Introduction to Priority Queue

A priority queue is a type of queue where each element is associated with a priority value, and elements are served based on their priority rather than their insertion order.

• Elements with higher priority are retrieved or removed before those with lower priority.
• When a new item is added, it is inserted according to its priority.

The binary heap is the most common implementation of a priority queue:

• A min-heap allows quick access to the element with the smallest value.
• A max-heap allows quick access to the element with the largest value.
• Binary heaps are complete binary trees, making them easy to implement using arrays.
• Using arrays provides cache-friendly memory access, improving performance.

Priority queues are widely used in algorithms such as Dijkstra’s shortest path algorithm, Prim’s minimum spanning tree algorithm, and Huffman coding for data compression.

Types of Priority Queue

• Min-Heap: In this queue, elements with lower values have higher priority. For example, with elements 4, 6, 8, 9, and 10, 4 will be dequeued first since it has the smallest value, and the dequeue operation will return 4.
• Max-Heap: Elements with higher values have higher priority. The root of the heap is the highest element, and it is dequeued first. The queue adjusts by maintaining the heap property after each insertion or deletion.

Array Representation of Binary Heap:

Since the heap is maintained in the form of a complete binary tree, so it can be represented in the form of an array. To keep the tree complete and shallow, while inserting a new element insert it in the leftmost vacant position in the last level i.e., at the end of our array. Similarly, while extracting maximum replace the root with the last leaf at the last level i.e., the last element of the array.

Implementation of Priority Queue Using Heap :

A Binary Heap is ideal for priority queue implementation as it offers better performance The largest key is at the top and can be removed in O(log n) time, with the heap property restored efficiently. If a new entry is inserted immediately, its O(log n) insertion time may overlap with restoration. Since heaps use contiguous storage, they efficiently handle large datasets while ensuring logarithmic time for insertions and deletions.

• insert(p): Inserts a new element with priority p.
• pop(): Extracts an element with maximum priority.
• getMax(): Returns an element with maximum priority.

Time Complexity: O(log n), for all the operation, except getMax(), which has time complexity of O(1).
Space Complexity: O(n)

Difference between Priority Queue and Queue

There is no priority attached to elements in a queue, the rule of first-in-first-out(FIFO) is implemented whereas, in a priority queue, the elements have a priority. The elements with higher priority are served first.

Library Implementation of Priority Queue

Operations on a Priority Queue

A typical priority queue supports the following operations:

1) Insertion (push) : When a new item is inserted in a Max-Heap, if it has the highest value, it becomes the root; in a Min-Heap, if it has the smallest value, it becomes the root. Otherwise, it is placed so that all higher-priority elements (larger in Max-Heap, smaller in Min-Heap) are accessed before it.

2) Deletion(pop) : We usually remove the highest-priority item, which is always at the top. After removing it, the next highest-priority item automatically takes its place at the top.

3) top : This operation only returns the highest priority item (which is typically available at the top) and does not make any change to the priority queue.

Applications of Priority Queue 

• CPU Scheduling
• Graph algorithms like Dijkstra's shortest path algorithm, Prim's Minimum Spanning Tree, etc.
• All queue applications where priority is involved.
• Data compression in Huffman code
• Event-driven simulation such as customers waiting in a queue.