Find the longest palindromic substring

longest_palindromic_substring.py

"""
Given a string s, return the longest palindromic substring in s

Example 1:
Input: s = "babad"
Output: "bab"
Note: "aba" is also a valid answer.

Example 2:
Input: s = "cbbd"
Output: "bb"

Example 3:
Input: s = "a"
Output: "a"

Example 4:
Input: s = "ac"
Output: "a"
"""
def longestPalindrome(s):
    start = 0 # start index of the longest substring
    max_length = 1
    n = len(s)
    for i in xrange(1, n):
        # First, look for the longest even palindrome,
        # i.e. repeated characters at the centre
        l = i-1
        h = i
        while l >= 0 and h < n and s[l] == s[h]:
            if max_length < h - l + 1:
                start = l
                max_length = h - l + 1
            l -= 1
            h += 1     

        l = i-1
        h = i+1
        while l >= 0 and h < n and s[l] == s[h]:
            if max_length < h - l + 1:
                start = l
                max_length = h - l + 1
            l -= 1
            h += 1

    return s[start:start+max_length]