Leetcode - Add Digits

Question

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

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Example

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

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Follow up

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

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Hint

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

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Java Code

/** *  * 同余定理公式： * (a + b)%n = (a%n + b)%n = (a + b%n)%n = (a%n + b%n)%n * (a * b)%n = (a%n * b)%n = (a * b%n)%n = (a%n * b%n)%n *  *///版本一：利用理论计算public int addDigits(int num) {    if(num == 0) return 0;    return (num %= 9) == 0 ? 9 : num;}//版本二：对num依次对10取余取整，得到各个数位，计算的和重新赋值给num，直到num为个位数public int addDigits2(int num) {    int sum = num;    while(num > 9) {        sum = num % 10;        while((num /= 10) > 0)            sum += num % 10;        num = sum;    }    return sum;}

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