Lecture 5

Learning objectives

After this class, you should be able to:

1. Prove the Master Theorem for recurrences, when n = bi.
2. Given a recurrence, either solve it using the Master theorem, or show why the Master theorem does not apply to it.

Reading assignment

1. Lectures 3-5 slides.
2. CLR: Sections 4.5 and 4.6 (until, and including, sec 4.6.1).
3. CLR: Chapter 6 - Sections 6.1-6.2, and Page 160.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 4.5-1.

• Questions on next lecture's material
  1. (Post your solution on the discussion board) Give an array of 6 integers, and show how BUILD-MAX-HEAP (page 160) will make it a heap. You may find it difficult to draw the tree representation, as in fig. 6.4, on Blackboard. Instead, give the array representation for each step.