There are many ways to find the `longest palindromic substring`. One can find it in $O(N ^ 3)$ and also in $O(N ^ 2)$ time complexity. But using `Manacher's Algorithm ...

This method has a time complexity of O(n³): one layer for the start index, one for the end index, and another for checking if the substring itself is a palindrome (which takes O(n) time). Clearly, ...