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

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

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

Steps: 6

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 calls (how many times the function can call itself before reaching a base case) is related to the number of times the list can be divided in half.
Step 5: Understand that the number of times you can divide a list of size n 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 represents the space complexity due to recursion.