Small script demonstrating how we can generate combinations from arrays of arrays

combinatoins.rb

def pretty_print(array_of_arrays)
  array_of_arrays.each do |array|
    puts "[#{array.join(",")}]"
  end
end

def combinations_for_free(array_of_arrays)
  array_of_arrays[0].product(*array_of_arrays[1...])
end

def combinations(array_of_arrays)
  array_of_arrays.reverse.reduce([[]]) do |solutions, arr|
    cross_product(arr, solutions)
  end
end

def cross_product(arr, array_of_arrays)
  products = []
  arr.each do |elem|
    array_of_arrays.map do |array|
      products.push(array.clone.unshift(elem))
    end
  end
  products
end

# Let's test it ...

require 'minitest/autorun'
require 'debug'

class CombinationsTest < Minitest::Test

  def cases
    [
      [[0,1],[2,3],[4,5]],
      [[1,2,3],[5],[6]],
      [[0,1,2],[3,4],[5,6,7]]
    ]
  end

  def test_combinations
    cases.each do |test_case|
      assert combinations(test_case).sort == test_case[0].product(*test_case[1..]).sort
    end
  end
end