Math::Counting - Combinatorial counting operations
use Math::Counting ':student';
printf "Given n=%d and r=%d:\nFact=%d\nPerm=%d\nComb=%d\n",
$n, $r, factorial($n), permutation($n, $r), combination($n, $r);
use Math::Counting ':big';
printf "n=%d, r=%d:\nBig F=%d\n Big P=%d\nBig C=%d\n",
$n, $r, bfact($n), bperm($n, $r), bcomb($n, $r);
Compute the numerical factorial, number of n,r permutations and number of n,r combinations using Math::BigInt and also the technique of "tail call elimination" as described in Higher Order Perl and Mastering Algorithms with Perl.
$f = factorial($n);
Return the number of arrangements of n according to the "student" version using real arithmetic.
$f = bfact($n);
Return the value of the "bfac" in Math::BigInt function, which is the "Right Way To Do It."
$p = permutation($n, $r);
Return the number of arrangements of r elements drawn from a set of n elements. nPn is the same as n!. This function employs the "student" version using real arithmetic.
$p = bperm($n, $r);
Return the Math::BigInt computation: n!/(n-r)!.
$c = combination($n, $r);
Return the number of ways to choose r elements from a set of n elements. This function employs the "student" version using real arithmetic.
$c = bcomb($n, $r);
Return the Math::BigInt computation: n!/r!(n-r)!.
Figure out how to allow the use of different Math::BigInt variations, like GMP.
Provide the gamma function for the factorial of non-integer numbers?
Higher Order Perl by Mark Jason Dominus (http://hop.perl.plover.com/).
Mastering Algorithms with Perl by Orwant, Hietaniemi & Macdonald (http://www.oreilly.com/catalog/maperl/).
String::OrderedCombination for nPk list generation.
Math::Combinatorics for nPn and nCr list generation.
http://en.wikipedia.org/wiki/Factorial
http://en.wikipedia.org/wiki/Permutation
http://en.wikipedia.org/wiki/Combination
Gene Boggs <gene@cpan.org>
Copyright 2005-2008 Gene Boggs All Rights Reserved
You may use this package under the same terms as Perl itself.
