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Postfix Expression • Infix expression is the form AOB – A and B are numbers or also infix expression – O is operator ( +, -, *, / ) • Postfix expression is the form ABO

Infix and postfix expressions1 - Stonehill College

Infix and postfix expressions In a postfix expression, • an operator is written after its operands • the infix expression 2+3 is 23+ in postfix notation • For postfix expressions, operations are performed in the order in which they are written (left to right) • No parentheses are necessary ‘ • the infix expression 2+3*4

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Postfix evaluation example zExpression: 5 4 + 8 * – Step 1: push 5 – Step 2: push 4 – Step 3: pop 4, pop 5, add, push 9 – Step 4: push 8 – Step 5: pop 8, pop 9, multiply, push 72 – Step 6: pop 72– the result zA bad postfix expression is indicated by: – Less than two operands to pop when operator occurs – More than one value on

PRODUCT DATA SHEET Sika® PostFix

Sika® PostFix is a two-part, pre-proportioned polyureth-ane resin which when mixed produces an expanding foam It has been specifically formulated and packaged to provide a lightweight, mix-in-the-bag, and fast-setting backfill for wooden, PVC and steel in-ground supports Sika® PostFix is based upon Sika’s proven foam techno-

Postfix: A Simple Stack Language - Wellesley College

CS251 Programming Languages Handout # 27 Prof Lyn Turbak March 3, 2005 Wellesley College Revised March 3, 2005 Postfix: A Simple Stack Language

Prefix, Infix, Postfix - Weebly

03-04 C4 Prefix/Infix/Postfix Evaluate the following prefix expression with A =20, B = 4, C =2, D = 5 + / * A B D C D 4 03-04 C4 Prefix/Infix/Postfix Translate the following infix expression to postfix R A AR S N 1 5 04-05 C4 Prefix/Infix/Postfix Evaluate the following prefix expression Note that all numbers are single digit

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Conversion from infix to postfix expression: Algorithm POSTFIX (Q, P) Suppose Q is an arithmetic expression written in infix notation This algorithm finds the equivalent postfix expression P Step1: Push “(” onto STACK and add ’’)’’ to the end of Q Step2: Scan Q from left to right and repeat step 3 to 6 for each element of Q, until

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In converting infix expressions to postfix notation, the following fact should be taken into consideration: In infix form, the order of applying operators is governed by the possible appearance of parentheses and the operator precedence relations; however, in postfix form, the order is simply the “natural” order – i e , the

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Converting infix to postfix •useful because evaluation of postfix is faster •humans usually apply the rules of precedence to set parentheses, i e , to determine the order of evaluation (and then build the postfix expression starting with the first operator), e g , 1*2+3 = (1*2)+3 leads to postfix 12*3+ •how do we apply the rules of

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CS251ProgrammingLanguagesHandout#27

Prof.LynTurbakMarch3,2005

WellesleyCollegeRevisedMarch3,2005

Postfix:ASimpleStackLanguage

wegiveabriefintroductiontoPostfix.

1Syntax

1.1Commands

form:

²Anyintegernumeral.E.g.,17,0,-3.

"Golf?Nosir--preferprisonflog!", "Yousay\"Goodbye\"\n\tandIsay\"Hello\"." ne,pop,pri,prs,put,rem,sel,sub,andswap. subcommandsseparatedbywhitespace. chicalstructure.

1.2Programs

(postfix10getmul) (postfix2add2div) (5sub)swapexecexec) (postfix1(2get0eq ("\n"prs) ("\nn="prs2getpri";ans="prs1getpri

2getmul2get1sub2put3getexec)

selexec) swap

13getexec)

1

1.3Abstractvs.ConcreteSyntax

typede¯nitions: typepgm=(*PostFixprograms*)

Pgmofint*comlist

andcom=(*PostFixcommands*)

Intofint(*pushintegernumeral*)

|Strofstring(*pushstringliteral*) |Seqofcomlist(*executablesequence*) |Pop(*poptopvaluefromstack*) |Swap(*swaptoptwovaluesofstack*) |Sel(*chooseoneoftwovaluesfromstack*) |Get(*pushvalueatgivenstackindex*) |Put(*storetopofstackatgivenstackindex*) |Prs(*printstring*) |Pri(*printinteger*) |Exec(*executesequenceattopofstack*) |Add|Sub|Mul|Div|Rem(*arithmeticops*) |LT|LE|EQ|NE|GE|GT(*relationalops*)

Forexample,theconcreteprogram

(5sub)swapexecexec)

Pgm(1,[Seq[Seq[Int2;Get;Swap;Exec];

Seq[Int3;Mul;Swap;Exec];

Swap];

Seq[Int5;Sub];

Swap; Exec;

Exec])

syntaxofPostfixisleftasanexercise.

2Semantics

termsofhowitmanipulatestheimplicitstack. 2

²Anintegernumeraln:Pushnontothestack.

²Astringliterals:Pushsontothestack.

therange[1;n]. sequencesareusedinconjunctionwithexec. stackvalueisn'tanexecutablesequence.

Figure1:SemanticsofPostfixcommands.

