The addAfter operation of an unordered list collection is A. O(log n) B. O(n) C. a higher order than O(n log n) D. O(n log n) E. O(1)

To determine the time complexity of the addAfter operation in an unordered list collection, we can analyze the nature of the operation in relation to the data structure used.

1. ### Break Down the Problem

• The operation addAfter typically involves finding a specified node in the list and adding a new node directly after it.
• In an unordered list, the nodes are not sorted, and we might have to traverse the list to locate the desired node.

2. ### Relevant Concepts

• In an unordered list (like a linked list or an array), finding a specific element can take up to $O(n)$ time in the worst case because we may have to check every element.
• Once the position to insert is found, inserting an element can be done in constant time $O(1)$ if we have a reference to the node and just update pointers or indices.

3. ### Analysis and Detail

• The search for the node where we want to add the new element takes $O(n)$ in the worst case.
• The insertion operation itself once the position is found takes $O(1)$.

Thus, the total time complexity for the addAfter operation in an unordered list collection is dominated by the searching part: $T(n) = O(n) + O(1) = O(n)$

4. ### Verify and Summarize

Given that searching is the most time-consuming part of the addAfter operation in an unordered list, and insertion is constant time, we conclude that the overall time complexity is $O(n)$.

Final Answer

The time complexity of the addAfter operation in an unordered list collection is B. O(n).