Homework 3

Background: Ch. 1.2, 1.3, 8.1, 8.2

Due September 25th:

• Solve the sparse matrix problems described in class.
• CLR Problem 1-2 (pg 17-18).
• CLR Problem 1-3 (pg 18).
• Low values of the insertion index are very common in practical applications. Why? Argue that insertion sort and bubblesort take O(kn) time on lists with insertion index k. Show that both can actually run even faster: for insertion index k=n/2 for some lists. Say why mergesort can take even for k=1. What simple change can we make to mergesort to help? Analyze the effect of this improvement for k=1. Can you extend your argument to arbitrary k to get a bound for mergesort?