LeetCode 1404: Number of Steps to Reduce Binary Number

🚀 #LeetCode 1404 — Number of Steps to Reduce a Number in Binary Representation to One | #Day150 of #365DaysOfCode Today’s problem looked innocent… until constraints said binary string length up to 500. That’s where brute force officially gets laid off from the company payroll. 🧠 Core Insight You are not allowed to convert the binary string into an integer. Why? Because the value can exceed 2^500 → way beyond long, BigInteger becomes slow, and simulation becomes the real game. This problem is actually about carry propagation, not arithmetic. ❌ Naive Thinking (What most people do) Convert binary → decimal Repeatedly divide by 2 / add 1 Count steps This fails: Overflow Time complexity explosion Wrong abstraction 🧩 Correct Model Operate directly on bits. Rules: Even → divide by 2 → shift right Odd → add 1 → causes carry chain So we simulate the effect of operations, not the number. ⚡ Optimal Greedy Approach (O(n)) We track a carry. For each bit from right to left: BitCarrySteps001102012111 Final answer = steps + carry 💻 Java Solution class Solution { public int numSteps(String s) { int steps = 0; int carry = 0; for(int i = s.length()-1; i > 0; i--) { int bit = s.charAt(i) - '0'; if(bit + carry == 1){ steps += 2; carry = 1; } else { steps += 1; } } return steps + carry; } } ⏱ Complexity Time: O(n) Space: O(1) 📊 Result Runtime: 0 ms (100%) Memory: 42.55 MB (93.81%) 🎯 Takeaway When constraints grow → switch from value thinking to representation thinking. You’re not solving math. You’re simulating hardware logic. #leetcode #leetcode1404 #dsa #algorithms #datastructures #coding #codinginterview #programming #softwareengineering #bitmanipulation #greedy #computerscience #competitiveprogramming #interviewprep #faang #faangprep #tech #developer #codinglife #100daysofcode #java #python #problemSolving #career #learning #students #engineering #placementpreparation #techcommunity #codingjourney #developerlife

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