Which of these Python code snippets correctly computes the middle index in binary search?

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BlackTom AI · Accepted Answer

Question restatement: Which of these Python code snippets correctly computes the middle index in binary search?

Option A: mid = (low + high) % 2
This uses the modulus operator with 2. It does not compute a middle index; it yields either 0 or 1 depending on the parity of the sum. Therefore it cannot be the correct middle index for a binary search.

Option B: mid = (low + high) / 2
Here, the division operator / in Python 3 returns a float when applied to integers. A middle index should be an integer position. Using a float would be invalid for indexing or array access, so this is incorrect unless you explicitly convert to int, which is not shown here.

Option C: mid = (low - high) // 2
This subtracts high from low before dividing, which moves the value away from the actual midpoint. It does not produce the correct middle index and would lead to wrong behavior in the binary search.

Option D: mid = (low * high) // 2
Multiplying low and high before dividing by 2 has no relation to the midpoint between low and high. This expression does not yield the correct middle index in general and is therefore incorrect.

Option E: mid = (high - low) * 2
Subtracting low from high gives a range width, but multiplying by 2 is not related to the middle position and would produce values far from the midpoint. This is not the middle index.

Option F: mid = (low + high) // 2
This expression adds the boundaries and uses floor division to produce an integer. It is the standard, correct way to compute the middle index in binary search in Python, ensuring an integer result that lies between low and high. The // operator guarantees an integer middle index, and in typical binary search implementations this is the desired behavior.

Summary of reasoning:
- Options A, B, C, D, and E fail to produce the correct middle index for the binary search either by using the wrong operation, returning a non-integer, or miscomputing the midpoint.
- Option F correctly computes the midpoint as the integer floor of the average of low and high, which aligns with the common binary search pattern in Python.

IS 4485-001 Fall 2025 Final Exam

Which of these Python code snippets correctly computes the middle index in binary search?

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