old_contents: # Time:  O(n)
  # Space: O(n)
  
  # TLE
  class Solution:
      # @param {string} s
      # @return {string}
      def shortestPalindrome(self, s):
          string = self.preProcess(s)
          palindrome = [0] * len(string) 
          center, right = 0, 0
          for i in xrange(1, len(string) - 1):
              i_mirror = 2 * center - i
              if right > i:
                  palindrome[i] = min(right - i, palindrome[i_mirror])
              else:
                  palindrome[i] = 0
  
              while string[i + 1 + palindrome[i]] == string[i - 1 - palindrome[i]]:
                  palindrome[i] += 1
  
              if i + palindrome[i] > right:
                  center, right = i, i + palindrome[i]       
          
          max_len = 0
          for i in xrange(1, len(string) - 1):
              if i - palindrome[i] == 1:
                  max_len = palindrome[i]
          return s[len(s)-1:max_len-1:-1] + s
          
      def preProcess(self, s):
          
          if not s:
              return "^$"
          string = "^"
          for i in s:
              string +=  "#" + i
          string += "#$"
          return string
          
  
new_contents: # Time:  O(n)
  # Space: O(n)
  
  # TLE
  class Solution:
      # @param {string} s
      # @return {string}
      def shortestPalindrome(self, s):
          string = self.preProcess(s)
          palindrome = [0] * len(string) 
          center, right = 0, 0
          for i in xrange(1, len(string) - 1):
              i_mirror = 2 * center - i
              if right > i:
                  palindrome[i] = min(right - i, palindrome[i_mirror])
              else:
                  palindrome[i] = 0
  
              while string[i + 1 + palindrome[i]] == string[i - 1 - palindrome[i]]:
                  palindrome[i] += 1
  
              if i + palindrome[i] > right:
                  center, right = i, i + palindrome[i]       
          
          max_len = 0
          for i in xrange(1, len(string) - 1):
              if i - palindrome[i] == 1:
                  max_len = palindrome[i]
          return s[len(s)-1:max_len-1:-1] + s
          
      def preProcess(self, s):
          if not s:
              return "^$"
          string = "^"
          for i in s:
              string +=  "#" + i
          string += "#$"
          return string
          
  
subject: Update shortest-palindrome.py