CS 253: Homework 1

Problem 1.  Design a program that allows you to experiment with 
different sort algorithms. This program should allow you to easily 
plug-in new sorting algorithms and compare them. For this homework, 
you will work with insertion, selection and bubble sorts (more
sorts will be added later).

Assume that input data is generated randomly and stored in a text file. 
You will experiment with your program in two steps:

Step 1: Experimenting with a prototype data (integers from 1 to 10) to 
ensure that your implementation works correctly. The results must be 
reported in a table format (not generated by the program, but collected 
manually from multiple program runs) in the a Word document as follows:

        best case         worst case        average case
      char.1...char.N   char.1...char.N   char.1...char.N

alg.1  ...       ....     ...     ...       ...      ...
alg.2  ...       ....     ...     ...       ...      ...
...
alg.N  ...       ....     ...     ...       ...      ...

Step 2: Experimenting with a large data set of 2000 elements.
The results must be reported in the same table format.

In adition, in the report, explain the empirical results generated
by your program comparing them to the known theoretical results
paying special attention to any inconsistensies.

Must submit for grading: an UML diagram of the program design, the java 
code, the random text file(s) generated by an independent module (you may 
need multiple random text files to better characterize the average efficiency 
of the respective algorithm), the report as a Word document.

Problem 2. Study, program, and compare the efficiencies of the following 
recursive algorithms:

-	Recursive binary search
-	Computing the factorial of N
-	Computing the N-th Fibonacci number.

Must submit the tree of recursive calls for each program (in any format as
long as I can open it for a reasonable N), the Big-O function with an 
explanation for each program, PLUS the java code and example runs to 
demonstrate the correctness of the implementation.  

ALL HOMEWORKS WILL BE POSTED ON THE COURSE WEBSITE, BUT SUBMITTED VIA BBLearn.
Remember that homework projects are individual assignments. Shared work will
be graded by the rule "Share the work, share the grade". However, you can get
some help from the code on my Web site. You may design your program in whatever 
environment you want, but the final version of your programs that you submit for 
grading must run in jdk. Test it, to make sure it does. Also, this in NOT a 
programming course -- you will be graded on your understanding of CONCEPTS and
THEORY that each programming project covers. That is, your perfect implementation
may result in 0 points, if you fail to explain your results, especially if they
are wrong.