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Authors:
Linda Null ,julia Lobur
Chapter:
Data Structures And The Computer
Exercise:
Exercises
Question:2 | ISBN:9780763704445 | Edition: 3

### Question

2. As stated in the text, a priority queue is a queue in which certain items are allowed to jump to the head of the line if they meet certain conditions. Devise a data structure and a suitable algorithm to implement a priority queue.

A suitable data structure to implement a priority queue is a binary heap. A binary heap is a binary tree-based data structure that satisfies the heap property, where each parent node has a value greater than or equal to its child nodes (in a max heap) or less than or equal to its child nodes (in a min heap).

Here's an outline of the data structure and algorithm to implement a priority queue using a binary heap:

1. Data Structure:

• Use an array-based representation to store the elements of the priority queue.
• Each element in the array represents a node in the binary heap.
• The first element of the array (index 0) is left empty for easier calculations.
• Maintain a variable to track the current size of the priority queue.
2. Operations: a) Insertion:

• Add the new element at the end of the array.
• Percolate the element up the heap by comparing it with its parent node and swapping if necessary to maintain the heap property.
• Update the size of the priority queue.

b) Deletion:

• Remove the root element (highest priority) from the array.
• Move the last element in the array to the root position.
• Percolate the element down the heap by comparing it with its child nodes and swapping if necessary to maintain the heap property.
• Update the size of the priority queue.

c) Peek:

• Return the value of the root element without removing it.
3. Algorithm Complexity:

• Insertion: O(log n)
• Deletion: O(log n)
• Peek: O(1)

Using a binary heap-based implementation allows efficient insertion and deletion of elements while maintaining the desired priority order.

It's important to note that the above outline provides a basic framework, and there are variations and optimizations possible based on specific requirements. For example, you can implement a min heap or a max heap depending on the desired priority order, and additional operations like changing the priority of an element can be added as well.

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