Leetcode #2535: Difference Between Element Sum and Digit Sum of an Array

In this guide, we solve Leetcode #2535 Difference Between Element Sum and Digit Sum of an Array in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Problem Statement

You are given a positive integer array nums. The element sum is the sum of all the elements in nums.

Quick Facts

• Difficulty: Easy
• Premium: No
• Tags: Array, Math

Intuition

There is a mathematical invariant or formula that directly leads to the result.

Using math avoids unnecessary loops and reduces complexity.

Approach

Derive the formula or update rule, then compute the answer directly.

Handle edge cases like overflow or zero carefully.

Steps:

• Identify the math relationship.
• Compute the result with a loop or formula.
• Handle edge cases.

Example

Python Solution

Complexity

The time complexity is $O(n \times \log_{10} M)$, where $n$ and $M$ are the length of the array $\textit{nums}$ and the maximum value of the elements in the array, respectively. The space complexity is $O(1)$.

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.