NAME

Math::Counting - Combinatorial counting operations

SYNOPSIS

  ## The algorithm-student versions:

  use Math::Counting ':long';
  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 ':short';
  printf "Given n=%d and r=%d:\nF=%d\nP=%d\nC=%d\n",
    $n, $r, f($n), P($n, $r), C($n, $r);

  ## The "Right way to do it":

  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);

DESCRIPTION

This package computes the factorial, number of (n,r) permutations and (n,r) combinations using either the Math::BigInt manpage and the technique of "tail call elimination" (TCE).

No functions are exported by default.

FUNCTIONS

f, factorial

  $f = f($n);
  $f = factorial($n);

Return the number of arrangements of n with TCE.

bfact

  $f = bfact($n);

Return the value of the bfact in the Math::BigInt manpage function, which is the "Right Way To Do It."

P, permutation

  $p = P($n, $r);
  $p = permutation($n, $r);

Return the number of arrangements of r elements drawn from a set of n elements with TCE. (nPn is the same as n!.)

bperm

  $p = bperm($n, $r);

Return the Math::BigInt computation: n!/(n-r)!.

C, choose, combination

  $c = C($n, $r);
  $c = choose($n, $r);
  $c = combination($n, $r);

Return the number of ways to choose r elements from a set of n elements with TCE.

bcomb

  $c = bcomb($n, $r);

Return the Math::BigInt computation: n!/r!(n-r)!.

TO DO

Figure out how to allow the use of different BigInt variations, like GMP.

Provide the gamma function for the factorial of non-integer numbers?

SEE ALSO

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/).

The bfac function of the Math::BigInt module.

the Algorithm::Combinatorics manpage

the String::OrderedCombination manpage for nPk list generation.

the Math::Combinatorics manpage for nPn and nCr list generation.

http://en.wikipedia.org/wiki/Factorial

http://en.wikipedia.org/wiki/Permutation

http://en.wikipedia.org/wiki/Combination

AUTHOR

Not me. I am but a pebble on the beach...

COPYRIGHT

Copyright 2007 Gene Boggs All Rights Reserved

You may use this package under the same terms as Perl itself.