Question

For an array-based list, for which of these operations is the worst-case running time different than the average case running time:

A. Retrieving the first item of the list.
B. Retrieving the last item of the list.
C. Adding an item to the beginning of the list.
D. Adding an item to the end of the list.
E. None of the above.

Answer 1

Adding an item to the beginning of an array-based list has a different worst-case time complexity (O(n)) compared to the constant time complexity (O(1)) of retrieving the first or last item or adding an item to the end of the list.

Step-by-step explanation:

Among the options provided for operations on an array-based list, the worst-case running time is different than the average case running time for the operation of adding an item to the beginning of the list (option C). When adding an item to the beginning of the list, we encounter the worst-case scenario because every element in the array must be shifted one position to make room for the new element, resulting in O(n) time complexity. On the other hand, retrieving the first item (A), the last item (B), or adding an item to the end of the list (D) typically have constant time complexity, O(1), assuming that we do not exceed the capacity of the underlying array and thus do not need to resize it, which is otherwise an infrequent operation.