Which is the longest palindromic substring?


In this tutorial, we are going to give you a knowledge momentum on the much-asked topic of longest palindromic substring! 

The longest palindromic substring often called the symmetric factor problem is a type of problem where you need to find the maximum length of the given contiguous substring of any given string which can be a palindrome. 


As if the needed longest palindromic substring for the ‘bananas’ would be the ‘anana’!


Though, the concept holds various approaches which you can follow to solve the given problems?


Do you want to learn about them in-depth?


If yes, stick to this tutorial till the end where we are going to unfold all the essential information related to the longest palindromic substring.


Without any type of ado, let’s get started! 



Longest palindromic substring - An overview 

In the problem of longest palindromic substring, you need to find out the length of any longest substring in the given string that can be a palindrome. This is one of the famous and commonly asked questions in a coding interview.


For example; the given input string with english alphabets would be present to you. You have to return its longest palindromic substring. A substring can be a string which would be formed by the removal of any number of characters which includes 0 from a given input string from the front to the back. 


Though, there is no guarantee that the longest palindromic substring would be unique in any case. In that case, you have to find whether it is a palindrome.




Approaches to find out the longest palindromic substring


To find the longest palindromic substring, take the help of below-mentioned approaches and learn to implement them in an ideal way. 



Manacher’s Algorithm


This is touted as the easy and efficient approach for finding the longest palindromic substring for any of the given strings. You may be needed to solve the given sub-problems of some of the hard problems. 


Consider the given problem statement:


The string s of the length n is given to you. You need to get its longest palindromic substring in a given string. The string in this case is palindrome and it can be completely reversed.


Manacher algorithm was first invented by the very famous Manacher for a list of all the available palindromes which can appear at the start of a string. Later it was observed that you can use the same algorithm in order to get any longest palindromic substring of a given string.


Manchester also invented the O[n] algorithm to list all the palindromes which appear at the start of a given string of the length n. In this case, you will get the O[n] time solution for the required longest palindromic substring. 


For example; consider a given input string as ‘abacaba’. By that time, you will get to the ‘c’ Manchester algorithms with the identified length of all its related algorithms. You can run a loop in order to identify the largest palindrome that can be centred around the letter to get the longest palindromic substring.



Brute force Approach 


This is another useful method to find the longest palindromic substring. Where a substring is considered the palindrome. To do it for the first time, you need to run any three available nested loops where the two outer loops will pick all the given substrings in order to fix them at the corner of the characters. 


An inner loop will first check if a picked substring is palindrome. 


The required time complexity for this approach would be the O [n ^3]. Here, you will get the three given nested loops where you need to find its longest palindromic substring for the approach so that you can get the required time complexity. 


Though, the auxiliary complexity in this case would be the O [1]. You may not need any type of extra space in this case. 




Dynamic programming Approach 


It would be the other ideal approach to find the longest palindromic substring. The given  time complexity in this case would be reduced when you store all the resultant elements in your substring.



  • First you need to maintain the boolean table that is [n] [n] which gets filled as in a bottom up manner 

  • The value of the given table [i] [j] would be true, if your required substring would be considered palindrome. Otherwise, return false 

  • In order for calculating the table, check its value [ i +1 [ j -1] as the values are true for the str [i] which stays same as the str [j], make that table [i] [j] as it made false 

  • You have to previously fill the tables as length 1 and length 2 to find if it is considered as true or a false in any given case 


The given time complexity in this case would be the  O [n^2] where the two nested traversals are needed. The auxiliary space in this case would be O [n^2] where the size of a matrix would be needed to store your array.



Using Loops 


Here, we are going to first run the loop in order to iterate all the characters. Then, we will check with the another loop as if there is any similar character in respect to that current character. 


If this is possible, you get both the first and the large character of your substring. Store the substring so as to check if it is longest or not. We keep on iterating it till we store our string.




Additional Learning - Top view of a binary tree 


A useful coding concept that you should know is the top view of binary tree. 

The top view of a binary tree is defined as the set of all visible nodes when a tree gets viewed from the bottom. The output from the given left most horizontal level will be till its rightmost horizontal level.




Wrapping up 


Learn the knits and grits of the longest palindromic substring with the help of this blog post and fill your knowledge bank in the right direction. 


All the best!

Comments

Post a Comment

Popular posts from this blog

What are the 5 types of inheritance?

Image
  The concept of inheritance is considered among the most crucial concepts of object-oriented programming. Inheritance in Java is considered as a process where one class inherits the property of its parent class. When we simply define inheritance, we call it the capability of a class that derives the properties or features of other classes. The new class will be created as the ‘ derived class’ and the existing class will be known as base or parent class. Talking about the types of inheritance, it is generally of five types. Here, in this blog we are going to discuss all these inheritance types in detail with the help of examples. Without any ado, let’s get started! Types of inheritance In case of inheritance, one class derives the properties from its parent class. Here, any new class will be derived from its existing class. This new class is the derived class and our current class will be termed as the base class. When we talk about inheritance in Java, there are mainly five types ...
Read more

Remove duplicates from a sorted linked list

Image
Introduction Before reading this article, It is recommended to have an understanding of the linked list and its implementation and some basic operations on the linked list. Problem Description Create a function that takes a non-descending list and removes any duplicate nodes. Only one traversal of the list is necessary. Eg. Consider the given linked list: 1->1->1->2->2->3, the function is expected to convert the linked list into 1->2->3. In this article, we will extensively discuss the Label Control in C# & how to  remove duplicates from sorted doubly linked list .  Important:  We are supposed to delete only the duplicates i.e. only one copy of nodes should be there. Intuition:  The biggest hint given is that the list is sorted or non-decreasing in nature. From this, we can deduce that if duplicates are present, then it has to be the next one in the chain. The ideal way to approach this problem is to simply loop through the first value i...
Read more

How often can you Buy and Sell the same stock?

Image
The stock market is notoriously unpredictable. It can be hard enough to guess whether or not a particular investment will pay off or not. We know that understanding all the nuances of rules and regulations involved when buying and selling stocks is difficult. One big question many people have is, “How often can you buy and sell the same stock with transaction fee ?”  Before you start trading, you are unaware of the steps to follow to start trading and what would be the best time to buy and sell stock with transaction fee.  No matter if this is your first time investing or if you’ve been around the block a few times before, we hope that our guide will help you understand briefly on how to sell and buy stocks with in same time. Let's start with understanding stock trading and the types of traders in detail. What is Stock trading? The term "stock trading" describes the purchasing and selling of equities on a stock market. Investors that purchase and sell stocks with the inte...
Read more