Question

Note

This is not a REBOL-specific question. You can answer it in any language.

Background

The REBOL language supports the creation of domain-specific languages known as ‘dialects’ in REBOL parlance. I’ve created such a dialect for list comprehensions, which aren’t natively supported in REBOL.

A good cartesian product algorithm is needed for list comprehensions.

The Problem

I’ve used meta-programming to solve this, by dynamically creating and then executing a sequence of nested foreach statements. It works beautifully. However, because it’s dynamic, the code is not very readable. REBOL doesn’t do recursion well. It rapidly runs out of stack space and crashes. So a recursive solution is out of the question.

In sum, I want to replace my meta-programming with a readable, non-recursive, ‘inline’ algorithm, if possible. The solution can be in any language, as long as I can reproduce it in REBOL. (I can read just about any programming language: C#, C, C++, Perl, Oz, Haskell, Erlang, whatever.)

I should stress that this algorithm needs to support an arbitrary number of sets to be ‘joined’, since list comprehension can involve any number of sets.

Answer 1

How about something like this:

#!/usr/bin/perl  use strict; use warnings;  my @list1 = qw(1 2); my @list2 = qw(3 4); my @list3 = qw(5 6);  # Calculate the Cartesian Product my @cp = cart_prod(\@list1, \@list2, \@list3);  # Print the result foreach my $elem (@cp) {   print join(' ', @$elem), '\n'; }  sub cart_prod {   my @sets = @_;   my @result;   my $result_elems = 1;    # Calculate the number of elements needed in the result   map { $result_elems *= scalar @$_ } @sets;   return undef if $result_elems == 0;    # Go through each set and add the appropriate element   # to each element of the result   my $scale_factor = $result_elems;   foreach my $set (@sets)   {     my $set_elems = scalar @$set;  # Elements in this set     $scale_factor /= $set_elems;     foreach my $i (0 .. $result_elems - 1) {       # Calculate the set element to place in this position       # of the result set.       my $pos = $i / $scale_factor % $set_elems;       push @{$result[$i]}, $$set[ $pos ];     }   }    return @result; } 

Which produces the following output:

1 3 5 1 3 6 1 4 5 1 4 6 2 3 5 2 3 6 2 4 5 2 4 6