A$)$ You are managing a task scheduling system for a company. Each task is assigned a priority

level, and the company wants to process tasks in order of their priority, with the highest$-$priority

tasks being handled first. Tasks with the same priority can be processed in any order.

You need to write a program that sorts the tasks using Heap Sort to ensure that the

highest$-$priority tasks are always at the front of the queue.

$($Real$-$World Context: Tasks in a company's project management system have varying levels of

urgency. Higher priority tasks $($like system updates or urgent client requests$)$ should be

completed before less critical ones. You must organize these tasks so that the highest priority task

is always the next to be executed.$)$

Input: An array of task objects, each with a priority $($higher value $=$ higher priority$)$ and a

description.

$[\{$ "priority": $3,$ "description": "Respond to emails" $\},\{$ "priority": $5,$ "description": "Fix server

issue" $\},\{$ "priority": $2,$ "description": "Update documentation" $\},\{$ "priority": $4,$ "description":

"Prepare meeting agenda" $\},\{$ "priority": $1,$ "description": "Clean workspace" $\}]$

Output: The tasks sorted by priority in descending order, so that the highest$-$priority tasks come

first.

B$)$ What is the time complexity of Heap sort in the Worst case? What are the advantages and

disadvantages of using Heap Sort over other sorting algorithms? $(30$ points$)$