Lecture 36: Priority queues; dijkstra’s algorithm

Lecture video

Textbook chapters

9.1; 14.6

Priority Queue ADT

A priority queue is similar to a queue, except that when we remove from it, we remove the highest priority item, not the item that has been in the queue the longest.

We store data in a priority queue as an entry, with fields for data (value v) and priority (key k). Ususally we say that smaller numbers are higher priority.

A priority queue must support the following operations:

• insert(k,v): create an entry with key k and value v
• min(): return (but do not remove) the min entry (k, v) having minimal key k
• removeMin() remove and return the min entry
• size(): return the number of entries
• isEmpty(): return a boolean indicating whether the priority queue is empty

Priority queues can be implemented with heaps (as we’ve seen). They can also be implemented using sorted or unsorted lists as the internal data store.

Dijkstra’s algorithm

Dijkstra’s algorithm is an example of an algorithm that uses a priority queue.

It takes in a graph and finds the shortest path distance from a given node to every other node in the graph.

Additional exercises

• Suppose that you implement a priority queue using an unsorted list as the internal data store. What is the runtime of insert(k,v)? What about min() and removeMin()?
• Same as the above, but suppose you use sorted list (meaning that you have to maintain the sorted list every time an entry is added). What are the runtimes?