## Description

https://leetcode.com/problems/longest-palindromic-substring/description/

Given a string **s**, find the longest palindromic substring in **s**. You may assume that the maximum length of **s** is 1000.

**Example:**

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Input: "babad" Output: "bab" Note: "aba" is also a valid answer. |

**Example:**

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Input: "cbbd" Output: "bb" |

## Explanation

A palindromic string meets two criteria:

- first and the last character are the same
- the inner word between the first and the last character is a palindromic string

The basic idea is to use dynamic programming to determine whether a substring is palindromic string base on above criteria.

Need to be careful that when returning the result, the end index need to plus 1, because java substring method doesn’t include the ending index.

## Video Tutorial

## Java Solution

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class Solution { public String longestPalindrome(String s) { if (s == null || s.length() < 2) { return s; } int length = s.length(); boolean[][] isPalindrome = new boolean[length][length]; int left = 0; int right = 0; for (int j = 1; j < length; j++) { for (int i = 0; i < j; i++) { boolean isInnerWordPalindrome = isPalindrome[i + 1][j - 1] || j - i <= 2; if (s.charAt(i) == s.charAt(j) && isInnerWordPalindrome) { isPalindrome[i][j] = true; if (j - i > right - left) { left = i; right = j; } } } } return s.substring(left, right + 1); // Time Complexity: O(n ^ 2) // Space Complexity: O(n ^ 2) } } |

I have the same question in python but the platform accepts input only in this format. The problem is Test Case with 12 as length and abcbcabbacba as string is resulting in 12 and same string as output , it should be 8, bcabbacb. Can you tell where I misunderstood the logic and syntax. My code is as follows:

#input length, string

N=int(input())

w=input()

if w == ” or len(w)<=2:

print(len(w))

print(w)

if N<=5000:

isPallindrome = [[0]*N]*N

left=0

right=0

for j in range(1,N):

for i in range(0,j):

isInnerWordPallindrome = isPallindrome[i+1][j-1] or j-i right-left:

left = i

right = j

var1 = len(w[left:right+1])

var2 = w[left:right+1]

print(var1)

print(var2)

Thank you in advance!

Can you please explain why are you taking j from 1 to length and not from 0 to length inside the first loop?

Please elaborate both the ranges for i and j.

Thanks in advance.

Try thinking about it simply, i is the left index and j is the right index of a word.

In order to get at least one character of a word, j has been to at least one index after i. If i’s index is 0, then j’s index would be 1.

For i, its value could start from 0 to j – 1.

For j, its value could start from 1 to the last character index of the input string (s.length() – 1).