CS7800 12F: Homework 01

Assigned: Wed 12 Sep 2012
Due: Wed 19 Sep 2012

Instructions

1. Please review the grading policy outlined in the course information page.

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: 5 of the following 6 problems
Points: 20 pts per problem

1. Problem 4-3 (b,h)

   Note: Part (h) is essentially a problem on bounding a summation; consider the technique we discussed in class.

2. Problem 4-3 (f,j)

3. Problem 4-3 (d)

   Hint: Do you think that the "-2" in the T(n/3 - 2) makes any difference, asymptotically? What about the "/2" in the additive term "n/2"? Perhaps you can come up with a good guess and then prove that guess correct...

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

   

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

   

   See CLRS pg. 58 for the definition of lg^*.

6. 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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