How to determine the time complexity of inserting an element into the middle of a linked list or array-like list?

The time complexity of inserting an element depends on the data structure:

• Linked list: To insert an element in the middle, you first need to traverse the list to the desired position — this takes O(n) time, where n is the number of elements before the insertion point. The actual insertion process (changing pointers) is O(1).

• Array-like list (e.g., Python list): Inserting in the middle requires shifting all subsequent elements to the right to make space, which takes O(n) time. Accessing the index itself is O(1).

Thus, for both structures, inserting in the middle is an operation with a time complexity of O(n), but the reasons differ: in a linked list — searching for the position, in an array — shifting elements.