Add Digits

Easymath
Category: Fundamentals
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Approach

Add Digits

Approach

Use digital root formula: 1 + (num - 1) % 9

Algorithm

  1. If num is 0, return 0
  2. Otherwise return 1 + (num - 1) % 9
  3. This gives digital root in O(1)

Complexity

  • Time: O(1) - constant time formula
  • Space: O(1) - constant space

Key Insights

  • Digital root pattern: 1→1, 2→2, ..., 9→9, 10→1, 11→2, etc.
  • Formula avoids iterative digit addition
  • Based on modulo 9 arithmetic

Solution

java
1class Solution {
2    public int addDigits(int num) {
3        if (num == 0) return 0;
4        return 1 + (num - 1) % 9;
5    }
6}
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