Final answer:
The worst-case time complexity for adding an item to the end of an array-based list is O(1) if space is available. If the array needs to be resized, the complexity becomes O(n), where 'n' is the number of elements in the array.
Step-by-step explanation:
When considering an array-based implementation of a list, the worst-case time complexity of adding an item to the end of the list is typically O(1), meaning it's a constant-time operation. However, this complexity assumes that there is enough space in the array to accommodate the new element without the need for resizing the array.
If the underlying array is full and needs to be resized to accommodate the new item, the time complexity becomes O(n), where 'n' is the number of elements in the array. This is because all elements have to be copied to a new, larger array. This resizing operation is an infrequent cost, so when amortized over a large number of insertions, the average time complexity can still be considered O(1), often referred to as amortized constant time. But strictly speaking, the worst-case time complexity for a single operation when resizing is necessary is indeed O(n).