Math::Counting - Combinatorial counting operations
use Math::Counting ':student'; printf "Given n=%d, k=%d:\nF=%d\nP=%d\nC=%d\n", $n, $k, factorial($n), permutation($n, $k), combination($n, $k);
use Math::Counting ':big'; printf "Given n=%d, k=%d, r=%d:\nF=%d\nP=%d\nD=%d\nC=%d\n", $n, $k, $r, bfact($n), bperm($n, $k, $r), bderange($n), bcomb($n, $k, $r);
Compute the factorial, number of permutations, number of derangements and number of combinations.
:big functions are wrappers around "bfac" in Math::BigInt with a bit of arithmetic between.
The student versions exist to illustrate the computation "in the raw" as it were. To see these computations in action, Use The Source, Luke.
$f = factorial($n);
Return the number of arrangements of n, notated as
This function employs the algorithmically elegant "student" version using real arithmetic.
$f = bfact($n);
Return the value of the function "bfac" in Math::BigInt, which is the "Right Way To Do It."
$p = permutation($n, $k);
Return the number of arrangements, without repetition, of k elements drawn from a set of n elements, using the "student" version.
$p = bperm($n, $k, $r);
Return the computations:
n^k # with repetition $r == 1 n! / (n-k)! # without repetition $r == 0
"A derangement is a permutation in which none of the objects appear in their "natural" (i.e., ordered) place." -- wolfram under "SEE ALSO"
Return the computation:
!n = n! * ( sum (-1)^k/k! for k=0 to n )
$c = combination($n, $k);
Return the number of ways to choose k elements from a set of n elements, without repetition.
This is algorithm expresses the "student" version.
$c = bcomb($n, $k, $r);
Return the combination computations:
(n+k-1)! / k!(n-1)! # with repetition $r == 1 n! / k!(n-k)! # without repetition $r == 0
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).
Naturally, there are a plethora of combinatorics packages available, take your pick:
Algorithm::Combinatorics, Algorithm::Loops, Algorithm::Permute, CM::Group::Sym, CM::Permutation, Games::Word, List::Permutor, Math::Combinatorics, Math::GSL::Permutation, Math::Permute::List, String::Glob::Permute, String::OrderedCombination
Special thanks to:
* Paul Evans
* Mike Pomraning
* Petar Kaleychev
* Dana Jacobsen
Gene Boggs <firstname.lastname@example.org>
This software is copyright (c) 2015 by Gene Boggs.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.