02 Stacks Queues

8/9/2019 02 Stacks Queues

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DATA STRUCTURESCOL 106

AMIT KUMAR, SHWETAAGRAWAL


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Why are we study!" DataStru#tures $


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M%der! w%r&d a&& a'%ut (DATA


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Dea&!" wth data(

H%w t% use t $

H%w t% st%re t $

H%w t% )r%#ess t $

H%w t% "a! *+!%w&ed"e

-r%. t $ H%w t% +ee) t se#ret$


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Dea&!" wth data(

H%w t% use t $

H%w t% st%re t $

H%w t% )r%#ess t $

H%w t% "a! *+!%w&ed"e

-r%. t $ H%w t% +ee) t se#ret$


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H%w sh%u&d data 'e

st%red$De)e!ds %! y%urre/ure.e!t


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ut we hae s%.e 'u&d!"'&%#+s

Data s derse 22


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T% st%re %ur '" data


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10

E&e.e!tary Data*Stru#tures

Arrays

Lists

Stacks Queues

Trees

RF

1

2

3 4

5 6

7 8

I! s%.e &a!"ua"es these are 'as# data ty)es 3 !%thers they !eed t% 'e .)&e.e!ted

head


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Stacks


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Sta#+

A &st -%r wh#h I!sert a!d De&ete area&&%wed %!&y at %!e e!d %- the &st4the top5 LIO 3 Last !, rst %ut

Push

Pop Pop


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What s ths "%%d -%r $

7a"e8sted hst%ry ! a We''r%wser


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U!d% se/ue!#e ! a te9t edt%r


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U!d% se/ue!#e ! a te9t edt%r Sa!" &%#a& ara'&es whe! %!e

-u!#t%! #a&&s a!%ther, a!d ths

%!e #a&&s a!%ther


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H%w sh%u&d we re)rese!tt $

Wrte #%de ! )yth%! $


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Wrte #%de ! C $


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Wrte #%de ! C $

Wrte #%de ! :aa $

Are!;t we esse!ta&&y d%!"the sa.e th!"$


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1e#ts,

wth %)erat%!sde=!ed %! the.


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?0

E9a.)&es

as# Ty)es !te"er, rea&4@%at!" )%!t5, '%%&ea!

40,15, #hara#ter Arrays

A022


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?1

A .a))!" -r%. a! !de9 set, su#h as{0,1,2,,n}, !t% a #e&& ty)e

O'>e#tsset %-#e&&sO)erat%!s

create(A,n)

put(A,v,i) %rA[i] = v vaue(A,i)

ADT Array


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A'stra#t Data Ty)es 4ADTs5

A! a'stra#t data ty)e 4ADT5 sa! a'stra#t%! %- a data

stru#ture

A! ADT s)e#=es

Data st%redO)erat%!s %! the data

Err%r #%!dt%!s ass%#ated

wth %)erat%!s


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23

ADT -%r st%#+ trade

The data st%red are 'uyse&& %rders

The %)erat%!ssu))%rted are

%rder 'uy 4st%#+, shares5 %rder se&&4st%#+, shares 5

%d #a!#e&4%rder5

Err%r #%!dt%!s uyse&& a !%!e9ste!t st%#+

Ca!#e& a !%!e9ste!t %rder


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Objects:

A =!te se/ue!#e %- !%des

Operations:

Create

7ush I!sert e&e.e!t at t%)

T%) Retur! t%) e&e.e!t 7%) Re.%e a!d retur! t%) e&e.e!t

IsE.)tytest -%r e.)ty!ess

Sta#+ ADT


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E9#e)t%!s

Atte.)t!" the e9e#ut%! %- a!%)erat%! %- ADT .ay s%.et.es#ause a! err%r #%!dt%!, #a&&ed a!

e9#e)t%! E9#e)t%!s are sad t% 'e *thr%w! 'y

a! %)erat%! that #a!!%t 'e e9e#uted

I! the Sta#+ADT, %)erat%!s )%)a!dt%)#a!!%t 'e )er-%r.ed - the sta#+ se.)ty

Atte.)t!" the e9e#ut%! %- )%)%r t%)

%! a! e.)ty sta#+ thr%ws a!


