Palindrome Number Challenge

Given an integer, determine if it is a palindrome. A palindrome is a number that reads the same forwards and backward. This is a fundamental problem in computer science that tests your understanding of number manipulation and algorithmic thinking.

Problem Description

The task is to write a function or program that accepts a single integer as input and returns True if the integer is a palindrome, and False otherwise. You should not convert the integer to a string to solve this problem.

Key Requirements:

• The function should accept an integer.
• The function should return a boolean value (True or False).
• The solution must avoid converting the integer to a string for the primary palindrome check.

Expected Behavior:

• If the number reads the same forwards and backward, return True.
• If the number does not read the same forwards and backward, return False.

Edge Cases to Consider:

• Negative numbers: How should negative numbers be treated?
• Single-digit numbers: Are single-digit numbers palindromes?
• Numbers ending in zero (but not zero itself): Can a palindrome end in zero if it's not just zero?

Examples

Example 1:

Input: 121
Output: True
Explanation: The number 121 reads the same forwards (121) and backward (121).

Example 2:

Input: -121
Output: False
Explanation: From left to right, the number is -121. From right to left, it becomes 121-. Therefore, it is not a palindrome.

Example 3:

Input: 10
Output: False
Explanation: Reads 01 from right to left. Therefore it is not a palindrome.

Example 4:

Input: 0
Output: True
Explanation: Single-digit numbers are palindromes.

Constraints

• The input integer will be within the range of standard integer types supported by most programming languages.
• The input will always be a single integer.
• Performance is important; aim for an efficient solution that doesn't exceed reasonable time complexity.

Notes

• Consider how you can reverse a number mathematically.
• Think about what happens if the reversed number becomes larger than the original number during the process.
• Be mindful of potential integer overflow issues if you are reversing the entire number. There might be a more optimized way to check for palindromes.