Table of Contents

Corning Community College

CSCS1320 C/C++ Programming

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, starting with values composed of exactly 2 sets of factor pairs.

Reading

In “The C Book”, please read through Chapter 8.

Review needed concepts in this tutorial and also this one

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).

grabit

There is a grabit for this project, which will provide you with some files pertinent for performing this project.

Run 'grabit' on lab46 in the appropriate manner to obtain the files.

Compiling

Since there is a provided Makefile in the project grabit, we can use that to compile, either regularly:

yourpi:~/src/SEMESTER/DESIG/cnv0$ make

Or, with debugging support:

yourpi:~/src/SEMESTER/DESIG/cnv0$ make debug

Program

It is your task to write a program that, upon accepting various pieces of input from the user, computes the number of factor pairs of a given number, displaying its eligibility as a secondary number.

Specifications

Your program should:

Some additional points of consideration:

Execution

Secondary number output

yourpi:~/src/SEMESTER/DESIG/cnv0$ ./cnv0
Enter a number: 6
6 is a secondary number
yourpi:~/src/SEMESTER/DESIG/cnv0$ 

Non-secondary number output

yourpi:~/src/SEMESTER/DESIG/cnv0$ ./cnv0
Enter a number: 7
7 is NOT a secondary number

Additional outputs

yourpi:~/src/SEMESTER/DESIG/cnv0$ ./cnv0
Enter a number: 8
8 is a secondary number
yourpi:~/src/SEMESTER/DESIG/cnv0$ ./cnv0
Enter a number: 16
16 is NOT a secondary number
yourpi:~/src/SEMESTER/DESIG/cnv0$ ./cnv0
Enter a number: 21
21 is a secondary number
yourpi:~/src/SEMESTER/DESIG/cnv0$ 

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

Reference

Copied as part of the grabit, inside your cnv0/ subdirectory, will be a copy of my implementation (in executable form, by the name ref_cnv0), which abides by the project specifications. Please compare its output against that of your implementation. You can invoke the reference implementation by running the following:

yourpi:~/src/SEMESTER/DESIG/cnv0$ make check
Enter a number: 6
6 is a secondary number
yourpi:~/src/SEMESTER/DESIG/cnv0$ 

Verification

In addition, I have also placed a cnv0verify script in that same subdirectory, which will test your program against a range of values, to determine overall correctness. You can run the verify script using the Makefile, as follows:

yourpi:~/src/SEMESTER/DESIG/cnv0$ make verify
[  1] you have: err, should be: err    [  2] you have:  no, should be:  no
[  3] you have:  no, should be:  no    [  4] you have: yes, should be: yes
[  5] you have:  no, should be:  no    [  6] you have: yes, should be: yes
[  7] you have:  no, should be:  no    [  8] you have: yes, should be: yes
[  9] you have: yes, should be: yes    [ 10] you have: yes, should be: yes
[ 11] you have:  no, should be:  no    [ 12] you have:  no, should be:  no
[ 13] you have:  no, should be:  no    [ 14] you have: yes, should be: yes
[ 15] you have: yes, should be: yes    [ 16] you have:  no, should be:  no
[ 17] you have:  no, should be:  no    [ 18] you have:  no, should be:  no
[ 19] you have:  no, should be:  no    [ 20] you have:  no, should be:  no
[ 21] you have: yes, should be: yes    [ 22] you have: yes, should be: yes
[ 23] you have:  no, should be:  no    [ 24] you have:  no, should be:  no
[ 25] you have: yes, should be: yes    [ 26] you have: yes, should be: yes
[ 27] you have: yes, should be: yes    [ 28] you have:  no, should be:  no
[ 29] you have:  no, should be:  no    [ 30] you have:  no, should be:  no
[ 31] you have:  no, should be:  no    [ 32] you have:  no, should be:  no
[ 33] you have: yes, should be: yes    [ 34] you have: yes, should be: yes
[ 35] you have: yes, should be: yes    [ 36] you have:  no, should be:  no
yourpi:~/src/SEMESTER/DESIG/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:

lab46:~/src/SEMESTER/DESIG/cnv0$ make submit

And make sure you get no error messages.

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:

91:cnv0:final tally of results (91/91)
*:cnv0:resources obtained via grabit by Sunday before deadline [13/13]
*: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: