C++ Program:

For this project, you will practice decomposing a problem into functions. In the final part, you will also get some practice with pass-by-reference functions. As

part of this lab is to also gain experience with integer operations, you are NOT allowed to convert numbers into strings and use string processing primitives.

TASK 0

Consider the standard decimal representation of a non-negative integer num. You wish to write a function that repetitively adds up the digits of a number until it eventually

results in a single-digit number. For example, given the number 234567, the first iteration results in 27 (=2+3+4+5+6+7), and the 2nd iteration results in 9 (=2+7). Since 9 is

a single-digit number, no more iterations are needed and 9 is returned. Write a function with the following prototype to do this: // Precondition: num > 0 // Postcondition: the

return value is the iterated sum of digits of num int sumDigits(int num); To do this, we first need to identify functions that are useful to doing this. In this case, a list of useful

function prototypes might be: int getDigit(int num, int index); // return the index'th digit of num int numDigits(int num); // return the number of digits in num You should have at

least these three functions, though you may have additional functions if you wish. Don't forget to write pre/post conditions for these functions. You may use library functions

defined in cmath (such as pow) if you wish, though you don't need to.

TASK 1 You need a driver program to test your above program. To do this, write a main function that

prompts for and input num, calls sumdigits and outputs the result. You may assume that the input is a positive number and do not need to do any error checking (but realize

that you would have to for a real program).

TASK 2 A well-known theorem of math states that the above sum is 9 iff the number is divisible by 9. Write a function that

modifies its argument number so that its divisible by 9. The function should add something to the right-most digit of the number if possible; otherwise it should subtract

something from that digit. An example use of this function might be: transformNum(n); cout << n; // prints 234567 if n was originally 234565 Write the transformNum function.

You should be able to reuse most of the code from earlier. Also modify the driver program to output the transformed number.