Priority Queue

In computer science, a priority queue is an abstract data type which is like a regular queue or stack data structure, but where additionally each element has a "priority" associated with it. In a priority queue, an element with high priority is served before an element with low priority. If two elements have the same priority, they are served according to their order in the queue.

• stack — elements are pulled in last-in first-out-order (e.g. a stack of papers)
• queue — elements are pulled in first-in first-out-order (e.g. a line in a cafeteria)

It is a common misconception that a priority queue is a heap. A priority queue is an abstract concept like "a list" or "a map"; just as a list can be implemented with a linked list or an array, a priority queue can be implemented with a heap or a variety of other methods.

A priority queue must at least support the following operations:

• insert_with_priority: add an element to the queue with an associated priority
• pull_highest_priority_element: remove the element from the queue that has the highest priority, and return it (also known as "pop_element(Off)", "get_maximum_element", or "get_front(most)_element"; some conventions consider lower priorities to be higher, so this may also be known as "get_minimum_element", and is often referred to as "get-min" in the literature; the literature also sometimes implement separate "peek_at_highest_priority_element" and "delete_element" functions, which can be combined to produce "pull_highest_priority_element")

More advanced implementations may support more complicated operations, such as pull_lowest_priority_element, inspecting the first few highest- or lowest-priority elements (peeking at the highest priority element can be made O(1) time in nearly all implementations), clearing the queue, clearing subsets of the queue, performing a batch insert, merging two or more queues into one, incrementing priority of any element, etc.