题目描述

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:

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

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

分析

公式：

dr(n)=n−9⌊n−19⌋

代码

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