Algorithm::Numerical::Shuffle - Shuffle a list.

    use Algorithm::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;

CWshuffle 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.

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.

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

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.

[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.

    $Date: 2000/03/08 05:57:40 $

    $Log: Shuffle.pm,v $
    Revision 1.4  2000/03/08 05:57:40  abigail
    Fixed bug that prevented in situ shuffling.
    Changed the wording of the license once again. (MIT/X style)

    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

This package was written by Abigail.

Copyright 1998, 1999, 2000 by Abigail.

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