Lecture 21

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. Write code implementing self-restructuring BSTs, using single rotations and move-to-root.
4. Given a sequence of insert and search operations on a BST, draw the resulting tree when one of the self-restructuring techniques mentioned above is used.
5. Given an application, suggest a suitable self-restructuring technique for it (which may be different from those discussed in class).
6. Given a BST and probabilities of searching for nodes in it, derive the average search time.

Reading assignment

1. Section 6.7.2 (deletion) and section 6.8, up to (and including) 6.8.1.
2. Pages 271-272.

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. Insert the following data into a self-restructuring BST: 8, 4, 10, 2, 6, 9. Show the tree that results from searching for 6 using each of the following techniques: (i) single rotation, and (ii) move to the root.
  4. Assume that the probabilities of searching for the nodes of a complete BST of height h are all equal. Give the average time to search for a node as a function of the number of nodes in the BST.

• Questions on next lecture's material
  1. Draw the array corresponding to figure 6.51 (c) (the bigger tree).