Alternating Digit Sum

Alternating Digit Sum - Problem

Math Easy

You are given a positive integer n. Each digit of n has a sign according to the following rules:

The most significant digit is assigned a positive sign.
Each other digit has an opposite sign to its adjacent digits.

Return the sum of all digits with their corresponding sign.

Input & Output

Example 1 — Three Digit Number

$ Input: n = 521

› Output: 4

💡 Note: Digits are 5, 2, 1. Signs are +, -, +. So we get +5 + (-2) + (+1) = 5 - 2 + 1 = 4

Example 2 — Four Digit Number

$ Input: n = 111

› Output: 1

💡 Note: Digits are 1, 1, 1. Signs are +, -, +. So we get +1 + (-1) + (+1) = 1 - 1 + 1 = 1

Example 3 — Single Digit

$ Input: n = 886

› Output: 6

💡 Note: Digits are 8, 8, 6. Signs are +, -, +. So we get +8 + (-8) + (+6) = 8 - 8 + 6 = 6

Constraints

1 ≤ n ≤ 10⁹

Visualization

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Asked in

LC LeetCode 15 M Microsoft 8

The key insight is to process each digit with alternating signs starting positive for the most significant digit. Both string conversion and mathematical digit extraction work well. Best approach is string conversion for simplicity. Time: O(d), Space: O(d) for string or O(1) for math approach.

Common Approaches

✓ Mathematical Digit Extraction

⏱️ Time: O(d) Space: O(1)

Instead of converting to string, extract digits mathematically from right to left using modulo operations. Since we need to process from left to right (most significant first), we can either reverse the digits or determine the sign based on the total number of digits.

String Conversion Approach

⏱️ Time: O(d) Space: O(d)

Convert the integer to a string to easily access each digit. Iterate through each character, convert it back to integer, apply the appropriate sign (positive for first digit, then alternating), and sum them up.

Mathematical Digit Extraction — Algorithm Steps

Count total digits to determine sign pattern
Extract digits from right to left using n % 10
Determine sign based on digit position
Sum all signed digits

Visualization

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Step-by-Step Walkthrough

Count Digits

Determine total number of digits for sign calculation

Extract Right to Left

Use modulo to get digits, but apply signs based on position

Calculate Result

Sum all digits with their correct signs

Code -

solution.c — C

#include <stdio.h>

int solution(int n) {
    // Count digits
    int temp = n;
    int digitCount = 0;
    while (temp > 0) {
        digitCount++;
        temp /= 10;
    }
    
    int result = 0;
    int position = 0;
    
    while (n > 0) {
        int digit = n % 10;
        // Most significant digit should be positive
        if ((digitCount - position - 1) % 2 == 0) {
            result += digit;
        } else {
            result -= digit;
        }
        
        n /= 10;
        position++;
    }
    
    return result;
}

int main() {
    int n;
    scanf("%d", &n);
    int result = solution(n);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(d)

Where d is the number of digits, we process each digit once

✓ Linear Growth

Space Complexity

O(1)

Only uses constant extra space for variables

✓ Linear Space

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Input & Output

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Common Approaches

Mathematical Digit Extraction — Algorithm Steps

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Code -

Time & Space Complexity

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