CS 253:  Homework # 2

Part 1:

Consider the following loop construct:

X := 1
repeat
   Y := N
   while Y > 0 do

     . . .          // something (the ellipsis)

     Y := Y - 1
   endwhile
   X := X + X
until X > N * N

Categorize its efficiency in terms of the variable N using 
big-O notation. Also, assume that the statements represented
by the ellipsis require four main memory accesses with each
access requiring 1 microsecond, and two disk file accesses
with each requiring 1 millisecond. Express in milliseconds 
the amount of time this construct would require to execute
if N = 1000.

Part 2:

Extend your sorting framework with two advanced sorting 
methods of your choice: (Shell Sort OR Radix Sort) AND 
(Merge Sort OR Quick Sort). If you choose Shell Sort,
experiment with different incremental sequences to see 
how they affect the algorithm's run time efficiency (count
the number of comparisons and exchanges). If you choose to
implement Radix Sort, answer the following question as well: 
Can you write a version of Radix Sort to work with real 
numbers? If yes, show me how. If not, explain why.

Compare the advanced sorting methods that you have
implemented to elementary sorts from homework 1. Explain
the results generated by your program (do not forget to
experiment with best / worst / avarage cases, if applicable).