Description :
Given sets S(1), S(2), ..., S(k), each of cardinality n(1), n(2), ..., n(k)
respectively, the cross product of the sets is the set CP of ordered tuples
such that { < s1, s2, ..., sk> | s1 => S(1), s2 => S(2), .... sk => S(k). }
If you do not like that description, how about:
Create a list by taking one item from each array, and do that for all
possible ways that can be done, so that the first item in the list is
always from the first array, the second item from the second array, and so
on.
If you need to see it:
A => ( a, b, c )
B => ( 1, 2, 3 )
C => ( foo, bar )
The cross product of A and B and C, A x B x C, is the set of tuples shown:
( a, 1, foo )
( a, 1, bar )
( a, 2, foo )
( a, 2, bar )
( a, 3, foo )
( a, 3, bar )
( b, 1, foo )
( b, 1, bar )
( b, 2, foo )
( b, 2, bar )
( b, 3, foo )
( b, 3, bar )
( c, 1, foo )
( c, 1, bar )
( c, 2, foo )
( c, 2, bar )
( c, 3, foo )
( c, 3, bar )
In code, it looks like this:
use v5.26;
use Set::CrossProduct;
my $cross = Set::CrossProduct->new( {
A => [ qw( a b c ) ],
B => [ qw( 1 2 3 ) ],
C => [ qw( foo bar ) ],
} );
while( my $t = $cross->get ) {
printf \"( %s, %s, %s )\
\", $t->AATT{qw(A B C)};
}
If one of the sets happens to be empty, the cross product is empty too.
A => ( a, b, c )
B => ( )
In this case, A x B is the empty set, so you\'ll get no tuples.
This module combines the arrays that give to it to create this cross
product, then allows you to access the elements of the cross product in
sequence, or to get all of the elements at once. Be warned! The cardinality
of the cross product, that is, the number of elements in the cross product,
is the product of the cardinality of all of the sets.
The constructor, \'new\', gives you an iterator that you can use to move
around the cross product. You can get the next tuple, peek at the previous
or next tuples, or get a random tuple. If you were inclined, you could even
get all of the tuples at once, but that might be a very large list. This
module lets you handle the tuples one at a time.
I have found this module very useful for creating regression tests. I
identify all of the boundary conditions for all of the code branches, then
choose bracketing values for each of them. With this module I take all of
the values for each test and create every possibility in the hopes of
exercising all of the code. Of course, your use is probably more
interesting. :)
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