Add Digits (Digital Root) Explained

Problem Statement

Given a non-negative integer num, repeatedly add its digits until the result has only one digit. This single digit is called the digital root. For example, for 38, 3 + 8 = 11, then 1 + 1 = 2, so the digital root is 2. This problem can be solved iteratively or using a mathematical congruence formula.

Example

Input: num = 38

Output: 2

Explanation: 3 + 8 = 11, 1 + 1 = 2.

Code

public class Solution {
    public int addDigits(int num) {
        return num == 0 ? 0 : 1 + ((num - 1) % 9);
    }

    public static void main(String[] args) {
        Solution sol = new Solution();
        System.out.println(sol.addDigits(38)); // 2
    }
}
            

def add_digits(num):
    if num == 0:
        return 0
    return 1 + ((num - 1) % 9)

# Example usage
print(add_digits(38))  # 2
            

function addDigits(num) {
    if (num === 0) return 0;
    return 1 + ((num - 1) % 9);
}

// Example usage
console.log(addDigits(38)); // 2
            

Explanation

• Use the congruence formula: digital root of num is 1 + ((num - 1) % 9) unless num is 0.
• This formula derives from the fact that num % 9 equals the sum of its digits modulo 9.
• For num = 0, the digital root is 0.
• The formula avoids iterative digit summing for efficiency.

Note