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CUET PG 2026 — DSA PYQ

CUET PG | DSA | 2026

What is the worst-case auxiliary space complexity of a recursive Binary Search implementation on an array of size N?

Choose the correct answer:

Explanation

In a recursive implementation of Binary Search, the algorithm repeatedly divides the search space into half ( $N /2, N /4, N /8, \dots$ ).

Call Stack Space:
- Each recursive call is stored in the function call stack until the base case is reached or the target element is found.
- The maximum depth of the call stack corresponds to the maximum number of times $N$ can be divided by 2 before reaching 1.
- Maximum recursion depth $= ⌊ lo g_{2} N ⌋ + 1$ .
Space Requirement:
- Since each call frame uses $O (1)$ space, a recursion depth of $O (lo g N)$ requires $O (lo g N)$ auxiliary space.

(Note: While iterative Binary Search requires $O (1)$ auxiliary space, recursive Binary Search requires $O (lo g N)$ auxiliary space due to the recursion call stack.)

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