Longest Pallindromic Substring

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This video is a comprehensive tutorial on solving the 'Longest Palindromic Substring' problem, a common algorithmic challenge. The instructor begins by presenting the problem statement from a coding platform, explaining that the goal is to find the longest substring within a given string that reads the same forwards and backwards. The core of the lesson is the 'Expand Around Center' algorithm, which is explained both conceptually and through a step-by-step implementation. The instructor uses a digital whiteboard to illustrate the method, showing how to treat each character (and each gap between characters) as a potential center of a palindrome and expand outwards to find the longest possible palindrome. This is followed by a detailed walkthrough of the Python code, where the `expand_around_center` function is defined to handle both odd-length (e.g., 'aba') and even-length (e.g., 'abba') palindromes. The main function iterates through each possible center, calls the helper function, and keeps track of the longest palindrome found. The video concludes with the instructor writing the complete, working code in an online IDE, demonstrating its execution and showing the accepted solution with performance metrics.

Chapters

1. 0:00 – 2:00 00:00-02:00

   The video opens on a coding platform, leetcode.com, displaying the problem '5. Longest Palindromic Substring'. The problem description, examples, and constraints are visible. The instructor explains the task: given a string, return the longest palindromic substring. The code editor on the right shows a skeleton of a Python class with a method `longestPalindrome` that takes a string `s` and returns a string. The instructor then transitions to a digital whiteboard to begin the explanation.

2. 2:00 – 5:00 02:00-05:00

   On the digital whiteboard, the instructor writes the problem title '26 Longest Palindromic Substring'. They introduce the core concept: 'Expand around centre'. Using the example string 'babad', they demonstrate how to treat each character as a potential center of a palindrome and expand outwards. They draw diagrams showing the expansion for the center at 'b' (resulting in 'bab') and at 'a' (resulting in 'aba'). They also illustrate the concept of even-length palindromes by showing the center between 'b' and 'a' in 'baab'.

3. 5:00 – 10:00 05:00-10:00

   The instructor continues on the whiteboard, explaining the algorithm in more detail. They write the pseudocode for the main function `longestPalindrome(s)` and the helper function `expand_around_center(left, right)`. They emphasize that the algorithm must handle both odd and even length palindromes by calling the helper function twice for each center: once with `i` and `i` (for odd), and once with `i` and `i+1` (for even). They write the logic for the `expand_around_center` function, which uses a while loop to expand as long as the characters at the left and right pointers are equal and within bounds.

4. 10:00 – 15:00 10:00-15:00

   The instructor completes the pseudocode on the whiteboard. They write the `expand_around_center` function, which returns the substring from `left` to `right` (inclusive). They then write the main loop of `longestPalindrome`, which iterates through each index `i` in the string. For each `i`, it calls `expand_around_center(i, i)` and `expand_around_center(i, i+1)`, compares the lengths of the resulting palindromes, and updates the `longest` variable if a longer one is found. They also write the base case for a single character string.

5. 15:00 – 20:00 15:00-20:00

   The instructor transitions back to the coding environment. They begin to write the actual Python code based on the whiteboard pseudocode. They define the `expand_around_center` function, which takes `left` and `right` indices and returns the substring. They implement the while loop to expand the palindrome, checking bounds and character equality. They then define the `longestPalindrome` function, initialize `longest` to an empty string, and loop through the string to find the longest palindrome by calling the helper function for both odd and even cases.

6. 20:00 – 25:00 20:00-25:00

   The instructor completes the code in the IDE. They write the logic to compare the lengths of the two palindromes found at each center and update the `longest` variable accordingly. They add a final return statement for the `longestPalindrome` function. The complete code is shown, and the instructor runs it, which results in an 'Accepted' status with a runtime of 276 ms and memory usage of 16.70 MB.

7. 25:00 – 26:13 25:00-26:13

   The video concludes with a final view of the accepted solution in the online IDE. The code is fully written and has passed all test cases. The instructor's final comment is to 'submit' the solution. The screen shows the accepted status, the runtime, and memory usage, confirming the successful implementation of the 'Expand Around Center' algorithm.

The video provides a clear, step-by-step guide to solving the Longest Palindromic Substring problem. It effectively combines a conceptual explanation using a whiteboard to illustrate the 'Expand Around Center' method with a practical implementation in Python. The instructor methodically breaks down the problem, first explaining the core idea of treating each character as a center, then detailing the code structure, and finally showing the complete, working solution. This approach ensures a deep understanding of both the algorithm's logic and its practical application, making it an excellent resource for learning this classic algorithmic challenge.