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Master binary search in Java with a clear, one-shot explanation that covers intuition, implementation, and pitfalls: understand that binary search works on sorted arrays by repeatedly halving the search space using two pointers and a mid index, ensuring O(log n) time complexity; implement iteratively to avoid stack overhead, compute mid as low + (high - low) / 2 to prevent overflow, and handle duplicates with lower_bound and upper_bound style variants to find first or last occurrence; extend the pattern to solve problems like finding insertion index, peak in mountain array, square root floor, or capacity minimization via predicate checks; always validate boundaries carefully, maintain loop invariants (search space inclusive or exclusive), and test edge cases like empty arrays, single elements, all-equal values, and targets outside range to build bug-free, interview-ready solutions.
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