Priority Queue in C++

Priority Queues are found to be similar to stack and regular queue data structures. It is considered an abstract data type. This Priority Queue prioritizes the elements in the queue to execute them based on the importance they carry. The elements with higher priority are executed first, and those with lower priorities are executed at the later stages. Some Priority Queue implementations remain undefined if any two elements are prioritized at the same level. 

In some of the other implementations of the Priority Queue, like trees, if the same priority elements occur, they are executed based on the position they are placed at. Programmers often use heap sort most of the time to implement Priority Queues. There are other data structures like trees, sets, arrays, linked lists, and more through which we can achieve Priority Queue. You can also make use of an unordered array. There are operations like insert, delete, top, empty, which help you with the smoother function of the Priority Queue. 

There is also an operation called peek that allows you to find the highest and lowest priority elements. This operation doesn’t modify the queue and is very frequently utilized by the developers. It also completes its operation in O(1)time which helps the tasks that require excellent performance improve their applications. You can also implement Priority Queue using stack. You will pull out the highest to lowest elements in the queue through the stack based on the priority. You can also clear, merge, or batch insert the elements in the queue with the help of stack data structure. 

Even if you can implement Priority Queue with the help of these data structures, they are still different from it. Stack and queues differ from Priority Queue. Stack and queue are dependent on the ordering of the elements in it whereas, in Priority Queue the more importance is given to the element being added. Hence, it is intrinsic to the ordering of data. All the data structures complement each other and help in better implementation. They have their own importance and should be implemented with the right solution to the problem to get better performances.

The Priority Queue differs from the regular queue. In the regular queue, you will notice it is first-in-first-out where the importance falls on the ordering of the element. The Priority Queue is what values the importance of the element being added. The elements added to the Priority Queue are ordered based on priority. The elements with the highest priority get executed first, and the next highest priority elements fill in, and the process continues until the goal is reached. This mechanism can also be seen as an abstract data type that acts like a container that prioritizes its elements.

Most frequently, we see Heap sort is being used for implementing the Priority Queue. There are many applications of Priority Queue, which include:

• Prim’s Algorithm : Priority Queue is used in Prim’s algorithm to store the nodes’ keys and extract the minimum key node at each step.

• Heapsort : Heapsort is based on heaps which is an implementation of the Priority Queue. 

• Data Compression(Huffman Codes) : Priority Queue can be utilized in Huffman codes. This is used for compressing the data on priority.

• Used in A* Search Algorithm of Artificial Intelligence : A* Search Algorithm is known for finding the shortest path between the two vertices of a graph. It utilizes a priority queue to prioritize the path between the defined vertices and find the shortest path. Priority Queue also allows you to keep track of the unexplored routes.

• Operating Systems : Priority Queue holds an upper hand in the operating system as it helps handle process management, load balancing, interrupt handling, and more. In process management, Priority Queue plays a crucial role in prioritizing processes and executing accordingly.

• Bandwidth Management : Priority Queues come in handy in networking as well. It allows you to prioritize the data packets based on their importance. This enables the network to make sure that these data packets reach their destination quicker.
  
  You can picture Priority Queue as an extension of the regular queue where it holds an extra value called priority, and elements are processed based on their respective priority values. There are three crucial operations that you must be aware of:

• ADD : The add operation in the Priority Queue allows you to add elements to the Priority Queue. 

• REMOVE : The remove operation in the Priority Queue allows you to eliminate the unwanted elements that are added to the queue. 

• PEEK : Peek is one of the most known operations in the Priority Queue, allowing you to get the highest priority element without deleting the node.

Characteristics of the Priority Queue include:

• Every element in the Priority Queue is associated with these elements respectively. 

• In Priority Queue, the element with the highest priority is placed at the top and executed first.

• If any two elements are on the same priority, then these elements are served with First-In-First-Out(FIFO) principle.

There are two types of Priority Queue:

• Max-Priority Queue : The elements with maximum priority are placed at the top, and the elements with the lowest priority are placed at the end of the queue. For example, elements 1,6,4,9 are placed as 9,6,4,1 in the Priority Queue.

• Min-Priority Queue : The elements with the lowest priority are put on the highest priority in the Priority Queue, and the highest priority elements are put at the end of the queue. For example, elements 11,23,42,10 are placed as 10,11,23,42 in the Priority Queue.

You can use Heapsort to implement the Priority Queue. Binary heap, which is also known as a binary tree, is used to implement Priority Queue. One significant rule here is that every node’s value must be greater than the values of its children node. It has the most diminutive possible height as it is a complete tree. You can implement Priority Queue using heapsort in the programming languages like C++, C, Java, and more.   

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