18.2. Rebalancing After Insertions

Try these first

1. 1.

   What is the maximum slope for a balanced binary search tree?

   Hint

   Think about the conditions for a balanced tree.

2. 2.

   What action do we take if the slope at a unbalanced node is +2?

   Hint

   What rotations are performed based on the child's slope?

3. 3.

   What is the maximum imbalance slope for a node to be considered balanced?

   • 2
   • 3
   • 1

   Hint

   Remember the definition of balance in trees.

4. 4.

   True or False: After inserting a node with a slope of -2, we first perform a right rotation.

   • True
   • False

   Hint

   Think carefully about how rotations are determined.

5. 5.

   Construct a balanced binary tree after inserting the values 50, 30, 20, 40, 70, 60, 80. Illustrate the rebalancing steps taken after each insertion.

   Hint

   Draw diagrams to see visual shifts for better understanding.

6. 6.

   Given an initial imbalance with a slope of +3, explain how you would address it with appropriate rotations and height updates.

   Hint

   Use slope calculations to guide your rotation strategy.