File recursive$\_$functions.c contains an incomplete definition of a function named num$\_$digits

that returns the number of digits in integer n$,$ n $>=0.$ The function prototype is:

SYSC $2006$: Foundations of Imperative Programming

$10$

int num$\_$digits$($int n$)$;

If n $<10,$ it has one digit, which is n$.$ Otherwise, it has one more digit than the integer n $/10.$ For

example, $7$ has one digit. $63$ has two digits, which is one more digit than $63/10($which is $6).$

$492$ has three digits, which is one more digit than $492/10,$ which is $49.$

Define a recursive formulation for num$\_$digits. You'll need a formula for the recursive case

and a formula for the stopping $($base$)$ case. Using this formulation, implement num$\_$digits as a

recursive function. $($Recall that, in C$,$ if a and b are values of type int, a $/$ b yields an int,

and a $\%$ b yields the integer remainder when a is divided by b$.)$ Your num$\_$digits function

cannot have any loops.

Function test$\_$exercise$\_1$ has seven test cases for your num$\_$digits function. It calls

test$\_$num$\_$digits seven times, once for each test case. Notice that test$\_$num$\_$digits has

two arguments: the value that will be passed to num$\_$digits, and the value that a correct

implementation of num$\_$digits will return $($the expected result$).$

Use the console output to help you identify and correct any flaws. Verify that num$\_$digits

passes all of its tests.