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*.