[LeetCode] 258. Add Digits

Problem : https://leetcode.com/problems/add-digits/

A naive solution:

class Solution:
    def addDigits(self, num: int) -> int:
        sums = 0
        
        while num > 0:
            sums += num % 10
            num = num // 10
        
        return sums if sums < 10 else self.addDigits(sums)

A mathematic solution:

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

Assume there is a 3 digits number   abc.

Then abc = a * 100 + b * 10 + c

Let sums =  a + b + c,  then  abc - sums = 99 * a + 9 * b

So, sums = abc - (99 * a  +  9 *b) 

Because  (99 * a + 9 * b)  is divisible by 9,     sums % 9 = abc % 9.

So we return  num % 9 as result.  If num % 9 = 0,  return 9.  As we only need to repeatedly add all digits until the result has only one digit.