***** C++ program 5*********

create a program that can do various math functions (GCD, LCM, average, factorial, etc.). You will have a main.cpp file that contains a simple menu-based main loop. You will have a separate functions.cpp file that contains implementations for the different math functions that you implement.

-- Getting started

Before getting too involved in writing the code you should start by creating the three files you need (main.cpp, functions.h, functions.cpp) and make sure you can compile all of them. Start with a main.cpp file. This file was included in the lab setup files (I saved you a bunch of typing). Use your text editor to review the main.cpp and make sure you understand how it works.

Next you need to create a functions.cpp file. This file will contain all of the functions that you implement. We'll start with a relatively simple function: average. This function sums the two input values and divides by 2. The average function will look like this:

void doAverage(int x,int y) {

int sum = x+y; int average = sum/2;

cout << "Average of " << x << " and " << y << " is " << average << endl; }

Create functions.cpp and type that function in. You will also need to include iostream and the appropriate using statement in functions.cpp.

After you have created functions.cpp you can compile both main.cpp and functions.cpp together using the following command:

g++ -o mathfun main.cpp functions.cpp

If you run this program you will see that it doesn't do anything different. At this point main.cpp doesn't know about functions.cpp. We have to do two more things. First, you need to create a header file, functions.h, that holds the function prototype for your average function. Create functions.h and include in it:

void doAverage(int x,int y);

Now, main.cpp needs to have access to this. Add the following line in main.cpp:

#include "functions.h"

This would go near the other include statement. Now you can compile main and functions as shown above. The last thing you need to do is to uncomment the call to doAverage() in main. Once you do that your program will work to calculate the average of two numbers.

After you get that working you should add the GCD function. The Greatest Common Denominator is easy to calculate using the Euclid method. The basic idea is quite simple. Given two numbers, replace the largest by the difference between the largest and the smallest. Keep going until the two numbers are the same or one of them gets to 0. At this point you have the GCD.

Here is an example for the numbers 252 and 105:

252 105 -- 252 is largest so replace it with 252-105 147 105 -- 147 is largest so replace it with 147-105 42 105 -- 105 is largest so replace it with 105-42 42 63 -- 63 is largest so replace it with 63-42 42 21 -- 42 is largest so replace it with 42-21 21 21 -- they are the same. 21 is the GCD

Write the doGCD() function in your functions.cpp file using this algorithm. Then enable it in main.cpp and check your results. Once you have GCD then LCM is also easy. The LCM (least common multiple) of two numbers, a, b, is just the GCD of the product of a and b. So you can reuse your GCD algorithm in LCM.

Finally, if you finish GCD and LCM add the factorial function. And if you are very ambitious you can add more functions (whatever you can think of).

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main.cpp

#include

using namespace std;

void getValues(int& x,int& y) {

cout << "Enter the first integer: ";

cin >> x;

cout << "Enter the second integer: ";

cin >> y;

}

int main() {

int choice;

bool done = false;

int x,y;

cout << "Welcome to the math functionator!" << endl << endl;

do {

cout << "1) GCD" << endl;

cout << "2) LCM" << endl;

cout << "3) average" << endl;

cout << "0) quit" << endl;

cout << "Enter choice: ";

cin >> choice;

if (choice != 0) {

getValues(x,y);

}

switch (choice) {

case 1:

//doGCD(x,y);

break;

case 2:

//doLCM(x,y);

break;

case 3:

//doAverage(x,y);

break;

case 0:

done = true;

}

} while (!done);

cout << "Bye" << endl;

return(0);

}