Sample Recursion Problems, P. Conrad

1. Write a function with the following prototype that returns the sum of the digits of an integer.

   int sumOfDigits(int x);
   

   If x is 234, the function should return 2 + 3 + 4, that is, 9.

   If x is 12, the function should return 1 + 2, which is 3.

   If x is 39, the function should return 12.

   If x is negative, ignore the minus sign. For example, -12 and 12 both return 3.

   Use recursion.

   Hints:

   • The base case is a number between 0 and 9.
   • If x is negative, just multiply it by -1 as soon as you enter the function.
   • For the recursive call, consider how computing the values x/10 and x%10 might be useful.
2. Write a recursive function (use no while loops or for loops) that prints all the elements of an array of integers, one per line. The parameters to the function should be int a[], and int size.

   Hint :

   • The return type is void
3. Same problem as the last one, but print out the elements in reverse order.

   Hint :

   • All you have to do is "flip" two lines of code. Which two lines?
4. Find the sum of the integers from 1 through n. Use recursion.
5. Find the product of the integers from 1 through n (this is called the factorial function). If n is zero, return 1. Use recursion.
6. Count the number of zeros in an array of integers. Use recursion.
7. Find the minimum element in an array of integers. Use recursion.