dc presentation on stack representation

8/3/2019 DC Presentation on Stack Representation

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By:--

1. Himanshu Bhagat

2. Kazi Mostafizur Rahman

3. K. Badash

4. Lal Bahadur Mishra

5. Nipun Bhardwaj

6. Nitesh Kumar

7. Rakesh Ranjan Choudhary


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A stack is a list of elements/items.

The elements may be inserted only at one end called the top of the stack.

In other words,A stack is collection/ organization

of data in a way such that the last element/datainserted is the first one to bedeleted/removed/taken out.


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For Example:-

1) a bunch ofbooks placed on each other on a table.

2) a lady wearing bangles.

3) A stack of coins (pennies).

Basic operations:-

1) Push:-

A push operation is used to insert an element into thestack.

2) Pop:-

A Pop operation is used to delete an item from the stack.

Note:- A pointer variable is used to point the top of the stack where theinsertion & deletion of elements takes place.


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Operations:- Stack contents

1. Push A* A is inserted into the stack.* Top points to the locationcontaining A.

ATop

B

ATop

2. Push A* B is inserted into the stack.* Top points to the locationcontaining B.

3. Pop* B is deleted from the stack.* Top points to the locationcontaining A.

ATop


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Stacks may be represented in computers as both statically as well asdynamically.

A representation of stack by means of an array is called staticrepresentation of sack.

A dynamic representation of stack include linked lists.

Stack Implementation

Static Dynamic

Using linear

array

Using linked

list


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Example:-

77

23

5

77 * 23 * 5 *

Array representation

Linked representation

|

V


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An array is used to represent a stack statically.

A pointer variable top is used which contains the locationof the top element of the stack.

Another variable MAXSIZE can be used to specify themaximum no of elements that the stack can hold.

Note:-

* Top= 0/NULL indicate that the stack is EMPTY.

* Top= MAXSIZE indicate that the stack is full.

Operations:-

1. Push 2. Pop

STATIC IMPLEMENTATION


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PUSH(STACK,TOP,MAXSIZE,ITEM)1. IFTOP=MAXSTK then print OVERFLOW and return

2. Set TOP=TOP+1[increase top by one]

3. SetSTACK[TOP]=ITEM, Increase ITEM in new TOP position

4. return

POP(STACK,TOP,ITEM)

1. IF TOP=0, PRINT underflow and return

2. Set ITEM=STACK[TOP] [Assign top element to item]

3. Set TOP=TOP-1[Decrease TOP By one]

4. Return

Push operation

Pop operation


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In a static representation, We must specify the size of stack before its use.

Which results in:-

* Memory wastage,

* Increase of the chance of overflow.

Limitations of static representation


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The Dynamic represntation or linked representation of a stack,commonly known as linked stack is a stack that is implementedusing a singly linked list.

The INFO field of the node hold the elements of the stack.

The LINK field holds pointers to the neighboring element.

The START pointer of the linked list behaves as the TOP pointer ofthe stack.

DYNAMIC IMPLEMENTATION


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PUSH_LINKSTACK(INFO,LINK,TOP,AVAIL, ITEM)1. If AVAIL=NULL , then write OVERFLOW and exit.

2. [Remove first node from AVAIL list]

Set NEW=AVAIL and AVAIL=LINK[AVAIL].

3.Set INFO[NEW]=ITEM [Copies ITEM into new node]

4.Set LINK[NEW]=TOP[New node points to the original TOP node inthe stack]

5.Set TOP=NEW[Reset TOP to point to the new node at the TOP of thestack]

6.Exit

Push operation

7 * 11 * 2 *

For Example:- pushin an element 5 in a list containing the elements :- 7, 11, 2

Top

7 * 11 * 2 *

Top

5 *


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POP_LINKSTACK(INFO,LINK,TOP,AVAIL,ITEM)

1.If TOP=NULL then write UNDERFLOW and exit.

2. Set ITEM=INFO[TOP] [Copies the TOP element of stack intoITEM]

3. Set TEMP=TOP andTOP=LINK[TOP]

[Remember the old value of the Top pointer in TEMP and reset TOP

to point to the next element in the stack]4.[Return delete node to the AVAIL list]

Set LINK[TEMP]=AVAIL and AVAIL=TEMP

5. Exit

Pop operation

7 * 11 * 2 *

Top

Example:-

11 * 2 *

Top


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An Arithmetic expression is a combination of operand & operator.

The representation of an arithmetic expression can be done inthree ways:-

1. Infix notation/ Infix Expression.

2. Polish/prefix notation.

3. Reverse polish/Postfix notation.

If an operator is placed between two operands, then theexpression is called as infix expression.

Example:-

(A+B)*C

ARITHMETIC EXPRESSION

Infix notation


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The notation in which the operator is placed before itstwo operands is called a polish/prefix notation.

For Example:-

*+ABC

The notation in which the operator isplaced before its two operands is called a polish/prefix notation.

For Example:-

AB+c*

Prefix notation

Postfix notation


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POLISH(Q,P)

1. Push ( onto stack & add a) to the end of Q

2. Scan Q from left to right & repeat step 3. & 4. for each element untilthe Stack is EMPTY.

3. If an operand is encountered, add it to P.

4. If a left parenthesis is encountered, push it onto the stack.

5. if an operator is encountered, then:

a) Repeatedly pop from the stack & add it to p, eachoperator which has same as or higher precedence then the operatorencountered.

b) Add operator to stack.

TRANSFORMING INFIX INTOPOSTFIX

Procedure


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6. If a right parenthesis is encountered, then:

a) Repeatedly pop from the stack & add it to P, eachoperator until a left parenthesis is encountered.

b) Remove left parenthesis from the stack.

7. EXIT.

For Example:-Q:-A+(B*C-(D/E^F)*G)*H

Symbol scanned STA

CKP

A ( A

+ (+ A

( (+( A

B (+( AB

* (+(* AB

C (+(* ABC

) (+ ABC*

- (- ABC*+

D (- ABC*+

) EMPTY ABC*+-


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1. Add ) at the end of P.

2. Scan P from left to right and repeat step 3. & 4. until thesentinel ) is encountered.

3. If an operand is encountered, push it on STACK.

4. If an operator is encountered, then:

a) Remove the top 2 elements of stack, where A

is the top element & B is the next to top element.

b) Evaluate a * b

c) Place the result ofb)back on stack.5. Set VALUE=Top element on stack.

6. EXIT.

EVALUATINGPOSTFIX EXPRESSION

Procedure


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For Example:-

consider p:-5, 6, 2,+,*, 12, 4, /, -

SYMBOL SCANNED STACK

5 5

6 5, 6

2 5, 6, 2

+ 5, 8

* 40

12 40, 12

4 40, 12, 4

/ 40, 3- 37

)

VALUE= 37


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Expression evaluation

Backtracking (game playing, finding paths, exhaustivesearching)

Memory management, run-time environment for nestedlanguage features.

APPLICATIONSOF STACKS


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Thus we can say that a stack is an effective way of

representing data that maybe used in expressionevaluation, backtracking, memory management.

CONCLUSION


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dc presentation on stack representation

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