What is the space complexity of the binary search algorithm?
Practice Questions
Q1
What is the space complexity of the binary search algorithm?
O(n)
O(log n)
O(1)
O(n log n)
Questions & Step-by-Step Solutions
What is the space complexity of the binary search algorithm?
Step 1: Understand what space complexity means. Space complexity measures how much memory an algorithm uses as the input size grows.
Step 2: Know that binary search is an algorithm used to find an item in a sorted list by repeatedly dividing the search interval in half.
Step 3: Recognize that binary search can be implemented in two ways: iteratively (using loops) and recursively (using function calls).
Step 4: For the iterative implementation, binary search only uses a few variables to keep track of the current position and the search boundaries. This means it uses a constant amount of space, regardless of the size of the input list.
Step 5: Therefore, the space complexity for the iterative version of binary search is O(1), which means it uses constant space.
Step 6: If binary search is implemented recursively, it uses additional space for each function call on the call stack, leading to a space complexity of O(log n), where n is the number of elements in the list.
Step 7: Conclude that the space complexity of binary search is O(1) for the iterative version.
