Lec-4 C Programming

8/19/2019 Lec-4 C Programming

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1Dept. of CSE, IIT KGP

FunctionsFunctions

CS10001:CS10001: Programming & Data StructuresProgramming & Data Structures

Pallab DasguptaPallab Dasgupta

Professor, Dept. of ComputerProfessor, Dept. of ComputerSc. & Engg.,Sc. & Engg.,

Indian Institute ofIndian Institute ofTechnology KharagpurTechnology Kharagpur


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IntrouctionIntrouction

• FunctionFunction – ! se"f#containe program segment t$at carries out some! se"f#containe program segment t$at carries out some

specific, %e""#efine tas.specific, %e""#efine tas.

• Some properties:Some properties: – E'er( C program consists of one or more functions.E'er( C program consists of one or more functions.

• )ne of t$ese functions must *e ca""e +)ne of t$ese functions must *e ca""e + main main..

• E-ecution of t$e program a"%a(s *egins *( carr(ing out t$eE-ecution of t$e program a"%a(s *egins *( carr(ing out t$e

instructions in +instructions in + main main..

– ! function %i"" carr( out its intene action %$ene'er it is! function %i"" carr( out its intene action %$ene'er it is

called called oror invoked invoked ..


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– In genera", a function %i"" process information t$at is passeIn genera", a function %i"" process information t$at is passe

to it from t$e ca""ing portion of t$e program, an returns ato it from t$e ca""ing portion of t$e program, an returns a

sing"e 'a"ue.sing"e 'a"ue.

• Information is passe to t$e function 'ia specia" ientifiersInformation is passe to t$e function 'ia specia" ientifiersca""eca""e argumentsarguments oror parameters parameters..

• T$e 'a"ue is returne *( t$e +T$e 'a"ue is returne *( t$e +returnreturn statement. statement.

– Some functions ma( not return an(t$ing.Some functions ma( not return an(t$ing.

• eturn ata t(pe specifie as +eturn ata t(pe specifie as +void void ..


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/inc"ue stio.$/inc"ue stio.$

int factoria" 2int m3int factoria" 2int m3

44

int i, temp516int i, temp516

for 2i516 i5m6 i773for 2i516 i5m6 i773

temp 5 temp 8 i6temp 5 temp 8 i6

return 2temp36return 2temp36

99

main23main23

44

int n6int n6

for 2n516 n5106 n773for 2n516 n5106 n773

printf 2+; 5


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A$( FunctionsBA$( FunctionsB

• FunctionsFunctions

– !""o%s one to e'e"op a program in a mou"ar fas$ion!""o%s one to e'e"op a program in a mou"ar fas$ion..

• Di'ie#an#conuer approac$.Di'ie#an#conuer approac$.

–!"" 'aria*"es ec"are insie functions are "oca" 'aria*"es!"" 'aria*"es ec"are insie functions are "oca" 'aria*"es

.

.

• Kno%n on"( in function efine.Kno%n on"( in function efine.

• T$ere are e-ceptions 2to *e iscusse "ater3.T$ere are e-ceptions 2to *e iscusse "ater3.

– ParametersParameters

• Communicate information *et%een functions.Communicate information *et%een functions.

• T$e( a"so *ecome "oca" 'aria*"es.T$e( a"so *ecome "oca" 'aria*"es.


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• enefitsenefits – Di'ie an conuer Di'ie an conuer

• anagea*"e program e'e"opment.anagea*"e program e'e"opment.

• Construct a program from sma"" pieces orConstruct a program from sma"" pieces or

components.components.

– Soft%are reusa*i"it(Soft%are reusa*i"it(

• se e-isting functions as *ui"ing *"ocs for ne%se e-isting functions as *ui"ing *"ocs for ne%

programs.programs.

• !*straction: $ie interna" etai"s 2"i*rar( functions3.!*straction: $ie interna" etai"s 2"i*rar( functions3.


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Defining a FunctionDefining a Function

• ! function efinition $as t%o parts:! function efinition $as t%o parts:

– T$e first "ine.T$e first "ine.

