CPSC 231: Assignment 3 (Due Monday Oct. 21)

Weighting = 3%

Fibonacci Numbers

The Fibonacci numbers are a sequence of numbers that was developed by the European mathematician Leonardo of Pisa for biological simulations.  The first two numbers in sequence are both one.  All other numbers in this sequence are calculated as the sum of the previous two numbers i.e.,

f (0) = 1

f (1) = 1

f (2)  = f (1) + f (0) = 1 + 1 = 2

f (3) =  f (2) + f (1) = 2 + 1 = 3

f (4) = f (3) + f (2) = 3 + 2 = 5

f (5) = f (4) + f (3) = 5 + 3 = 8

f (6) = f (5) + f (4) = 8 + 5 = 13

f (7) = f (6) + f (5) = 13 + 8 = 21

f (8) = f (7) + f (6) = 21 + 13 = 34

f (9) + f (8) + f (7) = 34 + 21 = 55

f (10) = f (9) + f (8) = 55 + 34 = 89

   :           :          :   

f (n) = f (n-1) + f (n-2) for n = 2, 3, 4 ... 

For this assignment you are to write a program that calculates Fibonacci numbers from n = 0 up to and including n = 45.  The value for n will be entered by the user of the program.  You are to implement your assignment with an iterative solution that employs looping and decision making constructs.  You are not to submit a recursive solution for this assignment.

Grading

B+ Version

For any number entered by the user from one up to some arbitrary nth value (maximum of 45), your program will calculate the final Fibonacci number in that sequence.  For example, if the user of the program entered six, the program would show the result for f(6) which is thirteen.  A sample solution that implements a B+ solution can be found under the path: /home/231/assignments/assignment3/Bplus.

A+ Version

Your program will not only calculate the Fibonacci number for any value from one up to some arbitrary nth value (maximum of 45), your program will not only show the last Fibonacci number, but will also show intermediate values.  For example, if the person using the program typed in six then the program would show all the Fibonacci numbers from zero  to six.  A program that implements an A+ solution can be found under the path: /home/231/assignments/assignment3/Aplus.

Requirements for both versions

Minor requirements

Both versions of your assignment must fulfill the following minor requirements.  Failure to satisfactorily meet each minor requirement will result in the loss of one letter "step" (e.g., "A+" to "A", "A" to "A-" etc.)

1. Error checking: Your program should ensure that the value entered by the user of the program is within the range of 0 - 45 (inclusive).  If this is not the case then the program should present a helpful and polite error message e.g., "Fibonacci numbers must be within the range of zero to forty five, please enter in a value within that range".
2. Neat and legible formatting: All results must be neatly formatted when displayed onscreen (see the sample solutions for some formatting examples).

Major requirement

Both versions of your assignment must also be accompanied by a either a flowchart or pseudo-code that correctly specifies the algorithm for your solution.  Failure to include to include the algorithm will result in the loss of a letter grade (e.g., "A+" to "B+", "B+" to "C+").   It is highly recommended that you layout the algorithm on paper prior to writing your program.

 

Learning Objectives

Learning how to apply the concepts of structured programming, decision-making and repetition, in a Pascal program.