17.2.1. Single Rotation

Try these first

1. 1.

   Define an AVL tree.

   Hint

   Consider the properties that make it 'balanced'.

2. 2.

   What is the significance of the balance factor in AVL trees?

   Hint

   Think about how height differences affect tree operations.

3. 3.

   What is the maximum height difference allowed in an AVL tree?

   • 0
   • 1
   • 2
   • 3

   Hint

   Think about the balance condition discussed.

4. 4.

   After a left-heavy tree insertion, which type of rotation is needed?

   • Left Rotation
   • Right Rotation
   • No Rotation
   • Rebalance

   Hint

   Consider the direction of imbalance.

5. 5.

   Given an AVL tree that has become unbalanced after several insertions, describe the process of identifying which rotations to perform to restore balance.

   Hint

   Evaluate the height differences carefully to make an informed decision.

6. 6.

   Construct an AVL tree by inserting the following sequence of numbers: 30, 20, 40, 10, 25, 22. Illustrate each step including any necessary rotations.

   Hint

   Keep track of height after each insertion to visualize balance.