Determine whether an integer reads the same backward as forward.

Interview question: Palindrome Number

Given an integer `x`, return `true` if `x` is a palindrome, and `false` otherwise.

An integer is a palindrome when it reads the same forward and backward. For example, `121` is a palindrome while `123` is not.

Note that negative numbers are never palindromes because of the leading minus sign.

Try to solve it without converting the integer to a string.

- Negative numbers are not palindromes because the minus sign appears only on the left.
- Positive numbers ending in `0` cannot be palindromes unless the number itself is `0`.
- These checks avoid extra work and prevent misleading reversals.

Handle Impossible Cases First

- Reversing the whole number works, but reversing half avoids unnecessary work and possible overflow in some languages.
- Repeatedly move the last digit of `x` into `reversed_half`.
- Stop when `reversed_half` is greater than or equal to the remaining `x`.

Reverse Only Half of the Number

- For an even number of digits, the remaining left half should equal the reversed right half.
- For an odd number of digits, the middle digit is irrelevant.
- Dropping the middle digit with `reversed_half // 10` handles odd lengths.

Compare Even and Odd Lengths

- The algorithm uses arithmetic only, so it satisfies the no-string follow-up.
- It processes about half the digits of the input.
- Time complexity is O(log10 n), and extra space complexity is O(1).