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E9er#se Sta#+s

Des#r'e the %ut)ut %- the -%&&%w!" seres %- sta#+%)erat%!s

7ush45

7ush4F5

7%)45

7ush4?5

7ush45

7%)45

7%)45

7ush4


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C Ru!8t.e Sta#+

The C ru!8t.e syste.+ee)s tra#+ %- the #ha! %-a#te -u!#t%!s wth a sta#+

Whe! a -u!#t%! s #a&&ed, the

ru!8t.e syste. )ushes %! thesta#+ a -ra.e #%!ta!!" L%#a& ara'&es a!d retur! a&ue

7r%"ra. #%u!ter, +ee)!" tra#+%- the state.e!t 'e!" e9e#uted

Whe! a -u!#t%! retur!s, ts-ra.e s )%))ed -r%. thesta#+ a!d #%!tr%& s )assed t%the .eth%d %! t%) %- the sta#+

main() {

int i;

i = 5;

foo(i);

}

foo(int j)

{

int k;

k = j+1;

bar(k);

}

bar(int m)

{

}

bar

PC = 1

m = 6

foo

PC = 3

j = 5

k = 6

main

PC = 2

i = 5


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Sta#+s ?

7are!theses Mat#h!"

Ea#h *4, *, %r * .ust 'e )aredwth a .at#h!" *5, *J, %r * correct: 4 544 5544 5B5J

correct: 444 544 5544 5B5J

incorrect: 544 5544 5B5J

incorrect: 4 B5J

incorrect: 4


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Sta#+s ?e#t %5 !serts

e&e.e!t % at the e!d %-the /ueue

de/ueue45 re.%es a!dretur!s the e&e.e!t at the-r%!t %- the /ueue

Au9&ary /ueue%)erat%!s -r%!t45 retur!s the

e&e.e!t at the -r%!twth%ut re.%!" t

se45 retur!s the!u.'er %- e&e.e!tsst%red

sE.)ty45 retur!s a%%&ea! a&ue !d#at!"whether !% e&e.e!ts are

st%red E9#e)t%!s

Atte.)t!" the e9e#ut%!%- de/ueue %r -r%!t %! a!e.)ty /ueue thr%ws a!E.)tyQueueE9#e)t%!


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E9er#se Queues

Des#r'e the %ut)ut %- the -%&&%w!" seres %- /ueue%)erat%!s

e!/ueue45

e!/ueue4F5

de/ueue45

e!/ueue4?5

e!/ueue45

de/ueue45

de/ueue45

e!/ueue4


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A))at%!s %- Queues

Dre#t a))at%!s Wat!" &!es

A##ess t% shared res%ur#es 4e2"2,

)r!ter5

I!dre#t a))at%!s

Au9&ary data stru#ture -%r a&"%rth.s C%.)%!e!t %- %ther data stru#tures


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49

Array8'ased Queue

Use a! array %- se N! a #r#u&ar -ash%!

Tw% ara'&es +ee) tra#+ %- the -r%!t a!d rear f !de9 %- the -r%!t e&e.e!t

r !de9 ..edate&y )ast the rear e&e.e!t

Array &%#at%! rs +e)t e.)ty

Q

0 1 ! rf

norma" config/ration

Q

0 1 ! fr

ra++e#aro/n# config/ration


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5

Queue O)erat%!s

We use the.%du&%%)erat%r

4re.a!der %-ds%!5

Algorithmsize()

return(N + r f) mod N

AlgorithmisEmpty()

return(f = r)

