COP 4531: Lecture 6

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. CLR: Sections 4.3 and 4.4 (until, and including, sec 4.4.1).
2. Review amortized time complexity analysis of vector inserts from COP 4530.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 4.3-1.
  2. Exercise 4.3-4.

• Questions on next lecture's material
  1. Give the amortized time required for n push_back operations on a vector, assuming that the size of the vector is increased by a factor of 3 each time it needs to be resized. Assume that the starting size of the vector is 1, and that increasing the size of a vector from m to p takes time p.