Given a string, your task is to count how many palindromic substrings in this string.



The substrings with different start indexes or end indexes are counted as different substrings even they consist of same characters. 


Example 1:

Input: "abc"
Output: 3
Explanation: Three palindromic strings: "a", "b", "c".



Example 2:

Input: "aaa"
Output: 6
Explanation: Six palindromic strings: "a", "a", "a", "aa", "aa", "aaa".



Note:

The input string length won't exceed 1000.

Source: leetcode | Difficulty: MEDIUM_HARD
Tags: String algorithms

Dynamic programming

Starter code: class Solution:
    def countSubstrings(self, s: str) -> int:
        

Solutions:
class Solution:

	def countSubstrings(self, s):
		ret = 0
		(left, right) = (0, 0)
		while left < len(s):
			while right < len(s) and s[right] == s[left]:
				right += 1
			ret += self.sum(right - left)
			(l, r) = (left - 1, right)
			while l >= 0 and r < len(s) and (s[r] == s[l]):
				ret += 1
				l -= 1
				r += 1
			left = right
		return ret

	def sum(self, n):
		s = 0
		for i in range(1, n + 1):
			s += i
		return s


class Solution:

	def countSubstrings(self, s):
		s = '^#' + '#'.join(s) + '#$'
		Z = [1] * len(s)
		(center, right) = (0, 0)
		for i in range(len(s) - 1):
			if i < right:
				i_mirror = 2 * center - i
				Z[i] = min(Z[i_mirror], right - i + 1)
			while s[i + Z[i]] == s[i - Z[i]]:
				Z[i] += 1
			if i + Z[i] - 1 > right:
				(center, right) = (i, i + Z[i] - 1)
		return sum((z // 2 for z in Z))


class Solution:

	def countSubstrings(self, s):

		def manachers(S):
			A = '@#' + '#'.join(S) + '#$'
			Z = [0] * len(A)
			center = right = 0
			for i in range(1, len(A) - 1):
				if i < right:
					Z[i] = min(right - i, Z[2 * center - i])
				while A[i + Z[i] + 1] == A[i - Z[i] - 1]:
					Z[i] += 1
				if i + Z[i] > right:
					(center, right) = (i, i + Z[i])
			return Z
		return sum(((v + 1) // 2 for v in manachers(s)))


class Solution:

	def countSubstrings(self, s):
		t = '@#' + '#'.join(s) + '#$'
		n = len(t)
		r = [0] * n
		c = 0
		for i in range(1, n - 1):
			if i - c < r[c]:
				if r[c - (i - c)] < r[c] - (i - c):
					r[i] = r[c - (i - c)]
				else:
					r[i] = r[c] - (i - c)
					while t[i - r[i] - 1] == t[i + r[i] + 1]:
						r[i] += 1
					c = i
			else:
				r[i] = 0
				while t[i - r[i] - 1] == t[i + r[i] + 1]:
					r[i] += 1
				c = i
		return sum(((i + 1) // 2 for i in r))


class Solution:

	def countSubstrings(self, s):
		ss = '$#'
		for i in s:
			ss += i + '#'
		ss += '@'
		r = [0] * (len(ss) + 1)
		pos = 0
		ma = 0
		for i in range(1, len(ss) - 1):
			if ma > i:
				r[i] = min(r[pos - (i - pos)], ma - i)
			else:
				r[i] = 1
			while ss[i + r[i]] == ss[i - r[i]]:
				r[i] += 1
			if r[i] + i > ma:
				(pos, ma) = (i, r[i] + i)
		ans = sum((int(l / 2) for l in r))
		return ans


class Solution:

	def countSubstrings(self, s):
		s = ',' + s + '.'
		ans = 0
		for i in range(1, len(s) - 1):
			j = 1
			while s[i + j] == s[i - j]:
				j += 1
			ans += j
		for i in range(1, len(s) - 1):
			j = 0
			while s[i - j] == s[i + 1 + j]:
				j += 1
			ans += j
		return ans