𝐁𝐢𝐧𝐚𝐫𝐲 𝐒𝐞𝐚𝐫𝐜𝐡 — 𝐌𝐨𝐫𝐞 𝐓𝐡𝐚𝐧 𝐉𝐮𝐬𝐭 𝐌𝐢𝐝𝐝𝐥𝐞 𝐈𝐧𝐝𝐞𝐱𝐞𝐬 When I first began exploring Binary Search, I thought it was a simple algorithm — find the middle, adjust 𝘭𝘰𝘸 and 𝘩𝘪𝘨𝘩, and repeat until done. But as I started solving more problems, I realized something deeper: 𝐁𝐢𝐧𝐚𝐫𝐲 𝐒𝐞𝐚𝐫𝐜𝐡 𝐢𝐬𝐧’𝐭 𝐣𝐮𝐬𝐭 𝐚𝐧 𝐚𝐥𝐠𝐨𝐫𝐢𝐭𝐡𝐦 — 𝐢𝐭’𝐬 𝐚 𝐦𝐢𝐧𝐝𝐬𝐞𝐭. It teaches how to 𝐧𝐚𝐫𝐫𝐨𝐰 𝐮𝐧𝐜𝐞𝐫𝐭𝐚𝐢𝐧𝐭𝐲, 𝐚𝐧𝐚𝐥𝐲𝐳𝐞 𝐛𝐨𝐮𝐧𝐝𝐚𝐫𝐢𝐞𝐬, 𝐚𝐧𝐝 𝐭𝐡𝐢𝐧𝐤 𝐢𝐧 𝐡𝐚𝐥𝐯𝐞𝐬 rather than wholes. Over the last few weeks, I explored several patterns of Binary Search — each bringing its own twist, confusion, and “aha!” moment: 1. 𝐂𝐥𝐚𝐬𝐬𝐢𝐜 𝐁𝐢𝐧𝐚𝐫𝐲 𝐒𝐞𝐚𝐫𝐜𝐡: Finding a target in a sorted array — the purest form. This pattern builds the base for all other variations. 2. 𝐁𝐢𝐧𝐚𝐫𝐲 𝐒𝐞𝐚𝐫𝐜𝐡 𝐨𝐧 𝐀𝐧𝐬𝐰𝐞𝐫: Used when the array isn’t sorted, but the 𝐚𝐧𝐬𝐰𝐞𝐫 𝐫𝐚𝐧𝐠𝐞 𝐢𝐬. Problems like “Capacity to ship packages in D days” or “Find smallest divisor under a threshold” don’t need sorted data — they need a 𝘴𝘦𝘢𝘳𝘤𝘩 𝘰𝘷𝘦𝘳 𝘭𝘰𝘨𝘪𝘤, not over array elements. It reshaped how I think about optimization and feasibility checks. 3. 𝐁𝐨𝐮𝐧𝐝𝐚𝐫𝐲 𝐏𝐫𝐨𝐛𝐥𝐞𝐦𝐬: Finding the 𝐟𝐢𝐫𝐬𝐭 or 𝐥𝐚𝐬𝐭 occurrence of an element. This looks simple until you realize how mid condition placement and < vs <= make or break your logic. These taught me precision, patience, and how to control loop boundaries. 4. 𝐏𝐞𝐚𝐤 / 𝐏𝐢𝐯𝐨𝐭 𝐏𝐫𝐨𝐛𝐥𝐞𝐦𝐬: Like searching in a rotated array or mountain array — here, you don’t just look for a number, you look for the point where direction changes. These problems strengthen your 𝐩𝐚𝐭𝐭𝐞𝐫𝐧 𝐫𝐞𝐜𝐨𝐠𝐧𝐢𝐭𝐢𝐨𝐧 and push you to visualize array behavior beyond indexes. 5. 𝐁𝐢𝐧𝐚𝐫𝐲 𝐒𝐞𝐚𝐫𝐜𝐡 𝐁𝐞𝐲𝐨𝐧𝐝 1𝐃: Even in 2D arrays, infinite arrays, or implicit search spaces — Binary Search appears again and again. It reminded me that 𝐬𝐞𝐚𝐫𝐜𝐡 𝐬𝐩𝐚𝐜𝐞 𝐢𝐬 𝐧𝐨𝐭 𝐚𝐥𝐰𝐚𝐲𝐬 𝐯𝐢𝐬𝐢𝐛𝐥𝐞, sometimes you just define it logically. Each of these problems deepened my understanding — not only of algorithms but of how analytical thinking evolves through practice. Every wrong mid-point, every off-by-one mistake, and every successful dry-run became a small teacher — guiding me toward clarity. This phase of my DSA journey reaffirmed something simple yet powerful: 𝐁𝐢𝐧𝐚𝐫𝐲 𝐒𝐞𝐚𝐫𝐜𝐡 𝐝𝐨𝐞𝐬𝐧’𝐭 𝐣𝐮𝐬𝐭 𝐟𝐢𝐧𝐝 𝐚𝐧𝐬𝐰𝐞𝐫𝐬, 𝐢𝐭 𝐡𝐚𝐥𝐯𝐞𝐬 𝐜𝐨𝐧𝐟𝐮𝐬𝐢𝐨𝐧.