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**Assigned:**
Wed 16 Sep 2009

**Due:**
Wed 23 Sep 2009

- Please review the course syllabus and make sure that you understand the course policies for grading, late homework, and academic honesty.
- 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 followingProblem 01 02 03 04 05 06 07 08 09 ... Credit RC RC RC EC RC RC NA RC RC ... 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.

- 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.

**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 (2^{nd} or 3^{rd}) will be indicated if the numbering differs.

- Problem 3-3
- Problem 3-4
- Solve the following recurrences and justify your result. (These are in problem 4.3 of the 3
^{rd}edition of CLRS. They do not appear in the 2^{nd}edition.- (a)
*T*(*n*) = 4*T*(*n*/3) +*n*lg*n*. - (b)
*T*(*n*) =*T*(*n - 2*) + 1 / lg*n*

- (a)
- Solve the following recurrences and justify your result.
- (a)
*T*(*n*) = 3*T*(*n*/3 - 2) +*n*/2

This is 4-3*d*in the 3^{rd}edition of CLRS. - (b)4-4
*j*in the 2^{nd}edition of CLRS or

4-3*j*in the 3^{rd}edition of CLRS. (They are the same.)

- (a)
- 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."

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