Problem Statement
Palindromic Substring Finder
You are a software developer working on a text analysis tool for a publishing company. The company wants to identify palindromic patterns in manuscripts to study the author's writing style.
Given a string s, your task is to find the longest substring that is a palindrome. A palindrome is a string that reads the same forward and backward.
Unlike the subsequence problem, a substring is a contiguous sequence of characters within a string. For example, in the word "babad", the substrings "bab" and "aba" are palindromes, but "babad" is not.
Examples
Example 1:
Input: s = "babad"
Output: "bab"
Explanation: The longest palindromic substring is "bab" or "aba". Both have length 3, but we return the first one we find, which is "bab".
Example 2:
Input: s = "cbbd"
Output: "bb"
Explanation: The longest palindromic substring is "bb", which has a length of 2.
Example 3:
Input: s = "racecar"
Output: "racecar"
Explanation: The entire string "racecar" is a palindrome, so it is the longest palindromic substring.
Constraints
- 1 <= s.length <= 1000
- s consists only of lowercase English letters.
Problem Breakdown
To solve this problem, we need to:
- A palindrome reads the same forward and backward, so we need to find a contiguous substring with this property.
- We can check each possible center of a palindrome and expand outward to find the longest palindrome.
- There are two types of palindromes: odd-length (with a single character at the center) and even-length (with two identical characters at the center).
- Dynamic programming can also be used to solve this problem by building up solutions for smaller substrings.
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Palindromic Substring Finder
You are a software developer working on a text analysis tool for a publishing company. The company wants to identify palindromic patterns in manuscripts to study the author's writing style.
Given a string s, your task is to find the longest substring that is a palindrome. A palindrome is a string that reads the same forward and backward.
Unlike the subsequence problem, a substring is a contiguous sequence of characters within a string. For example, in the word "babad", the substrings "bab" and "aba" are palindromes, but "babad" is not.
Examples
Example 1:
The longest palindromic substring is "bab" or "aba". Both have length 3, but we return the first one we find, which is "bab".
Example 2:
The longest palindromic substring is "bb", which has a length of 2.
Example 3:
The entire string "racecar" is a palindrome, so it is the longest palindromic substring.
Problem Breakdown
Constraints:
- 1 <= s.length <= 1000
- s consists only of lowercase English letters.
Key Insights:
A palindrome reads the same forward and backward, so we need to find a contiguous substring with this property.
We can check each possible center of a palindrome and expand outward to find the longest palindrome.
There are two types of palindromes: odd-length (with a single character at the center) and even-length (with two identical characters at the center).
Dynamic programming can also be used to solve this problem by building up solutions for smaller substrings.
Real-World Application
This problem has several practical applications:
Text Analysis
Used in linguistic analysis to identify patterns and symmetries in texts.
Bioinformatics
Finding palindromic sequences in DNA and RNA which often indicate biological significance.
String Processing
Used in various string processing algorithms and applications.