If a binary search algorithm is implemented recursively, what is the space compl

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Question: If a binary search algorithm is implemented recursively, what is the space complexity due to recursion?

Options:

Correct Answer: O(log n)

Solution:

The space complexity of a recursive binary search is O(log n) due to the call stack used for recursion.

If a binary search algorithm is implemented recursively, what is the space complexity due to recursion?

If a binary search algorithm is implemented recursively, what is the space complexity due to recursion?

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: Know that 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: Realize that the maximum depth of these recursive calls is related to how many times you can divide the list in half until you reach a single element.
Step 5: Understand that the number of times you can divide n elements in half is log base 2 of n, which is written as log(n).
Step 6: Conclude that the space used by the call stack for these recursive calls is O(log n), which is the space complexity of the recursive binary search.

Space Complexity – The amount of memory space required by an algorithm as a function of the input size.
Recursion – A programming technique where a function calls itself to solve smaller instances of the same problem.
Binary Search – An efficient algorithm for finding an item from a sorted list of items by repeatedly dividing the search interval in half.
Call Stack – A stack data structure that stores information about the active subroutines of a computer program.