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?

 

12 ms

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

8 ms

class Solution {
    public:
    int addDigits(int num) {
        while(true){
            if(num<10) return num;
            else num = reduce(num);
        }
    }
    
    int reduce(int num){
        if(num<10) return num;
        else return num%10+addDigits(num/10);
    }
};

为什么递归的方法更快呢？