Priority Queue Implementations

Unsorted Array

Like the unsorted array implementation of a dictionary, we can do:

• Insertion in constant time.
• Find-min/max in linear time.
• Delete-min/max can be done in linear time by combining find-minimum and then deleting.

Sorted Array

• Insertion in linear time.
• Find-min/max in constant time.
• Delete-min/max is constant time, as we decrement the number of items n.
  • If this is a min-priority queue, we should sort in reverse order!

Balanced Binary Search Tree

• Insertion is $O(\log n)$ – we traverse the tree to the correct location.
• Find-min/max is $O(\log n)$ – we traverse to either the left-most or right-most node.
• Delete-min/max is also just $O(\log n)$.

Find-min/max can actually be improved to constant time for all 3 data structures if we store a pointer/index to the minimum entry.

• This pointer is updated upon insertion of a new value iff the new value is less than the current minimum.
• In this case, Delete-min/max would become involve delete that minimum element we point to, and then doing a search to restore this canned value. The time complexity of this would just be whatever the time complexity of searching is.

Heap