Add Digits

Problem

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

Example:

Input: 38
Output: 2
Explanation: 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?

Accepted Non-optimal

The O(N) solution involves using some bitwise operations.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
class Solution {
public:
    int addDigits(int number) {
      while(number > 9) {
        int n = number;
        int sum = 0;
        while (n) {
          int digit = n % 10;
          sum += digit;
          n /= 10;
        }
        number = sum;
      }
      return number;
    }
};

Optimal

The best solution works in O(1) time! Because of a mathematical property. However, I need to fully get it before I can discuss it further. Stay tuned.