8 posts tagged with "dynamic-programming"

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 Minimum Coin Combination problem that reveals why greedy algorithms sometimes fail—and how recognizing overlapping subproblems is the foundation of dynamic programming thinking.

Want to truly understand dynamic programming? This isn't just another tutorial with code solutions. We'll explore why these algorithms work, how they connect to other problems, and when to apply them. By the end, you'll think like a DP expert.

A curated collection of breakthrough moments and essential insights from my algorithm learning journey.

This page highlights the most important revelations and "aha moments" from my learning journey. These are the posts where fundamental concepts finally clicked, where confusion turned into clarity.

A casual conversation between two software engineers about the subtle differences between recursion, memoization, and "real" DP.

The Setup​

It's late afternoon at the office. Alex just finished implementing a memoized solution to Min Cost Climbing Stairs and walks over to Jamie's desk with their laptop.

Alex: Hey Jamie, can I bug you for a second? I'm confused about something with DP.

Jamie: [looks up from code review] Sure, what's up?

Alex: So I wrote this solution for the climbing stairs problem. I started with recursion, then added memoization like everyone says. But now I'm wondering... is this actually DP? Or is it still just recursion?

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.

The Student's Confusion​

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:

A dialogue between an engineer learning DP and a professor clarifying the optimal learning path

The Question​

Engineer: Professor, I've been breaking down how to approach dynamic programming problems, and I want to validate my thinking. Here's my approach:

1. First, I solve the problem using recursion in the worst possible way - not worrying about time or space complexity at all
2. Then, I optimize that recursive solution with memoization, which gives me a top-down DP solution
3. Finally, I convert it to bottom-up DP for an even better solution in terms of both time and space complexity

Am I thinking about this correctly? Or am I missing something critical?