Binary Search Mid Calculation Overflow

I use left plus the quantity right minus left divided by two instead of left plus right divided by two because the simpler version can overflow. In Java an int is a 32-bit signed value, so it maxes out around two point one billion. If left and right are both large, and that really happens when you binary search an answer space that can go up to about two billion rather than just a small array, then adding them together produces a sum bigger than the maximum an int can hold. The dangerous part is that Java doesn't throw an exception when this happens. It silently wraps around to a negative number, so your middle index becomes negative and the search either crashes with an out-of-bounds access or quietly returns the wrong answer. The safe formula avoids ever forming that oversized sum. Right minus left is just the size of the current range, which is always smaller than either endpoint, so it can't overflow. I halve that gap and add it back to left, and the result is exactly the same midpoint, just computed in a way that stays within bounds. What I'd emphasize in an interview is that this costs nothing. It's the same number of operations, so there's no reason not to write it the safe way every time. It signals that I think about edge cases and that I know integer overflow in Java is silent rather than something the runtime will catch for me. It's a one-line habit that prevents a rare but genuinely hard-to-debug failure in production code that handles large ranges.