A priority queue is an abstract data type that operates similar to a regular queue or stack data structure, but with an added feature: each element has a “priority” associated with it. In a priority queue, elements with higher priority are served before elements with lower priority. If two elements have the same priority, they are served according to their order in the queue (typically FIFO order).
All the basic operations of a queue can be applied to a priority queue, but with additional constraints to maintain the priority property. The common operations include:
- Remove (or Dequeue): Removes and returns the element with the highest priority from the priority queue. If multiple elements have the same highest priority, the one that was added first is removed.
- Insert (or Enqueue), top, isEmpty: These operations function the same way as in a regular queue.
A priority stack is not a commonly used data structure because the concept of priority conflicts with the fundamental behaviour of a stack, which is Last In First Out (LIFO). In a stack, the most recently added element is always the first one to be removed, regardless of its priority. Introducing priority into a stack would undermine this core principle, making it less useful and harder to understand.
The elements stored in a priority queue must be comparable.
Priority queues are particularly useful for solving problems that need to quickly access the highest (or lowest) priority element. Some common use cases include:
- Task scheduling: Managing tasks in a way that high-priority tasks are executed before low-priority ones.
- Dijkstra’s algorithm: Finding the shortest path in a graph by always expanding the least costly node.
- Huffman coding: Building optimal prefix codes for data compression by repeatedly merging the least frequent elements.
- Event simulation: Managing events in a simulation where events with higher priority (e.g., earlier timestamps) need to be processed first.