If a binary search is performed on a sorted array of size n, what is the space c

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Question: If a binary search is performed on a sorted array of size n, what is the space complexity?

Options:

Correct Answer: O(1)

Solution:

The space complexity of binary search is O(1) when implemented iteratively, as it uses a constant amount of space.

If a binary search is performed on a sorted array of size n, what is the space complexity?

If a binary search is performed on a sorted array of size n, what is the space complexity?

Step 1: Understand what binary search is. It is a method to find an element in a sorted array by repeatedly dividing the search interval in half.
Step 2: Know that binary search can be implemented in two ways: iteratively (using loops) and recursively (using function calls).
Step 3: Focus on the iterative implementation first. In this method, you only need a few variables to keep track of the current position, the start, and the end of the search interval.
Step 4: Since the number of variables used does not change with the size of the array (n), the space used is constant.
Step 5: Therefore, the space complexity for the iterative binary search is O(1), meaning it uses a constant amount of space regardless of the size of the array.
Step 6: Now, consider the recursive implementation. Each recursive call adds a new layer to the call stack, which can use more space depending on the depth of the recursion.
Step 7: In the worst case, the depth of recursion can go up to log(n), which means the space complexity for the recursive version is O(log n).
Step 8: Conclude that the space complexity of binary search is O(1) for the iterative version and O(log n) for the recursive version.

Space Complexity – Space complexity measures the amount of working storage an algorithm needs.
Binary Search – Binary search is an efficient algorithm for finding an item from a sorted list of items.
Iterative vs Recursive Implementation – The space complexity can differ based on whether the binary search is implemented iteratively or recursively.