Table of Contents

Corning Community College

CSCS2330 Discrete Structures

Project: COMPUTATION - CALCULATING N-ARY VALUES (cnv0)

Objective

To create a program that can calculate and determine the number of factor pairs of a given number, in a specified range of numbers.

Background

In mathematics, you have likely encountered the notion of “prime” numbers, those values which are divisible only by 1 and the number itself.

Expanding our view on the situation, when considering factors of a number, we have the presence of a “factor pair”; ie a pair of two values that are evenly divisible into that number.

For 17, a prime number, we have just ONE factor pair: 1 and 17:

All other values (2-16) when we divide them into 17 results in a non-zero value for the remainder.

In this way, prime, or primary, numbers, have exactly ONE factor pair. To further simplify matters, we can call it an N-ary(1) or nary(1) value. Where the number indicates the number of factor pairs.

A secondary, or nary(2) number, on the other hand, has exactly TWO sets of factor pairs.

Take the number 6, for instance:

Where 17 was a primary number, 6 is a secondary number.

Determining factor pairs

We are going to be exploring a basic, brute force, method of determining factors for a number, and that is the “trial by division” method.

Here, we successively divide a number by potential factors, to see if the factor evenly divides into the number. For convenience, we will assume the 1 and number factor pair, because EVERY number is evenly divisible by 1 and itself.

So, the number 5:

No other evenly divisible factors were found in the range 2-(N-1), therefore we are only left with the factor pair of 1 and N, making 5 an nary(1) value.

The number 14:

Because factor pairs ALWAYS come in a set of 2, we have the factor pairs of 1 and 14, along with 2 and 7.

How about 12:

There are 4 additional factors discovered here, giving us a total of 6 factors, or three factor pairs:

Notice also how the factors are nested: 1 and 12 are the outermost, 2 and 6 are encapsulated within that, and inside there, 3 and 4.

Because there are 3 factor pairs, 12 would be considered an nary(3) value (or a tertiary number).

Program

It is your task to write a program that, upon accepting various pieces of input from the command-line, computes the number of factor pairs of a given number or range of numbers, displaying to STDOUT all the numbers in that range that qualify as a nary number of the specification.

Program run-time usage

Your program should accept command-line arguments as follows:

$ ./cnv0 NARY START END

All are mandatory. If any are lacking or incorrect, display an error and exit with a non-zero value.

Specifications

Your program should:

Some additional points of consideration:

Execution

Secondary number output

lab46:~/src/discrete/cnv0$ ./cnv0 2 3 12
4 6 8 9 10
lab46:~/src/discrete/cnv0$ 

The execution of the program is short and simple- obtain the input, do the processing, produce the output, and then terminate.

Compiling

As we have been doing all along, use the following options to gcc when compiling:

lab46:~/src/discrete/cnv0$ gcc -Wall --std=gnu99 -o cnv0 cnv0.c
lab46:~/src/discrete/cnv0$ 

Submission

To successfully complete this project, the following criteria must be met:

To submit this program to me using the submit tool, run the following command at your lab46 prompt:

$ submit discrete cnv0 cnv0.c
Submitting discrete project "cnv0":
    -> cnv0.c(OK)

SUCCESSFULLY SUBMITTED

You should get some sort of confirmation indicating successful submission if all went according to plan. If not, check for typos and or locational mismatches.

What I'll be looking for:

78:cnv0:final tally of results (78/78)
*:cnv0:proper error checking and status reporting performed [13/13]
*:cnv0:correct variable types and name lengths used [13/13]
*:cnv0:proper output formatting per specifications [13/13]
*:cnv0:runtime tests of submitted program succeed [13/13]
*:cnv0:no negative compiler messages for program [13/13]
*:cnv0:code is pushed to lab46 repository [13/13]

Additionally: