Reverse Number

Given a signed 32-bit integer x, return x with its digits reversed. Input: 123 → Output: 321. Input: -123 → Output: -321. Input: 120 → Output: 21 (no leading zeros). Solve this using math only — no string conversion allowed.

The key mathematical insight is that you can extract digits from right to left using modulo (% 10) and build the reversed number by multiplying the accumulator by 10 before adding each digit. This is the digit extraction pattern: repeatedly divide by 10 (integer division) to strip the last digit, and use modulo 10 to capture it.

1. Handle the sign separately: store the sign, then work with the absolute value. 2. Initialize reverse = 0. 3. While x > 0: extract the last digit with digit = x % 10, then build reverse = reverse * 10 + digit, then remove the last digit with x = x // 10. 4. Multiply the result by the stored sign and return.

- Converting to string and reversing (str(x)[::-1]) — this bypasses the mathematical technique the problem is testing - Forgetting to handle the sign: -123 reversed as 321- is invalid - Not handling trailing zeros in the input: 120 should become 21, not 021 - In languages with fixed integer sizes, not checking for 32-bit overflow after reversal

The digit extraction pattern (% 10 to get, // 10 to remove) is fundamental. You will use it again in palindrome number checking, Armstrong numbers, and many other number theory problems. Master this loop pattern here.