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Introduction
A Priority Queue is a specialized data structure that efficiently manages elements based on their associated priority levels. Unlike standard queues, where elements are processed in the order they arrive (FIFO), a priority queue ensures that elements with higher precedence are served first, regardless of their insertion sequence. This makes it highly useful in scenarios where tasks or processes must be handled according to their importance rather than their arrival time, such as job scheduling, load balancing, or network routing. In this blog, we'll explore how priority queues work, their key characteristics, and common use cases.
Priority queues are similar to queues. The difference is that the elements do not come out in FIFO (First In, First Out) order. They come out based on their “priority.”
A priority is a value that marks the “importance” of a queue element. In a priority queue, the order of entry is not of much concern; the order of exit is. Each component of the priority queue is dequeued based on its priority. The priority can be of two types, depending on the situation.
Type 1: Lower value, higher priority
Type 2: Higher value, higher priority.
How is Priority Assigned to the Elements in a Priority Queue?
Each element is associated with a priority value in a priority queue that determines its processing order. The priority can be assigned based on various factors such as urgency, importance, or numerical ranking, depending on the specific use case. There are generally two types of priority queues:
Max-Priority Queue: In this type, the element with the highest priority (maximum value) is dequeued first.
Min-Priority Queue: Here, the element with the lowest priority (minimum value) is dequeued first.
Priorities can be assigned dynamically based on factors like processing time, task importance, or predefined rules. For example, in a hospital emergency room system, patients with more critical conditions receive higher priority, ensuring they are attended to before less critical cases.
Operations of a Priority Queue
The priority queue supports several key operations that facilitate its functionality:
Insert (Enqueue): This operation allows for adding a new element to the priority queue along with its priority value. The position of the element is determined by its priority, rather than its insertion order.
Extract-Max / Extract-Min (Dequeue): This operation removes and returns the element with the highest or lowest priority, depending on whether it’s a max-priority or min-priority queue.
Peek: This operation returns the element with the highest or lowest priority without removing it from the queue, allowing you to check the next element to be processed.
Increase / Decrease Key: This allows adjusting the priority of an existing element, either by increasing or decreasing its priority, based on the queue type.
Each of these operations ensures that the elements in the priority queue are processed by their priority, making the data structure optimal for time-sensitive tasks.
Characteristics of a Priority Queue
The following are some characteristics of a priority queue:-
Elements are stored based on their associated priority values.
Highest and lowest priority elements can be accessed in constant time, irrespective of the number of elements present in the queue.
After every insertion or deletion, depending on the underlying Data structure, the queue is reorganized to maintain the order.
Only the highest priority element can be removed from a priority queue. You should use multisets to support removal of intermediary elements.
It can be implemented with binary search tree, binary heap, linked list or array, they all have different advantages and disadvantages.
In the next section you will learn about the different types of priority queues.
Types of Priority Queues
Priority queues are of two types, based on the priority given to the elements depending on their numerical values:-
Ascending Order Priority Queue
In this types of priority queue, numbers with smaller values are given higher priorities, i.e. the smallest element is at front of the queue.
Descending Order Priority Queue
In this types of priority queue, numbers with larger values are given higher priorities, i.e. the largest element is at front of the queue.
In the next section, you will look at the comparison between different implementations of priority queues.
Implementation of Priority Queues
You can implement priority queues in many ways. Implementation using binary search tree, linked list, array, and binary heap tree are most common. Out of these, the most efficient way to implement priority queues is using the heap data structure.
The following image shows the worst-case time complexities of various ways to implement the priority queues.
Analysis of complexities using different implementations
Operation
Using Unsorted Arrays
Using Unsorted Linked List
Using BST
Using Heap
Enqueue
O(1)
O(1)
O(logN)
O(logN)
Dequeue
O(N)
O(N)
O(logN)
O(logN)
What is Heap?
A heap is a specialized tree data structure which is commonly used for implementing priority queues. The nodes are stored in a hierarchical order based on their values. It is usually implemented using an array, and the parent child relationships are maintained by their indices.
There are two types of heaps:
Max Heap
In a max heap, the value of each parent node is greater than or equal to the values of its children. This makes sure that the maximum value is at the root.
Min Heap
In a min heap, the value of each parent node is less than or equal to the values of its children. This makes sure that the minimum value is at the root.
In the next section, you will learn about some applications of priority queues.
Now a question arises, how are priority queues different from normal queues? Let’s find out.
Imagine a scenario where ten people need to exit a room. The people are numbered according to their time of entry as P1, P2, P3 …. P5. That means that P1 entered first and P5 entered last.
If it were a normal queue exit, P1 would have exited first, then P2, P3, and so on. Look at the image that follows to visualize it.
