(Latest Revision: 03/10/2000)
03/10/2000 -- added a few simple examples.
Using Recursion to Compute Greatest Common Divsors
Discussion of Greatest Common Divisors:
Suppose that m and d are positive integers. We say d is a
divisor of m (or d divides m) if m = d * k for some positive
Example: d=5 is a divisor of m=50, because 50 = 5 * 10.
If m and n are positive integers then a positive integer d is
a common divisor of m and n if d divides m and d
Example: d=2 is a common divisor of m=78 and n=48, because 78 =
2 * 39 and 48 = 2 * 24.
If m and n are positive integers then m and n have a greatest
common divisor c. The number c is a positive integer which
is a common divisor of m and n. Also, c is a multiple of every
common divisor of m and n. In other words, c divides both m
and n, and if k is some other integer that divides both m and
n, then k divides c too.
Example: 6 is the greatest common divisor of 78 and 48. 78 = 6
* 13 and 48 = 6 * 8. Other common divisors of 78 and 48, such
as 2 and 3, are divisors of 6.
Notation: If m and n are positive integers, we denote their
greatest common divisor c as c = gcd(a,b).
Example: 6 = gcd(78,48)
Theorem: If m and n are positive integers and m <= n then
- m divides n and m=gcd(m,n), or
- gcd(m,n) = gcd(n%m,m)
Your assignment is to write a program that contains a function
that uses the idea of the theorem above to recursively compute
greatest common divisors.
A sample run of such a program is included in this directory.
You can view it by clicking
The function that computes greatest common divisors must input
(as parameters) any two positive int's m and n and return a
positive int that is a greatest common divisor of m and n.
Here is a sample prototype for the function:
/* Recursive function that returns gcd(m,n) */
int gcd (int m, int n) ;
The function must be a recursive function. Also, the
function must print the messages you saw in the
having the form:
Working on <<first param>> and <<second
To get those messages, you just put a cout statement at the
very beginning of the body of the function. The cout statement
writes the values of the actual parameters of the function.
Because the function is recursive, the user sees a report on
the parameter values for each level of the recursion. This is
printed as an aid to understanding what is happening during the
execution of the recursive function.
I can give more details concerning the information above in
As you can see from examining the
of the program, your program is required to run interactively
in a loop. It prompts the user to enter two positive
integers. If the user complies then the program computes the
gcd by executing the recursive function. The program then
reports the gcd of the two integers, which is the value
returned by the function. The program then prompts again.
This continues while the user's input is two positive
integers. When the user enters two zero's, the program
terminates. Your program must not prompt for any other inputs,
or attempt to read any other inputs.
I plan to test your program by preparing some new sample inputs
and placing them in a file. My file will contain only pairs of
integers. It will be a file that looks similar to this:
Of course the file above is only a sample. The actual test
file(s) may have more or fewer pairs of positive integers
before the sentinel line of two integers. (There will always
be a sentinel line of two zero's at the end.)
I will test your program by running it in this manner:
a.out < myTestFile
where "myTestFile" is the name of the file I created that
contains the list of pairs of integers. Your program has to
work correctly under those conditions. To make sure, make some
test files of your own and try your program on them.
What To Turn In:
This is not going to be a large program. It's probably going
to be a level two program with only about three functions,
including the main function. Therefore, I am not requiring you
to turn in a preliminary version.
Turn in a final-level program. Before midnight on the due
date, send via e-mail
Important! Use the following subject lines for
- a source file,and
- a test script showing adequate data coverage.
for the source file: "CS2500P2Source"
for the script file: "CS2500P2Script"
It will really help me a lot in sorting my mail if you use
exactly those subject lines. (Note there are no
For the due date, see
the class schedule.