<ALIGN="CENTER">CS1044 Assignment 4

CS 1044, Assignment 4, Schuetz

Spring 1998

Due Date: 11:59 pm, March 31, 1998

Roots of quadratic equations

Assignment 4 may be done jointly with one other class member. In that case, both names must appear in the program header, and only one grader account may be used. To request to work together, submit a collaboration request form (no Email) to the instructor by 5:00 Thursday, March 26. This form is found on the class web page.

Introduction

Write a program to find the roots of a quadratic equation, using the following design which involves the use of four functions. Recall that for a quadratic equation

                          Ax² + Bx + C = 0

the roots are given by

	-B + sqrt (B² - 4AC)    and    -B - sqrt (B² - 4AC)
         -------------------             -------------------
                 2A                              2A

Note that the quantity (B² - 4AC) is called the discriminant (D). If A != 0, then there are three distinct possibilities for D.

(1) If D > 0, then there are two distinct real roots. For example, if A = B = 1 and D = 4, then we have the two roots

        -1 + sqrt (4)       -1 + 2
         -----------    =    -----   =    0.5   and
              2                2

        -1 - sqrt (4)       -1 - 2
         -----------    =    -----   =   -1.5
              2                2

(2) If D = 0, then both roots are real and have the same value. For example, if A = 1, B = 2, and D = 0, then the roots are both

        -2 - sqrt (0)
         -----------    =   -1.0
              2

(3) If D < 0, then there are two complex number solutions of the form M + Ni and M - Ni. For example, if A = B = 1 and D = -4, then we have the two roots

        -1 + sqrt (-4)       -1 + 2i
         ------------    =    ------   =   -0.5 + 1.0i   and
               2                 2

        -1 - sqrt (-4)       -1 - 2i
         ------------    =    ------   =   -0.5 - 1.0i
               2                 2

-------------------------------

Note: If A = 0 but B != 0, then the equation becomes Bx + C = 0 which has the single real solution -C / B. If A = B = 0, then the coefficients do not form a valid equation, and an error message should be written. In your program, all the floating point numbers and coefficients in your equations should be stored as type double to avoid loss of precision.

Input

The input for your program is to be read from the file, asgn4.in. Each line of this file has three real numbers that represent the equation coefficients A, B, and C, respectively. It is unknown how many equations are to be solved. A typical input file might have the following data:

1.0     -2.0     -3.0
1.0     -2.0     10.0
1.0     -2.0      1.0
0.0     -0.0      1.0
0.0      2.0      4.0

Functions

This problem is to be solved using the following four functions:

Print_Heading (output_stream) does nothing but print the 4 lines of header information for the tabular output.
Get_Coefficients (input_stream, A, B, C, valid, endOfFile) reads an input data line containing the three coefficients of the quadratic equation. The function should place the value true in valid if the coefficients form a valid equation, and endOfFile will contain true if there are no more coefficients to be processed, in other words, if no A, B, and C values are available.
Solve (A, B, C, num1, num2, numrealsolns) actually solves the quadratic equation with coefficients A, B, and C. numrealsolns is an integer which is either 0, 1, or 2 to prepresent the number of real solutions to the equation. If the data is invalid (when A = B = 0) then Solve should not be called at all.
(a) If numrealsolns = 2 (D >= 0) then num1 and num2 are the two roots which may be identical if D=0.
(b) If numrealsolns = 1 (A = 0) then num1 is the single real root and num2 is meaningless.
(c) If numrealsolns = 0 (D < 0) then num1 and num2 are the real and imaginary parts of the complex solutions (M and N). You may assume that num2 is positive. Then the answers are num1 + num2 i and num1 - num2 i.
Write_line (output_stream, A, B, C, num1, num2, numrealsolns, valid) This procedure prints the output line according to the results provided by Solve. If valid is false, then Write_line will print the invalid coefficients message shown below.

Output

The output must be written to the file, asgn4.out. The output generated by the input data above is

                                    Number
                                      of
        A        B        C        Solutions        Root 1        Root2
-------------------------------------------------------------------------
     1.00    -2.00    -3.00         2 Real            3.00        -1.00
     1.00    -2.00    10.00        2 Complex      1.00 + 3.00i  1.00 - 3.00i
     1.00    -2.00     1.00         2 Real            1.00         1.00
     0.00     0.00     1.00     ***** Error: Invalid coefficients ! *****
     0.00     2.00     4.00         1 Real           -2.00

Documentation

As with every program you will write this semester, your code will need to conform to the departmental standards, which include prettyprinting such as whitespace and indentation, a documentation header for each function you write including main, and readable inline documentation that describes the function of each chunk of code. All function parameters must also be documented so that a user will understand how they are used.

Your Submission

Your programs are to be submitted to the automatic grader; they are archived by the grader and will be hand graded for conformance to departmental standards on a random basis. No other materials need be submitted with this assignment. This assignment should be submitted as Project Number 4. You can earn two bonus points per day (24 hours) for each day early you submit your program, up to three days (total of 6 points).