From Length to Sequences: Backtracking Through the LCS Table
Finding the LCS length was one thing. But what if the question asks for ALL possible longest subsequences? That's where backtracking enters the picture.
LeetCode problem solutions
View All TagsFinding the LCS length was one thing. But what if the question asks for ALL possible longest subsequences? That's where backtracking enters the picture.
I thought I had DP figured out. I'd solved house robber with that sweet max(rob_this_house + dp[i-2], skip_this_house) logic. I'd reversed linked lists by imagining "the rest is already solved." But when I faced Longest Common Subsequence, all my mental models fell apart.
No decision tree. No "imagine the rest" logic. No clever way to use previous answers. Just... confusion.
Here's how I finally cracked it.
A conversation about solving the Widest Binary Tree Level problem that reveals how mathematical position formulas and DFS traversal create an elegant solution—and why we need to track both min and max positions at each level.
A dialogue between Professor Chen and Alex, a senior Computer Science student, as they unravel why some DP problems resist the standard recursive → memoization → tabulation pipeline.
Alex: [walks into office hours with laptop open] Professor Chen, I'm really confused about this LeetCode problem I'm working on. I thought I understood DP, but something's not clicking.
Professor Chen: Let's see what you've got. Walk me through it.
Alex: It's LC 740: Delete and Earn. Here's the problem:
The Remove Linked List Elements problem is a fundamental linked list manipulation challenge that teaches essential pointer handling techniques. This problem is excellent for understanding when and why to use dummy nodes in linked list operations.
The Minimum Subarray Sum problem (also known as "Minimum Size Subarray Sum") is an excellent introduction to the sliding window technique. This problem demonstrates how we can optimize from a brute force O(n³) solution to an elegant O(n) solution.
The Maximum Depth of Binary Tree problem is a classic tree traversal challenge that introduces fundamental concepts of tree algorithms. This problem is perfect for understanding the relationship between recursion and tree structures.
The "Length of Last Word" problem is a fundamental string processing challenge that tests your understanding of string manipulation and edge case handling. Let's explore multiple approaches to solve this problem efficiently.