Algorithms for Inserting and Deleting Keys in a Priority Queue

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Introduction

In computer science, priority queues are abstract data types that manage a collection of elements, ensuring that each element has a priority. These data structures find applications in various domains, including scheduling, graph algorithms, and simulation systems. This article explores the algorithms used to insert and delete keys efficiently in a priority queue, focusing on the binary heap implementation, which is commonly used due to its optimal time complexity.

Understanding Priority Queues

• Definition: A priority queue is a data structure where each element is assigned a priority. Elements are served based on priority, not just order of insertion, making it different from regular queues.
• Applications: Priority queues are critical in scenarios such as task scheduling in operating systems, managing the jobs in print queues based on importance, and finding the shortest path in algorithms like Dijkstra’s.

Binary Heap: The Foundation of Priority Queues

• Structure: A binary heap is a complete binary tree that maintains a specific order property. In a max-heap, each parent node is greater than or equal to its children, while a min-heap has parent…