Which of the following is a potential issue when computing mid = (low + high) // 2 for very large lists?

Question

BlackTom AI · Accepted Answer

To address this question, we first consider what the expression mid = (low + high) // 2 attempts to do: it finds the midpoint between low and high using integer division.

Option 1: Floating point error. Since the calculation uses integers (low and high) and the division is integer division (//), there is no floating point arithmetic involved, so floating point errors are not a concern here. This option is not a potential issue for integer midpoint computation.

Option 2: Syntax error. The expression is syntactically valid in many programming languages (e.g., Python, where // denotes floor division). There is no inherent syntax error in (low + high) // 2, assuming the variables exist and are numbers. This would not be a general issue with the approach.

Option 3: No issues with this approach. In practice, there can be an overflow issue in languages with fixed-size integers when low and high are very large, so stating there are no issues is incorrect.

Option 4: Logic error. The midpoint calculation itself is not a logical error; it correctly yields a midpoint. The logic error would come from overflow or incorrect handling, not from the midpoint formula itself. Hence, this option is not the primary issue described.

Option 5: Integer overflow. This is the classic potential problem: if low and high are large, (low + high) can exceed the maximum representable integer, causing overflow in languages with fixed-size integers. This can lead to incorrect mid values or runtime errors.

Option 6: Division by zero. The division by two is constant (2), so division by zero does not occur in this expression. This would not be a risk here.

In summary, the plausible, concrete issue tied to computing the midpoint with (low + high) // 2 for very large lists is the possibility of integer overflow, while the other options do not describe a real drawback of this specific calculation across common programming contexts.

IS 4485-001 Fall 2025 Final Exam Practice 1

Which of the following is a potential issue when computing mid = (low + high) // 2 for very large lists?

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