We all know classic binary search:
 Sorted array → divide → conquer → find the target.
 But what if the array isn’t sorted?
 Or worse—what if we’re not even searching for an index, but an answer?
 That’s where Modified Binary Search comes in 💡
✅ Classic Binary Search
▫️ Works on sorted arrays
▫️ Finds exact index of target
▫️ Time complexity: O(log N)
while (low <= high) {
 int mid = low + (high - low) / 2;
 if (nums[mid] == target) return mid;
 else if (nums[mid] < target) low = mid + 1;
 else high = mid - 1;
}
⚡ Modified Binary Search
▫️ No sorted array required
▫️ Search happens in the answer space
▫️ Used in problems like:
 🔹 Min/max capacity
 🔹Kth smallest/largest
 🔹Optimal time, distance, or cost
Think:
 🧠 “What’s the smallest value that satisfies the condition?”
 That’s binary search on the answer range.
*💡 Spot the Pattern *
 If the problem says:
 ➡️ “Find the minimum…”
 ➡️ “What’s the max capacity…”
 ➡️ “Can we do this in X time…”
You’re in modified binary search territory.
Binary search isn’t just a search—it’s a strategy.
 Master both flavors, and you’ll unlock a whole new level of algorithmic thinking.
 


 
    
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