Combine array of array into all possible combinations, forward only, in Ruby

I have an array of arrays, like so:

[['1','2'],['a','b'],['x','y']]

I need to combine those arrays into a string containing all possible combinations of all three sets, forward only. I have seen lots of examples of all possible combinations of the sets in any order, that is not what I want. For example, I do not want any of the elements in the first set to come after the second set, or any in the third set to come before the first, 开发者_开发知识库or second, and so on. So, for the above example, the output would be:

['1ax', '1ay', '1bx', '1by', '2ax', '2ay', '2bx', '2by']

The number of arrays, and length of each set is dynamic.

Does anybody know how to solve this in Ruby?

---

Know your Array#product:

a = [['1','2'],['a','b'],['x','y']]
a.first.product(*a[1..-1]).map(&:join)

---

Solved using a recursive, so-called "Dynamic Programming" approach:

• For n-arrays, combine the entries of the first array with each result on the remaining (n-1) arrays
• For a single array, the answer is just that array

In code:

def variations(a)
  first = a.first
  if a.length==1 then
    first
  else
    rest = variations(a[1..-1])
    first.map{ |x| rest.map{ |y| "#{x}#{y}" } }.flatten
  end
end

p variations([['1','2'],['a','b'],['x','y']])
#=> ["1ax", "1ay", "1bx", "1by", "2ax", "2ay", "2bx", "2by"]

puts variations([%w[a b],%w[M N],['-'],%w[x y z],%w[0 1 2]]).join(' ')
#=> aM-x0 aM-x1 aM-x2 aM-y0 aM-y1 aM-y2 aM-z0 aM-z1 aM-z2 aN-x0 aN-x1 aN-x2
#=> aN-y0 aN-y1 aN-y2 aN-z0 aN-z1 aN-z2 bM-x0 bM-x1 bM-x2 bM-y0 bM-y1 bM-y2
#=> bM-z0 bM-z1 bM-z2 bN-x0 bN-x1 bN-x2 bN-y0 bN-y1 bN-y2 bN-z0 bN-z1 bN-z2

You could also reverse the logic, and with care you should be able to implement this non-recursively. But the recursive answer is rather straightforward. :)

---

Pure, reduce with product:

a = [['1','2'],['a','b'],['x','y']]
a.reduce() { |acc, n| acc.product(n).map(&:flatten) }.map(&:join)
#  => ["1ax", "1ay", "1bx", "1by", "2ax", "2ay", "2bx", "2by"]