But now, there is a catch. Everyone in the room has different “statuses” or “priorities.” For example, P1 has priority 3, and P5 has priority 1. That means that P5 is of higher importance than P1. In this case, P5 will exit the room first (provided the priorities are in increasing order and lower values have more preference). The following image can help you visualize it better.
Applications of Priority Queue
The following are some applications of the priority queues.
In Dijkstra’s algorithm, stores the graph in an adjacency list to use a priority queue.
In Prim’s Algorithm, uses a priority queue to store the keys of nodes.
In Artificial Intelligence, uses a priority queue to implement the A* search algorithm.
In Data compression, it uses a priority queue in Huffman Encoding to implement the min-heap.
In Operating Systems, use priority queues in the load-balancing algorithms.
In bandwidth management, Priority queues are used to prioritize important data packets.
In Dijkstra’s algorithm We all know that if we want to find the minimum cost path from a source to a destination vertex, we use Dijkstra’s Algorithm. In the efficient approach of Dijkstra’s Algorithm, we store the graph in an adjacency list. We then use a priority queue to extract the minimum path. To learn more about this approach, go to Dijkstra's Algorithm.
In Prim’s Algorithm In the case of Prim’s Algorithm, we use a priority queue to store the keys of nodes. Then we extract minimum key nodes at every step.
In Artificial Intelligence We use a priority queue to implement the A* search algorithm. The A* search algorithm first attempts the most promising routes to discover the shortest path between two vertices in a weighted graph. This type of queue ( also known as the fringe in the A* algorithm) keeps track of the unexplored routes. The one with the shortest lower bound on the total path length receives the most priority.
In data compression We use a priority queue in Huffman Encoding to implement the min-heap. Huffman Encoding is one of the famous data compression techniques used in compression formats like PKZIP and GZIP.
In Operating Systems We use priority queues in the load balancing algorithms. It maintains the flow of operations. Good load-balancing algorithms ensure a smoother flow. They optimize the response time in various computations. Interrupt handling also uses priority queues. The interrupts that have more priority are handled first.
In bandwidth management Priority queues are used to prioritize essential data packets. The network can ensure that such packets reach their destination as soon as feasible.
Advantages of Priority Queue
Efficient Task Management: Priority queues ensure that high-priority tasks are completed first, which is crucial in time-sensitive applications like job scheduling or real-time systems.
Flexible Prioritization: They allow dynamic reassignment of priority values, making them adaptable to changing conditions or requirements.
Optimal for Dijkstra's Algorithm: Priority queues are commonly used in graph algorithms, such as Dijkstra's shortest path algorithm, due to their ability to efficiently handle edge relaxation.
Real-time Processing: In scenarios like interrupt handling in operating systems, a priority queue enables immediate attention to critical tasks, ensuring smoother operation.
Supports Both Max and Min Priority: Priority queues can be configured as either max or min priority queues, offering flexibility based on the type of application.
Disadvantages of Priority Queue
No Direct Sorting: While priority queues process elements based on priority, they do not inherently maintain a sorted list of elements, making them unsuitable for applications requiring full element ordering.
Insertion Overhead: Depending on the implementation (e.g., using a heap), inserting elements may require reordering the data structure, which can result in performance overhead for large datasets.
Limited Access to Elements: In a priority queue, only the highest or lowest priority element can be accessed directly, restricting random access to other elements within the queue.
Complex Implementation: Efficient priority queues, especially those implemented using heaps or other advanced data structures, can be complex to implement and maintain compared to simpler queue structures.
Not Always Optimal for Real-Time Systems: In certain real-time systems, the need to reorder elements with changing priorities may lead to delays, which can impact system performance.
What is the difference between priority queue and dequeue?
A priority queue processes elements based on their priority, serving the highest or lowest priority first, while a dequeue (double-ended queue) allows insertion and removal from both ends, but without any prioritization of elements based on their importance.
Why is priority queue better?
A priority queue is better for scenarios where task importance or urgency matters, as it ensures higher-priority elements are processed first. This makes it ideal for scheduling, resource allocation, and real-time system management, where timing and priority are critical.
What is priority queue pattern?
The priority queue pattern is a design pattern where elements are managed in a queue-like structure but are processed based on priority. Tasks with higher precedence are dequeued and handled before lower-priority tasks, ensuring efficient prioritization of processes or events.
Conclusion
In this article, we discussed the priority queue in Data structure. The priority queue is a powerful and versatile data structure that plays a crucial role in managing tasks based on priority rather than arrival order. Its ability to efficiently handle processes where urgency or importance matters makes it ideal for numerous applications, including task scheduling, network routing, and real-time system management.
You can refer to these articles to learn more about the priority queues.