Lecture 17

Learning objectives

After this class, you should be able to:

1. Given a sequence of n integers, a number k in [1,n], and a sequence of random numbers, show the steps involved in applying the randomized selection algorithm discussed in class to find the k th smallest of these numbers.
2. Analyze the time complexity of the randomized selection algorithm discussed in class.

Reading assignment

1. Class notes on randomized selection.
2. Review binary search trees and balanced binary search trees (CLR: Chapters 12 and 13).

Exercises and review questions

• Questions on current lecture's material
  1. Show how the randomized selection algorithm that we discussed in class would determine the 4 th smallest number of the following sequence: 1 4 3 2 6 0 7 5. Use a sequence of random numbers generated by any of the Unix random number generators, and show this sequence too.

• Questions on next lecture's material
  1. (Post your answer on the discussion board) Give an example of a binary tree with at least eight nodes, and show how you would search for an element in that tree.
  2. What is the time complexity of a search in a binary search tree?