I have a problem involving combinatorics and permutations and my brain
The problem: I have a hash of products in input. I then build an array
of equivalent products for each input product. I end up with an array
such as this:
:input_prod_1 => [:p1_1, :p1_2, … , p1_x],
:input_prod_2 => [:p2_1, :p2_1, …, p2_y],
:input_prod_m => [:pm_1, :pm_1, …, pm_z]
I need all the unique combinations of each product from the first group
with each of the second. For example:
given: [ [:p1, :p2], [:p3, p4] ]
I need to obtain: [ [:p1, :p3], [:p1, :p4], [:p2, :p3], [:p2, :p4] ]
Given: [ [:p1], [:p2, :p3, :p4] ]
I need: [ [:p1, :p2], [:p1, :p3], [:p1, :p4] ]
The number of input products is in the order of tens (max); the same
goes for the number of equivalent products. This means the total number
of partitions is pretty large and I need to weed out the equivalent ones
soon/fast enough to reduce the total number.
I’ve been making attempts with the permutation gem all morning; looks
like it’s doing the “right thing”, but frankly my maths skills are
lacking and I can’t really figure out how to use it (should I?).
Also: order is not important for the result arrays.
This is easy, right? :-/