Homework 4 (incomplete)

Background: Ch. 10.

Due October 2nd:

• 4.1: Given a list L of n numbers, we want to compute . Prove that x equal to the median of L minimizes the expression. [Extra Credit!]
• 4.2: Given a list L of n numbers, we want to compute . Prove that x equal to the mean of L minimizes the expression. [Extra Credit!]
• 4.3: Give an algorithm for computing the mode of a list of numbers (not necessarily sorted).
• 4.4: Give an algorithm for efficiently computing the rank of GPA x both when the list L of GPAs is sorted and when it is not. Give tight worst-case running time bounds.
• 4.5: Show that the expected running time of SELECT is O(n).
• 4.6: CLR Exercise 10.3-3 (pg. 192).
• 4.7: CLR Exercise 10.3-7 (pg. 192).