Problem $1$:

Purpose of Big O notation in algorithm analysis and its significance in evaluating algorithm efficiency.

Provide $2-3$ paragraphs referring to books, journals or other web literature

B$.$ Consider the following code snippet:

for i in range$($n$)$:

print$("$Hello$,$ World!"$)$

a$)$ What is the time complexity of the above code snippet in Big O notation?

Give the time complexity by writing a code and executing it$.$ Provide screenshots of the code.

b$)$ Explain your answer.

Based on the above code explain the above time complexity for each steps. Refer to literature for justification

C$.$ Determine the Big O notation representing their time complexity with a brief explanation: $3$ marks each

a$)$ f$($n$)=5$n$^2+2$n $+1$

Big O Notation:

Explanation Refer to literature for justification

b$)$ g$($n$)=$ log$($n$)+10$

Big O Notation:

Explanation Refer to literature for justification

c$)$ h$($n$)=2^$n

Big O Notation:

Explanation Refer to literature for justification

Problem $2$:

A$.$ Implementing a file system structure using a tree data structure.

Code of the this can be implemented using Tree not necessarily Binary Search Tree

Explanation

Screenshot of the code snippets

B$.$ Implement a binary search tree $($BST$)$ : Insert, Search delete and Traversal $.$

Step by step explanation of the code for all the functions $,$ classes with the screenshots of the code and output

C$.$ Singly linked list and a doubly linked list

Singly Linked List: insert$\_$front$($value$),$ insert$\_$end$($value$),$ delete$($value$)$ and display$()$ Step by step explanation of the code for all the functions $,$classes with the screenshots of the code and output

Doubly Linked List: insert$\_$front$($value$),$ delete$($value$),$ display$()$ and reverse$\_$display$()(5$ Marks$)$

Step by step explanation of the code for all the functions $,$ classes with the screenshots of the code and output

Problem $3$:: Stack data structure

push$($item$),$ pop$(),$ peek$(),$ is$\_$empty$()$ and get$\_$min$()$

Step by step explanation of the code for all the functions $,$ classes

output and its justification as required