PriorityQueue Implementation
Contrast the efficiency of alternative implementation approaches.
Suppose we want to implement the operations of PriorityQueue using a linked list or an array-based implementation.
Exercise Provide an example of core operations, for each underlying data structure, where the operation cannot be implemented better than $\Omicron(n)$.
Hint: We have, generally, two choices: keeping the underlying data ordered (sorted) or not.
Solution
Keeping the underlying data sorted will enable us to perform remove and best in constant time. However, the insert will be $\Omicron(n)$ since an array implementation will require shifting elements around. Even a linked list implementation will require a linear search to find where to insert.
Keeping the underlying data unordered (unsorted) will require us to perform a linear search for finding/removing the best (whether we use an array or a linked list implementation).