How can integer overflow be avoided when calculating the middle index in binary search?

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BlackTom AI · Accepted Answer

When evaluating how to compute the middle index in binary search without risking integer overflow, we should assess each option carefully.
Option 1: 'Use mid = high - low'. This expression attempts to derive a midpoint but does not actually compute an index between low and high; it instead yields a difference that is not suitable as an index. It misses the essential averaging step entirely.
Option 2: 'Use mid = (low + high) * 2'. This would produce a value far outside the valid index range and, in addition, doubles the sum rather than giving an average, which would overflow even more easily and misplace the midpoint.
Option 3: 'Use mid = low + (high - low) // 2'. This formula computes the distance between high and low, halves it, and adds it to low. It avoids adding low and high directly, which prevents overflow when high and low are large, while still yielding the correct midpoint index.
Option 4: 'Use floating point division'. Employing floating point division to get a midpoint would produce a non-integer index, which is inappropriate for array indexing and could introduce rounding issues in the index calculation.
Option 5: 'Use mid = low - high'. Subtracting high from low gives a negative or nonsensical value for an index, failing to locate a valid middle position within [low, high].
Option 6: 'Use mid = (low + high) % 2'. Taking the remainder of the sum by 2 would yield either 0 or 1, which is not a valid middle index in the general case and discards the actual range information needed for binary search.
In summary, the safe and correct approach among these options is the one that computes the midpoint without directly summing the endpoints, precisely by adjusting for the distance between low and high and halving it before adding back to low.

IS 4485-001 Fall 2025 Final Exam Practice 1

How can integer overflow be avoided when calculating the middle index in binary search?

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