Latest Revision: February 11, 2013

Directions for Lab #2

Read and study these directions before the day of the lab. Read this document all the way through at least once before trying to perform any of the steps. After that, rehearse some of the steps, mentally and/or by getting online and doing them.

The goal of this exercise is to develop an interactive program that performs arithmetic on integers, using the C++ int data type.

A Pythagorean triple is a set of three positive integers that represent the sides of a right triangle. Such triples -- X, Y, Z -- satisfy the relation: 
X*X + Y*Y = Z*Z
-- which means: "The square of X plus the square of Y equals the square of Z." The common notation for expressing this idea in math books is:
(X2 + Y2 = Z2)
You can make Pythagorean triples by using the following recipe:

First pick any two positive integer 'seeds' M and N, with M > N, then determine the lengths of the sides of a right triangle like this: 
Side One of the Triangle Equals:    M*M - N*N 
Side Two of the Triangle Equals:    2*M*N
Hypotenuse of the Triangle Equals:  M*M + N*N
For example if we choose seeds M=2 and N=1, then M is larger than N, as required, and

Side One = M*M - N*N = 2*2 - 1*1 = 3,
Side Two = 2*M*N = 2*2*1 = 4, and
the Hypotenuse = M*M + N*N = 2*2 + 1*1 = 5.

So using M=2 and N=1 as seeds, the recipe gives us the Pythagorean Triple: (3,4, 5)

Below is a "shell" or "skeleton" of a C++ program. It is not finished. It has only comments where most of the executable statements need to be. The intended purpose of the program is to read values for M and N from the user (M > N), and to then calculate and display a Pythagorean triple. 
/*  start of file lab02.cpp */
/*
    lab02.cpp.  This program reads two positive integer seeds
    M and N with M > N and displays a Pythagorean triple, 
    which consists of three positive integers that represent 
    the sides of a right triangle.
*/

#include <iostream>

using namespace std ;

int main(void)
{
    /* ***a*** Declare M and N and comment on their meanings */

    /* ***b*** Display this text: "A Program to Calculate Pythagorean Triples" */

    /* ***c*** Prompt for a positive integer seed N, and then read it */
    /* ***c*** Prompt for a positive integer seed M > N, and then read it */

    /* ***b*** Display this text: "The Pythagorean Triple" */

    /* ***d*** Calculate and display Side one */
    /* ***d*** Calculate and display Side two */
    /* ***d*** Calculate and display Hypotenuse */

   return 0;
}   
/*  end of file lab02.cpp */
Below is an example of an interactive session. It illustrates what you should see on the screen when you run the program. To make it easy for you to figure out which characters the user of the program entered, and which characters the program printed on the screen, the characters entered by the user are shown underlined and in boldface. 
john@vega: a.out

A Program to Calculate Pythagorean Triples

  Enter an integer N:         2
  Enter an integer M > N:     5

The Pythagorean Triple

  Side One       =  21
  Side Two       =  20
  Hypotenuse     =  29

john@vega:

Individual steps:

  1. Save a copy of the program shell lab02.cpp (see above). Give the file the same name: lab02.cpp. To make the file you can just select the program text, copy it, paste it into a window running an editor, and save it.

  2. Below the comment in file lab02.cpp that begins with ***a***, insert a declaration of integer variables M and N and comment on their meanings. (See your C++ textbook for examples of this kind of declaration.) Save, compile and execute the program. Correct any errors.

  3. Below each comment that begins with ***b***, insert the indicated output statement -- one to display "A Program to Calculate Pythagorean Triples" and one to display "The Pythagorean Triple". Construct the statements so that the program output will be just as in the example interactive session shown above. Make sure that your code creates blank lines just as in the example. Re-run the program (i.e. save, compile and execute it again). Correct any errors. Notice the output you get.

  4. Under each comment that begins with ***c***, insert the indicated code, to prompt for and read the integer N, or to prompt for and read the integer M. Construct the code so that the program will behave just as in the example interactive session. (Notice that each prompt is indented in that example.) Re-run the program. Correct any errors. Notice the output you get.

  5. Under each comment that begins with ***d***, put the code for the appropriate output statement. Construct the code, so that the program will display the Pythagorean triple corresponding to the values of N and M that were input. The numbers output must be M*M-N*N, 2*M*N, and M*M+N*N.

    Get the indentation (spacing) right, as in the example.

    Don't use any new variables for this part of the code. Perform the computations in the output statements. (As an example of the general idea: cout << 3*A+6*4 << endl; is an output statement that computes 3A+24 and outputs it without using any new variables.)

    Re-run the program. Correct any errors. Notice the output you get. Verify that the numbers in the output do form a Pythagorean triple. For example, if the output contains the numbers 21, 20, and 29, then verify using a calculator (or pencil and paper) that 21*21 + 20*20 = 29*29. (This is a critical step! The whole point of learning to program is to make the computer give us what we want. The output has to be correct.)

  6. Run the program and enter numbers that violate the directions in the following way: Enter one negative integer and one positive one. Does the program produce a Pythagorean triple? Refer to the program code. Can you point out what made the program succeed or fail?

  7. Run the program and enter numbers that violate the directions in a different way: Enter two positive numbers but have M < N. Does the program produce a Pythagorean triple? Refer to the program code. Can you point out what made the program succeed or fail?

  8. Make a script (you could call it lab02.script) where you run the program and enter 2 and 7 for N and M. Refer to the directions of the "Hello World! assignment" if you need help with the directions for making a script.

  9. E-mail me a copy of the program source code (the file lab02.cpp) with subject line:

    CS1500Lab02Source

    E-mail me a copy of the script with subject line:

    CS1500Lab02Script

    (A word about the subject lines - it is important that you use the exact subject lines I specify. It assures I will be able to find your message in my inbox. There may be hundreds of messages there. You will lose a significant amount of credit for this assignment if you don't use the correct subject line. The easiest way to make sure you are using the correct subject line is to just select, copy, and paste it into the appropriate location when you are composing the command to send the e-mail.)

    You may refer to the directions of the "Hello World!" assignment if you need help with sending the e-mail. If you need help, please ask.