Can someone suggest some method to count the number of prefixes of a given string which are also palindromes? It would be even helpful if I can get a boolean array of the length of string where a true denotes that a prefix up to this index is a palindrome.

Right now I have a simple 2d dp approach where dp[i][j] is true if string i to j is a palindrome, but this is O(n2). Is there some O(n) or O(nlog(n)) method thankyou.