[NEW ALGORITHM] : Longest Palindromic String

[tanushrigoel]

Description:

The Longest Palindromic Substring (LPS) algorithm is used to find the longest contiguous substring in a given string that reads the same forward and backward. This is an efficient solution with a time complexity of O(n²).

Key Steps:

• 2D DP Table: A 2D table is used to mark whether a substring is a palindrome.
• Base Case: Single-character substrings are always palindromes.
• Dynamic Update: For longer substrings, characters at both ends must match, and the inner substring must also be a palindrome.
• Tracking: The algorithm keeps track of the longest palindrome found.

Complexity:

• Time Complexity: O(n²)
• Space Complexity: O(n²)

This algorithm is useful for text analysis and efficiently handles edge cases such as empty strings and single characters.

Checklist:

• [x] Contributor in GSSoC-ext
• [x] Want to work on it

Additional Information:

Longest Palindromic Substring (Dynamic Programming)

Overview:

This algorithm finds the longest contiguous palindromic substring within a given string using dynamic programming.

Key Steps:

1. DP Table: A 2D table tracks whether substrings are palindromes.
2. Base Cases: Single-character substrings are palindromes. For two-character substrings, check if both characters match.
3. Dynamic Update: For longer substrings, check if both ends match and if the inner substring is a palindrome.
4. Efficiency: Time complexity is O(n²).

[tanushrigoel]

please add hacktoberfest label as well