Latest Revision: September 14, 2014

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.

proof by picture of pythag theorem A Pythagorean triple is a set of three positive integers that represent the sides of a right triangle. Such triples -- a, b, c -- satisfy the relation: 
a*a + b*b = c*c
-- which means: "The square of a plus the square of b equals the square of c." The common notation for expressing this idea in math books is: 
(a2 + b2 = c2)
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), and we can verify it is a Pythagorean Triple by noting that 3*3 + 4*4 = 9+16 = 25 = 5*5.

Please notice that the seeds and the sides are different things. In our example the seeds are 1 and 2, and the sides calculated from the seeds are 3, 4, and 5.

Another example: Let M=5 and N=3, then M > N, and

Side One = M*M - N*N = 5*5 - 3*3 = 16,
Side Two = 2*M*N = 2*5*3 = 30, and
the Hypotenuse = M*M + N*N = 5*5 + 3*3 = 34.

So using M=5 and N=3 as seeds, the recipe gives us the Pythagorean Triple: (16, 30, 34), and we can verify it is a Pythagorean Triple by noting that 16*16 + 30*30 = 256+900 = 1156 = 34*34.

Below is a "skeleton" of a C++ program. It is not finished. It has only comments where the C++ statements need to be. The intended purpose of the program is to read values for M and N from the user (M is required to be larger than 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 int variables M and N */

    /* ***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 skeleton program 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. In the next four steps, you will make additions to the skeleton, as directed. Don't delete anything. Just add what the directions say to add. (In particular, don't delete the comments.)

  3. Immediately below the comment in file lab02.cpp that begins with ***a***, insert a declaration of integer variables M and N. (See section 2.1 of your C++ textbook for examples of this kind of declaration.) Save, compile and execute the program. Correct any errors.

  4. Just under each of the two comments that begin with ***b***, insert the indicated output statement. In other words, insert the "cout statement" that is needed. Under one of the ***b*** comments you must make a cout statement that displays the string "A Program to Calculate Pythagorean Triples" and under the other ***b*** comment you'll make a cout statement that displays "The Pythagorean Triple". You've made cout statements in the previous two labs. There are many examples in the text, on page 20, for instance. Construct the cout statements so that the program output will be exactly 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.

  5. Directly under each of the two comments that begin with ***c***, insert the indicated C++ statements, to prompt for and read the integer N, or to prompt for and read the integer M. This will require two statements under each comment, first a cout statement that puts the prompt on the screen for the user to read, and then a cin statement that reads the input from the user and copies it to the desired variable. Refer to lines 7-8 and 9-10 of Display 1.8 on page 20 of your text for examples of such pairs of statements. Construct your C++ statements so that the program will behave exactly as in the example interactive session shown above. (Notice that each prompt is indented in that example, and each has a long run of blanks in a specific area) Re-run the program. Correct any errors. Notice the output you get.

  6. Under each of the three comments that begin with ***d***, put the code for the appropriate output (cout) statement. Construct the code, so that the program will display the correct Pythagorean triple - the triple corresponding to the values of N and M that were input by the user. 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. Write cout statements that contain the expressions to be calculated. (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. There's another example at the bottom of page 50 of your text.)

    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 you might verify using a calculator (or pencil and paper) that 21*21 + 20*20 = 441+400 = 841 = 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. Before the lab starts, have a look at the program called triple_check.cpp that is included in the assignment directory. It will probably help you do the lab assignment better if you read and understand it. Also you may use triple_check.cpp to check the correctness of the output of the program you write for this lab. )

  7. Make a script showing a run of the program in which you enter 2 and 7 for N and M. Filter the script. Refer to the directions of the "Hello World! assignment" if you need help with the directions for making and filtering a script.

  8. 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

    (Be sure to use the exact subject lines specified above. 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 just to 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 additional help, please ask.