Add Digits LeetCode

Given a non-negative integer num, repeatedly add all its digits until the result has only one digit.

Example

• Given num = 38, the process is like: 3 + 8 = 11, 1 + 1 = 2. Since 2 has only one digit, return it.

Follow up: 

• Could you do it without any loop/recursion in O(1) runtime?

The Wikipedia and LeetCode pages give the detailed overview of the problem if you want to explore further. A collection of hundreds of interview questions and solutions are available in our blog at Interview Question

It helps to see the digital root of a positive integer as the position it holds with respect to the largest  multiple of 9 less than the number itself. For example, the digital root of 11 is 2, which means that 11 is the second number after 9. Likewise, the digital root of 2035 is 1, which means that 2035 − 1 is a multiple of 9. 

If a number produces a digital root of exactly 9, then the number is a multiple of 9. With this in mind the digital root of a positive integer n may be defined by using floor function as 

dr(n)=n-9( {n-1}/{9}).

Solution