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.
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.
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 Lowest Common Ancestor problem that reveals one of the most elegant patterns in tree recursion—using return values to communicate information upward through the call stack.
A conversation about solving the Minimum Coin Combination problem that reveals why greedy algorithms sometimes fail—and how recognizing overlapping subproblems is the foundation of dynamic programming thinking.
A conversation about solving the LRU Cache problem that reveals one of the most elegant hybrid data structure designs—and why sometimes the "crazy" idea of combining two data structures is actually brilliant.
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 conversation about solving the Subarray Sum Equals K problem that reveals how cumulative sums and hashmaps create an elegant O(n) solution—and why we need that mysterious map.put(0, 1) initialization.
I just made a commit, so why does VS Code still show that asterisk (*) on my branch name? A debugging journey through Git's "deleted" file status and what to do about it.
A conversation between two engineers about the Range Sum Query problem that reveals why some algorithmic techniques exist—and when they actually matter.
Frontend Dev: "I just finished working on my frontend branch and want to merge it into main. Someone told me to use rebase, but when I ran git rebase main, it said 'Current branch frontend is up to date.' What does that mean? Should I use merge instead?"
Git Mentor: "Ah, this is one of the most confusing topics in Git! Let me show you the difference between fast-forward merge and rebase, and when to use each one. Your 'up to date' message actually tells us something important!"