Homework 1

Short Description:

Continue to explore algorithms to extract the k^th item.

This assignment is worth 15 points.

Goals

When you finish this homework, you should:

Gain some experience timing programs
Gain some experience analyzing timing results
Gain an appreciation for the weakness of wall clock performance analysis.

Formal Description

Write a program that implements algorithm 2 from the notes. Perform a timing analysis on this program similar to the one done in the notes.

Next you should implement the following algorithm:

FindItemK(A,n,k)

 for i<-0 to k-1 do
     position = FindPositionOfMinimum(A,i, n)
     exchange(A[i], A[position])
 return A[k-1]

Perform a similar timing analysis on this algorithms.

Finally, recompile your programs on cslab103 and redo your timing experiments on one of the algorithms.

When you are finished produce a report summarizing your results. This report should be produced using a word processor, and contain the following sections:

Introduction: briefly introduce your experiment.

Algorithms: List the important algorithms in both English (with a high level description of the algorithm) and in pseudo code.

Algorithm 1:

This algorithm finds the k^th item in a list by 
first sorting the list then extracting the item.

(place pseudo-code here)

Methods: Explain what you did and how you did it. Describe the computing environment, input, output and other conditions which might effect the experiment.
Data: Give tables summarizing your results. Make sure that your tables are labeled. Reference your tables in the text.
Analysis: Describe what you discovered. Include graphs to help interpret the data. Make sure that any graphs are labeled. Reference any graphs or tables in your text.
Verification: Describe how you verified that your algorithms, code, and methods are valid.
Conclusions: Summaries your results. Make recommendations on which algorithms to employ and under what conditions they should be employed.
Further Investigation: Describe further experiments or investigations your work might suggest to you.
References: Cite references to any material used.
Appendices: Items which you feel are required to make your report complete. For example, if you wish to include code, or code fragments, this is the place to do it.

Input

The size of the array and the item to find.

Output

The time spent in the algorithm.

Discussion

If you don't understand how to do any portion of this assignment, make sure you ask for assistance. Makefiles and tar are a standard part of most projects in the unix world. They are not hard to use and I will be more than happy to help you with them.

Required Files

Your code, a README file , and a Makefile.

The README file should contain personal information (your name, email, ...) as well as a description of the assignment. It should discuss the algorithms and data structures you employed in accomplishing the assignment. You should also discuss any unique features contained in your program, problems with the program, and special instructions for compiling or using your program. If you wish to provide feedback on the assignment, ask questions, or compose poetry, this is probably the place to do it.

Your makefile for this program should be derived from the following Makefile. To use this file, you should name your program alg2.C. To use this makefile, simply type make and your program should compile. By typing make clean your executables and object files will be removed. If you wish to see what commands make will issue when run you can type make -n. You can edit a make file with any editor. The file should be called Makefile with an uppercase M.

Extra Credit

You may receive up to five points extra credit for implementing and testing any other algorithm to find the k^th item. One such algorithm might involve examining k and if it is less than n/2 search for the k^th smallest, otherwise search for the n-k^th largest.

Remember, if you search the net, or a book for an algorithm, you must document the source.

Submission

This assignment is due Sept 11 at class time. You should email a tar file of your homework directory to dbennett@edinboro.edu. Furthermore you should submit, before class begins, a hardcopy of your lab report.

To create a tar file, you should place all of the files you want to submit into a single directory, for example hw1. One level above this directory type the command:

tar cvzf hw1.tgz hw1

This will create the file hw1.tgz in the current working directory. To check the contents of this file, type :

tar tzf hw1.tgz

To extract the contents of this file, type:

tar xvzf hw1.tgz

Tar is the Tape Archive utility for unix. It was originally intended to copy a file system to the tape device.