– T$e *o( of t$e function.T$e *o( of t$e function.

return-value-type function-namereturn-value-type function-name (( parameter-list parameter-list ))

{{

declarations and statementsdeclarations and statements

}}


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• T$e first "ine contains t$e return#'a"ue#t(pe, t$e functionT$e first "ine contains t$e return#'a"ue#t(pe, t$e functionname, an optiona""( a set of comma#separate argumentsname, an optiona""( a set of comma#separate arguments

enc"ose in parent$eses.enc"ose in parent$eses.

– Eac$ argument $as an associate t(pe ec"aration.Eac$ argument $as an associate t(pe ec"aration.

– T$e arguments are ca""eT$e arguments are ca""e formal argumentsformal arguments or or formalformal

parameters parameters..

• E-amp"e:E-amp"e:

int gc 2int !, int 3int gc 2int !, int 3

• T$e argument ata t(pes can a"so *e ec"are on t$e ne-t "ine:T$e argument ata t(pes can a"so *e ec"are on t$e ne-t "ine:

int gc 2!, 3int gc 2!, 3

4 int !, 6 ##### 94 int !, 6 ##### 9


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• T$e *o( of t$e function is actua""( a compoun statementT$e *o( of t$e function is actua""( a compoun statementt$at efines t$e action to *e taen *( t$e functiont$at efines t$e action to *e taen *( t$e function..


44

int temp6int temp6%$i"e 22 !3 ;5 03 4%$i"e 22 !3 ;5 03 4

temp 5 !6temp 5 !6

5 !6 5 !6

! 5 temp6! 5 temp6

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return 2!36return 2!36

99

)D)D


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• A$en a function is ca""e from some ot$er function, t$eA$en a function is ca""e from some ot$er function, t$e

corresponing arguments in t$e function ca"" are ca""ecorresponing arguments in t$e function ca"" are ca""e

actual argumentsactual arguments oror actual actual parameters parameters..

– T$e forma" an actua" arguments must matc$ in t$eirT$e forma" an actua" arguments must matc$ in t$eir

ata t(pes.ata t(pes.

– T$e notion of positiona" parameters is importantT$e notion of positiona" parameters is important

• Point to note:Point to note:

– T$e ientifiers use as forma" arguments are +"oca".T$e ientifiers use as forma" arguments are +"oca".

• Hot recognie outsie t$e function.Hot recognie outsie t$e function.

• Hames of forma" an actua" arguments ma( iffer.Hames of forma" an actua" arguments ma( iffer.


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/inc"ue stio.$/inc"ue stio.$ J8 Compute t$e GCD of four num*ers 8J J8 Compute t$e GCD of four num*ers 8J

main23main23

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int n1, n=, n>, n, resu"t6int n1, n=, n>, n, resu"t6

scanf 2+ , &n1, &n=, &n>, &n36scanf 2+ , &n1, &n=, &n>, &n36

resu"t 5 gc 2 gc 2n1, n=3, gc 2n>, n3 36resu"t 5 gc 2 gc 2n1, n=3, gc 2n>, n3 36

printf 2+T$e GCD of , , an is


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Function Hot eturning !n( La"ueFunction Hot eturning !n( La"ue

• E-amp"eE-amp"e: ! function %$ic$ prints if a num*er is i'isi*"e *(: ! function %$ic$ prints if a num*er is i'isi*"e *(M or not.M or not.

'oi i'M 2int n3'oi i'M 2int n3

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if 22n M3 55 03if 22n M3 55 03

printf 2+ is i'isi*"e *( M, n36printf 2+ is i'isi*"e *( M, n36

e"see"se

printf 2+ is not i'isi*"e *( M, n36printf 2+ is not i'isi*"e *( M, n36

return6return6

99

OPTIONAL


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• eturning contro"eturning contro"

– If not$ing returneIf not$ing returne

• returnreturn;; • or, unti" reac$es rig$t *raceor, unti" reac$es rig$t *race

– If somet$ing returneIf somet$ing returne •

returnreturn

expressionexpression;;


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Some PointsSome Points

• ! function cannot *e efine %it$in anot$er function.! function cannot *e efine %it$in anot$er function. – !"" function efinitions must *e isNoint!"" function efinitions must *e isNoint..

