Assignment 2

CS 270/680 Mathematical Foundations of Computer Science
Instructor: Jeremy Johnson 
Due date: (Beginning of class on Oct. 12)

1. Exercise 2.5.3 from the text
2. Exercise 2.7.7 from the text
3. Exercise 2.9.4(a) from the text
4. In this question you will investigate the a recursive program to simultaneously compute the minimum and maximum element in a vector of integers.
   1. Write a main program that calls the function minmax and counts the number of comparisons used when called with a vector of size n (you can use the vector whose elements are 0,1,...,n-1).
   2. Use the program you wrote to determine the number of comparisons used for vectors of size 2^k, for k=1,...,10.
   3. Write a recurrence relation for the number comparisons used by minmax for vectors of size 2^k. Use the recurrence to compute the values for size 2^k, for k=1,...,10 and compare to those obtained from your program.
   4. Use repeated substitution to convert the recurrence relation to a sum and find a closed form solution for the sum (you will have seen the sum before).

      Graduate Student Problem

      1. Exercise 3.11.11 from the text
         

      How to submit

      Students should submit their solution electronically.  Use a word processor (e.g. word with the equation editor or latex) to create your solution and submit either 1) a text file, 2) a word document, or 3) a pdf file. Alternatively, you can submit a pdf file containing a scan of a handwritten solution. You should also submit the program you wrote to determine the number of comparisons used by minmax (make sure you have a readme file explaining how to compile and use the program). You should submit your assignment using WebCT. Bring a paper copy of your homework to the class meeting when it is due. WebCT will be set up to accept assignments on Thursday.