explain why linear search and binary search space complexity is O(1)
Actually, the space complexity of both linear search and binary search is not O(1), but rather O(n) and O(log n) respectively.
Linear search is a basic search algorithm that checks each element in a list until it finds the target value or reaches the end of the list. The space complexity of linear search is O(1) for the algorithm itself because it does not require any additional space. However, the space complexity of linear search overall is O(n), where n is the size of the list, because the list itself takes up memory space.
On the other hand, binary search is a more efficient search algorithm that works on a sorted list by repeatedly dividing the list in half and discarding the half where the target value cannot be present. The space complexity of binary search is O(1) for the algorithm itself because it only requires a few variables to keep track of the search range. However, the space complexity of binary search overall is O(log n), where n is the size of the list, because its recursion depth corresponds to the number of times the list can be halved.
To summarize:
- Linear search has a space complexity of O(1) for the algorithm itself and O(n) overall due to the space required for the list.
- Binary search has a space complexity of O(1) for the algorithm itself and O(log n) overall due to the recursion depth.