The DP Mistake Most Developers Make

The DP Mistake Most Developers Make Most developers approach Dynamic Programming by tracking only the maximum value . It feels natural. But in some problems… that approach fails. 🧩 The Problem I was solving: 👉 Maximum Non-Negative Product in a Matrix You start from (0,0) and can move only right or down. The goal is to find the path with the maximum non-negative product . At first glance, it seems simple: Just track the maximum product path. That’s exactly what I did. And it didn’t work. ❌ Why Tracking Only Max Fails The issue comes from negative numbers . Because: Negative × Negative = Positive This changes everything. A path that has a very small (negative) value now can become the maximum later. So if you only track the maximum… you lose important information. 💡 The Key Insight To solve this problem, you must track both : ✅ Maximum product ✅ Minimum product Why? Because: min × negative → max max × negative → min This is the core idea. ⚙️ Approach Use Dynamic Programming. At each cell