If the binary search algorithm is implemented recursively, what is the space com
Practice Questions
Q1
If the binary search algorithm is implemented recursively, what is the space complexity due to recursion?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
If the 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 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.
Space Complexity – Space complexity refers to the amount of memory space required by an algorithm as a function of the input size.
Recursive Algorithms – Recursive algorithms call themselves with a subset of the original problem, which can lead to additional space usage on the call stack.
Binary Search – Binary search is an efficient algorithm for finding an item from a sorted list of items, which divides the search interval in half repeatedly.
