Class 34: Priority Queues

Held: Monday, 1 November 2004

Summary: Today we investigate priority queues, linear structures in which the policy is highest-priority first, which usually translates into smallest first.

Related Pages:

• EBoard.
• Sample Code.

Assignments

• Homework for class 35: List positions.

Notes:

• I will reserve time for questions on the exam at the start of each class this week (except Friday).

Overview:

• Priority queue basics.
• Java Detour: Abstract classes.
• Implementing priorty queues.
• Efficiency.
• Looking ahead: Lists.

Priority queue basics

• Priority queues are the third basic linear structure.
• The policy for priority queues is get returns the highest-priority object.
• How do we determine priority? Typically, we use the smallest or largest element.
  • If the objects in our priority queue are all Comparable, we use the compareTo method associated with those objects.
  • We can also choose a Comparator to use when we create the priority queue.

Java Detour: Abstract classes

• Suppose we make the latter choice (using a Comparator). Presumably, the comparator should be a parameter to the constructor. How do we specify that in the interface?
• We can't!
• However, it doesn't make sense to write just one PriorityQueue class, since there are different implementation.
• The solution: A compromise between interfaces and fully specified classes.
• In Java, this compromise is an abstract class.
• Like regular classes, abstract classes may include fields, constructors, and method definitions.
• Like interfaces, abstract classes may leave some methods declared but undefined.
• Class declarations for abstract classes include the keyword abstract.
• Undefined methods must also include the keyword abstract (unless they are implicitly taken from an interface).

Implementing priorty queues

• Didn't seem to do it: Becking, Conor, Gonnerman, McMillian, O'Neil
• Ahlgren,Miller,Poythress: Use a linked set of nodes, as in LinkedQueue. When inserting, look at each node in turn until you find the correct place.
• Ahlgren,Miller,Poythress: As an array with elements stored in increasing order.
• Billups: Unsure of details.
• Claveria,Poythress: A binary tree.
• Gupta,Namai: Don't change put. When you get an element, search for the smallest.
• Namai: Find some way to use binary search.

Runtime Analysis

• Store in sorted order: O(n) insert, O(1) get.
  • Binary search doesn't help, since it requires an array and we'll need to fill that hole in the array.
• Get searches for smallest: O(1) insert, O(n) get.
• Binary tree: Depends on details. If the tree is perfectly balanced, O(logn) get, O(logn) insert.

Looking ahead: Lists

• What is a list? A collection of values you can iterate.
• What methods might we provide for lists?
  • Create a new list.
  • Get an element of the list (first, last, other?)
  • Insert at a particular position?
  • Delete something from the list (params?)