Palindrome Number

Plus One

Longest Valid Parentheses

Determine whether a base-10 integer reads identically in reverse.

Return whether the decimal digits of integer `x` read the same left-to-right and right-to-left. Negative values are not palindromes.

**Input / output**
- Input: `x: integer`
- Output: boolean

**Examples**
1. `121` returns `true`.
2. `-121` and `10` return `false`.

**Constraints**
- `-2,147,483,648 <= x <= 2,147,483,647`

**Follow-up**
Can you reverse only half the digits to avoid strings and integer overflow?

- 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).