Lecture 7

Learning objectives

After this class, you should be able to:

1. Given an array and a sequence of random numbers, show how randomized quicksort will sort the array.
2. Analyze the worst case and average case time complexities of quicksort.
3. Given a problem, choose a suitable sorting algorithm that will be efficient for that problem.

Reading assignment

1. Lectures 6-9 slides.
2. CLR: Sections 7.3 - 7.4.
3. CLR: Chapter 8, page 192.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 7.3-2
  2. Show that q2 + (n-1-q)2, 0 < q < n-1, is maximized when q = 0 or q = n-1.

• Questions on next lecture's material
  1. (Post your solution on the discussion board) Give an example of an array that is not already in sorted order, and give the permutation corresponding to this array. Note: The desired permutation is the set of values of pi(1), pi(2), pi(3), ... , as presented on page 192, and in particular, in figure 8.1.
  2. What is the maximum number of leaves in a binary tree of height h?