If a binary search algorithm is implemented recursively, what is its space compl
Practice Questions
Q1
If a binary search algorithm is implemented recursively, what is its space complexity due to recursion?
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 its space complexity due to recursion?
Step 1: Understand what binary search is. It is an algorithm that finds the position of a target value within a sorted array 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 array.
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 these recursive calls is determined by how many times we can divide the array in half until we reach a single element. This is logarithmic in relation to the size of the array.
Step 5: Therefore, the maximum number of recursive calls (or the height of the call stack) is log base 2 of n, where n is the number of elements in the array.
Step 6: Since each call takes up space in the call stack, the total space used by the recursive calls is O(log n).
Space Complexity – The amount of memory required by an algorithm in relation to the input size, particularly focusing on the additional space used by the call stack in recursive functions.
Binary Search Algorithm – An efficient algorithm for finding an item from a sorted list of items, which works by repeatedly dividing the search interval in half.
Recursion – A programming technique where a function calls itself in order to solve a problem, often leading to increased space usage due to the call stack.
