Assistant System Engineer

Understanding the problem: Recognize that a palindromic substring reads the same backward as forward. The problem asks to find the longest palindromic substring in a given string.

Brute force approach: Start with each character in the string and expand outwards to check if the substring is a palindrome. Track the longest palindrome found.

Optimized approach: Utilize dynamic programming to optimize the solution. Create a boolean table dp[i][j] where dp[i][j] is true if the substring from index i to j is a palindrome.

Initialize base cases: Set dp[i][i] to true for all single characters, and dp[i][i+1] to true for all adjacent characters if they are the same.

Dynamic programming recurrence: Use the recurrence relation dp[i][j] = (s[i] == s[j] && dp[i+1][j-1]) to check if the substring from i to j is a palindrome based on the characters at indices i and j.

Update the maximum length: Keep track of the maximum length of palindromic substrings found during the process.