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 , 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.