PPractick

The problem

A ticketing system gives "lucky" status to any booking reference that reads the same forwards and backwards, like 12321 or 4554. References are stored as integers, and converting each one to a string just to check it creates millions of throwaway strings a day. Your task: decide whether an integer is a palindrome using arithmetic only. The elegant solution reverses just the second half of the number and compares it with the first half, which also avoids any risk of overflow.

Example: 121 → true, -121 → false (it reads 121- backwards), 10 → false.

Function signature

bool isPalindrome(int x);  // true if x reads the same forwards and backwards

Test cases

Input x	Output	Explanation
121	true
-121	false	Negative numbers have a leading '-' that no digit can match
10	false	Ends in 0 but doesn't start with 0
0	true	A single digit is a palindrome
12321	true	Odd number of digits; the middle digit is ignored
1221	true	Even number of digits
123	false
2147447412	true	Close to INT_MAX; reversing only half never overflows

(Confirm: x is a 32-bit signed integer; solve without converting to a string.)

How interviewers phrase it

• "Check whether an integer is a palindrome without converting it to a string" (LeetCode 9).
• A string-based version is often accepted as a first answer, followed by "Now do it without extra space."

Clarifying questions to ask

1. Are negative numbers palindromes? (Usually no.)
2. Can I convert to a string, or should I use arithmetic?
3. What's the input range? (Reversing the full number could overflow.)

Follow-ups to expect

1. "Why not reverse the whole number?"
2. "How do you know when you've reached the middle?"
3. "How do you handle an odd number of digits?"
4. "Why reject numbers ending in 0 upfront?"
5. "Complexity?"

Related questions

• Count all Digits of a Number Easy
• Reverse a number Easy
• GCD of Two Numbers Easy
• Check if the Number is Armstrong Easy
• Print all Divisors Easy
• Check for Prime Number Easy

All 474 dsa interview questions

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