18.7. Efficient Height Management

Try these first

1. 1.

   What does a slope of -1 indicate in a binary search tree?

   Hint

   Think about the definition of slope.

2. 2.

   What is the main purpose of performing rotations in BSTs?

   Hint

   Consider why tree operations can slow down.

3. 3.

   What action do we take if the slope of a tree node is -2?

   • Perform a left rotation
   • Perform a right rotation
   • Rotate at the child first

   Hint

   Think about which direction needs to be adjusted first.

4. 4.

   True or False: A slope of 0 means both the left and right subtrees are of equal height.

   • True
   • False

   Hint

   Consider the definition of slope.

5. 5.

   Given a series of insertions into a binary search tree, track the changes in slopes and the necessary rotations needed after each insertion.

   Hint

   Document each step with a simple tree diagram.

6. 6.

   Create a balanced binary search tree with a specific set of nodes and explain how to maintain its balance through rotations during subsequent operations.

   Hint

   Focus on tree height and slopes after each alteration.