Add Digits

How it works

A number has the same remainder modulo nine as the sum of its decimal digits, because ten is congruent to one modulo nine. Repeating digit sums therefore yields its digital root: zero stays zero, and a positive multiple of nine maps to nine.

Steps

1. Return zero for input zero.
2. For positive input compute 1 + (num - 1) % 9.
3. Return the single-digit result.

Complexity

• Time: O(1) for fixed-width input.
• Space: O(1).

Things to watch for

• A positive multiple of nine returns nine, rather than zero.
• Keep zero as its own case.
• The input is nonnegative.

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

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