Write a function that, given a string, returns the longest palindromic substring. Optimize for time and space complexity.

Use the CIRCLES framework: Context (problem definition), Input (string), Constraints (time/space), Reasoning (choose center‑expansion), List (edge cases), Execute (code outline), Summary (complexity). Provide a concise 120‑150 word strategy without narrative.

The problem is to find the longest contiguous palindrome in a string. I choose the center‑expansion technique because it runs in O(n²) time and O(1) space, which is optimal for this task. I iterate over each character as a potential center, expanding outward for both odd and even length palindromes. For each expansion, I track the maximum length and its start index. Edge cases include empty strings and single‑character strings, which I handle by returning the input directly. Finally, I slice the original string from the start index to the maximum length and return it. This solution is concise, handles all cases, and meets the required complexity constraints.