Heaps vs Priority Queue

Before attempting to understand the difference between a heap and a priority queue, it is important to distinguish between an abstract data type and a data structure. So what is the difference.

Abstract data type (ADT)

In simple terms, an abstract data type (ADT) is a blueprint or idea, while a data structure (DS) is the concrete implementation of that blueprint. Here is a list of how an ADT can be implemented through a data structure:

• Stacks, queues, and heaps are examples of abstract data types. They are simply ideas, or "black boxes," with a defined behavior. To implement them, To implement abstract data types, you must select suitable concrete data structures. And there can be more than one ways to implement an ADT using a DS

Abstract Data Type	Example Data Structure Implementation
Stack	Array, Linked List
Queue	Array, Linked List
Priority Queue	Heap
Set	Hash Table, Binary Search Tree
Map	Hash Table, Binary Search Tree

What is a queue?

Here is an implementation of a queue using lists in Python. This can also be implemented using linked lists:

class Queue:
    def __init__(self):
        self.items = []

    def is_empty(self):
        return self.items == []

    def enqueue(self, item):
        self.items.insert(0, item)

    def dequeue(self):
        return self.items.pop()

    def size(self):
        return len(self.items)

This implementation uses a list to store the items in the queue. The enqueue method adds an item to the end of the list, while the dequeue method removes an item from the front of the list. The is_empty method checks if the queue is empty, and the size method returns the number of items in the queue. Is this implementation of a queue now considered a data structure? Yes, it is, as it goes beyond just being an abstract idea.

What is a priority queue?

A priority queue is a type of queue that removes the entry with the highest priority first, regardless of when it was added, unlike a normal queue that operates on a first-in, first-out basis.

Is it possible to implement a priority queue using a list, similar to how we implemented a basic queue? The answer is yes, but it may not be the most efficient approach. This is because when adding an element, we do not know its priority and we would need to sort the list every time to determine the correct location of that element. Instead, we can use heap data structures to implement a data type that meets the requirements of a priority queue. A heap allows us to retrieve the maximum (or highest priority) element in O(1) time and rearrange itself to give us the updated maximum in log(n) time when a new item and its priority are added.

To understand more about implemetation of heaps go to A heap upclose: Simulating a max heap

Here is an implementation of a priority queue in Python using a heapq module that has a concrete implementation of a heap built into it.

import heapq

class PriorityQueue:
    def __init__(self):
        self._queue = []
        self._index = 0

    def is_empty(self):
        return len(self._queue) == 0

    def put(self, item, priority):
        heapq.heappush(self._queue, (priority, self._index, item))
        self._index += 1

    def get(self):
        if self.is_empty():
            return None
        return heapq.heappop(self._queue)[-1]

This implementation uses the heapq module to maintain a heap-based priority queue. The put method adds an item to the queue with a given priority, and the get method removes and returns the item with the highest priority.

In essence, a priority queue is a concept that can be implemented using the heap data structure. The heapq module provides an implementation of the heap data structure.

A question for clarification?

Is a heap an ADT or a DS? Similar to a PQ, it can be both: in specification, it is an ADT, and in implementation, it is a DS. The ADT definition will usually not change, but the concrete implementation might change considerably depending on how it is implemented. It's like a house with the same function but built using either wood or concrete.

Dedications

Difference between ADT and DS (Stackoverflow)

https://anmolsehgal.medium.com/heap-vs-priority-queues-vs-queues-b03398312c87

https://simplesnippets.tech/what-is-abstract-data-types-in-data-structures-adt/

https://stackoverflow.com/questions/10267084/what-is-adt-abstract-data-type

https://cs.stackexchange.com/questions/6678/what-is-the-difference-between-abstract-and-concrete-data-structures/6687#6687