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Palindrome Number

Difficulty: Easy

Problem Description

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

Key Insights

  • A palindrome is a number that reads the same forwards and backwards.
  • Negative numbers are not palindromes due to the presence of the negative sign.
  • Numbers ending in 0 (except for 0 itself) cannot be palindromes because they would start with 0 when reversed.

Space and Time Complexity

Time Complexity: O(log10(n)) - The number of digits in the number determines how many iterations we need. Space Complexity: O(1) - We only use a constant amount of space.

Solution

To determine if a number is a palindrome without converting it to a string, we can reverse half of the number and compare it with the other half. We can do this by repeatedly extracting the last digit and building the reversed number. If the original number is equal to the reversed number or the original number without its last digit (in the case of odd digit counts), then it is a palindrome.

Code Solutions

def isPalindrome(x: int) -> bool:
    # Negative numbers and numbers ending with 0 (except 0 itself) are not palindromes
    if x < 0 or (x % 10 == 0 and x != 0):
        return False
    
    reversed_number = 0
    while x > reversed_number:
        # Build the reversed number by taking the last digit of x
        reversed_number = reversed_number * 10 + x % 10
        x //= 10  # Remove the last digit from x
    
    # Check if the original number is equal to the reversed number
    return x == reversed_number or x == reversed_number // 10
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