CEG220: Introduction to C Programming for Engineers – I

Section 2

 

Project 2: Calculating Cube Roots

 

Program Background:

By now, most of you have used square roots often in equations, and have heard of Newton’s method to approximate square roots.  But we sometimes need to calculate the cube root of a number – and math.h doesn’t have a function in its library for that[1]. As you will find out when solving many problems, this happens frequently; so, we’ll need to improvise – and write it ourselves.

 

The algorithm to incrementally approach the cube root of a positive number n with a guess g is:

 

Guessnew = (2/3) * Guessold + ( (1/3) * (n / (g2) ). Please note the decimal points involved!

 

Program Description:

Your task is to write pseudo code for this algorithm and implement it as a program. Given a guess as the square root of x, experiment with the number of iterations that is required to get an accurate value for the cube root of x. Is the square root of x a good guess for this algorithm? What might be a better guess (a function of x)? Why?

 

Program Requirements:

1)      Your program must comply with the class programming standard

2)      You must submit a hand-written program specification detailing (1) your approach to solving the problem, (2) the algorithm(s) you used, and (3) justifying the data types you have used

 

Grading Standard:

This project is worth 100 points. Please note that programs that do not compile or do not link will lose all points related to run-time requirements (examples of run-time requirements includes but is not limited to correct run output, handling certain cases adequately, etc.). Grading standard will be followed strictly:

 

20 points:         Preparatory Requirements

·        Compliance with class coding standard (5 points each)

·        adequate comments – clear, concise, useful; not excessive

·        well-named identifiers

·        follows program specification

·        hand-written document / program specification (5 points)

·        Uses pseudo-code to express the problem and how to solve it

 

40 points:         Run-time Requirements

·        cubert(x) returns the cube root of x (20 points)

·        uses appropriate style of loop, where appropriate (5 points)

·        NOTE: if you correctly substantiate why you used a certain loop in your program specification and/or your code, I will be more lenient in this category.

·        Handles all cases of n properly (10 points)

·        Uses modular design when appropriate (5 points)

 

15 points          Written Requirements

·        questions are answered satisfactorily and substantiated in words and by the results of your program

 

Due Date:

This project is due on 9/22 at the beginning of class. If your assignment is late – by 5 minutes or (the maximum) 2 days, the penalty is 30% (see syllabus).


[1] math.h DOES have a function called pow(x, y) which returns xy. You are supposed to calculate cubert(x) using the formula given, and NOT return pow(x, (1.0/3)) = x^1/3 = cubert(x).