Stack Applications

Stacks Application Areas of Stacks

When functions are called.

To convert a infix expression to postfix.

To evaluate a postfix expression.

Stacks are used : Application Areas of Stacks

Algorithm to convert INFIX to POSTFIX expression

Postfix Expression involving LOGICAL OPERATORS/CONSTANTS

LOGICAL OPERATORS

NOT : Complementation (Unary Operator) (HIGHEST PRIORITY)

Result is TRUE if operand is FALSE and vice versa.

AND : Logical multiplication (PRIORITY LESS THAN NOT

Result is TRUE if both operands are TRUE otherwise FALSE hi

OR : Logical Addition (LOWEST PRIORITY)

Result is FALSE if both operands are FALSE otherwise TRUE

LOGICAL CONSTANTS

YES / TRUE

NO / FALSE

Just For Reference

Q= A*(B+(C+D)*(E+F)/G)*H Convert INFIX Expression into POSTFIX Expression Following the algorithm showing stack status at each step ) Extra Bracket added 22 H 21 * 20 ) 19 G 18 / 17 ) 16 F 15 + 14 E 13 ( 12 * 11 ) 10 D 9 + 8 C 7 ( 6 + 5 B 4 ( 3 * 2 A 1 ( P (Postfix Expression) Description Stack Status Input Element STEP

Evaluation of POSTFIX Expression

Postfix Expression is without parenthesis.

Postfix Expression has only Operands and Operators

Stack is used to hold operand/intermediate results (STACK APPLICATION)

Expression Evaluated from left to right

Some points to remember regarding POSTFIX expressions:

Evaluation of POSTFIX Expression (Algorithm)

Let P be the expression in POSTFIX notation

Expression is Evaluated from left to right

Add ; at the end to mark end of expression P

Scan the postfix expression from left to right taking one element at a time

While (element !=‘;’) repeat the steps 2.1 and 2.2

2.1 if (element = Operand ) it is PUSHed in STACK

2.2 If (element == Operator )

{

POP first element from TOP call it A

POP second element from TOP call it B

Perform OPERATION B operator A

PUSH Result in STACK

}

Pop the value from stack TOP which is result of the expression

{ {

Assignment Stack Applications

post fix , infix notation (2 marks)

Give postfix form of the following expression:

(i) A*(B+(C+D)*(E+F)/G)*H

(ii) A+[(B+C)*(D+E)*F]/G

(iii) A*(B+D)/E-F-(G+H/K)

(iv) ((A-B)*(D/E))/(F*G*H)

(v) (True && false) || !(false||true)

Evaluate the following postfix expression using a stack and show the Contents of stack after each step:

(i) 50,40,+, 18,14,-,4,*,+

(ii) 100,40,8,+,20,10,-,+,*

(iii) 5,6,9,+,80,5,*,-,/

(iv) 120,45,20,+,25,15,-,+,*

(v) 20,45,+,20,10,-,15,+,*

(vi) TRUE,FALSE, TRUE FALSE, NOT, OR, TRUE , OR,OR,AND

3. Write the equivalent infix expression for :

i. 10,3,*,7,1,-,*,23,+

ii. /+a*bc-c*db

iii. abc*+cdb*-/

The End

Stack Applications

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