Difference Between Element Sum and Digit Sum of an Array

Problem Description

You are given a positive integer array nums. The element sum is the sum of all the elements in nums. The digit sum is the sum of all the digits (not necessarily distinct) that appear in nums. Return the absolute difference between the element sum and digit sum of nums.

Key Insights

• The element sum is straightforward: simply sum all the integers in the array.
• The digit sum requires breaking down each integer into its constituent digits and summing those digits.
• The final result is the absolute difference between the element sum and digit sum.

Space and Time Complexity

Time Complexity: O(n * d) where n is the number of elements in the array and d is the maximum number of digits in the largest number in the array.

Space Complexity: O(1) since we are using a constant amount of space regardless of the input size.

Solution

To solve this problem, we will follow these steps:

1. Initialize two variables, element_sum and digit_sum, to zero.
2. Iterate through each number in the array. For each number:
   • Add the number to element_sum to calculate the element sum.
   • Convert the number to a string to iterate through its digits, converting each character back to an integer, and add these to digit_sum.
3. Calculate the absolute difference between element_sum and digit_sum.
4. Return the result.

We will use simple arithmetic operations and string manipulation to achieve this.

Code Solutions