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Difference Between Element Sum and Digit Sum of an Array

Number: 2624

Difficulty: Easy

Paid? No

Companies: Amazon

Problem Description

Given an array of positive integers, calculate two sums: the element sum (sum of all numbers in the array) and the digit sum (sum of every digit contained within the numbers). Return the absolute difference between these two sums.

Key Insights

  • The element sum is the straightforward sum of all numbers in the array.
  • The digit sum requires iterating through each number and summing each individual digit.
  • Converting each integer to a string can make digit extraction simple.
  • The input size is small (nums.length up to 2000), so a simple iterative solution is efficient.

Space and Time Complexity

Time Complexity: O(n * k), where n is the number of elements and k is the average number of digits per element
Space Complexity: O(1) – only a few extra variables are used regardless of input size

Solution

The solution involves two main steps:

  1. Iterate over the array to compute the element sum.
  2. For each number, convert it to a string (or repeatedly divide by 10) to sum its digits, thereby computing the digit sum. Finally, compute the absolute difference between the two sums.

Data Structures and Approaches:

  • Use a simple loop to traverse the array.
  • For digit extraction, either convert the number to a string and iterate over its characters or use arithmetic operations (modulus and division).
  • Use built-in functions where available (e.g., sum in Python) for clear and concise code.

Code Solutions

# Python solution with detailed line-by-line comments

def differenceOfSum(nums):
    # Calculate the element sum by summing all numbers in the list.
    element_sum = sum(nums)
    
    # Initialize the digit sum to 0.
    digit_sum = 0
    
    # Iterate over each number in the list.
    for num in nums:
        # Convert the number to a string to iterate over each digit.
        for digit in str(num):
            # Convert the digit back to an integer and add to digit_sum.
            digit_sum += int(digit)
    
    # Return the absolute difference between element_sum and digit_sum.
    return abs(element_sum - digit_sum)

# Example usage:
print(differenceOfSum([1, 15, 6, 3]))  # Output: 9
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