Pai Ch04 Stack

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PROPRIETARY MATERIAL. 2008 The McGraw-Hill Companies, Inc. All rights reserve. !o part o" this #ower#oint slie ma$ %e ispla$e, repro&ce or istri%&tein an$ "orm or %$ an$ means, witho&t the prior written permission o" the p&%lisher, or &se %e$on the limite istri%&tion to teachers an e&cators permitte %$ McGraw-Hill

"or their inivi&al co&rse preparation. I" $o& are a st&ent &sing this #ower#oint slie, $o& are &sing it witho&t permission.

c raw- ucat on

Copyrighted Material-Additional resource material supplied with the book Data Structures and Algorithms : Concepts, echni!ues and Applications authored "y G#A#$# %ai and published by

Tata McGraw Hill. This resource material is for Instructor's use only.

Stacks

(Chapter 4)


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Introduction - definitions

Stack Operations (Push & Pop)

Stack Implementation (Array & Linked List)

Algorithms of Push and Pop operationsApplications

Recursie Programming

!aluation of !"pressions

ADT for stacks

Outline of Chapter 4


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1. Stack : Denition


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A stackis an ordered list with therestriction that elements are addedor deleted from only one end of thelist termed top of stack.

The other end of the list which lies

inactive is termed bottom of stack.

The stack data structure oeys theprinciple ofLast In First Out(!"#$).

"n other words% elements inserted oradded into the stack &oin last andthose that &oined last are the 'rst toe removed.

What is Stack? Denition

Top of stack ottom ofstack


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The two operations which stack data structure

supports (i) "nsertion or addition of elements known as Push.(ii) eletion or removal of elements known as Pop.

Stack Operations

Top of stack ottom of

stack


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Certain prolems * applications

need stack mechanism+

(i) Simulation of people enterin,* leavin, a lift in a uildin,.(ii) -eap memory mana,ement

in $S.(iii) ana,in, data in recursion(iv) ana,in, arithmetice/pressions

0e shall see some e/ampleslater.

Why use Stack?

1nters !eaves


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2. Stack Ipleentation


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2 A common and a asic method of

implementin, stacks is to makeuse of another fundamental datastructure vi3.% arrays.

2 0hile arrays are sequential datastructures the other alternative

of employin, linked datastructures have eensuccessfully attempted andapplied.

2 An array ased implementation of

stacks is fairly convenientconsiderin, the fact that stacksare unidimensional ordered listsand so are arrays which despitetheir multidimensional structureare inherently associated with aonedimensional consecutive set

Stack Ipleentation

Top of stack

ottom ofstack

55 "n 6ava

"nt top789 55 currentlocation% top78+ stackempty.int:; Stack7 new int:8


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Algorithm 4.1 Implementation of push

operation on a stack// Stack is the array

// n=max size; top=current location;

// item=data to be pushed

procedure PUSH(S!"#$ n$ top$ item% if(top = n% thenS!"#&'U; else

) top = top * +;

S!"#,top- = item; /.store

item as top element of STACK */

endPUSH

Stack : !l"orith of P#S$


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Algorithm 4.2 :Implementation ofpop operation on a stack

// S!"# is the array

// top=current location;

// item=data retrie0edprocedure P1P(S!"#$ top$ item% if(top = 2+% thenS!"#&34P5; else) item = S!"#,top-;

top = top 2 +;

endP1P

Stack : !l"orith of POP


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%. &'aples of Stack

!pplications


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urin, the e/ecutionof a recursive pro,ram% to keep trackof the callsmade to itself and to record the status of theparameters at the time of the call% a stackdata structure isused

Tail recursionor Tail end recursionis a special case ofrecursion where a recursive call to the function turns out toe the last action in the callin, function. >ote that therecursive call needs to e the last executed statement in

the function and not necessarily the last statement in thefunction.

&'aple(1: Stack !pplication

)ecursi*e pro"rain"

.'


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"n a stack implementation of a recursive call% allthe local variales of the function that are to e?rememered@% are pushed into the stack whenthe call is made.

pon termination of the recursive call% the localvariales are popped out and restored to theirprevious values.

