LeetCode:Add Digits

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

For 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?

Hint:

1. A naive implementation of the above process is trivial. Could you come up with other methods?
2. What are all the possible results?
3. How do they occur, periodically or randomly?
4. You may find this Wikipedia article useful.

这道题很蛋疼，想了好久怎么能不用循环算，后来百度了下原来有公式。。怪我数学不怎么样咯。。

class Solution {public:    int addDigits(int num) {        return (num-1)%9+1;    }    };