Solving Longest Palindromic Substring: A Multi-Language Approach
The Longest Palindromic Substring problem is a classic algorithmic challenge that tests your understanding of string manipulation and dynamic programming. Let's solve it in multiple programming languages and explore different approaches. For more on string manipulation, check out our guide on memoization in ruby for optimization.
Problem Statement
Given a string s
, return the longest palindromic substring in s
.
Example 1:
Example 2:
Understanding the Problem
A palindrome is a string that reads the same forward and backward. The challenge is to find the longest such substring within a given string. There are several approaches to solve this:
- Brute Force (O(n³))
- Dynamic Programming (O(n²))
- Expand Around Center (O(n²))
- Manacher's Algorithm (O(n)) - advanced
We'll implement the "Expand Around Center" approach as it's both efficient and intuitive. For more on performance optimization, see our guide on performance bottlenecks in rails applications.
TypeScript Implementation
Ruby Implementation
For more on Ruby optimization techniques, check out our guide on memoization in ruby performance improvement.
Python Implementation
Code Walkthrough
Let's break down the key components of our solution. For more on code optimization, see our guide on optimize large lists tables rendering performance.
-
Base Case
- If string length is less than 2, return the string itself
- A single character is always a palindrome
-
Expand Around Center Function
- Takes left and right pointers as parameters
- Expands outward while characters match
- Updates global tracking of longest palindrome found
-
Main Loop
- Iterates through each character
- Checks for both odd and even length palindromes
- Uses two separate expansions for each position
-
Time and Space Complexity
- Time Complexity: O(n²)
- Space Complexity: O(1)
Performance Optimization Tips
For more on performance optimization, check out our guide on optimize database queries rails application.
-
Early Termination
- If remaining string length is less than current max, stop searching
- Implement bounds checking before expansion
-
Memory Management
- TypeScript/JavaScript: Use substring instead of slice
- Python: Use string slicing efficiently
- Ruby: Use proper string range operations
-
Language-Specific Optimizations
- TypeScript: Use type annotations for better performance
- Python: Consider using memoryview for large strings
- Ruby: Use frozen string literals when possible
Threading Considerations
When implementing this in a web application, consider threading implications. For more details, see our guide on multithreading vs multiprocessing in ruby.
Related Problems
- Palindromic Substrings (LeetCode 647)
- Valid Palindrome (LeetCode 125)
- Palindrome Pairs (LeetCode 336)
Related Resources
Performance and Optimization
- Memoization in ruby for optimization
- Memoization in ruby performance improvement
- Performance bottlenecks in rails applications
Implementation and Best Practices
- Optimize large lists tables rendering performance
- Optimize database queries rails application
- Multithreading vs multiprocessing in ruby
Conclusion
The Longest Palindromic Substring problem demonstrates the importance of efficient algorithm design and language-specific implementations. While the core logic remains similar across languages, each implementation takes advantage of language-specific features for optimal performance. For more on optimizing Ruby applications, check out our guide on optimize rails app for high traffic.
Remember to practice this problem with different input sizes and edge cases to fully understand its complexity and optimization opportunities.