Stack - tnbedcsvips.in · example that shows evaluation of the Postfix expression using stack as...

V.MANIKANDAN. M.Sc.,B.Ed.,M.Phil.,CCNA. Paavai Engineering College, Namakkal-18. E_Mail ID:- [email protected]

Stack What is Stack?

1. Stack is LIFO Structure [ Last in First Out ]

2. Stack is Ordered List of Elements of Same Type.

3. Stack is Linear List

4. In Stack all Operations such as Insertion and Deletion are permitted at only one end

called Top

Visual Representation of Stack:

Field Value

Size of the Stack 6

Maximum Value of Stack Top 5

Minimum Value of Stack Top 0

Value of Top when Stack is Empty -1

Value of Top when Stack is Full 5

Basic Operations Performed on Stack :

1. Create

2. Push

3. Pop

4. Empty

Creating Stack:

1. Stack can be created by declaring the structure with two members.

2. One Member can store the actual data in the form of array.

3. Another Member can store the position of the topmost element.

typedef struct stack { int data[MAX]; int top; }stack;

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Push on Stack:

We have declared data array in the above declaration. Whenever we add any element in the

‘data’ array then it will be called as “Pushing Data on the Stack”.

Suppose “top” is a pointer to the top element in a stack. After every push operation, the value of

“top” is incremented by one.

Pop on Stack :

Whenever we try to remove element from the stack then the operation is called as POP Operation

on Stack.

Some basic terms :

Concept Definition

Stack Push The procedure of inserting a new element to the top of the stack is known as Push Operation

Stack Overflow Any attempt to insert a new element in already full stack is results into Stack Overflow.




Concept Definition

Stack Pop The procedure of removing element from the top of the stack is called Pop Operation.

Stack Underflow Any attempt to delete an element from already empty stack results into Stack Underflow.

When Stack is Empty

When Stack is said to empty then it does not contain any element inside it. Whenever the Stack

is Empty the position of topmost element is -1.

When Stack is Not Empty

Whenever we add very first element then topmost position will be incremented by 1. After

adding First Element top = 0.

After Deletion of 1 Element Top Will be Decremented by 1

Position of Top and Its Value:

Position of Top Status of Stack

-1 Stack is Empty

0 First Element is Just Added into Stack

N-1 Stack is said to Full

N Stack is said to be Overflow

Values of Stack and Top:

Operation Explanation

top = -1 -1 indicated Empty Stack

top = top + 1 After push operation value of top is incremented by integer 1

top = top – 1 After pop operation value of top is decremented by 1

Check Whether Stack is Empty or Not ?

We are using Empty Function for Checking whether stack is empty or not –

1. Function returns “True” if Stack is Empty.

2. Function returns “False” if Stack is Non-Empty.

3. Function Takes “Pointer to Stack”

int empty (stack *s)




1. Return Type : Integer. [Empty Stack Return 1 , Non Empty Stack Return 0 ]

2. Parameter : Address of Variable of Type Stack .

3. How to Call this Function From Main ?

typedef struct stack{ int data[MAX]; int top;

} stack;

Empty Function :

int empty(stack *s) { if(s->top == -1) //Stack is Empty return(1); else return(0); }stack;

Check Whether Stack is Full or Not ?

We are using Empty Function for Checking whether stack is full or not –

1. Function returns “True” if Stack is Full

2. Function returns “False” if Stack is Not Full.

3. Function Takes “Pointer to Stack”

int full (stack *s)

1. Return Type : Integer. [If full Stack Return 1 , not full Stack Return 0 ]

2. Parameter : Address of Variable of Type Stack .

How to Call this Function From Main ?

typedef struct stack { int data[MAX]; int top; }stack; void main() { stack s; // Declare Stack Variable ------- ------- i = full(&s); // Pass By Reference ------ ------ }

1. Pass “Stack” Variable to “full Function” using pass by reference.

2. As full Function returns integer , we have facility to store returned value into some

integer variable so we have written [ i = full(&s) ]




Complete Code

int full(stack *s) { if(s->top == MAX-1) //Stack is Full return(1); else return(0); }

Push Operation:

1. Push Refers as “Adding Elements onto Stack“.

2. Push Operation carried out in following 2 steps –

o First Increment Variable “top“ so that it now refers to next memory location.

o Secondly Add Element Onto Stack by accessing array.

3. Main Function Should ensure that stack is not full before making call to push() in order to

prevent “Stack Overflow“

Push Function

void push(stack *s,int num) { s->top = s->top + 1; s->data[s->top] = num; }

Pop Operation Arguments and Return Type :

1. Argument : Variable of Type Stack.

2. Return Type : Integer [ Removed Element ]

Steps in Pop Operation :

1. Store Topmost Element in another Variable.

2. Decrement Top by 1

3. Return Topmost Element .

Pre-requisites : Stack Type Definition .: Click Here

Pop Function :

int pop(stack *s) { int x; x = s->data[s->top]; s->top = s->top - 1; return(x); }




Application of Stack :

1. Parsing

2. Recursive Function

3. Calling Function

4. Expression Evaluation

5. Expression Conversion

I. Infix to Postfix

II. Infix to Prefix

III. Postfix to Infix

IV. Prefix to Infix

6. Towers of hanoi

Expression Representation Techniques :

1. Infix Expression

2. Prefix Expression

3. Postfix Expression

Evaluation of Postfix Expression : [ Click Here ]

Expression Example Note

Infix a + b Operator Between Operands

Prefix + a b Operator before Operands

Postfix a b + Operator after Operands

Generally postfix expressions are free from Operator Precedence thats why they are preferred in

Computer system.Computer System Uses Postfix form to represent expression. Following is the

example that shows evaluation of the Postfix expression using stack as data structure.

Algorithm for Evaluation of Postfix Expression

Initialize(Stack S)

x = ReadToken(); // Read Token

while(x)

{

if ( x is Operand )

Push ( x ) Onto Stack S.

if ( x is Operator )




{

Operand2 = Pop(Stack S);

Operand2 = Pop(Stack S);

Evaluate (Operand1,Operand2,Operator x);

}

x = ReadNextToken(); // Read Token

}


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