Lecture 24

Learning objectives

After this class, you should be able to:

1. Formally prove properties of different types of trees and algorithms on them.
2. Formally prove that algorithms with certain time complexities are impossible, using the fact that comparison-based sorting cannot be done faster than Theta(n log n) time.

Reading assignment

1. Class notes.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Prove that if a node x has a right child, then the successor of x must be the smallest valued node in the right subtree of x.
  2. Prove that if a node x has no right child, then the successor of x must be one of the ancestors of x, if x has a successor.
  3. Prove that a rotation preserves the BST property.
  4. Prove that it is impossible to develop a O(n) time BST initialization algorithm.
  5. Prove that it is impossible to develop a O(1) time AVL tree insertion algorithm.

• Questions on next lecture's material
  1. None. Please work on assignment 6.