# CS5800 09F: Homework 02

Created: Sat 12 Sep 2009

Assigned: Wed 16 Sep 2009
Due: Wed 23 Sep 2009

## Instructions

1. Please review the course syllabus and make sure that you understand the course policies for grading, late homework, and academic honesty.

2. On the first page of your solution write-up, you must make explicit which problems are to be graded for "regular credit", which problems are to be graded for "extra credit", and which problems you did not attempt. Please use a table something like the following

Problem01020304 0506070809...
CreditRCRCRCECRC RCNARCRC...

where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not applicable" (not attempted). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.

3. You must also write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.

## Problems

Required: 4 of the following 5 problems.
Points: 20 pts per problem
Unless otherwise indicated, problems are from Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein. The edition (2nd or 3rd) will be indicated if the numbering differs.

1. Problem 3-3
2. Problem 3-4
3. Solve the following recurrences and justify your result. (These are in problem 4.3 of the 3rd edition of CLRS. They do not appear in the 2nd edition.

• (a) T(n) = 4T(n/3) + n lg n.

• (b) T(n) = T(n - 2) + 1 / lg n

4. Solve the following recurrences and justify your result.
• (a) T(n) = 3T(n/3 - 2) + n/2
This is 4-3 d in the 3rd edition of CLRS.

• (b)4-4 j in the 2nd edition of CLRS or
4-3 j in the 3rd edition of CLRS. (They are the same.)

5. Derive an asymptotically tight bound on the following recurrence.

Hint: This problem has a five line solution. You'll need to think "out of the box."

### Switch to:

Harriet Fell
College of Computer Science, Northeastern University
360 Huntington Avenue #340 WVH,
Boston, MA 02115
Email: fell@ccs.neu.edu
Phone: (617) 373-2198 / Fax: (617) 373-5121
The URL for this document is: http://www.ccs.neu.edu/home/fell/CS5800/F09/Homeworks/hw.02.html