Dynamic Programming Solution for Stable Binary Arrays

🚀 Day 185 of #200DaysOfCoding Today I solved a very interesting Dynamic Programming problem: “Find All Possible Stable Binary Arrays”. 🔍 Problem Idea We are given three integers: zero, one, and limit. We need to build binary arrays that: • Contain exactly the given number of 0s and 1s • Do not allow more than limit consecutive 0s or 1s The challenge is to count all possible valid arrays while respecting the constraint on consecutive elements. 💡 Key Learning To solve this efficiently, I used Dynamic Programming with the following idea: Track arrays that end with 0 and arrays that end with 1 Ensure the limit constraint is maintained Subtract invalid states where consecutive elements exceed the allowed limit This approach reduces complexity and handles larger inputs efficiently. ⚙️ Concepts Practiced ✅ Dynamic Programming ✅ State Transition Logic ✅ Handling Constraints on Consecutive Elements ✅ Optimizing DP using mathematical adjustments 📈 What I Learned Today This problem taught me how to carefully design DP states and transitions when additional constraints are involved. It also showed how powerful DP becomes when combined with smart state pruning. Consistency is the key — one step closer to completing the #200DaysOfCoding challenge! 💪 #coding #programming #leetcode #datastructures #algorithms #dynamicprogramming #cpp #learning #softwaredevelopment

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