JAMIA 2025 — Computer PYQ

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Question

JAMIA 2025 — Computer PYQ

JAMIA | Computer | 2025

What is the time complexity of binary search in a sorted array?

Choose the correct answer:

Explanation

Derivation

Let $n$ be the number of elements in the array. In each step, the search space is reduced by half.

Step 1: $n$
Step 2: $\frac{n}{2}$
Step 3: $\frac{n}{4} = \frac{n}{2^2}$
Step $k$ : $\frac{n}{2^k}$

The search ends when the remaining search space is reduced to 1:

\frac{n}{2^k} = 1

n = 2^k

To solve for $k$ (the number of steps), we take the logarithm on both sides:

\log_2(n) = \log_2(2^k)

k = \log_2(n)

2. Time Complexities

Case	Complexity	Description
Best Case	$O(1)$	Target element is the middle element.
Average Case	$O(\log n)$	Target is found after several splits.
Worst Case	$O(\log n)$	Target is at the ends or not in the array.

3. Space Complexity

Iterative: $O(1)$ (constant space).
Recursive: $O(\log n)$ (due to the recursion stack).

Final Answer:

The time complexity of binary search is $O(\log n)$ .