5.py

# Name: Longest Palindromic Substring
# Link: https://leetcode.com/problems/longest-palindromic-substring/
# Method: DP, is string from [i,j] a palindrome (alternatively, expand from middle)
# Time: O(n^2)
# Space: O(n)
# Difficulty: Medium


class Solution:
 def longestPalindrome(self, s: str) -> str:
 max_pal_len = 1
 max_val_idx = [0, 0]

 # Optimised DP using only 2 lines
 is_pal_line = [False for _ in range(len(s))]
 is_pal_line[-1] = True

 for i in range(len(s) - 1, -1, -1): # From bottom up, looking after diagonal
 is_pal_now = [False for _ in range(len(s))]
 is_pal_now[i] = True
 for j in range(i + 1, len(s)):
 if s[i] == s[j] and (j - i == 1 or is_pal_prev[j - 1]):
 is_pal_now[j] = True
 if j - i + 1 > max_pal_len:
 max_pal_len = j - i + 1
 max_val_idx = [i, j]
 is_pal_prev = is_pal_now

 return s[max_val_idx[0] : max_val_idx[1] + 1]