Question: If a binary search algorithm is implemented recursively, what is the space complexity?
Options:
O(1)
O(log n)
O(n)
O(n log n)
Correct Answer: O(log n)
Solution:
The space complexity is O(log n) due to the recursive call stack.
If a binary search algorithm is implemented recursively, what is the space compl
Practice Questions
Q1
If a binary search algorithm is implemented recursively, what is the space complexity?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
If a binary search algorithm is implemented recursively, what is the space complexity?
Step 1: Understand what binary search is. It is an algorithm used to find an item in a sorted list by repeatedly dividing the search interval in half.
Step 2: Recognize that a recursive implementation of binary search means the function calls itself to search in the left or right half of the list.
Step 3: Each time the function calls itself, it adds a new layer to the call stack, which is a structure that keeps track of function calls.
Step 4: The maximum depth of the call stack in a binary search occurs when the search space is halved each time, which happens log(n) times, where n is the number of elements in the list.
Step 5: Therefore, the space used by the call stack is proportional to the maximum depth, which is O(log n).
Step 6: Conclude that the space complexity of a recursive binary search algorithm is O(log n) because of the recursive call stack.
Binary Search Algorithm – A search algorithm that finds the position of a target value within a sorted array by repeatedly dividing the search interval in half.
Recursion – A programming technique where a function calls itself to solve smaller instances of the same problem.
Space Complexity – A measure of the amount of working storage an algorithm needs.
Call Stack – A stack data structure that stores information about the active subroutines of a computer program.
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