1. Objectives In this lesson, you will learn to: Define stacks
Identify applications of stacks
Implement stacks using linked lists
Define queues
Identify the two types of queues:
Deques
Priority queue
Implement queues using linked lists

2. Stacks
Are a form of single linked lists in which addition and deletion are performed in the beginning of the list
Are also called push-down lists

3. Stacks (Contd.)
Enable the item which is added last to be removed first (Last In First Out i.e. LIFO)
DataC
DataB
DataA
TOP
PUSH
POP

4. Stacks (Contd.) Example: Function calls stored in a stack substring()
main()
PUSH the calling function values & addresses when the function is invoked
POP out the calling function values once the called function execution is over

5. Stacks (Contd.) Operations that can be carried out on stacks are:
Addition (PUSH)
Removal (POP)

6. Applications of Stacks
Parameter tracking and passing values with function calls
Validating arithmetic expressions
Evaluating prefix and postfix notations

7. Towers of Hanoi
PIN 1
PIN 2
PIN 3

8. Towers of Hanoi
Rules:
Only one disc at a time should be moved, specifically the topmost disc from any pin
A larger disc should never be placed on a smaller disc

9. Infix Notation Is denoted as ‘1+2’
Is evaluated using general mathematics rules
Requires usage of parenthesis to change operator precedence

10. Postfix Notation Is denoted as ‘12+’
Is used by computers to evaluate an expression
Does not require usage of parenthesis

11. Conversion of an Infix Expression to a Postfix Expression
Is done by following the listed steps:
1. Scan the expression from left to right and execute steps 2 to 5 until the stack is empty
2. If the scanned item is an operand, add it to the postfix string, which is the string that will contain the final converted postfix expression
3. If the scanned item is a parenthesis, PUSH it to the stack
4. If the scanned item is an operator, add the current operator to the stack

12. Conversion of an Infix Expression to a Postfix Expression (Contd.)
5. If a right parenthesis is encountered then,
5.1 POP each operator from the top of the stack until the left parenthesis is encountered
5.2 Remove the left parenthesis from the stack
6. Exit

13. Evaluation of a Postfix Expression
Is done by following the listed steps:
1. Add a ')' to the end of the postfix expression
2. Scan the expression from left to right
3. Repeat steps 4 and 5
4. If an operand is encountered, PUSH every operand encountered to the stack
5. If an operator is encountered,
5.1 POP the top two elements
5.2 Evaluate the expression of the two elements
5.3 PUSH the result to the stack

14. Evaluation of a Postfix Expression (Contd.)
6. Set RESULT = top of the stack
7. Exit on encountering the ')' value

15. Implementing Stacks Using linked lists
Is preferred because of dynamic allocation of memory
Using arrays
Is disadvantageous because it requires the size of the array to be pre-defined

16. Implementing Stacks (Contd.)
Example:
class Stack {
private:
//Member data
Node *top;
public:
Stack();
void PUSH(node *);
Node *POP();
~Stack(); };

17. Problem Statement 12.D.1
Create an application that implements stack by using single linked list and prints the accepted input in reverse order.

18. Problem Statement 12.P.1
Create an application that accepts an expression with round brackets and validates it. The application should ensure that the number of opening brackets should be equivalent to the number of closing brackets.
Hint: An expression (2+3)*5 can be used to evaluate the given program.

19. Queues
Are sequential lists in which items are inserted into the tail end of the queue and taken from the head
Example:
Printer queue

20. Queues (Contd.) Are also called First In First Out (FIFO) lists B REARX D G
FRONT

21. Types of Queues
Deques
Priority queues

22. Deques Stands for double-ended queues
Are queues in which elements can be added or removed from both the ends of the queue
Example:
FRONT
REAR
Ann
Bob
Tim
Joe
Ken

23. Deques (Contd.) Are of two types: Input restricted deques
Output restricted deques

24. Priority Queues
Are queues which have priority associated with the items added to the queue that determines the order in which the elements are processed and deleted
Are used in a time-sharing system
Are used by printing applications

25. Priority Queues (Contd.)
In priority queues:
An element with a higher priority is processed first
If two elements share the same priority, then the element that came in first is processed first

26. Priority Queues (Contd.) Are used in:
Time-sharing systems
Operating system schedulers for scheduling activities to be processed by the microprocessor
Simulation applications

27. Operations on Queues Primitive operations are: Insertion of nodes
Deletion of nodes
Additional operations are:
Checking if a queue is empty
Emptying a queue
Counting the number of elements in a queue

28. Problem Statement 12.D.2
Create an application that will accept the applicant names as and when they appear for interview. The list of applicants should be updated every hour.

29. Problem Statement 12.P.2
Create an application that will print the details of the first five early bird prize winners.
Hint: The details to be accepted are the name and id.

30. Summary In this lesson, you learned that:
A stack is a data structure in which operations like adding and removing data are performed from only one end called as TOP
Stacks can be used to:
Validate arithmetic expressions
Evaluate infix and postfix notation
Store function arguments and address whenever a function calls another function

31. Summary (Contd.) The operations that can be carried out on stacks are:
Push
Pop
In computers where rules for precedence do not exist, the evaluation of an arithmetic expression written in infix is done in two steps:
Conversion of an infix expression to a postfix expression
Evaluation of the postfix expression
Stacks can be implemented using arrays or linked lists

32. Summary (Contd.)
Defining stacks by using linked list is preferred because of dynamic memory allocation
A queue is a sequential list where items are inserted into the tail end of the queue and taken from the head
The "tail" is referred to as the REAR element and the "head" is the FRONT element of a queue, where each element is deleted from the end called FRONT and added at the other end called REAR
Queues are called First In First Out (FIFO) lists
Queues can be categorized into two types:
Deques (pronounced either deck or deQueue)
Priority queue

33. Summary (Contd.)
A deques is also called a double-ended queue. In this, elements are added or removed from both ends of the queue
The two types of deques are:
Output-restricted
Input-restricted
Often, the items added to a queue have a priority associated with them that determines the order in which the processing and deletion of the each element in the queue happens. Such a kind of queue is called a priority queue

34. Summary (Contd.) The different applications of queues are:
Time-sharing systems
Operating system schedulers for scheduling
activities to be processed by the microprocessor
Simulation applications
A queue can be implemented using arrays or linked list
A queue when implemented using linked lists is called a linked queue