CSOR 4231 07F: Homework 2

Required : 5 of the following 7 problems
Points: 10 pts per problem

General Instructions

1. Please review the homework and 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 attempted" (not applicable). 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.
4. Start early, be concise but rigorous, and enjoy!

Specific Instructions

1. All logs are base 2 unless otherwise specified.
2. Unless otherwise specified, all problems and exercises are from CLRS, Introduction to Algorithms, 2nd edition.

Problems

1. Exercise 6-4.2. Correctness of heapsort
2. Problem 6-3. Young Tableaux
3. Exercise 8.1-4. Lower Bound on Sorting.
4. Suppose we modify counting sort so that the loop in line 9 through 11 goes from 1 upto length[A].
   1. Is the modified counting sort still correct? Why or why not?
   2. Is the modified counting sort still stable ? Why or why not?
   3. If it is not stable explain how to modify the rest of counting sort so that the modified counting sort is stable.
5. Problem 8-5. Average Sorting.
6. Exercises 5.3-2, 5.3-4. Random Permutations
7. Exercises 5.2-4, 5.2-5. Indicator Random Variables.

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• Homework 1
• CSOR 4231 07F Home Page
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