[LeetCode] 258. Add Digits 加数字

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.

找规律，每9个一循环(1~9)，res = (num - 1) % 9 + 1

数根是将一正整数的各个位数相加（即横向相加），若加完后的值大于10的话，则继续将各位数进行横向相加直到其值小于十为止[1]，或是，将一数字重复做数字和，直到其值小于十为止，则所得的值为该数的数根。

in out   in out
0   0    10  1
1   1    11  2
2   2    12  3
3   3    13  4
4   4    14  5
5   5    15  6
6   6    16  7
7   7    17  8
8   8    18  9
9   9    19  1

Java: Trivial and naive

public class Solution {
    public int addDigits(int num) {
        while (num > 9) {
            num = getInt(num);
        }
        return num;
    }

    private int getInt(int num) {
        int result = 0;
        while (num >= 10) {
            result += num % 10;
            num /= 10;
        }
        result += num;
        return result;
    }
}

Java: T: O(1), S: O(1)

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

Python: Trivial and naive

class Solution:
    def addDigits(self, num):
        while num > 9:
            c = 0
            while num:
                c += num % 10
                num /= 10
            num = c
        return num

Python: T: O(1), S: O(1)

class Solution:
    def addDigits(self, num):
        return (num - 1) % 9 + 1 if num > 0 else 0

C++: Trivial and naive

class Solution {
public:
    int addDigits(int num) {
        while (num / 10 > 0) {
            int sum = 0;
            while (num > 0) {
                sum += num % 10;
                num /= 10;
            }
            num = sum;
        }
        return num;
    }
};

C++: T: O(1), S: O(1)

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

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