**Problem Statement:**
Given the required input arguments, write an efficient algorithm to solve the **Longest Palindromic Substring** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge.
**Hint / Expected Approach:**
Expand around center O(n²) or Manacher O(n)
**Edge Cases to Consider:**
- (1) Single character
- (2) All same characters
- (3) Even vs odd palindromes