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Diffstat (limited to 'lib/Math')
| -rw-r--r-- | lib/Math/Cartesian/Product.pm | 262 |
1 files changed, 0 insertions, 262 deletions
diff --git a/lib/Math/Cartesian/Product.pm b/lib/Math/Cartesian/Product.pm deleted file mode 100644 index eedcf1e..0000000 --- a/lib/Math/Cartesian/Product.pm +++ /dev/null @@ -1,262 +0,0 @@ -=head1 Name - -Math::Cartesian::Product - Generate the Cartesian product of zero or more lists. - -=head1 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 - - print "@$_\n" for - cartesian {"@{[reverse @_]}" eq "@_"} - ([' ', '*']) x 8; - - # * * - # * * - # * * * * - # * * - # * * * * - # * * * * - # * * * * * * - # * * - # * * * * - # * * * * - # * * * * * * - # * * * * - # * * * * * * - # * * * * * * - # * * * * * * * * - -=cut - -package Math::Cartesian::Product; - -use Carp; -use strict; - -sub cartesian(&@) # Generate the Cartesian product of zero or more lists - {my $s = shift; # Subroutine to call to process each element of the product - - my @C = @_; # Lists to be multiplied - my @c = (); # Current element of Cartesian product - my @P = (); # Cartesian product - my $n = 0; # Number of elements in product - -# return 0 if @C == 0; # Empty product per Philipp Rumpf - - @C == grep {ref eq 'ARRAY'} @C or croak("Arrays of things required by cartesian"); - -# Generate each Cartesian product when there are no prior Cartesian products. -# The first variant builds the results array, the second does not per Justin Case - - my $p; $p = wantarray() ? sub - {if (@c < @C) - {for(@{$C[@c]}) - {push @c, $_; - &$p(); - pop @c; - } - } - else - {my $p = [@c]; - push @P, bless $p if &$s(@$p); - } - } : sub # List not required per Justin Case - {if (@c < @C) - {for(@{$C[@c]}) - {push @c, $_; - &$p(); - pop @c; - } - } - else - {++$n if &$s(@c); - } - }; - -# Generate each Cartesian product allowing for prior Cartesian products. - - my $q; $q = wantarray() ? sub - {if (@c < @C) - {for(@{$C[@c]}) - {push @c, $_; - &$q(); - pop @c; - } - } - else - {my $p = [map {ref eq __PACKAGE__ ? @$_ : $_} @c]; - push @P, bless $p if &$s(@$p); - } - } : sub # List not required per Justin Case - {if (@c < @C) - {for(@{$C[@c]}) - {push @c, $_; - &$q(); - pop @c; - } - } - else - {++$n if &$s(map {ref eq __PACKAGE__ ? @$_ : $_} @c); - } - }; - -# Determine optimal method of forming Cartesian products for this call - - if (grep {grep {ref eq __PACKAGE__} @$_} @C) - {&$q - } - else - {&$p - } - - $p = $q = undef; # Break memory loops per Philipp Rumpf - wantarray() ? @P : $n # Product or count per Justin Case - } - -# Export details - -require 5; -require Exporter; - -use vars qw(@ISA @EXPORT $VERSION); - -@ISA = qw(Exporter); -@EXPORT = qw(cartesian); -$VERSION = '1.009'; # Tuesday 18 Aug 2015 - -=head1 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. - -C<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 -C<cartesian()> function, otherwise false. - -2. Zero or more lists. - -C<cartesian()> returns an array of references to all the n-tuples selected by -the code block supplied as parameter 1 if called in list context, else it -returns a count of the selected n-tuples. - -C<cartesian()> croaks if you try to form the Cartesian product of -something other than lists of things or prior Cartesian products. - -The cartesian product of lists A,B,C is associative, that is: - - (A X B) X C = A X (B X C) - -C<cartesian()> respects associativity by allowing you to include a -Cartesian product produced by an earlier call to C<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 - # ... - -C<cartesian()> is easy to use and fast. It is written in 100% Pure Perl. - -=head1 Export - -The C<cartesian()> function is exported. - -=head1 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 - -=head1 Author - -Philip R Brenan at gmail dot com - -http://www.appaapps.com - -=head1 Acknowledgements - -With much help and good natured advice from Philipp Rumpf and Justin Case to -whom I am indebted. - -=head1 See Also - -=over - -=item L<Math::Disarrange::List> - -=item L<Math::Permute::List> - -=item L<Math::Permute::Lists> - -=item L<Math::Permute::Partitions> - -=item L<Math::Subsets::List> - -=item L<Math::Transform::List> - -=back - -=head1 Copyright - -Copyright (c) 2009-2015 Philip R Brenan. - -This module is free software. It may be used, redistributed and/or -modified under the same terms as Perl itself. - -=cut |