Binary Search Explained: How Halving a Sorted Array Cuts Search Time to O(log N)

A software developer shares how understanding the core logic behind binary search transformed it from a dreaded interview topic into a reliable problem-solving tool. The key insight is that a sorted array allows each comparison to eliminate half the remaining search space, reducing runtime to O(log N) rather than O(N). The technique extends beyond simple equality checks to any monotonic predicate — a condition that flips from false to true exactly once across the dataset. A classic interview application is finding the first bad software version in a sequence, where binary search minimizes costly API calls by narrowing the search window with each step. Common implementation pitfalls include integer overflow when computing the midpoint and failing to handle the final index when searching for an exact match.