Write a function to find the longest palindromic substring in a given string

Sure, here is a Python function that finds the longest palindromic substring in a given string:

def longest_palindrome(s):
    def expand_around_center(s, left, right):
        while left >= 0 and right < len(s) and s[left] == s[right]:
            left -= 1
            right += 1
        return s[left + 1:right]

    longest = ""
    for i in range(len(s)):
        # Find a longer odd length palindrome with s[i] at its center
        palindrome_odd = expand_around_center(s, i, i)
        if len(palindrome_odd) > len(longest):
            longest = palindrome_odd

        # Find a longer even length palindrome with s[i] and s[i+1] at its center
        palindrome_even = expand_around_center(s, i, i + 1)
        if len(palindrome_even) > len(longest):
            longest = palindrome_even

    return longest

This function works by iterating over each character in the string, and for each character, it tries to expand around that character to find a palindrome. It does this twice for each character: once for palindromes of odd length (with the character at the center), and once for palindromes of even length (with the character and the next character at the center). It keeps track of the longest palindrome it has found so far, and returns that at the end.