Add Digits

LeetCode 258 | Difficulty: Easy

Easy

Problem Description

Given an integer num, repeatedly add all its digits until the result has only one digit, and return it.

Example 1:

Input: num = 38
Output: 2
Explanation: The process is
38 --> 3 + 8 --> 11
11 --> 1 + 1 --> 2 
Since 2 has only one digit, return it.

Example 2:

Input: num = 0
Output: 0

Constraints:

- `0 <= num <= 2^31 - 1`

Follow up: Could you do it without any loop/recursion in O(1) runtime?

Topics: Math, Simulation, Number Theory

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Approach

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

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Solutions

Solution 1: C# (Best: 52 ms)

Metric	Value
Runtime	52 ms
Memory	N/A
Date	2018-04-12

Solution

public class Solution {
    public int AddDigits(int num) {
        if(num/10==0) return num;
    else
    {
        int ret = 0;
        while(num!=0)
        {
            int rem = num%10;
            ret = ret+rem;
            num/=10;
        }
        if(ret/10==0) return ret;
        else return AddDigits(ret);
    }
    }
}

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Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.
• LeetCode provides 4 hint(s) for this problem — try solving without them first.

💡 Hints

Hint 1: A naive implementation of the above process is trivial. Could you come up with other methods?

Hint 2: What are all the possible results?

Hint 3: How do they occur, periodically or randomly?

Hint 4: You may find this Wikipedia article useful.