CS7800 12F: Homework 02

Assigned: Wed 19 Sep 2012
Due: Wed 26 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: 6 of the following 7 problems
Points: 18 pts per problem

1. Exercise 8.1-3

2. Exercise 8.1-4

3. Exercises 8.2-4, 8.3-4, and the following problem:

   Suppose that you are given the task of devising an algorithm for sorting n records and that the basic operation in your algorithm is an exchange: Exchange[i,j] swaps the data records in positions i and j. (Bubble-sort, Insertion-sort, Heapsort, Quicksort, and Shell-sort are all examples of such algorithms.) The width of an exchange is defined to be the distance across which data records are moved, i.e., j - i for Exchange[i,j]. Prove that any algorithm for sorting which uses only constant width exchanges must run in Omega(n²) time in the worst case.

   • Hint: Bound the total amount of "data movement" that must be performed in the worst case.
   • FYI: Insertion sort and bubble sort are examples of constant-width-exchange sorting algorithms.

4. Problem 8-1 (a, b, c, d, e)

5. Problem 8-3

6. Exercises 9.3-7 and 9.3-9

7. Problem 9-2 (a, b, c)

Switch to:

• Homework 01
• Homework 03