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