18.3. Handling Nodes with Height +2

Try these first

1. 1.

   What indicates a height imbalance of +2 at a node?

   Hint

   Think about the heights of both subtrees.

2. 2.

   What is a rotation in the context of binary trees?

   Hint

   Consider what happens to the structure of the tree during rotation.

3. 3.

   What does a height of +2 in a binary tree node indicate?

   • A balanced tree
   • A right-heavy imbalance
   • Left-heavy balance

   Hint

   Think about what balance means for each subtree.

4. 4.

   True or False: A single rotation can fix any height imbalance.

   • True
   • False

   Hint

   Consider the complexity of imbalances.

5. 5.

   You are given an unbalanced binary tree where a node has a height of +3. Describe the steps to rebalance this tree using rotations.

   Hint

   Consider the roles every node plays in a binary tree.

6. 6.

   Design an algorithm in pseudo-code for inserting a node into an AVL tree while ensuring rebalancing through rotations.

   Hint

   Think about how the insertion affects the tree balance and the corresponding rebalancing operations after every insertion.