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ruby - Sort an array according to the elements of another array

I have an array of ids

a1 = [1, 2, 3, 4, 5]  

and I have another array of objects with ids in random order

a2 = [(obj_with_id_5), (obj_with_id_2), (obj_with_id_1), (obj_with_id_3), (obj_with_id_4)]  

Now I need to sort a2 according to the order of ids in a1. So a2 should now become:

[(obj_with_id_1), (id_2), (id_3), (id_4), (id_5)]  

a1 might be [3, 2, 5, 4, 1] or in any order but a2 should correspond to the order of ids in a1.

I do like this:

a1.each_with_index do |id, idx|
  found_idx = a1.find_index { |c| c.id == id }
  replace_elem = a2[found_idx]
  a2[found_idx] = a2[idx]
  a2[idx] = replace_elem
end  

But this still might run into an O(n^2) time if order of elements of a2 is exactly reverse of a1. Can someone please tell me the most efficient way of sorting a2?

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I'll be surprised if anything is much faster than the obvious way:

a2.sort_by{|x| a1.index x.id}

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