Stacks and queues using aaray line .pptx

Module 2 : Stack and Queues
Refer Module 2 of Syllabus [CSC303 (SE AI&DS/ SE Comps)]
2.1 Introduction, ADT of Stack, Operations on Stack, Array
Implementation of
Stack, Applications of Stack-Well form-ness of Parenthesis, Infix
to Postfix Conversion and Postfix Evaluation, Recursion.
2.2 Introduction, ADT of Queue, Operations on Queue, Array
Implementation of Queue, Types of Queue-Circular Queue,
Priority Queue, Introduction of Double
Ended Queue, Applications of Queue.

Stack
Definition - A stack is an ordered collection of homogeneous data
elements, where the insertion and deletion takes place at one end,
known as TOP.
⮚The stack is also called LAST IN FIRST OUT(LIFO)
⮚It means: the element which is inserted last must be deleted first
⮚Example
1.pile of plates in cafeteria
2.Chapati stack in round box
3.stack of coins

❖ Stack maintains a pointer called top, which keeps track of the top
most element in the stack.
❖ Any insertions or deletions should be based upon the value of top.
❖ It works on the basis of LIFO (Last in First out).
❖ According to the definition, new elements are inserted from top
and the elements are deleted from same end i.e again top.
❖ This suggests that the element inserted most recently can only be
deleted.
❖ In the stack, the elements are removed in the reverse order of
that in which they were added to the stack i.e last element
inserted is to be deleted first. So it is called last in first out.

Basic operations:
❖The basic operations are insertion, deletion ,display.
❖In stacks, special terms are given for insert and delete. i.e push for
insert and pop is for delete.
❖Push: inserting or adding element into the stack is called push.
❖Pop: deleting or removing element from the stack is called
pop.

❖Elements are inserted in the order as A,B,C,D,E
❖It represents the stack of 5 elements.
❖The top most element in the stack is E
❖If we want to delete element E has to be deleted
first

❖Pop operation- delete element from the stack

Implementing stack using arrays
Algorithm for creating empty stack:
Step 1 - Include all the header files which are used in the program and define a
constant 'SIZE' with specific value.
Step 2 - Declare all the functions used in stack implementation.
Step 3 - Create a one dimensional array with fixed size (int stack[SIZE])
Step 4 - Define a integer variable 'top' and initialize with '-1'. (int top = -1)
Step 5 - In main method, display menu with list of operations and make
suitable function calls to perform operation selected by the user on the stack.

Algorithm for inserting element into the stack:
push(value) - Inserting value into the stack
Step 1 - Check whether stack is FULL. (if top = SIZE-1)
Step 2 - If it is FULL, then display "Stack is FULL!!! Insertion is not possible!!!" and
terminate the function.
Step 3 - If it is NOT FULL, then increment top value by one (top top +1
🡨 ) and set
stack[top] to value (stack[top] value
🡨 ).

Explanation for Push
❖ The stack is of size max. This procedure inserts an
element item on to the top of a stack which is represented
by an array stack.
❖ The first step of this algorithm checks for an
overflow condition.
❖ Overflow means inserting element into a stack which
is full.
❖ If the top value reaches to maximum size of the stack
then elements cannot be inserted into the stack i.e. stack
is full.
❖ Otherwise top is incremented by one and element is
inserted into the stack.

Algorithm to delete elements from the stack:
pop() - Delete a value from the Stack
Step 1 - Check whether stack is EMPTY. (if top = -1)
Step 2 - If it is EMPTY, then display "Stack is EMPTY!!! Deletion is not
possible!!!" and terminate the function.
Step 3 - If it is NOT EMPTY, then delete stack[top] and decrement top value by
one (top top -1
🡨 ).

