Lab Project #6 - Perfect Sums

THE PROBLEM: Design and write a program in C++ that will solve the perfect sums problem for the values of 1 to 100 inclusive. A number is said to be perfect if the sum of its divisors (except for itself) is equal to itself. For example, 6 is a perfect number because the sum of its divisors (1+2+3) is 6. The number 8 is said to be deficient because the sum of its divisors (1+2+4) is only 7. The number 12 is said to be abundant because the sum of its divisors (1+2+3+4+6) is 16. Write a program that lists all the divisors of the numbers between 1 and 100 and classifies each number as perfect, deficient, or abundant.

Example Output:

Number: Divisors: Classification:

1 () Deficient

2 (1) Deficient

3 (1) Deficient

4 (1+2) Deficient

100 (1+2+4+5+10+20+25+50) Abundant

THE DESIGN: Recall the steps in problem-solving, go through each one in this project. Your top-down design should be included as comments at the top of your source code. The design must be complete. Your design will be compared to your program.

IMPLEMENTATION: You should use many functions to write this program. There is no input, only output. Essentially, you must loop from 1 to 100, calling a function that prints out the divisors of a number, then adds them up and figures out if the number is deficient, perfect or abundant. Write a function that handles one line of the output, given the number to classify. Write a function to print out the list of divisors. Write a function that classifies the number based on the sum of its divisors. Write a function to find the next greatest divisor. Write a function that returns a boolean that tells whether or not a given value is a divisor of another value. Other functions are possible as well.

Note: To get full credit, you must format the output as above. That is, you must make each of the 100 answers take a single line, and you must get the columns to line up as they do in the example.

Hint: This problem is a short one, but takes an understanding of loops and functions, and how to call a function with a loop in it from another function.