How do you solve Add Digits on LeetCode?

Add Digits (LeetCode #258) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: The digital root can be computed in constant time using properties of numbers.

What is the brute force solution for Add Digits?

The brute force approach for Add Digits is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves repeatedly summing the digits of the number until we get a single-digit result. This is straightforward but can be inefficient for larger numbers. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Add Digits?

Add Digits uses the following concepts: Math, Simulation, Number Theory. The recommended patterns to study are: Mathematical Properties, Modulo Operations.

What are the interview tips for Add Digits?

Always consider if there's a mathematical shortcut before diving into loops or recursion. Explain your thought process clearly, especially when transitioning from brute force to optimal solutions. Practice recognizing patterns in problems, such as the use of modulo for digit-related tasks.

What are common mistakes when solving Add Digits?

Forgetting to handle the case when num is 0. Overcomplicating the problem by trying to implement loops or recursion when a mathematical formula exists.

#258

Add Digits

Easy

MathSimulationNumber TheoryMathematical PropertiesModulo Operations

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(1)
Space	O(1)	O(1)

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Intuition

Time O(1)Space O(1)

The optimal approach uses a mathematical property known as the digital root, which allows us to compute the result in constant time without loops or recursion. This is based on the fact that the result can be derived using modulo operations.

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Algorithm

2 steps

1Step 1: If num is 0, return 0.
2Step 2: If num is not 0, return 1 + (num - 1) % 9. This formula derives from properties of numbers in base 10.

solution.py6 lines

1# Full working Python code
2
3def add_digits(num):
4    if num == 0:
5        return 0
6    return 1 + (num - 1) % 9

ℹ

Complexity note: The time complexity is O(1) because we are using a constant-time mathematical formula to compute the result, and space complexity is O(1) since we are not using any additional data structures.

1The digital root can be computed in constant time using properties of numbers.
2Understanding the relationship between digits and modulo operations can simplify problems significantly.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.