Name
Math::Cartesian::Product - Generate the Cartesian product of zero or
more lists.
Synopsis
use Math::Cartesian::Product;
cartesian {print "@_\n"} [qw(a b c)], [1..2];
# a 1
# a 2
# b 1
# b 2
# c 1
# c 2
cartesian {print "@_\n"} ([0..1]) x 8;
# 0 0 0 0 0 0 0 0
# 0 0 0 0 0 0 0 1
# 0 0 0 0 0 0 1 0
# ...
# 1 1 1 1 1 1 1 0
# 1 1 1 1 1 1 1 1
Description
Generate the Cartesian product of zero or more lists.
Given two lists, say: [a,b] and [1,2,3], the Cartesian product is the
set of all ordered pairs:
(a,1), (a,2), (a,3), (b,1), (b,2), (b,3)
which select their first element from all the possibilities listed in
the first list, and select their second element from all the
possibilities in the second list.
The idea can be generalized to n-tuples selected from n lists where all
the elements of the first list are combined with all the elements of the
second list, the results of which are then combined with all the member
of the third list and so on over all the input lists.
It should be noted that Cartesian product of one or more lists where one
or more of the lists are empty (representing the empty set) is the empty
set and thus has zero members; and that the Cartesian product of zero
lists is a set with exactly one member, namely the empty set.
"cartesian()" takes the following parameters:
1. A block of code to process each n-tuple. this code should return true
if the current n-tuple should be included in the returned value of the
"cartesian()" function, otherwise false.
2. Zero or more lists.
"cartesian()" returns an array of references to all the n-tuples
selected by the code block supplied as parameter 1.
"cartesian()" croaks if you try to form the Cartesian product of
something other than lists of things.
The cartesian product of lists A,B,C is associative, that is:
(A X B) X C = A X (B X C)
"cartesian()" respects associativity by allowing you to include a
Cartesian product produced by an earlier call to "cartesian()" in the
set of lists whose Cartesian product is to be formed, at the cost of a
performance penalty if this option is chosen.
use Math::Cartesian::Product;
my $a = [qw(a b)];
my $b = [cartesian {1} $a, $a];
cartesian {print "@_\n"} $b, $b;
# a a a a
# a a a b
# a a b a
# ...
"cartesian()" is easy to use and fast. It is written in 100% Pure Perl.
Export
The "cartesian()" function is exported.
Installation
Standard Module::Build process for building and installing modules:
perl Build.PL
./Build
./Build test
./Build install
Or, if you're on a platform (like DOS or Windows) that doesn't require
the "./" notation, you can do this:
perl Build.PL
Build
Build test
Build install
Author
PhilipRBrenan@appaapps.com
http://www.appaapps.com
Acknowledgements
With much help and good natured advice from Philipp Rumpf to whom I am
greatly indebted.
See Also
Math::Disarrange::List
Math::Permute::List
Math::Subsets::List
Math::Transform::List
Copyright
Copyright (c) 2009 Philip R Brenan.
This module is free software. It may be used, redistributed and/or
modified under the same terms as Perl itself.