17.1. Balanced Search Trees

Try these first

1. 1.

   Define an AVL tree.

   Hint

   Consider the height difference criterion!

2. 2.

   What does it mean for a tree to be balanced?

   Hint

   Think about how balance affects tree operations.

3. 3.

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

   • 0
   • 1
   • 2
   • 3

   Hint

   Recall the properties of AVL trees.

4. 4.

   True or False: All AVL trees are complete binary trees.

   • True
   • False

   Hint

   Think about the definition of 'complete' versus 'balanced.'

5. 5.

   Construct an AVL tree by inserting the following values in order: 10, 20, 30, 40, 50, and 25. Demonstrate all the rotations that might be needed.

   Hint

   Draw the tree at each insertion to see where the imbalances lie.

6. 6.

   Explain how the AVL tree would look after deleting node 30 from the previous tree. What rotations might be necessary?

   Hint

   Visualize the tree post-deletion, check heights and explore necessary rotations.