Lecture 18

Learning objectives

After this class, you should be able to:

1. Write code to implement deletion from an AVL tree, and give its time complexity.
2. Given a sequence of insertions into an AVL tree, and deletions from it, draw the tree.
3. Explain the correctness of the algorithms for insertion and deletion in an AVL tree.

Reading assignment

1. Section 4.4.
2. Lecture: Trees: Part 4 -- AVL trees.
3. None.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Insert the following elements into an AVL search tree in the order given below: 8, 4, 10, 2, 6, 9, 11, 12, 1, 3, 5, 7, 0, 1.1, 2.1, 3.1, 4.1, 5.1, 6.1, 7.1. Show the AVL tree that results from deleting the node with key value 9.
  2. Insert the following elements into an AVL search tree in the order given below: 8, 4, 10, 2, 6, 9, 12, 11, 1, 3, 5, 7, 0, 1.1, 2.1, 3.1, 4.1, 5.1, 6.1, 7.1 (note that 11 and 12 are inserted in a different order than in the previous question). Show the AVL tree that results from deleting the node with key value 9.
  3. Complete the figures for case 2 in insertion and deletion by giving the heights of all the vertices.
  4. Let the balance factor of a node be defined by | Height of right sub tree - Height of left sub tree |. Give the balance factor for the nodes in slides 27-30. Instead of storing the heights of the nodes, can we store the balance factors of the nodes and update an AVL tree (for insertion and deletion) based on this information?

• Questions on next lecture's material
  1. None.