"LeetCode #1611: Minimum Bit Operations to Zero"

🚀 LeetCode #1611 – Minimum One Bit Operations to Make Integers Zero Today, I tackled one of the more fascinating bit-manipulation problems on LeetCode — "Minimum One Bit Operations to Make Integers Zero". 🧩 Problem Overview Given an integer n, you must transform it into 0 using two operations: Flip the rightmost (0th) bit. Flip the ith bit if the (i−1)th bit is 1 and all lower bits are 0. The goal is to find the minimum number of operations required. The challenge is to transform an integer n into 0 using specific bit operations that flip bits based on certain constraints. At first glance, it seems like a complex recursive search problem, but the key insight lies in recognizing the pattern of Gray codes. 🔍 Key Insight: The problem follows the structure of reflected Gray code transformations. By analyzing how bits flip in the Gray code sequence, we can derive a recursive relationship that efficiently computes the minimum operations. 💡 Recursive Relation: If f(n) is the minimum number of operations for integer n: f(0) = 0 f(n) = (1 << (k + 1)) - 1 - f(n ^ (1 << k)) where k is the position of the most significant bit (MSB) in n. 🧠 Example Walkthrough n = 3 → binary 11 → result = 2 n = 6 → binary 110 → result = 4 ⚙️ Complexity Time: O(log n) Space: O(log n) (due to recursion depth) 🧩 Takeaway This problem was a great reminder that: Many bit-manipulation problems have elegant recursive or mathematical patterns hidden beneath them. Recognizing symmetry and recursion in binary transformations often leads to O(log n) solutions. #LeetCode #Python #BitManipulation #GrayCode #Algorithms #DataScience

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