🧩 The Problem

Given an integer x, determine whether it’s a palindrome — that is, whether it reads the same forwards and backwards.

🔗 Problem Link: LeetCode 9. Palindrome Number

Examples

Input:  x = 121   → Output: True
Input:  x = -121  → Output: False
Input:  x = 10    → Output: False

Bonus: Can you solve it without converting the integer to a string?

🔍 The Three Approaches I Explored

1. 💡 Direct Solution with String Conversion

def isPalindrome(x: int) -> bool:
    return str(x) == str(x)[::-1]
  • Simple and fast (4 ms on LeetCode)
  • But does not satisfy the follow-up constraint of avoiding strings

2. 📐 Mathematical Reversal Using log10 and Closed-Form Formula

Inspired by this StackExchange post, this solution uses a formula to reverse digits without strings:

reverse(x) = x × 10ⁿ − 99 × Σₖ floor(x / 10ᵏ) × 10ⁿ⁻ᵏ
  • ✅ No string conversion
  • ✅ Mathematically elegant
  • ⚠️ Slightly slower due to log10() and exponentiation
  • ⚠️ Can suffer from floating-point rounding issues

3. ⚙️ Iterative Arithmetic Reversal (Preferred)

def reverse(x: int) -> int:
    result = 0
    while x > 0:
        result = result * 10 + x % 10
        x //= 10
    return result
  • ✅ No strings
  • ✅ Fast and stable
  • ✅ Easy to understand and debug

⏱️ Benchmark Results

Tested on values like 11, 101, 1001, ..., 10000001

Iterative method:    ~0.000009 seconds
Math (log10) method: ~0.000033 seconds

✅ Both produce the correct result 📌 Iterative is about 3.7× faster and more robust for real-world use

🧠 What I Learned

  • How to reverse integers purely with arithmetic
  • How to benchmark small Python functions using time.perf_counter()
  • That elegance can sometimes come at a performance cost
  • How to choose the right tradeoff between readability, correctness, and efficiency

🌍 Real-World Applications

Palindrome logic pops up in places like:

  • Input validation (e.g. palindromic IDs)
  • Data compression using symmetry
  • Embedded systems that don’t allow string types
  • Constraints in coding interviews or systems-level code (like drivers/firmware)

📂 Code Repository

You can find my full source code for this solution on GitHub:

✍️ Final Thoughts

Solving the same problem in multiple ways helps me grow not only as a developer, but as a technical communicator. Being able to solve is great. Being able to explain clearly — that’s where the real value is.

“Hope it helps! I’m learning to write more elegant solutions with Python 3.13 and Clean Code.” 🚀

👨‍💻 Like this post? Let’s connect on LinkedIn or check out more on GitHub!