Computer System Priority

Imagine you are managing a queue of tasks in a computer system. Each task has a priority level assigned to it$,$ ranging from $1($highest priority$)$ to $5($lowest priority$).$ Tasks need to be processed in order of their priority, with higher priority tasks taking precedence over lower priority ones. You also need to efficiently add new tasks to the queue and update the priorities of existing tasks as needed.

$$ Task $1$: Priority level $3,$ "Update user profiles"

$$ Task $2$: Priority level $1,$ "Critical system bug fix"

$$ Task $3$: Priority level $2,$ "Database optimization"

$$ Task $4$: Priority level $4,"$UI redesign"

$$ Task $5$: Priority level $1,$ "Emergency server restart"

What data structure would be suitable for managing this task queue, and how can it be used to efficiently find and process the task with the highest priority?

Assuming that the data structure is correctly implemented, the task with the highest priority should be processed first.

$($Do Not Use java.util.$*$ package$)$

Contact Management

You are tasked with designing a data structure for a contact management system that allows users to store and retrieve contact information efficiently. Contacts have a name, phone number, and email address. Users should be able to perform operations like adding a new contact, searching for a contact by name, and deleting a contact.

$1.$ How would you design the underlying structure to store contact information efficiently?

$2.$ critically analyze how you would implement adding a new contact and ensuring it can be retrieved later.

$3.$ Describeyourapproachforsearchingforacontactbyname.

$4.$ Whatconsiderationswouldyoutakeintoaccountfordeletingacontact?

$5.$ Compare the advantages and disadvantages of your chosen design in terms of

memory usage and time complexity for the given operations.

Sample Data Set

Name: John Doe

Phone Number: $(555)123-4567$ Email: john.doe@example.com

Name: Jane Smith

Phone Number: $(555)987-6543$ Email: jane.smith@example.com

Name: Alice Johnson

Phone Number: $(555)456-7890$ Email: alice.johnson@example.com

Name: Bob Brown

Phone Number: $(555)789-0123$ Email: bob.brown@example.com

Bookstore

Imagine you are working as a software developer for a bookstore. Your task is to create and manage a stack data structure to keep track of books in the store's inventory. Each book has the following information: title, author, publication year, and ISBN $($International Standard Book Number$).$ You need to implement the stack operations to maintain and update this inventory.

Sample Data Set:

Stack: $[]$

Book $1$: Title: "The Great Gatsby", Author: $"$F$.$ Scott Fitzgerald", Year: $1925,$ ISBN: $"978-0743273565"$

Book $2$: Title: $"$To Kill a Mockingbird", Author: "Harper Lee", Year: $1960,$ ISBN: $"978-0061120084"$

Book $3$: Title: $"1984",$ Author: "George Orwell", Year: $1949,$ ISBN: $"978-0451524935"$ Book $4$: Title: "Pride and Prejudice", Author: "Jane Austen", Year: $1813,$ ISBN: $"978-0141439518"$

Now, let's perform some operations on the stack:

$1.$ Addthefirsttwobookstotheinventory.Thestackwilllooklikethis: Stack: $[$Book $2,$ Book $1]$

$2.$ A customer purchases $"$To Kill a Mockingbird" $($Book $2).$ Remove this book from the inventory. What does the stack look like now?

$3.$ Anewbookarrives:Title:"TheCatcherintheRye",Author:"J$.$D$.$Salinger",Year: $1951,$ ISBN: $"978-0316769174".$ Add it to the inventory. What does the stack look like now?

$4.$ Another customer purchases "The Great Gatsby" $($Book $1).$ Remove this book from the inventory. What does the stack look like now?

Question: Provide the updated stack after each operation, and critically analyze how the stack data structure behaves in this inventory management scenario. How would you implement the push and pop operations to ensure books are added and removed correctly?

Please describe the stack's state and the steps involved in each operation as you answer the question.

Algorithms

$1.$Organizing Books in a Library: A Practical Approach to Efficient Sorting

Suppose you are the librarian of a busy public library, and you have received a shipment of new books. The shipment consists of $100$ books, each with various attributes such as title, author, genre, and publication date. Here is a simplified example data set of $10$ books from the shipment:

$$ Title: "The Great Gatsby" $|$ Author: F$.$ Scott Fitzgerald $|$ Genre: Classic $|$ Publication Date: $1925$

$$ Title: $"$To Kill a Mockingbird" $|$ Author: Harper Lee $|$ Genre: Classic $|$ Publication Date: $1960$

$$ Title: $"1984"|$ Author: George Orwell $|$ Genre: Dystopian $|$ Publication Date: $1949$

$$ Title: "The Catcher in the Rye" $|$ Author: J$.$D$.$ Salinger $|$ Genre: Coming$-$of$-$Age $|$

Publication Date: $1951$

$$ Title: "Pride and Prejudice" $|$ Author: Jane Austen $|$ Genre: Classic $|$ Publication Date:

$1813$

$$ Title: "The Hobbit" $|$ Author: J$.$R$.$R$.$ Tolkien $|$ Genre: Fantasy $|$ Publication Date: $1937$

$$ Title: "Brave New World" $|$ Author: Aldous Huxley $|$ Genre: Dystopian $|$ Publication Date:

$1932$

$$ Title: "The Hunger Games" $|$ Author: Suzanne Collins $|$ Genre: Dystopian $|$ Publication

Date: $2008$

$$ Title: "Harry Potter