CS5800 09F: Homework 02

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

   Problem	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.

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 (2^nd or 3^rd) 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 3^rd edition of CLRS. They do not appear in the 2^nd 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 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.)

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."

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