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 for String objects?
If yes, explain how. If not, explain why.

Follow the same design methodology as in homework 1: experiment
with the EXACT SAME prototype data first (all data is already 
stored in text files), report the results in the same table (use 
the one from hw1 and extend it), then experiment with EXACT SAME 
large data sets (already stored in text files), report the 
results in hw1 table by extending it).

Compare the advanced sorting methods that you have implemented 
to elementary sorts from homework 1. Explain yourfindings. 
Remember,you are graded on how well you understand theory and 
concepts, NOT how sophisticated your code is -- this is NOT a 
programming course, but we do need a tool to study algorithms and 
data structures.