LeetCode 3666: Minimum Operations to Equalize Binary String

🚀 Day 517 of #750DaysOfCode 🔥 LeetCode 3666 – Minimum Operations to Equalize Binary String (Hard) Today’s problem was a parity + math-based greedy optimization challenge that looks simple at first glance but requires deep observation. 🧠 Problem Summary You are given: A binary string s An integer k In one operation, you must flip exactly k different indices. Goal: Make the entire string equal to '1' using the minimum number of operations. If impossible → return -1. 💡 Key Observations 1️⃣ Let zero = number of '0' in the string. 2️⃣ Each operation flips exactly k bits. 3️⃣ Flipping changes parity (even/odd behavior becomes important). 4️⃣ We must carefully handle: When k == length When parity of k and number of zeros mismatch When operations must be even or odd This becomes a mathematical bound + parity correction problem, not a brute-force simulation. 🛠️ Approach Used Count total zeros. Handle edge cases: If no zeros → answer = 0 If len == k → only one full flip possible Compute minimum operations for: Odd number of operations Even number of operations Adjust based on parity constraints. Return minimum valid answer. Time Complexity: O(n) Space Complexity: O(1) 🎯 What I Learned ✔️ Hard problems often reduce to mathematical constraints ✔️ Parity (even/odd) reasoning is powerful in bit-flip problems ✔️ Always check feasibility conditions before optimizing ✔️ Avoid brute force when constraints go up to 10⁵ This problem really tested logical thinking beyond implementation. On to Day 518 🚀 #LeetCode #Java #DataStructures #Algorithms #ProblemSolving #HardProblems #CodingJourney #750DaysOfCode

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