DIY: Palindromic Substrings

Problem Statement

Given a string s, your task is to implement the algorithm that will return the number of palindromic substrings in it.

Note: A string is a palindrome when it reads the same backward as forward, and a substring is a contiguous sequence of characters within the string.

Consider the string "abb". The substrings of "abb" are "a", "b", "b", and "bb". Of these, all four are palindromes, so the algorithm should return 4.