Binary Search. Based

Before writing binary search, ask what is monotonic: a sorted array comparison, a rotated-array condition, or a feasibility predicate over possible answers. Choose one interval convention and say it aloud. For a first true predicate, use low and high as inclusive candidates; if predicate(mid) is true, keep mid by setting high to mid, otherwise set low to mid plus one. The invariant is that the first true answer remains in [low, high]. For exact lookup, return when equal and otherwise discard only the half that cannot contain the target. Calculate mid as low plus (high minus low) divided by two to avoid overflow in fixed-width languages. Test empty input, one element, target below or above range, duplicates, and an answer at either endpoint. A standard search performs O(log n) comparisons and uses O(1) space, but binary search on answer is O(log R) feasibility checks where R is the numeric range.