Concatenating/Merging/Joining two AVL trees

Question

Assume that I have two AVL trees and that each element from the first tree is smaller then any element from the second tree. What is the most efficient way to concatenate th

Answer 1

One ultra simple solution (that works without any assumptions in the relations between the trees) is this:

1. Do a merge sort of both trees into one merged array (concurrently iterate both trees).
2. Build an AVL tree from the array - take the middle element to be the root, and apply recursively to left and right halves.

Both steps are O(n). The major issue with it is that it takes O(n) extra space.