Final answer:
Index-based lists allow operations such as insertion, deletion, access, search, and update, with time complexities ranging from O(1) for simple access and updates, to O(n) for insertion and deletion that may require shifting elements. The space complexity for these operations is generally O(1).
Step-by-step explanation:
Operations of an Index-Based List
An index based list is a data structure that allows access to elements by their index position. Here are the main operations and their complexity:
Access: Retrieving an element by its index, which has a time complexity of O(1) since direct access is possible. The space complexity is O(1).
Update: Changing the element at a specific index. This operation is O(1) for time complexity since it's a simple substitution. Space complexity remains O(1).
The complexities mentioned are for average or worst-case scenarios, and actual performance can depend on the specific implementation of the index-based list and underlying data structure.