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Reverse Integer

This question is asked by Apple. Given a 32-bit signed integer, reverse it and return the result.

Note: You may assume that the reversed integer will always fit within the bounds of the integer data type.

Example(s)​

Example 1:

Input: num = 550
Output: 55
Explanation:
Reverse of 550 is 055, which becomes 55 (leading zeros are dropped).

Example 2:

Input: num = -37
Output: -73
Explanation:
Reverse of -37 is -73 (sign is preserved, digits are reversed).

Example 3:

Input: num = 123
Output: 321
Explanation:
Reverse of 123 is 321.

Example 4:

Input: num = 120
Output: 21
Explanation:
Reverse of 120 is 021, which becomes 21 (leading zeros are dropped).

Solution​

The solution uses digit extraction and reversal:

  1. Handle sign: Store the sign separately
  2. Extract digits: Extract digits using modulo and division
  3. Build reversed: Build reversed number digit by digit
  4. Apply sign: Apply the original sign to the result

JavaScript Solution

/**
* Reverse a 32-bit signed integer
* @param {number} num - Input integer
* @return {number} - Reversed integer
*/
function reverse(num) {
// Handle sign
const isNegative = num < 0;
let n = Math.abs(num);

let reversed = 0;

// Extract digits and build reversed number
while (n > 0) {
  const digit = n % 10;
  reversed = reversed * 10 + digit;
  n = Math.floor(n / 10);
}

// Apply sign
return isNegative ? -reversed : reversed;
}

// Test cases
console.log('Example 1:', reverse(550)); 
// 55

console.log('Example 2:', reverse(-37)); 
// -73

console.log('Example 3:', reverse(123)); 
// 321

console.log('Example 4:', reverse(120)); 
// 21

console.log('Test 5:', reverse(0)); 
// 0
Output:
Click "Run Code" to execute the code and see the results.

Alternative Solution (String-based)​

Here's a version that converts to string:

/**
 * String-based approach
 */
function reverseString(num) {
  const isNegative = num < 0;
  const numStr = Math.abs(num).toString();
  const reversedStr = numStr.split('').reverse().join('');
  const reversed = parseInt(reversedStr, 10);
  return isNegative ? -reversed : reversed;
}

Complexity​

  • Time Complexity: O(log₁₀ n) - Where n is the number of digits. We process each digit once.
  • Space Complexity: O(1) - Only using a constant amount of extra space.

Approach​

The solution uses digit extraction and reversal:

  1. Handle sign:

    • Store whether the number is negative
    • Work with absolute value

  2. Extract digits:

    • Use modulo 10 to get last digit
    • Divide by 10 to remove last digit
    • Repeat until number becomes 0

  3. Build reversed:

    • Multiply current reversed by 10
    • Add the extracted digit
    • This builds the reversed number from right to left

  4. Apply sign:

    • Apply the original sign to the result

Key Insights​

  • Digit extraction: Use modulo and division to extract digits
  • Build reversed: Multiply by 10 and add digit to build reversed number
  • Handle sign: Store sign separately, work with absolute value
  • Leading zeros: Automatically handled (055 becomes 55)
  • O(log n) time: Number of digits is log₁₀(n)

Step-by-Step Example​

Let's trace through Example 1: num = 550

num = 550
isNegative = false
n = 550
reversed = 0

Iteration 1:
  digit = 550 % 10 = 0
  reversed = 0 * 10 + 0 = 0
  n = 550 / 10 = 55

Iteration 2:
  digit = 55 % 10 = 5
  reversed = 0 * 10 + 5 = 5
  n = 55 / 10 = 5

Iteration 3:
  digit = 5 % 10 = 5
  reversed = 5 * 10 + 5 = 55
  n = 5 / 10 = 0

n = 0, exit loop
Result: 55

Visual Representation​

Example 1: num = 550

Original:  5  5  0
           ↑  ↑  ↑
         hundreds tens ones

Reverse:   0  5  5
           ↑  ↑  ↑
         hundreds tens ones

Leading zero dropped: 55

Example 2: num = -37

Original:  -  3  7
            ↑  ↑  ↑
          sign tens ones

Reverse:   -  7  3
            ↑  ↑  ↑
          sign ones tens

Result: -73

Example 3: num = 120

Original:  1  2  0
           ↑  ↑  ↑
         hundreds tens ones

Reverse:   0  2  1
           ↑  ↑  ↑
         hundreds tens ones

Leading zero dropped: 21

Edge Cases​

  • Zero: Returns 0
  • Negative numbers: Sign is preserved
  • Trailing zeros: Become leading zeros (automatically dropped)
  • Single digit: Returns the same digit
  • Powers of 10: Returns 1 (e.g., 100 → 1)

Important Notes​

  • 32-bit signed integer: Problem states it fits within bounds
  • Leading zeros: Automatically dropped when converting to integer
  • Sign handling: Store sign separately, work with absolute value
  • Digit extraction: Modulo 10 gets last digit, division removes it
  • O(log n) time: Based on number of digits

Why It Works​

Digit extraction:

  • n % 10 gives the last digit
  • n / 10 removes the last digit
  • Repeat until n = 0

Building reversed:

  • Start with reversed = 0
  • For each digit: reversed = reversed * 10 + digit
  • This builds the number from right to left

Example:

n = 123
reversed = 0

digit = 3: reversed = 0 * 10 + 3 = 3
digit = 2: reversed = 3 * 10 + 2 = 32
digit = 1: reversed = 32 * 10 + 1 = 321
  • Palindrome Number: Check if reversed equals original
  • Reverse Bits: Different problem (bit manipulation)
  • Add Two Numbers: Different problem
  • String to Integer: Different conversion

Takeaways​

  • Digit extraction using modulo and division
  • Build reversed by multiplying by 10 and adding digit
  • Handle sign separately from digit reversal
  • O(log n) time based on number of digits
  • Leading zeros are automatically dropped