Optimal sequence for AVL tree insertion (without any rotations)

Given an array of integers, the task is to find the sequence in which these integers should be added to an AVL tree such that no rotations are required to balance the tree.

Examples : 

Input : array = {1, 2, 3}
Output : 2 1 3

Input : array = {2, 4, 1, 3, 5, 6, 7}
Output : 4 2 6 1 3 5 7

Approach : 

• Sort the given array of integers.
• Create the AVL tree from the sorted array by following the approach described here.
• Now, find the level order traversal of the tree which is the required sequence.
• Adding numbers in the sequence found in the previous step will always maintain the height balance property of all the nodes in the tree.

Below is the implementation of the above approach : 

4 2 6 1 3 5 7 

Complexity Analysis:

• Time Complexity: O(N)
• Auxiliary Space: O(N)