diff --git a/0005-longest-palindromic-substring/0005-longest-palindromic-substring.py b/0005-longest-palindromic-substring/0005-longest-palindromic-substring.py
index f5895c2..d7f922c 100644
--- a/0005-longest-palindromic-substring/0005-longest-palindromic-substring.py
+++ b/0005-longest-palindromic-substring/0005-longest-palindromic-substring.py
@@ -2,28 +2,40 @@ class Solution:
     def longestPalindrome(self, s: str) -> str:
         """
         Complexities:
-        Time:  O(n^3)
+        Time:  O(n^2)
         Space: O(1)
 
         where n = len(s)
         """
 
-        # indicies inclusive - O(n)
-        def isPalindrome(startIndex: int, endIndex: int):
-            if startIndex >= endIndex:
-                return True
+        # Returns the longest palindrome centered at s[i] or (s[i], s[i + 1])
+        # - O(n)
+        def longestPalindromeFromCenter(i: int, evenCentered: bool):
+            offset = 1
+            evenOffset = 1 if evenCentered else 0
 
-            if s[startIndex] == s[endIndex]:
-                return isPalindrome(startIndex + 1, endIndex - 1)
-            return False
+            while i - offset >= 0 and i + offset + evenOffset < len(s) and s[i - offset] == s[i + offset + evenOffset]:
+                offset += 1
 
+            offset -= 1 # Account for off-by-one
+
+            return s[i - offset : i + offset + evenOffset + 1]
 
         maxPalindrome = s[0]
+        # For each letter, check if it is the center of a palindrome (or center with s[i+1])
+        # - O(n^2) = n * 2(O(n))
         for i in range(len(s)):
-            for j in range(i + 1, len(s)):
-                length = j - i + 1
-                if length > len(maxPalindrome) and isPalindrome(i, j):
-                    maxPalindrome = s[i:j+1]
+            # Check for an even length palindrome
+            if i + 1 < len(s) and s[i] == s[i+1]:
+                evenPalindrome = longestPalindromeFromCenter(i, True)
+
+                if len(evenPalindrome) > len(maxPalindrome):
+                    maxPalindrome = evenPalindrome
+            
+            oddPalindrome = longestPalindromeFromCenter(i, False)
+            if len(oddPalindrome) > len(maxPalindrome):
+                    maxPalindrome = oddPalindrome
+
 
         return maxPalindrome