Explanation for Pop()
❖This procedure deletes an element from the stack.
❖The first step of this algorithm checks
for underflow condition.
❖If the top value is -1 then stack is empty.
❖Empty stack is known as underflow.
❖Takeout the element from the location
where, the top is pointing and then decrement
top by one.

display() - Displays the elements of a Stack
We can use the following steps to display the elements of a stack
Step 1 - Check whether stack is EMPTY. (if top = -1)
Step 2 - If it is EMPTY, then display "Stack is EMPTY!!!" and terminate the
function.
Step 3 - If it is NOT EMPTY, then define a variable 'i' and initialize with top.
Display stack[i] value and decrement i value by one (i--).
Step 3 - Repeat above step until i value becomes '0'.

Image: Data Structures using C by Balagurusamy

⮚ Space complexity
⮚ Time complexity of push(), pop(),size(),
isEmpty(), isFull()
will take O(1).
⮚ Limitation in stack using array is that maximum size of the
stack must be pre defined and it cannot be changed(fixed).
⮚ When trying to add elements in the stack when the
stack is
full will rise the exception.

⮚ Consider size of the stack is 4
⮚ Insert following elements
A,B,C,D
Representing Stack with Dynamic array
A
A B
A B C
A B C D
A B C D E
Stack is full when E is inserted create a new stack with double size
and copy all the old stack elements to new
stack and named it as old stack

Representing Stack with Linked List
⮚ Disadvantage of using an array to implement a stack or queue
is the wastage of space.
⮚ Implementing stacks as linked lists provides a feasibility on
the number of nodes by dynamically growing stacks, as a
linked list is a dynamic data structure.
⮚ The stack can grow or shrink as the program demands it to.
⮚ A variable top always points to top element of the stack.
⮚ top = NULL specifies stack is empty.

⮚ In this representation, first node in the list is last inserted
element hence top must points to the first element on the stack
⮚ Last node in the list is the first inserted element in the stack.
⮚ Thus, push operation always adds the new element at front of
the list
⮚ And pop operation removes the element at front of the list.
⮚ Size of the stack not required.
⮚ Test for overflowis not applicable in this case.

10 NULL
150
0
1800
1200
1400
20 1400
30 1200
40 1800
50 1500 1100
top
Example:
⮚The following list consists of five cells, each of which holds a
data object and a link to another cell.
⮚A variable, top, holds the address of the first cell in the list.

Applications of stacks
⮚Balancing symbols
⮚Parenthesis matching.
⮚Infix to prefix conversions.
⮚Infix to postfix conversions.
⮚Evaluation of postfix expressions.
⮚Implementing function calls (Recursion)
⮚Undo operations in text editors
⮚Matching tags in HTML and XML
⮚Quick sort.

Conversion of expressions
Arithmetic expressions can be represented in three ways:
❖Infix notation
❖Prefix notation
❖Postfix notation

Conversion of expressions
1.Infix notation- In which operator should be placed in between the two
operands.
Example- A+B C-D E*F G/H.
2.Prefix notation (polish notation)-
•Operator preceded by the operand is called prefix notation
Examples
+AB -CD *EF GH.
3. Postfix notation(reverse polish notation or suffix notation)-
•Operator should be placed after operands.
AB+ CD-

Notation– Conversions (Infix to Prefix)
Consider the infix expression:
2 + 3 * (5 – 7) / 9
Let us insert implicit parentheses
(2 + ((3 * (5 – 7)) / 9))
Transfer the operators to the beginning of parentheses
(+ 2 (/ (* 3 (– 5 7)) 9))
Remove the parentheses:
+ 2 / * 3 – 5 7 9
This is the equivalent prefix expression.

Notations – Conversions (Infix to Postfix)
Consider the infix expression:
2 + 3 * (5 – 7) / 9
Let us insert implicit parentheses
(2 + ((3 * (5 – 7)) / 9))
Transfer the operators to the end of parentheses
(2 ((3 (5 7 –) *) 9 /) +)
Remove the parentheses:
2 3 5 7 – * 9 / +
This is the equivalent postfix expression.

