NAME

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

SYNOPSIS

``````    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;``````

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: 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``````

AUTHOR

This package was written by Abigail.

Copyright 1998, 1999, 2000 by Abigail.

LICENSE

This program is copyright 1998-2000 by Abigail.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.