O(n^2) time and O(1) space using concept of expansion around the center.

647. Palindromic Substrings/647. Palindromic Substrings_2.py

@@ -0,0 +1,15 @@
+class Solution:
+    def dfs(self, left, right,s):
+        final = 0
+        while left >= 0 and right < len(s) and s[left] == s[right]:
+            left -= 1
+            right += 1
+            final += 1
+        return final
+
+    def countSubstrings(self, s: str) -> int:
+        result = 0
+        for i in range(len(s)):
+            result += self.dfs(i,i,s)
+            result += self.dfs(i,i+1,s)
+        return result