An algorithm problem Discrete Mathematics class

CaptSamuelFrank · #1 $Old$ 08-26-2008, 12:53 PM

This is from the first day of class. We were given problems we should be able to do. The only one I had a problem with was this one as I have never really learned any programming yet nor modulus's.

Quote:

Input: A positive integer number a.
Output: A positive integer number s.

Let s = 0
While a > 0
Let s = s + (a mod 10)
Let a = a/10

In this algorithm, the word while indicates a loops, meaning that following indented steps are repeated as long as the loop condition of a > 0 holds. Also, note the operation a/10 is integer division, meaning that the fractional portion of the result is simply dropped (e.g. 10/4 = 2).

(a) What is the output of the algorithm if the input is a = 432765891
(b) One important characteristic of an algorithm is efficiency. Typically, this is measured by the number of operations the algorithm performs. How many additions does this algorithm perform given the input of some positive integer a? Express your answer as a function of a.

If someone could show me the steps to solving this problem and explain how to go about solving it I would be very pleased. I wish to be able to do these kind of things on my own and I am guessing it is probably quite simple.

Thanks so much for any help!
-CSF
peace.

Plato · #2 $Old$ 08-26-2008, 06:34 PM

Quote:

Originally Posted by CaptSamuelFrank $View Post$

This is from the first day of class. We were given problems we should be able to do. The only one I had a problem with was this one as I have never really learned any programming yet nor modulus's.
If someone could show me the steps to solving this problem and explain how to go about solving it I would be very pleased. I wish to be able to do these kind of things on my own and I am guessing it is probably quite simple

I will tell you that I do not know anything past a basic knowledge of programming.
But I am sure that the second line is incorrect. It must be While a >1.
Otherwise, we are in an infinite loop.
If that correction is made, then the program adds then the digits in the number a.
So that is the answer to part a.

For part (b), the number pf ‘sums’ is the number of places in the number a.