17.1.5. Slope and Rebalancing

Try these first

1. 1.

   Define height in the context of trees.

   Hint

   Think about paths from the top to the bottom of the tree.

2. 2.

   What does it mean for a tree to be balanced?

   Hint

   Consider how the slopes of subtrees affect balance.

3. 3.

   What is the maximum slope for a balanced AVL tree?

   • 0
   • 1
   • 2
   • -1

   Hint

   Consider the balance requirement in AVL trees.

4. 4.

   True or False: An AVL tree requires that the heights of left and right subtrees differ by at most 2.

   • True
   • False

   Hint

   Think about the AVL balancing rules.

5. 5.

   You have an initially balanced AVL tree. Describe how adding nodes can lead to an imbalance and the specific rotations needed to restore balance.

   Hint

   Consider example scenarios and what rotations apply.

6. 6.

   Given an AVL tree structure, demonstrate visually how the slope affects base operations and what actions to take when movements cause an imbalance.

   Hint

   Draw the tree before and after insertion to clarify the process.