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