Q

0 1 ! rf

Q

0 1 ! fr


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Queue O)erat%!s 4#%!t25

Algorithmenqueue(o)

ifsize()=N - 1then

throw

FullQueueException

else

Q[r]=o

r=(r + 1) mod N

O)erat%! e!/ueuethr%ws a! e9#e)t%! -the array s -u&&

Ths e9#e)t%! s.)&e.e!tat%!8

de)e!de!t

Q

0 1 ! rf

Q

0 1 ! fr


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Queue O)erat%!s 4#%!t25

O)erat%! de/ueuethr%ws a! e9#e)t%!- the /ueue s e.)ty

Ths e9#e)t%! ss)e#=ed ! the/ueue ADT

Algorithmdequeue()

ifisEmpty()then

throw

EmptyQueueException

else

o=Q[f]

f=(f + 1) mod N

returno

Q

0 1 ! rf

Q

0 1 ! fr


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7er-%r.a!#e a!d L.tat%!s8 array8'ased .)&e.e!tat%! %- /ueue ADT

7er-%r.a!#e Let n'e the !u.'er %- e&e.e!ts ! the

/ueue

The s)a#e used s O(n Ea#h %)erat%! ru!s ! t.e O(1

L.tat%!sThe .a9.u. se %- the /ueue .ust 'e

de=!ed a priori, a!d #a!!%t 'e #ha!"edTry!" t% e!/ueue a! e&e.e!t !t% a -u&&

/ueue #auses a! .)&e.e!tat%!8s)e#=#e9#e)t%!

Gr%wa'&e Array 'ased


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Gr%wa'&e Array8'asedQueue

I! a! e!/ueue %)erat%!, whe! thearray s -u&&, !stead %- thr%w!" a!e9#e)t%!, we #a! re)&a#e the array

wth a &ar"er %!e S.&ar t% what we dd -%r a! array8

'ased sta#+

The e!/ueue %)erat%! has a.%rtedru!!!" t.e O(nwth the !#re.e!ta& strate"y

O(1wth the d%u'&!" strate"y


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*ectors

E9er#se

Des#r'e h%w t% .)&e.e!t a/ueue us!" a s!"&y8&!+ed &st Queue %)erat%!s e!/ueue495,

de/ueue45, se45, sE.)ty45

%r ea#h %)erat%!, "e the ru!!!"t.e

Queue wth a S!"&y L!+ed


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Queue wth a S!"&y L!+edLst

We #a! .)&e.e!t a /ueue wth a s!"&y &!+ed &st The -r%!t e&e.e!t s st%red at the head %- the &st

The rear e&e.e!t s st%red at the ta& %- the &st

The s)a#e used s O(na!d ea#h %)erat%! %- the Queue ADTta+es O(1 t.e

NOTE we d% !%t hae the &.tat%! %- the array 'ased.)&e.e!tat%! %! the se %- the sta#+ '# the se %- the &!+ed

&st s !%t =9ed, I2e2, the /ueue s NEER -u&&2

f

r

no#es

e"ements

frontrear


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I!-%r.a& C Queue I!ter-a#e

I!-%r.a& C!ter-a#e -%r %urQueue ADT

Re/ures thede=!t%! %-#&assEmpty3ueueException

N%#%rres)%!d!"'u&t8! STL #&ass

template

class3ueue{

public:

int size();

bool isEmpty();

Objectront()t!ro"(Empty3ueueException);

voi#en4ueue(Object o);

Object #e4ueue()

t!ro"(Empty3ueueException);$;


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Queue Su..ary

Queue O)erat%! C%.)&e9ty -%rDPere!t I.)&e.e!tat%!s

1'29'15 4(54(5 $)

*ectors 58

ArrayFixed-Size

ArrayExpandable (doublin!"ra"ey#

$i!"Sinly-$in%ed

#e:/e/e,- .,1- .,1- .,1-

en:/e/e,o- .,1- .,n- orst Case.,1- %est Case.,1- $erage Case

.,1-

front,- .,1- .,1- .,1-

Sie,- ism+t,- .,1- .,1- .,1-

Th D '& E d d Q ADT


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The D%u'&e8E!ded Queue ADT42F5

