The problem is to determine if a given integer is a palindrome. One approach is to convert the number to a string, reverse the string, and compare it to the original string. This approach has a time complexity of O(n) and a space complexity of O(n) due to the creation of additional strings and arrays. A more efficient approach uses a mathematical method without string conversion. This approach has a time complexity of O(log n) because it only processes half the digits of the number. The space complexity is O(1) because it only uses two variables regardless of the input size. The optimized solution includes early returns for negative numbers and single digits, only reverses half the number, and uses constant extra space. It handles both even and odd length numbers and does not require string conversion. The solution is demonstrated with the example of the number 1221, which is determined to be a palindrome. Overall, the second approach is more efficient and preferred over the first approach.
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