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CSC341

/ISC361

CSC341

/ISC361

CSC341

/ISC361

CSC341

/ISC361

DataStru

ctures&Algorithm

s

DataStru

ctures&Algorithm

s

DataStru

ctures&Algorithm

s

DataStru

ctures&Algorithm

s

SORTING-QUICKSORT

QuickSort

-S

aceCom

lexit

8/22/2009 Sundar B.

CallStacksand

FunctionCallOverhead

-Recursive

Functions

-TailCa

llsandTailRecursion

QuickSort

-Function

CallOverhead

-TailCallElimination

-UseofExplicitStack

-ControllingStackSize

1

CSIS, BITS, Pilani

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QUICKSOR

TSPACECOM

PLEXITY

QuickSort

usesadditionals

pace

throughtherecursivecalls

forkeepingtrackofallthesub-liststhataretobesorted

Worstcas

e:Unbalancedpa

rtitioning

Exactly

N-1

framesoncalls

tack(atmaximumd

epth)

8/22/2009 Sundar B.

Averagec

ase:Balancedpartitioning(constantfactorbalance)

(logN

)framesoncallstac

k.

Bestcase:Equalpartitions

Exactly

logNframesoncall

stack(atmaximumdepth)

Isthisopt

imal?

Canwe

reducethecallstac

koverhead?

StackSize

Fram

eSize

2CSIS, BITS, Pilani

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CALLSTACK

8/22/2009 Sundar B.

Considerthefollowing

procedure:

quad(A,B,C

,sign)

{disc=B

*B-4*A*C;

if(disc=

-

Exercise:Drawthecallstack

foreachof

thefivepointsof

execution.Assumequadisthe

mainfunctionintheprogram.

CSIS, BITS, Pilani3

return

(-B+sign

*sqrt(disc))/(2*A);

}

Callsequence:

1.

quad

2.

quad

-->printError

3.

sqrt

5.

next);

len(ls){

len_

tl(ls,0);

} len_

tl(ls,acc){

CSIS, BITS, Pilani5

}

if(ls==null)returnacc;

elsereturn

len_

tl(ls

->next,acc+1)

Exercise:

Drawthes

tackforlen(ls)

wherelshas4elements

Exercise:

Drawthe

stackfor

len_

tl(ls)

wherelshas4

elements

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FUNCTION

CALLOVERHEADANDRECURSION

Observationsfromtheexample:

Doyou

needthecallfram

esonstackforlen_

tl?

Foratail

call,

thereisno

continuation

i.e.

no

computationtobedone(withinthe

callingfunction)

afterthereturn

8/22/2009 Sundar B.

i.e.

no

contextinformationisneeded

i.e.

no

stackframeneede

d

Foratail

recursivefunction/procedure,

Onlyonecallframeisne

eded

Argu

ments(values)can

beusedtoupdate

parameters

(variables)onthesame

frameforeveryca

ll.

i.e.

Costofatailrecursivefunction/proced

ureissameasan

iterativ

eprocedure.

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TAILRECURSIONELIMINATION-EXAMPL

E

len_

tl(ls,acc){

if(ls==null)returnacc;

elsereturn

len_

tl(ls

->next,acc+1)

len_

tl(ls,

acc){

B:if(ls==null)returnacc;

else{//ls!=NULL

ls=ls->nextacc=acc+1

7

goto

B;

}}

len_

tl(ls,a

cc){

while(ls!=null){

ls=

ls->next;

acc=acc+1;

} returnacc;

}

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QUICKSOR

T-CALLSTACK

OVERHEAD

Consider

thefollowingim

plementationo

fQuickSort

voidquic

kSort(Elementls[],

intstart,

intend)

{

if(start