LeetCode #2544 — EASY

Alternating Digit Sum

Build confidence with an intuition-first walkthrough focused on math fundamentals.

Solve on LeetCode

The Problem

Problem Statement

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.

Example 1:

Input: n = 521
Output: 4
Explanation: (+5) + (-2) + (+1) = 4.

Example 2:

Input: n = 111
Output: 1
Explanation: (+1) + (-1) + (+1) = 1.

Example 3:

Input: n = 886996
Output: 0
Explanation: (+8) + (-8) + (+6) + (-9) + (+9) + (-6) = 0.

Constraints:

1 <= n <= 10⁹

Step 01

Brute Force Baseline

Problem summary: 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Math

Example 1

Example 2

Example 3

Core Insight

What unlocks the optimal approach

The first step is to loop over the digits. We can convert the integer into a string, an array of digits, or just loop over its digits.
Keep a variable sign that initially equals 1 and a variable answer that initially equals 0.
Each time you loop over a digit i, add sign * i to answer, then multiply sign by -1.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2544: Alternating Digit Sum
class Solution {
    public int alternateDigitSum(int n) {
        int ans = 0, sign = 1;
        for (char c : String.valueOf(n).toCharArray()) {
            int x = c - '0';
            ans += sign * x;
            sign *= -1;
        }
        return ans;
    }
}

// Accepted solution for LeetCode #2544: Alternating Digit Sum
func alternateDigitSum(n int) (ans int) {
	sign := 1
	for _, c := range strconv.Itoa(n) {
		x := int(c - '0')
		ans += sign * x
		sign *= -1
	}
	return
}

# Accepted solution for LeetCode #2544: Alternating Digit Sum
class Solution:
    def alternateDigitSum(self, n: int) -> int:
        return sum((-1) ** i * int(x) for i, x in enumerate(str(n)))

// Accepted solution for LeetCode #2544: Alternating Digit Sum
impl Solution {
    pub fn alternate_digit_sum(mut n: i32) -> i32 {
        let mut ans = 0;
        let mut sign = 1;
        while n != 0 {
            ans += (n % 10) * sign;
            sign = -sign;
            n /= 10;
        }
        ans * -sign
    }
}

// Accepted solution for LeetCode #2544: Alternating Digit Sum
function alternateDigitSum(n: number): number {
    let ans = 0;
    let sign = 1;
    while (n) {
        ans += (n % 10) * sign;
        sign = -sign;
        n = Math.floor(n / 10);
    }
    return ans * -sign;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(log n)

Space

O(log n)

Approach Breakdown

ITERATIVE

O(n) time

O(1) space

Simulate the process step by step — multiply n times, check each number up to n, or iterate through all possibilities. Each step is O(1), but doing it n times gives O(n). No extra space needed since we just track running state.

MATH INSIGHT

O(log n) time

O(1) space

Math problems often have a closed-form or O(log n) solution hidden behind an O(n) simulation. Modular arithmetic, fast exponentiation (repeated squaring), GCD (Euclidean algorithm), and number theory properties can dramatically reduce complexity.

Shortcut: Look for mathematical properties that eliminate iteration. Repeated squaring → O(log n). Modular arithmetic avoids overflow.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Overflow in intermediate arithmetic

Wrong move: Temporary multiplications exceed integer bounds.

Usually fails on: Large inputs wrap around unexpectedly.

Fix: Use wider types, modular arithmetic, or rearranged operations.