#2535

Easy

LeetCode Problem Workspace

Difference Between Element Sum and Digit Sum of an Array

Find the absolute difference between element sum and digit sum of an array of integers.

Problem Statement

You are given a positive integer array nums. For each element in the array, calculate its digit sum, then compute the element sum (the sum of all numbers in the array). Finally, return the absolute difference between the element sum and the digit sum.

Note that the absolute difference between two integers x and y is defined as |x - y|. Make sure to handle numbers with multiple digits by splitting each number and adding its digits together.

Examples

Example 1

Input: nums = [1,15,6,3]

Output: 9

The element sum of nums is 1 + 15 + 6 + 3 = 25. The digit sum of nums is 1 + 1 + 5 + 6 + 3 = 16. The absolute difference between the element sum and digit sum is |25 - 16| = 9.

Example 2

Input: nums = [1,2,3,4]

Output: 0

The element sum of nums is 1 + 2 + 3 + 4 = 10. The digit sum of nums is 1 + 2 + 3 + 4 = 10. The absolute difference between the element sum and digit sum is |10 - 10| = 0.

Constraints

1 <= nums.length <= 2000
1 <= nums[i] <= 2000

Solution Approach

Iterate and Calculate Sums

The first step in solving this problem is to iterate through the array and calculate both the element sum and the digit sum. You can use a simple for loop to access each element, and for the digit sum, split each number into its digits and sum them.

Compute the Absolute Difference

Once you have both sums, subtract the digit sum from the element sum and take the absolute value of the result. This will give the correct answer as specified in the problem.

Optimize and Edge Case Handling

Ensure the solution handles cases with single-digit numbers, large numbers, and varying array sizes. Consider edge cases such as arrays with all single-digit numbers, or arrays where the element sum equals the digit sum.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity is O(n), where n is the length of the array. For each element, you iterate through its digits, and this is performed once for each element. The space complexity is O(1) if you ignore the space used for storing input.

What Interviewers Usually Probe

Tests ability to loop through an array efficiently.
Checks understanding of digit extraction from integers.
Evaluates correctness in calculating absolute differences.

Common Pitfalls or Variants

Common pitfalls

Forgetting to correctly sum the digits of numbers with multiple digits.
Not taking the absolute value of the difference between sums.
Incorrectly handling large numbers or edge cases with single-digit arrays.

Follow-up variants

Change the array to contain only single-digit numbers.
Increase the array size to test scalability.
Introduce negative integers to test how absolute values are handled.

FAQ

What is the key approach to solving the Difference Between Element Sum and Digit Sum of an Array?

The key approach is to compute both the element sum (the sum of all numbers) and the digit sum (the sum of all digits of each number), and then return the absolute difference.

What are common pitfalls when solving this problem?

Common pitfalls include forgetting to calculate the digit sum correctly, not handling the absolute value properly, and missing edge cases like arrays with single digits.

How can I optimize my solution for large arrays in this problem?

You can optimize by using a simple for loop to calculate both sums in one pass over the array. Additionally, avoid unnecessary space usage by performing calculations on the fly.

What time complexity should I expect when solving this problem?

The time complexity is O(n), where n is the length of the array, since you need to process each element and calculate its digit sum individually.

Is there a more efficient way to compute the digit sum?

A common way to compute the digit sum is to repeatedly extract the last digit using modulo 10 and then reduce the number by dividing it by 10.

terminal

Solution

Solution 1: Simulation

We traverse the array $\textit{nums}$, calculate the sum of the elements $x$ and the sum of the digits $y$, and finally return $|x - y|$. Since $x$ is always greater than or equal to $y$, we can directly return $x - y$.

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class Solution:
    def differenceOfSum(self, nums: List[int]) -> int:
        x = y = 0
        for v in nums:
            x += v
            while v:
                y += v % 10
                v //= 10
        return x - y

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