3 anexecution. andcalculatesa¢b¡2¢c: (postfix3mulswap2mulswapsub) ontheargumentlist[3;4;5]:

CommandsStack

mul swap 2 mul swap sub 3 4 5 swap 2 mul swap sub 12 5 2 mul swap sub 5 12 mul swap sub 2 5 12 swap sub 10 12 sub12 10 -2 4 andothersituations. stackoperations: (postfix0123pop)¡[]¡!2 (postfix012swap3pop)¡[]¡!1 programcommands. (postfix2swap)¡[3;4]¡¡!4 intheprogram. (postfix14sub)¡[3]¡!-1 (postfix14add5mul6sub7div)¡[3]¡!4 (postfix0173div)¡[]¡!5 (postfix0173rem)¡[]¡!2 (postfix034lt)¡[]¡!1 (postfix034gt)¡[]¡!0 (postfix034lt10add)¡[]¡!11 5 (postfix21get)¡[5;6]¡¡!5 (postfix22get)¡[5;6]¡¡!6

4getfgetxg

5getfgetxagain,atnewindexg

mulfpushx2onstackg

2getmulfmultiplyx2byag

5getfgetxagain,atnewestindexg

4getfgetbatnewindexg

mulfcalculatebxg addfaddax2andbxg

4getfgetcg

addfax2+bx+cisnowattopofstackg )¡[3;4;5;10]¡¡¡¡¡!345 ofotherlanguagesinPostfix.

3getfPushcg

mulfReplacecandabyacontopofstackg

2putfReplacecbyaconbottomofstackg

subfCalculateac-bg )¡[2;3;4]¡¡¡!5 6

CommandsStack

((3getswapexec)(2mulswapexec)swap) (5sub) swap exec exec 7 (5sub) swap exec exec ((3getswapexec)(2mulswapexec)swap) 7 swap exec exec (5sub) ((3getswapexec)(2mulswapexec)swap) 7 exec exec ((3getswapexec)(2mulswapexec)swap) (5sub) 7 (3getswapexec) (2mulswapexec) swap exec (5sub) 7 (2mulswapexec) swap exec (3getswapexec) (5sub) 7 swap exec (2mulswapexec) (3getswapexec) (5sub) 7 exec(3getswapexec) (2mulswapexec) (5sub) 7 3 get swap exec (2mulswapexec) (5sub) 7 get swap exec 3 (2mulswapexec) (5sub) 7 swap exec 7 (2mulswapexec) (5sub) 7 exec(2mulswapexec) 7 (5sub) 7 2 mul swap exec 7 (5sub) 7 mul swap exec 2 7 (5sub) 7 swap exec 14 (5sub) 7 exec(5sub) 14 7 5 sub 14 7 sub5 14 7 9 7 (postfix123sel)¡[1]¡!2 (postfix123sel)¡[0]¡!3 writteninPostfix: (postfix1(ffactorialloopcodeg

2get0eqfisn=0?g

()fifyes,we'redone;ansisontopofstackg

2get1sub2putfandnÃn-1;g

3getexec)fthenexecuteloopagaing

selexec) swapfswapnwithfactorialloopcodeg

1fpushinitialanswer=1g

3getexecfexecuteloopg

FactIter.

CommandsStack

FactIterswap13getexec3

swap13getexecFactIter3

13getexec3FactIter

3getexec13FactIter

getexec313FactIter execFactIter13FactIter :::manystepsomitted::: :::manystepsomitted::: :::manystepsomitted::: :::manystepsomitted:::

60FactIter

8 followingprogram: (postfix1(ffactorialrecursioncodeg

2get0eqfisn=0?g

(poppop1)fifyes,return1g (2get1subfpushn-1g

2get1getexecfcallfactrecursivelyg

swappopfdeletefactcodeg mulfmultiplyonwayoutg selexec)

1getexecfcallfactinitiallyg

CommandsStack

(1getexec)1getexec

1getexec(1getexec)

getexec1(1getexec) exec(1getexec)(1getexec)

1getexec(1getexec)

(postfix2

2getprifDisplay1stargg

"and"prsfDisplay``and''g

1getprifDisplay2ndargg

"\n"prsfDisplaynewlineg addfReturnsumofargsg 9

CommandsStack

FactRec1getexec3

1getexecFactRec

3 getexec0

FactRec

3 execFactRec

FactRec

3 :::manystepsomitted:::

2get0eq(poppop1)

(2get1sub2get1getexecswappopmul) selexecFactRec 3 :::manystepsomitted:::

2get0eq(poppop1)

(2get1sub2get1getexecswappopmul) selexec swappopmulFactRec 2

FactRec

3 :::manystepsomitted:::

2get0eq(poppop1)

(2get1sub2get1getexecswappopmul) selexec swappopmul swappopmulFactRec 1

FactRec

2

FactRec

3 :::manystepsomitted:::

2get0eq(poppop1)

(2get1sub2get1getexecswappopmul) selexec swappopmul swappopmul swappopmulFactRec 0

FactRec

1

FactRec

2

FactRec

3 :::manystepsomitted::: poppop1 swappopmul swappopmul swappopmulFactRec 0

FactRec

1

FactRec

2

FactRec

3 :::manystepsomitted::: swappopmul swappopmul swappopmul1

FactRec

1

FactRec

2

FactRec

3 :::manystepsomitted::: swappopmul swappopmul1

FactRec

2

FactRec

3 :::manystepsomitted::: swappopmul2

FactRec

3 :::manystepsomitted::: 6 10 oftheloop: (postfix1(2get0eq ("\n"prs) ("\nn="prs2getpri";ans="prs1getpri

2getmul2get1sub2put3getexec)

selexec) swap

13getexec)

consolewindow: n=5;ans=1 n=4;ans=5 n=3;ans=20 n=2;ans=60 n=1;ans=120 11quotesdbs_dbs7.pdfusesText_13