Counting palindromic substrings in O(n)

Question

Given a string (assume only English characters) S of length n, we can count the number of palindromic substrings with the following algorithm:

Answer 1

For "normal" strings it should be rather efficient to look at each character as the potential "center" of a palindrome and then check if the surrounding characters actually build one:

# check odd palindromes
for center in range(len(ls)):
   # check how many characters to the left and right of |center|
   # build a palindrome
   maxoffs = min(center, len(ls)-center-1)
   offs = 0
   while offs <= maxoffs and ls[center-offs] == ls[center+offs]:
      offs += 1
   offs -= 1
   print ls[center-offs : center+offs+1]                                    

# check for even palindromes
for center in range(len(ls)-1):
   maxoffs = min(center, len(ls)-center-2)
   offs = 0
   while offs <= maxoffs and ls[center-offs] == ls[center+offs+1]:
      offs += 1
   offs -= 1
   if offs >= 0:
      print ls[center-offs : center+offs+2]

For normal strings this should be about O(n), though in the worst case, for example if the string consists of only one character repeated over and over again, it will still take O(n²) time.