>ow for tail recursion% since the recursive callturns out to e the last e/ecuted statement% thereis no need that the local variales must e pushedinto a stack for them to e ?rememered@ and?restored@ on termination of the recursive call.

&'aple: Stack !pplication

)ecursi*e pro"rain" +cont,

.(


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&'aple: Data o*eent inStack for the recursi*e "cf+4-,

00 call gc12(,*3

00 a 4 (5 " 4 *5 answer 4 &

public static int gc1 int a! int b"

# if a $$ b" %% if a e&uals b

return a

if a ( b"

return gc1 a - b! b"

else %% if a ) b

return gc1a! b - a"

*

%6SH

gc1 +! ,"

%6SH

gc1+! "

gc1 +! ,"

%6SH

gc1! "

gc1+! "

gc1 +! ,"

%7%

return

gc1! "

gc1+! "

gc1 +! ,"

8stcall% BS-

a% BS-

aD% BS-a7% B$B

.)


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In' e'pression $perandD $peratorD $perandD

An aritmetic e/pression+

Post' e'pression $perandD $perandD $peratorD

Pre' e'pression $peratorD $perandD$perandD

dcba +

+ dabc

bcda '+

&'aple(2: Stack !pplication

&*aluation of &'pressions

.*


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Scenario: Given abc*+d- !e get ""b*c#+a#-d

Algorithm 4.$ : %rocedure to evaluate a post fi& e&pression '.(nput: '&pression ')utput: )riginal '&pression%rocedure 'A,%)S(/"'# & 0 get,ne&t,character "'#

*get the next character of expression E */ case & of

:& is an operand: %ush & into stac3 S

:& is an operator: %op out reuired number ofoperands from the stac3 S

evaluate the operator and pushthe result into the stac3 S

:& 0 567: %op out the result from stac3 S end case

end 'A-%)S(/.

.+


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Post' e'pression $perandD $perandD

$peratorD + (2)*

&'ercise: /racin" the Stackoperations to e*aluate Post'

&'pressions

232

732

212

? ? ?

.


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Pre' e'pression $peratorD $perandD $perandD

&'ercise: Can 0e use Stack toe*aluate Pre' &'pressions? /ry

it

? ? ? ? ? ? ?

bcda '+

.


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4. !D/ of Stack

&/


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Data o3ects:

A 'nite set of elements of the same type

Operations:Create an empty stack and initiali3e top of stack

"63!3(S!"#%Check if stack is empty

"H#&S!"#&34P5(S!"#%(oolean function)

Check if stack is full "H#&S!"#&'U(S!"#%(oolean function)

Bush I34into stack S!"#PUSH(S!"#$ I34%

Bop element from stack S!"#and output the elementpopped in I34

P1P(S!"#$ I34%

!D/ for Stack

&.


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&'ercises

&&


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(1 Write a a*a Interface 5 a*a pro"ra to ipleent the Stack!D/.

(2 Write a a*a pro"ra- usin" Stack in con*ertin" a 6ecialnuer into a inary nuerThe lo,ic for transformin, a decimal numer into a inary numer is asfollows+

Eead a numer

"teration (while numer is ,reater than 3ero)#ind out the remainder after dividin, the numer y FBrint the remainderivide the numer y F

1nd the iteration-owever% there is a prolem with this lo,ic. Suppose the numer% whose

inary form we want to 'nd is FG. sin, this lo,ic% we ,et the result as888


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PROPRIETARY MATERIAL. 2008 The McGraw-Hill Companies, Inc. All rights reserve. !o part o" this #ower#oint slie ma$ %e ispla$e, repro&ce or istri%&te

in an$ "orm or %$ an$ means, witho&t the prior written permission o" the p&%lisher, or &se %e$on the limite istri%&tion to teachers an e&cators permitte %$ McGraw-Hill

"or their inivi&al co&rse preparation I" $o& are a st&ent &sing this #ower#oint slie $o& are &sing it witho&t permission

Copyrighted Material-Additional resource material supplied with the book Data Structures and Algorithms : Concepts, echni!ues and Applications authored "y G#A#$# %ai and published by

Tata McGraw Hill. This resource material is for Instructor's use only.

1nd of

Stacks

(Chapter 4)

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