Examples
Infix
Expression
Prefix
Expression
Postfix
Expression
2 + 3 + 2 3 2 3 +
2 + 3 * 5 + 2 * 3
5
2 3 5
* +
(2 + 3) * 5 * + 2
3 5
2 3 +
5 *
2 * 3 – (5 + 9) – * 2 3+ 5 9 2 3 *
5 9 + -

Convert infix to postfix expression
1. (A-B)*(D/E)
2. (A+B^D)/(E-F)+G
3. A*(B+D)/E-F*(G+H/K)
4. ((A+B)*D)^(E-F)
5. (A-B)/((D+E)*F)
6. ((A+B)/D)^((E-F)*G)
7. 12/(7-3)+2*(1+5)
8. 5+3^2-8/4*3+6
9. 6+2^3+9/3-4*5
10. 6+2^3^2-4*5

Infix to post fix (RPN-Reverse Polish Notation) Conversion
Algorithm to convert infix expression to postfix expression(RPN):
1.Declare a stack and postfix array (output : postfix expression)
2.Repeat the following steps until the end of the infix expression is reached.
1. Get input token (constant, variable, arithmetic operator, left
parenthesis, right parenthesis) in the infix expression.
2. If the token is
i. A left parenthesis: Push it onto the stack.
ii. A right parenthesis:
○ Pop the stack elements and add to postfix array until a left
parenthesis is on the top of the stack.
○ Pop the left parenthesis also, but do not add to postfix array
iii. An operator:
○ While the stack is nonempty and token has lower or equal priority
than stack top element, pop and add to postfix array.
○ Else push token onto the stack.
iv. An operand: add to postfix array
3. When the end of the infix expression is reached, pop the stack elements and add to
postfix array until the stack is empty.
(Note: Left parenthesis in the stack has lowest priority)

Note
• the lower precedence operator never placed on top of the
higher precedence.

Infix expression- (A+B)^C-(D*E)/F
Infix Stack Post fix
( ( Empty
A ( A
+ (+ A
B (+ AB
) Empty AB+
^ ^ AB+
C ^ AB+C
- - AB+C^
( -( AB+C^
D -( AB+C^D
* -(* AB+C^D
E -(* AB+C^DE
) - AB+C^DE*
/ -/ AB+C^DE*
F -/ AB+C^DE*F
Empty AB+C^DE*F/-

Convert infix to postfix expression using stack
1. (A-B)*(D/E)
2. (A+B^D)/(E-F)+G
3. A*(B+D)/E-F*(G+H/K)
4. ((A+B)*D)^(E-F)
5. (A-B)/((D+E)*F)
6. ((A+B)/D)^((E-F)*G)
7. 12/(7-3)+2*(1+5)
8. 5+3^2-8/4*3+6
9. 6+2^3+9/3-4*5
10. 6+2^3^2-4*5

Appln 2 . Postfix expression evaluation
• Algorithm
1.Scan expression from left to right and repeat steps 2 and
3 for each element of expression.
2.If an operand is encountered, push it on to
stack.
3. If an operator is encountered then
i. remove the top two elements of stack, where A is the top
and B is the next top element.
ii. evaluate B operator A
iii.push the result back on to the stack.
4.set the top value on stack.
5.stop

Evaluate the
expression
• Postfix:-
5,6,2,+,*,12,4,/,-
Symbol scanned
5
6
2
+
stack content
5
5
6
5
6
2
5
8
40
*
12
4
40 12
40 12 4
/ 40 3
- 40-3
37

Evaluate the postfix expression
1. 5,3,+,2,*,6,9,7,-,/,-
2. 3,5,+,6,4,-,*,4,1,-,2,^,+
3. 3,1,+,2,^7,4,1,-,2,*,+,5.-

3.Parenthesis matching
❖The objective of this function is to check the
matching of parenthesis in an expression
i.e
❖ In an expression the no of left parenthesis
must be equal to no: of right parenthesis.
Ex: ((A+B)*C)
❖This is a valid expression because in this no of left
parenthesis (2) = no: of right parenthesis (2).

Stacks and queues using aaray line .pptx

More Related Content

Similar to Stacks and queues using aaray line .pptx

Recently uploaded

Stacks and queues using aaray line .pptx