Lecture 22

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 simple 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 and handout on randomized selection.

Exercises and review questions

• Questions on current lecture's material
  1. (Post your answer on the discussion board) 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.
  2. We showed that T(n) ≤ 4n. Instead, assume that T(n) ≤ cn, redo the derivation, and show that taking c = 4 will satisfy your assumption.

• Questions on next lecture's material
  1. None.