Dynamic Programming Solution for Maximum Earning Robot

🚀 Day 550 of #750DaysOfCode 🚀 💡 Problem Solved: Maximum Amount of Money Robot Can Earn Today’s problem was a great example of how Dynamic Programming + smart decision-making can turn a complex problem into a structured solution. 🧠 Problem Insight: A robot moves from the top-left to the bottom-right of a grid, collecting coins along the way. Positive values → gain coins 💰 Negative values → lose coins due to robbers 🥷 But here’s the twist: 👉 The robot can neutralize robbers up to 2 times ⚙️ Approach I Used: Instead of just tracking position, I added an extra dimension: Number of neutralizations used (0, 1, or 2) So for every cell, I tracked the maximum coins possible under each scenario. At each step, I had two choices: Take the value (gain or loss) If it’s negative → optionally neutralize (if power remains) This turns the problem into a state-based DP, where each decision impacts future outcomes. 🔥 What Made This Interesting: It’s not just about maximizing sum It’s about when to use limited resources Greedy won’t work — you must think ahead 👉 Sometimes taking a small loss now helps you avoid a bigger loss later. 📈 Complexity: Time: O(n × m) Space: O(n × m × 3) 💬 Key Takeaway: This problem reinforced an important lesson: When constraints are limited (like 2 neutralizations), always consider adding them as a DP state. ✅ Day 550 done — staying consistent and leveling up every day 🚀 #DSA #DynamicProgramming #LeetCode #ProblemSolving #Java #CodingJourney #Consistency #Tech #SoftwareEngineering #750DaysOfCode

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