Homework Assignment 2
This assignment is due by Tuesday February 12 (in class). Assignments should be handed in before
the class begins.
Problem 1: Solve exercises 7.1-3, 7.1-4 (page 174), 7.2-4 (page 178), and 7.4-4 (page 184) in the
textbook.
Problem 2: Solve the following recurrences using the master theorem. Clearly justify using the
various cases of the theorem.
•T(n) = 9T(n
3) + n2+n
2+ 1
•T(n) = 5T(n
2) + n2
•T(n) = 12T(n/4) + n2
Problem 3: Solve exercise 4.5-2 (page 97) in the textbook.
Problem 4: Explain why the recurrence T(n)=2T(n
2) + nlog ncannot be analyzed using the
Master Theorem. Then show using induction that T(n) = O(nlog2n).
Problem 5:
(i) Analyze the recurrence T(n) = √n T (√n) + nusing unfolding or recursion trees (use n= 2 for
the base case). You may be better able to track the terms by noting that √n=n1
2.
(ii) Now give an inductive proof that your bound from (i) is indeed correct. You may assume that
T(n)≤Cfor n≤16.
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