One of the most famous hard problems on LeetCode is Median of Two Sorted Arrays. At first glance, it looks straightforward—you just need the median of two sorted arrays. But the catch is that the required time complexity is O(log(m + n)), which rules out the obvious approach.

The main trick in this problem is realizing that even though the entire array is rotated, one side of the midpoint will always be sorted. Once we identify the sorted side, we can decide whether the target belongs there or not.

Binary search isn’t just for finding an element in a sorted array. One of its most powerful applications is searching for a boundary or turning point. LeetCode 153: Find Minimum in Rotated Sorted Array is a perfect example of this pattern.

Whenever you encounter a problem asking for the minimum or maximum value that satisfies a condition, consider whether the answer space is monotonic. If it is, binary search on the answer is often the optimal approach.

The two-step binary search solves by first finding the row and then searching inside it. The cleanest and most optimal solution is to treat the matrix as a virtual 1D sorted array and run one binary search over it.

Binary Search is one of the most fundamental algorithms every programmer should know. It’s fast, elegant, and appears frequently in coding interviews. Binary Search only works on sorted data.