New Stack Application

8/12/2019 New Stack Application

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STACK

APPLICATION


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MAIN OBJECTIVE

Postfix evaluation

Infix to Postfix conversion

Expression evaluation


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EVALATION O E!P"ESSIONS

Consists of operators an#

operan#s$

A pro%ra&&in% lan%ua%e supports

several 'in#s of operators (it)

so&e priorit* values$

X = A/B * * C + D X E A * C


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EVALATION O E!P"ESSIONS

I$ Or#erin% of operation+ priorit*

of operation$

II$ ,irection of operation


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,I"ECTION O OPE"ATIONS

I$ Left to ri%)t

II$ "i%)t to left

For Example:

A - - B - - C ./ A - - 0B- -C1


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EVAL2ATION O E!P"ESSIONS

Infix notation 3 A 4 B

Postfix notation 3 AB4

Prefix notation 3 4AB

5 6a*s to represent an expression3

Co&piler uses postfix notation for

evaluatin% expressions$


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EVAL2ATION O

E!P"ESSIONS

Examples:

71 Infix3 A- B+ C

Postfix 3 AB - C+

81 Infix 3 A + B - - C 4 , - E 9A - C

Postfix 3 ABC - - + , E - 4 AC - .


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A,VANTA:ES O POSTI!

NOTATIONS

7$ Nee# for parent)esis is eli&inate#$

For Example:T)e follo(in% expression

(it) an# (it)out t)e parent)esis (ill)ave t)e sa&e postfix notation

A + 0B - - C1 4 0, - E1 9 A - C


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A,VANTA:ES O POSTI!

NOTATIONS

8$ Priorit* of operators is eli&inate#$

5$ Evaluation process is &uc) si&pler

t)an atte&ptin% a #irect evaluation

fro& infix notation$


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EVAL2ATIN: A POSTI!

E!P"ESSION 2SIN: A STACK

E!P"ESSION3 5; 4 8 - 0Postfix Notation1

S*&


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POSTI! EVAL2ATION

AL:O"IT=M

Place operan#s on stac' until (e fin# an

operator$

"e&ove fro& t)e stac'> t)e correct

nu&


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,ECLA"ATION

? #efine MA!@STACK@SIE 7

? #efine MA!@E!P"@SIE 7

t*pe#ef enu& lparen> rparen> plus> &inus

ti&es> #ivi#e> &o#> eos> operan#D prece#ence

int stac'FMA!@STACK@SIEG +-%lo


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2NCTION TO EVAL2ATE A

POSTI! E!P"ESSION

int eval 0voi#1

+- evaluate a postfix expression> expr

&aintaine# as a %lo


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2NCTION TO EVAL2ATE A

POSTI! E!P"ESSION

prece#ence to'en

c)ar s*& op8

int n +-Counter t)e expression strin%

int top .7

to'en %et@to'en 0s*& n1


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POSTI! E!P"ESSION

EVAL2ATION3 2SIN: A STACK

()ile 0to'en eos1

if 0to'en operan#1

a## 0top> s*&


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POSTI! E!P"ESSION

EVAL2ATION

op8 #elete 0top1

op7 #elete 0top1

s(itc) 0to'en1

case plus3 a##0top> op74op81


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POSTI! E!P"ESSION

EVAL2ATION

to'en %et@to'en0s*& n1 D

return #elete 0top1 +- text-+

D


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2NCTION TO :ET A TOKEN "OM

INP2T ST"IN:

prece#ence %et@to'en0c)ar -s*& int -n1

+ - %et t)e next to'en > s*& t)e to'en is

represente# ()ic) is

returne# in t)e function na&e-+


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2NCTION TO :ET A TOKEN

"OM INP2T ST"IN:

s(itc) 0-s*&


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AL:O"IT=M O" INI! TO

POSTI! T"ANSLATION

I$ ull* parent)esie t)e expression

II$Move all operators so t)at t)e* replacet)eir correspon#in% ri%)t parent)esis

III$ ,elete all parent)eses


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POSTI! T"ANSLATION

E!AMPLE3

000A + 0B - - C11 4 0 , - E 1 1 9 0A - C 1 1

A B C - -+ , E - 4 A C - .


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POSTI! T"ANSLATION

,ra(


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POSTI! T"ANSLATION

Or#er of operan#s is t)e sa&e in

A+B--C4,-E.A-C is ABC--+,E -4AC-.

Postfix can


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POSTI! T"ANSLATION

Q T)e


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STACK BASE, AL:O"IT=M

E!AMPLE3 A4 B - C

Next to'en

A

+

B

*

C

Stac'

empty

+

+

+*

+*

Output

A

A

AB

AB

ABC

inal output A B C - - 0Postfix)


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E!AMPLE 83 A-0B4C1-, ABC4-,-

Next to'en

none

A

*

(

B

+C

Stac'

empty

empty

*

*(

*(

*(+*(+

Output

none

A

A

A

AB

ABABC


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At t)is point> (e (ant to unstac' #o(n

to t)e correspon#in% left parent)eses an#

t)en #elete t)e left an# ri%)t parent)eses$


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Next to'en

1

-

,

#one

Stac'

-

-

-

e&pt*

Output

ABC4

ABC4-

ABC4-,

ABC4-,-


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2NCTION TO CONVE"T "OM

INI! TO POSTI!

voi# postfix 0voi#1

+- output t)e postfix of t)e expressions fro& infix

expression> t)e expression strin%> t)e stac' an# top are%lo


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INI! TO POSTI!

for 0to'en %et@to'en0s*& n1

to'en eos to'en %et@to'en0s*&

n11

if 0to'en operan#1

printf0Qc> s*&


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INI! TO POSTI!

else

+- re&ove an# print s*& to'en1 DD



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INI! TO POSTI!

()ile 0to'en #elete0top11 eos1

printf@to'en0to'en1

printf 0Qn1

D

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