Counting and Summing Digits in an Integer



  The problem of counting the digits in a positive integer or summing those
  digits can be solved recursively. For example, to count the number of
  digits think as follows:

     * If the integer is less than 10 there is only one digit (the base
       case).

     * Otherwise, the number of digits is 1 (for the units digit) plus the
       number of digits in the rest of the integer (what's left after the
       units digit is taken off). For example, the number of digits in 3278
       is 1 + the number of digits in 327.

  The following is the recursive algorithm implemented in Java.
  
       public int numDigits (int num)
       {
           if (num < 10)
              return (1);   // a number < 10  has only one digit
           else
              return (1 + numDigits (num / 10));
       }

  Note that in the recursive step, the value returned is 1 (counts the units
  digit) + the result of the call to determine the number of digits in num /
  10. Recall that num / 10 is the quotient when num is divided by 10 so it
  would be all the digits except the units digit.

  The file DigitPlay.java contains the recursive method numDigits (note that
  the method is static -- it must be since it is called by the static method
  main). Copy this file to your directory, compile it, and run it several
  times to see how it works. Modify the program as follows:

     Add a static method named sumDigits that finds the sum of the digits
     in a positive integer. Also add code to main to test your method. The
     algorithm for sumDigits is very similar to numDigits; you only have to
     change two lines!