Problem
An AVL-2 tree is an AVL tree in which for each internal position the heights of the subtrees rooted by its children differ at most by 2. Build the AVL-2 tree resulting from the following key insertions, in that order, and answer the questions below. For internal and external nodes, consider only nodes that have a non-null key; in other words, take the resulting tree without the sentinel nodes. Also take the height of the tree without the sentinel nodes.
Keys for the AVL-2 tree: 1,2,5,12,6,7,4,3,0,14,11,8,13
Task
A. What is the height of the AVL-2 tree?
B. What is the key in the root node?
C. How many external nodes does this tree have?
D. What is the sum of the keys in the last 2 nodes of the left branch?
E. What is the sum of the keys in the last 2 nodes of the right branch?