.

COMPLEXITY

The running time of the algorithm is linear in the size of the list. For an in situ shuffle, the memory overhead is constant; otherwise, linear extra memory is used.

LITERATURE

The algorithm used is discussed by Knuth [3]. It was first published by Fisher and Yates [2], and later by Durstenfeld [1].

CAVEAT

Salfi [4] points to a big caveat. If the outcome of a random generator is solely based on the value of the previous outcome, like a linear congruential method, then the outcome of a shuffle depends on exactly three things: the shuffling algorithm, the input and the seed of the random generator. Hence, for a given list and a given algorithm, the outcome of the shuffle is purely based on the seed. Many modern computers have 32 bit random numbers, hence a 32 bit seed. Hence, there are at most 2^32 possible shuffles of a list, foreach of the possible algorithms. But for a list of n elements, there are n! possible permutations. Which means that a shuffle of a list of 13 elements will not generate certain permutations, as 13! > 2^32.

REFERENCES

[1]

R. Durstenfeld: CACM, 7, 1964. pp 420.

[2]

R. A. Fisher and F. Yates: Statistical Tables. London, 1938. Example 12.

[3]

D. E. Knuth: The Art of Computer Programming, Volume 2, Third edition. Section 3.4.2, Algorithm P, pp 145. Reading: Addison-Wesley, 1997. ISBN: 0-201-89684-2.

[4]

R. Salfi: COMPSTAT 1974. Vienna: 1974, pp 28 - 35.

HISTORY

$Date: 1999/03/01 20:54:06 $

$Log: Shuffle.pm,v $
Revision 1.3  1999/03/01 20:54:06  abigail
Changed package name to Algorithm::*
Changed license.

Revision 1.2  1998/09/09 20:48:12  abigail
- Make shuffle() work with empty lists.
- Changed license to Artistic only.

Revision 1.1  1998/04/23 17:58:07  abigail
Initial revision

AUTHOR

This package was written by Abigail.

COPYRIGHT

Copyright 1998, 1999 by Abigail.

LICENSE

This package is free and open software.

You may use, copy, modify, distribute and sell this package or any modifications there of in any form you wish, provided you do not do any of the following:

- claim that any of the original code was written by someone
  else than the original author(s).
- restrict someone in using, copying, modifying, distributing or
  selling this program or module or any modifications of it.

THIS PACKAGE IS PROVIDED "AS IS" AND WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.