Problem
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.
Notes
DP problem
-
States:
left_index, right_index, mark if
s[left_index, right_index+1]is palindromic -
Transition:
if s[l] == s[r]: # mark it only when both ends are same values dp[l][r] = 1 if r == l # if only one element dp[l][r] = 1 if r+1 == l # if only two elements dp[l][r] = 1 if dp[l+1][r+1] = 1 # if the string in between is palindromic results = results + 1 -
Base case:
initialize dp[i][j] = 0
Solution
class Solution:
def countSubstrings(self, s):
dp = [[0] * len(s) for i in range(len(s))]
res = 0
for r in range(len(s)):
for l in range(r+1):
if s[r] == s[l]:
if r == l or r+1 == l or dp[l+1][r-1] == 1:
dp[l][r] = 1
res += 1
return res
print(Solution().countSubstrings("aba"))