What is the Longest Palindromic Substring?
A common coding interview question involves finding the longest palindromic substring within a given string. A palindrome is a sequence that reads the same backward as forward, such as "madam" or "racecar." In this article, we will explore different methods to solve this problem, focusing on the most efficient one.
Brute Force Method
The brute force method involves checking all possible substrings of the given string to identify palindromic substrings, and then determining the longest among them. This approach has a time complexity of O(n^3), where n is the length of the string. Here’s how the basic algorithm works:
- Generate all possible substrings of the string.
- For each substring, check if it is a palindrome.
- Keep track of the longest palindromic substring found.
Here is a simple implementation in Python:
Python
Expand Around Center Method
A more efficient method to find the longest palindromic substring is the expand around center technique. The idea is to consider every character (or pair of characters) in the string as a potential center of a palindrome, and then expand outwards as long as we keep finding matching characters.
This approach works in O(n^2) time, which is much better than the brute force method. Below is a Python implementation:
Python
Dynamic Programming Approach
Another approach to find the longest palindromic substring is to use dynamic programming. This method stores the results of subproblems (i.e., whether a substring is a palindrome) in a table, to avoid redundant calculations.
The time complexity here is also O(n^2), but it uses O(n^2) space. Here’s an example of the dynamic programming approach in Python:
Python
These methods showcase different approaches to solving the longest palindromic substring problem. Each method has its pros and cons, and understanding them will enhance problem-solving skills in coding interviews.
