Understanding the longest palindromic substring problem

In many string-processing applications, finding patterns within text is a very common problem. One such pattern is a palindrome, a sequence of characters that reads the same both forwards and backwards. When analyzing a single string, we often want to identify the longest contiguous segment that reads the same forward and backwards. This is known as the longest palindromic substring problem, in which the objective is to find the longest substring in the input string that forms a palindrome.

The longest palindromic substring problem is a classic problem in dynamic programming and has practical applications in DNA sequence analysis for identifying genetic markers, text processing for pattern recognition, data compression algorithms, and natural language processing tasks.

In this lesson, we will learn about the longest palindromic substring problem and how it can be solved efficiently using a dynamic programming solution.

The longest palindromic substring problem

Consider we are given a string s of length n. A substring is defined as a contiguous sequence of characters within the string.

A palindrome is a string that reads the same forwards and backwards, such as "racecar" or "aba". We need to find the length of the longest substring of s that is also a palindrome.