Question

Which one of the following is the formula used to calculate the middle index in Binary Search?

• A. \(\frac{low + high}{2}\)
• B. \(low + high\)
• C. \(high - low\)
• D. \(\frac{high-low}{2}\)

Hint:

Modern implementations often use \(low+\frac{high-low}{2}\) to avoid overflow.

Answer 1

The Correct Option is A

Concept: Binary Search repeatedly divides a sorted list into two halves and checks the middle element.

Step 1: Understand Binary Search To locate an element efficiently, Binary Search first finds the middle position of the current search range.

Step 2: Apply middle index formula The middle index is calculated as: \[ mid=\frac{low+high}{2} \] where: \[ low = \text{starting index} \] \[ high = \text{ending index} \] Final Answer: \[ \boxed{\frac{low+high}{2}} \]