Difference Between Element Sum and Digit Sum of an Array

Difference Between Element Sum and Digit Sum of an Array

What is this problem about?

The Difference Between Element Sum and Digit Sum of an Array coding problem asks you to calculate two different sums from a given list of positive integers. The "element sum" is the standard sum of all numbers in the array. The "digit sum" is the sum of every individual digit of every number in the array. Finally, you need to return the absolute difference between these two sums.

Why is this asked in interviews?

This question is popular in initial screening rounds at companies like Amazon and Bloomberg. It tests basic programming skills, specifically your ability to iterate through an array and your mastery of Math interview patterns for digit extraction. It evaluations whether you can handle number-to-digit conversion without necessarily relying on expensive string conversions, which is a sign of a more technically proficient candidate.

Algorithmic pattern used

This problem uses Digit Extraction and Linear Iteration. To calculate the digit sum, you iterate through each number in the array. For each number, you repeatedly take the modulo by 10 to get the last digit and then divide the number by 10 to remove that digit. This process continues until the number becomes zero. Meanwhile, the element sum is gathered by a simple accumulation loop.

Example explanation

Suppose the array is [15, 9, 2].

1. Element Sum: $15 + 9 + 2 = 26$.
2. Digit Sum:
   • Digits of 15: $1 + 5 = 6$.
   • Digits of 9: $9$.
   • Digits of 2: $2$.
   • Total Digit Sum: $6 + 9 + 2 = 17$.
3. Difference: $|26 - 17| = 9$.

Common mistakes candidates make

• String Conversion: Converting each number to a string to sum the digits. While this works, it is generally slower and uses more memory than mathematical digit extraction.
• Absolute Value: Forgetting to take the absolute difference at the end, though since the element sum is always greater than or equal to the digit sum for positive integers, this might not always cause a failure.
• Initialization: Forgetting to reset the digit extraction logic for each element in the loop.

Interview preparation tip

Practice extracting digits using % 10 and / 10 in a while loop. This is a foundational Math interview pattern that appears in many problems, from reversing integers to checking for palindromes. Being able to write this snippet fluently shows you have a strong grasp of basic algorithmic building blocks.