NAME
    Math::Combinatorics - Perform combinations and permutations on lists

SYNOPSIS
    Available as an object oriented API.

      use Math::Combinatorics;

      my @n = qw(a b c);
      my $combinat = Math::Combinatorics->new(count => 2,
                                              data => [@n],
                                             );

      print "combinations of 2 from: ".join(" ",@n)."\n";
      print "------------------------".("--" x scalar(@n))."\n";
      while(my @combo = $combinat->next_combination){
        print join(' ', @combo)."\n";
      }

      print "\n";

      print "combinations of 2 from: ".join(" ",@n)."\n";
      print "------------------------".("--" x scalar(@n))."\n";
      while(my @permu = $combinat->next_permutation){
        print join(' ', @permu)."\n";
      }

      output:

    Or available via exported functions 'permute', 'combine', and
    'factorial'.

      use Math::Combinatorics;

      my @n = qw(a b c);
      print "combinations of 2 from: ".join(" ",@n)."\n";
      print "------------------------".("--" x scalar(@n))."\n";
      print join("\n", map { join " ", @$_ } combine(2,@n)),"\n";
      print "\n";
      print "permutations of 3 from: ".join(" ",@n)."\n";
      print "------------------------".("--" x scalar(@n))."\n";
      print join("\n", map { join " ", @$_ } permute(@n)),"\n";

    Output:

      combinations of 2 from: a b c
      ------------------------------
      a b
      a c
      b c

      combinations of 2 from: a b c
      ------------------------------
      a b c
      a c b
      b a c
      b c a
      c a b
      c b a

    Output from both types of calls is the same, but the object-oriented
    approach consumes much less memory for large sets.

DESCRIPTION
    Combinatorics is the branch of mathematics studying the enumeration,
    combination, and permutation of sets of elements and the mathematical
    relations that characterize their properties. As a jumping off point,
    refer to:

    http://mathworld.wolfram.com/Combinatorics.html

    This module provides a pure-perl implementation of nCk, nPk, and n!
    (combination, permutation, and factorial, respectively). Functional and
    object-oriented usages allow problems such as the following to be
    solved:

    nCk "Fun questions to ask the pizza parlor wait staff: how many possible
    combinations of 2 toppings can I get on my pizza?".

    nPk "Master Mind Game: ways to arrange pieces of different colors in a
    certain number of positions, without repetition of a color".

    Object-oriented usage additionally allows solving these problems by
    calling the new() entry elsewhere in this document with a frequency
    vector:

    nPRk "morse signals: diferent signals of 3 positions using the 2 two
    symbol - and .".

    nCRk "ways to extract 3 balls at once of a bag with black and white
    balls".

    nPRk "different words obtained permuting the letters of the word
    PARROT".

AUTHOR
    Allen Day <allenday@ucla.edu>, with algorithmic contributions from
    Christopher Eltschka and Tye.

ACKNOWLEDGEMENTS
    Thanks to everyone for helping to make this a better module.

    For adding new features: Carlos Rica, David Coppit

    For bug reports: Ying Yang, Joerg Beyer, Marc Logghe

LICENSE AND COPYRIGHT

    Copyright (c) 2004 Allen Day. All rights reserved. This program is
    free software; you can redistribute it and/or modify it under the same
    terms as Perl itself.