longest palindromic substring

class (object):
    def longestPalindrome(self, s):
        """
        :type s: str
        :rtype: str
        """
        max_length = 0
        max_str = ""
        for i in range(len(s)):
            
            left = i
            right = i
            while left >= 0 and right <= len(s) - 1 and s[left] == s[right]:
                left -= 1
                right += 1
            if right - left - 1 > max_length:
                max_length = right - left - 1
                max_str = s[left+1:right]
            # case 2 double center
            if i + 1 < len(s) and s[i] == s[i+1]:
                left = i
                right = i + 1
                while left >= 0 and right <= len(s) - 1 and s[left] == s[right]:
                    left -= 1
                    right += 1
                if right - left - 1 > max_length:
                    max_length = right - left - 1
                    max_str = s[left+1:right]
        return max_str