The D%u'&e8E!ded Queue, %rDe/ue,ADT st%res ar'trary%'>e#ts2 47r%!%u!#ed de#+;5

R#her tha! sta#+ %r /ueueADTs2 Su))%rts !sert%!s a!dde&et%!s at '%th the -r%!t

a!d the e!d2 Ma! de/ue %)erat%!s

!sertrst4%'>e#t %5 !sertse&e.e!t % at the 'e"!!!" %-the de/ue

!sertLast4%'>e#t %5 !sertse&e.e!t % at the e!d %- thede/ue

Re.%erst45 re.%es a!dretur!s the e&e.e!t at the-r%!t %- the /ueue

Re.%eLast45 re.%es a!dretur!s the e&e.e!t at thee!d %- the /ueue

Au9&ary /ueue %)erat%!s =rst45 retur!s the e&e.e!t

at the -r%!t wth%utre.%!" t

&ast45 retur!s the e&e.e!t at

the -r%!t wth%ut re.%!" t se45 retur!s the !u.'er %-

e&e.e!ts st%red

sE.)ty45 retur!s a %%&ea!a&ue !d#at!" whether !%e&e.e!ts are st%red

E9#e)t%!s Atte.)t!" the e9e#ut%! %-

de/ueue %r -r%!t %! a!e.)ty /ueue thr%ws a!E.)tyDe/ueE9#e)t%!


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D%u'&y L!+ed Lst

A d%u'&y &!+ed &st )r%des a!atura& .)&e.e!tat%! %- theDe/ue ADT

N%des .)&e.e!t 7%st%! a!dst%re

e&e.e!t

&!+ t% the )re%us !%de

&!+ t% the !e9t !%de

S)e#a& tra&er a!d header !%des

+re ne!t

e"em

trai"er0ea#er no#es'+ositions

e"ements

no#e

De/ue wth a D%u'&y L!+ed


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De/ue wth a D%u'&y L!+edLst

We #a! .)&e.e!t a de/ue wth a d%u'&y &!+ed &stThe -r%!t e&e.e!t s st%red at the =rst !%de

The rear e&e.e!t s st%red at the &ast !%de

The s)a#e used s O(na!d ea#h %)erat%! %- the

De/ue ADT ta+es O(1 t.e

"astfirst

e"ements

first


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6?

I.)&e.e!t!" De/ues wthD%u'&y L!+ed Lsts

Here;s asua&at%! %- the#%de -%rre.%eLast452

7 - d L


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7er-%r.a!#e a!d L.tat%!s8 d%u'&y &!+ed &st .)&e.e!tat%! %- de/ue ADT

7er-%r.a!#e Let n'e the !u.'er %- e&e.e!ts ! the

sta#+

The s)a#e used s O(n Ea#h %)erat%! ru!s ! t.e O(1

L.tat%!s NOTE we d% !%t hae the &.tat%! %- the

array 'ased .)&e.e!tat%! %! the se %-the sta#+ '# the se %- the &!+ed &st s !%t=9ed, I2e2, the de/ue s NEER -u&&2


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De/ue Su..ary

De/ue O)erat%! C%.)&e9ty -%rDPere!t I.)&e.e!tat%!s

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*ectors 64

ArrayFixed-Size

ArrayExpandable(doublin !"ra"ey#

$i!"Sinly-$in%ed

$i!"&oubly-$in%ed

remoe;irst,-remoe


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6

I.)&e.e!t!" Sta#+s a!d Queueswth De/ues

Stacks with Deques:

Queues with Deques:


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The Ada)t%r 7atter!

Us!" a de/ue t% .)&e.e!t a sta#+ %r /ueue s a!e9a.)&e %- the ada)t%r )atter!2 Ada)t%r )atter!s.)&e.e!t a #&ass 'y us!" .eth%ds %- a!%ther #&ass

I! "e!era&, ada)t%r #&asses s)e#a&e "e!era& #&asses

Tw% su#h a))at%!s88 S)e#a&e a "e!era& #&ass 'y #ha!"!" s%.e.eth%ds2

Ex: implementing a stack with a deque.88 S)e#a&e the ty)es %- %'>e#ts used 'y a "e!era&ass2

Ex: Defning an IntegerArrayStack class

02 Stacks Queues

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