Array combinatorics - arrays

Question

I am working in Ruby 2.7.
I have an Array, whose elements are one of three things: either a String or an Integer, or occasionally another Array with a pair of elements (this time, only Strings or Integers). There are no further levels of nesting for Arrays, by the definition of my problem.
Examples:
w = [1, 2, 'b', 4]
x = [[2, 'r'],[2, 'g']]
y = [[2, 'w']]
z = ['u', 6, [2, 'r']]
The context of the problem is that the inner arrays represent selectable alternatives for use in the outer array. I am looking for all possible ways to choose an element from each inner array, if present, and substitute that element into the outer array.
Examples:
f(w) = [ [1, 2, 'b', 4] ]
f(x) = [ [2, 2], [2, 'g'], ['r', 2], ['r', 'g'] ]
f(y) = [ [2], ['w'] ]
f(z) = [ ['u', 6, 2], ['u', 6, 'r'] ]
Order of elements in each selection (inner array of each solution) does not matter. Order of solutions in output also does not matter.
I can brute force an answer selecting/rejecting, transforming, and using Array#product; but I am looking for an approach that is as brief and elegant as possible.

Answer 1

The rules given in the question are unprecise and incomplete, so I've done my best to infer what they are.
Code
def doit(arr)
if arr.size == 1
e = arr.first
return e.is_a?(Array) ? (arr.map { |f| [f] }) : arr
end
(first, *rest), other = arr.partition { |e| e.is_a?(Array) }
return [arr] if first.nil?
prod = first.product(*rest)
return prod if other.empty?
prod.flat_map { |a| other.map { |e| [e, *a] } }
end
See Enumerable#partition, Array#product and Enumerable#flat_map.
Examples
doit [1, 2, 'b', 4]
#=> [[1, 2, "b", 4]]
doit [[2, 'r'],[2, 'g']]
#=> [[2, 2], [2, "g"], ["r", 2], ["r", "g"]]
doit [:a, [2, 'r'], :b, [2, 'g']]
#=> [[:a, 2, 2], [:b, 2, 2], [:a, 2, "g"], [:b, 2, "g"],
# [:a, "r", 2], [:b, "r", 2], [:a, "r", "g"], [:b, "r", "g"]]
doit [[2, 'w']]
#=> [[[2, "w"]]]
doit ['u', 6, [2, 'r']]
#=> [["u", 2], [6, 2], ["u", "r"], [6, "r"]]
doit [:a, [2, 3], :b, :c, [4, 5], :d, [6, 7]]
#=> [[:a, 2, 4, 6], [:b, 2, 4, 6], [:c, 2, 4, 6], [:d, 2, 4, 6],
# [:a, 2, 4, 7], [:b, 2, 4, 7], [:c, 2, 4, 7], [:d, 2, 4, 7],
# [:a, 2, 5, 6], [:b, 2, 5, 6], [:c, 2, 5, 6], [:d, 2, 5, 6],
# [:a, 2, 5, 7], [:b, 2, 5, 7], [:c, 2, 5, 7], [:d, 2, 5, 7],
# [:a, 3, 4, 6], [:b, 3, 4, 6], [:c, 3, 4, 6], [:d, 3, 4, 6],
# [:a, 3, 4, 7], [:b, 3, 4, 7], [:c, 3, 4, 7], [:d, 3, 4, 7],
# [:a, 3, 5, 6], [:b, 3, 5, 6], [:c, 3, 5, 6], [:d, 3, 5, 6],
# [:a, 3, 5, 7], [:b, 3, 5, 7], [:c, 3, 5, 7], [:d, 3, 5, 7]]
Note that the return value for doit [[2, 'w']] is different than that given in the question.
Explanation
The steps are as follows.
arr = [:a, [2, 'r'], :b, [2, 'g']]
(first, *rest), other = arr.partition { |e| e.is_a?(Array) }
#=> [[[2, "r"], [2, "g"]], [:a, :b]]
Ruby applies array decomposition to the above expression to obtain values for first, rest and other:
first
#=> [2, "r"]
rest
#=> [[2, "g"]]
other
#=> [:a, :b]
Continuing, because first.nil? #=> false in return [arr] if first.nil?, we do not return. Next:
prod = first.product(*rest)
#=> [[2, 2], [2, "g"], ["r", 2], ["r", "g"]]
other.empty? #=> false in return prod if other.empty? so we do not return.
I can best explain the remaining calculations by inserting puts statement in the code and running it.
prod.flat_map do |a|
puts "a = #{a}"
other.map do |e|
puts " e = :#{e}"
puts " [e, *a] = #{[e, *a]}"
[e, *a]
end
end
#=> [[:a, 2, 2], [:b, 2, 2], [:a, 2, "g"], [:b, 2, "g"],
# [:a, "r", 2], [:b, "r", 2], [:a, "r", "g"], [:b, "r", "g"]]
The following is displayed.
a = [2, 2]
e = :a
[e, *a] = [:a, 2, 2]
e = :b
[e, *a] = [:b, 2, 2]
a = [2, "g"]
e = :a
[e, *a] = [:a, 2, "g"]
e = :b
[e, *a] = [:b, 2, "g"]
a = ["r", 2]
e = :a
[e, *a] = [:a, "r", 2]
e = :b
[e, *a] = [:b, "r", 2]
a = ["r", "g"]
e = :a
[e, *a] = [:a, "r", "g"]
e = :b
[e, *a] = [:b, "r", "g"]