Ruby, remove super-arrays - ruby

Question

If I have an array of arrays, A, and want to get rid of all arrays in A who also have a sub-array in A, how would I do that. In this context, array_1 is a sub-array of array_2 if array_1 - array_2 = []. In the case that multiple arrays are simply rearranged versions of the same elements, bonus points if you can get rid of all but one of them, but you can handle this however you want if it's easier.
In python, I could easily use comprehension, with A being a set of frozen sets :
A = {a for a in A if all(b-a for b in A-{a})}
Is there a simple way to write this in ruby? I don't care if the order of A or it's arrays are preserved at all. Also, in my program, none of the arrays have duplicate elements, if that makes things any easier/faster.
Example
A = [[1,6],[1,2],[2,4],[3,5],[1,3,6],[2,3,6]]
# [1,6] is a subarray of [1,3,6], so [1,3,6] should be removed
remove_super_arrays(A)
> A = [[1,6],[1,2],[2,4],[3,5],[2,3,6]]
A = [[1,2,4],[2,3,4],[1,4,5],[2,6]]
# although there is overlap, there are no subarrays, so nothing should be removed
remove_super_arrays(A)
> A = [[1,2,4],[2,3,4],[1,4,5],[2,6]]
A = [[1],[2,1,3],[2,4],[1,4]]
# [1] is a subarray of [2,1,3] and [1,4]
remove_super_arrays(A)
> A = [[1],[2,4]]

Answer 1

Code
def remove_super_arrays(arr)
order = arr.each_with_index.to_a.to_h
arr.sort_by(&:size).reject.with_index do |a,i|
arr[0,i].any? { |aa| (aa.size < a.size) && (aa-a).empty? }
end.sort_by { |a| order[a] }
end
Examples
remove_super_arrays([[1,6],[1,2],[2,4],[3,5],[1,3,6],[2,3,6]] )
#=> [[1,6],[1,2],[2,4],[3,5],[2,3,6]]
remove_super_arrays([[1,2,4],[2,3,4],[1,4,5],[2,6]])
#=> [[1,2,4],[2,3,4],[1,4,5],[2,6]]
remove_super_arrays([[1],[2,1,3],[2,4],[1,4]])
#=> [[1],[2,4]]
Explanation
Consider the first example.
arr = [[1,6],[1,2],[2,4],[3,5],[1,3,6],[2,3,6]]
We first save the positions of the elements of a
order = arr.each_with_index.to_a.to_h # save original order
#=> {[1, 6]=>0, [1, 2]=>1, [2, 4]=>2, [3, 5]=>3, [1, 3, 6]=>4, [2, 3, 6]=>5}
Then reject elements of arr:
b = arr.sort_by(&:size)
#=> [[1, 6], [1, 2], [2, 4], [3, 5], [1, 3, 6], [2, 3, 6]]
c = b.reject.with_index do |a,i|
arr[0,i].any? { |aa| (aa.size < a.size) && (aa-a).empty? }
end
#=> [[1, 6], [1, 2], [2, 4], [3, 5], [2, 3, 6]]
Lastly, reorder c to correspond to the original ordering of the elements of arr.
c.sort_by { |a| order[a] }
#=> [[1, 6], [1, 2], [2, 4], [3, 5], [2, 3, 6]]
which in this case happens to be the same order as the elements of c.
Let's look more carefully at the calculation of c:
enum1 = b.reject
#=> #<Enumerator: [[1, 6], [1, 2], [2, 4], [3, 5], [1, 3, 6],
# [2, 3, 6]]:reject>
enum2 = enum1.with_index
#=> #<Enumerator: #<Enumerator: [[1, 6], [1, 2], [2, 4], [3, 5],
# [1, 3, 6], [2, 3, 6]]:reject>:with_index>
The first element is generated by the enumerator enum2 and passed to the block and assigned as values of the block variables:
a, i = enum2.next
#=> [[1, 6], 0]
a #=> [1, 6]
i #=> 0
The block calculation is then performed:
d = arr[0,i]
#=> []
d.any? { |aa| (aa.size < a.size) && (aa-a).empty? }
#=> false
so a[0] is not rejected. The next pair passed to the block by enum2 is [[1, 2], 1]. That value is retained as well, but let's skip ahead to the last element passed to the block by enum2:
a, i = enum2.next
#=> [[1, 2], 1]
a, i = enum2.next
#=> [[2, 4], 2]
a, i = enum2.next
#=> [[3, 5], 3]
a, i = enum2.next
#=> [[1, 3, 6], 4]
a #=> [1, 3, 6]
i #=> 4
Perform the block calculation:
d = arr[0,i]
#=> [[1, 6], [1, 2], [2, 4], [3, 5]]
d.any? { |aa| (aa.size < a.size) && (aa-a).empty? }
#=> true
As true is returned, a is rejected. In the last calculation the first element of d is passed to the block and the following calculation is performed:
aa = [1, 6]
(aa.size < a.size)
#=> 2 < 3 => true
(aa-a).empty?
#=> ([1, 6] - [1, 3, 6]).empty? => [].empty? => true
As true && true #=> true, a ([1, 3, 6]) is rejected.
Alternative calculation
The following is a closer match to the OP's Python equivalent, but less efficient:
def remove_super_arrays(arr)
arr.select do |a|
(arr-[a]).all? { |aa| aa.size > a.size || (aa-a).any? }
end
end
or
def remove_super_arrays(arr)
arr.reject do |a|
(arr-[a]).any? { |aa| (aa.size < a.size) && (aa-a).empty? }
end
end

Answer 2

This was a nice exercise for me. I have used the logic from here.
My code iterates over each subarray (except the first), then there is the magic substraction using the first index, when it is empty the other array contained both numbers.
def remove_super_arrays(arr)
arr.each_with_index.with_object([]) do |(sub_array, index), result|
next if index == 0
result << sub_array unless (arr.first - sub_array).empty?
end.unshift(arr.first)
end
arr = [[1,6],[1,2],[2,4],[3,5],[1,3,6],[2,3,6]]
p remove_super_arrays(arr)
#=> [[1, 6], [1, 2], [2, 4], [3, 5], [2, 3, 6]]