17.1.6. Case Analysis for Rebalancing

Try these first

1. 1.

   What is the height of a tree with only a root node?

   Hint

   Consider how we measure height in terms of nodes.

2. 2.

   What is an AVL tree?

   Hint

   Think about what properties an AVL tree has.

3. 3.

   What must be the maximum height difference between left and right children in an AVL tree?

   • 0
   • 1
   • 2

   Hint

   Think about the conditions that define an AVL tree.

4. 4.

   True or False: AVL trees can become very unbalanced after any insertion or deletion if not rebalanced immediately.

   • True
   • False

   Hint

   Remember the operations that can disturb the balance.

5. 5.

   Given a series of insertions into an AVL tree, illustrate the tree after each insertion and indicate any necessary rotations. Start with an empty tree and insert the values: 10, 20, 30, 25, 22.

   Hint

   Keep track of the slopes after each insertion.

6. 6.

   You have a balanced AVL tree. Describe the steps you would take to delete a node that causes an imbalance, ensuring to maintain the AVL property afterward.

   Hint

   Consider the case of a node deletion affecting the height balance throughout the tree.