Difference Between Element Sum and Digit Sum of an Array

Difference Between Element Sum and Digit Sum of an Array - Problem

Array Math Easy

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.

Note: The absolute difference between two integers x and y is defined as |x - y|.

Input & Output

Example 1 — Basic Case

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

› Output: 9

💡 Note: Element sum: 1 + 15 + 6 + 3 = 25. Digit sum: 1 + 1 + 5 + 6 + 3 = 16. Absolute difference: |25 - 16| = 9.

Example 2 — Single Digits

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

› Output: 0

💡 Note: Element sum: 1 + 2 + 3 + 4 = 10. Digit sum: 1 + 2 + 3 + 4 = 10. Absolute difference: |10 - 10| = 0.

Example 3 — Large Numbers

$ Input: nums = [99,88]

› Output: 153

💡 Note: Element sum: 99 + 88 = 187. Digit sum: 9 + 9 + 8 + 8 = 34. Absolute difference: |187 - 34| = 153.

Constraints

1 ≤ nums.length ≤ 2000
1 ≤ nums[i] ≤ 2000

Visualization

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Understanding the Visualization

Input Array

Given array [1, 15, 6, 3]

Calculate Sums

Element sum = 25, Digit sum = 16

Output

Absolute difference = 9

Key Takeaway

🎯 Key Insight: We can calculate both sums in a single pass for optimal efficiency

Asked in

a Amazon 15 G Google 12

The key insight is to calculate both sums simultaneously in a single pass. For each number, add it to the element sum and extract its digits for the digit sum. Best approach is the single-pass solution with Time: O(n × d), Space: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ Single-Pass Approach	O(n × d)	O(1)	Calculate both sums in one loop through the array
Two-Pass Approach	O(n × d)	O(1)	Calculate element sum and digit sum in separate loops

Single-Pass Approach — Algorithm Steps

Step 1: Initialize both sum variables
Step 2: For each number, add to element sum and extract digits
Step 3: Return absolute difference

Visualization

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Step-by-Step Walkthrough

Initialize

Start with elementSum = 0, digitSum = 0

Process Each Number

For each number: add to elementSum, extract digits for digitSum

Final Result

Return absolute difference: |25 - 16| = 9

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int solution(int* nums, int numsSize) {
    int elementSum = 0;
    int digitSum = 0;
    
    for (int i = 0; i < numsSize; i++) {
        // Add to element sum
        elementSum += nums[i];
        
        // Extract digits and add to digit sum
        int temp = nums[i];
        while (temp > 0) {
            digitSum += temp % 10;
            temp /= 10;
        }
    }
    
    int diff = elementSum - digitSum;
    return diff < 0 ? -diff : diff;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    // Parse array manually
    int nums[1000];
    int count = 0;
    char* token = strtok(line, "[,]\n");
    while (token != NULL) {
        nums[count++] = atoi(token);
        token = strtok(NULL, "[,]\n");
    }
    
    int result = solution(nums, count);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n × d)

Single loop through n elements, each digit extraction takes d operations where d is average digits per number

✓ Linear Growth

Space Complexity

O(1)

Only uses constant extra space for sum variables

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Single-Pass Approach — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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