• Heste function ca""s are a""o%e.Heste function ca""s are a""o%e.

– ! ca""s , ca""s C, C ca""s D, etc.! ca""s , ca""s C, C ca""s D, etc. – T$e function ca""e "ast %i"" *e t$e first to return.T$e function ca""e "ast %i"" *e t$e first to return.

• ! function can a"so ca"" itse"f, eit$er irect"( or in a c(c"e.! function can a"so ca"" itse"f, eit$er irect"( or in a c(c"e.

– ! ca""s , ca""s C, C ca""s *ac !.! ca""s , ca""s C, C ca""s *ac !.

– Ca""eCa""e recursive call recursive call or or recursionrecursion..


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E-amp"e::E-amp"e:: main main ca""sca""s ncrncr,, ncrncr ca""sca""s factfact


int ncr 2int n, int r36int ncr 2int n, int r36

int fact 2int n36int fact 2int n36

main23main23

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int i, m, n, sum506int i, m, n, sum506

scanf 2+ , &m, &n36scanf 2+ , &m, &n36

for 2i516 i5m6 i75=3for 2i516 i5m6 i75=3

sum 5 sum 7 ncr 2n, i36sum 5 sum 7 ncr 2n, i36

printf 2+esu"t:


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16

Laria*"eLaria*"e

ScopeScope

Output:

--------------

A = 3

A = 2

A = 1

/inc"ue stio.$

int !6

'oi main23

4 ! 5 16

m(Proc236

printf 2 O! 5


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at$ i*rar( Functionsat$ i*rar( Functions

• at$ "i*rar( functionsat$ "i*rar( functions – perform common mat$ematica" ca"cu"ationsperform common mat$ematica" ca"cu"ations

#include #include

• Format for ca""ing functionsFormat for ca""ing functionsFunctionName (argument);FunctionName (argument);

• If mu"tip"e arguments, use comma#separate "istIf mu"tip"e arguments, use comma#separate "ist

printf ("%f", sqrt(!!.!)); printf ("%f", sqrt(!!.!));

• Ca""s functionCa""s function sqrtsqrt, %$ic$ returns t$e suare root of its, %$ic$ returns t$e suare root of its

argument.argument.• !"" mat$ functions return ata t(pe!"" mat$ functions return ata t(pe doubledouble..

– !rguments ma( *e constants, 'aria*"es, or e-pressions!rguments ma( *e constants, 'aria*"es, or e-pressions ..


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double acosdouble !"double acosdouble !" # Compute arc cosine of !.# Compute arc cosine of !.

double asindouble !"double asindouble !" # Compute arc sine of !.# Compute arc sine of !.

double atandouble !"double atandouble !" # Compute arc tangent of !.# Compute arc tangent of !.

double atan$double y, double !"double atan$double y, double !" # Compute arc tangent of y%!.# Compute arc tangent of y%!.

double cosdouble !"double cosdouble !" # Compute cosine of angle in radians.# Compute cosine of angle in radians.

double coshdouble !"double coshdouble !" # Compute the hyperbolic cosine of !.# Compute the hyperbolic cosine of !.

double sindouble !"double sindouble !" # Compute sine of angle in radians.# Compute sine of angle in radians.double sinhdouble !"double sinhdouble !" # Compute the hyperbolic sine of !.# Compute the hyperbolic sine of !.

double tandouble !"double tandouble !" # Compute tangent of angle in radians.# Compute tangent of angle in radians.

double tanhdouble !"double tanhdouble !" # Compute the hyperbolic tangent of !.# Compute the hyperbolic tangent of !.


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double ceildouble !"double ceildouble !" # et smallest integral 'alue that e!ceeds !.# et smallest integral 'alue that e!ceeds !.

double floordouble !"double floordouble !" # et largest integral 'alue less than !.# et largest integral 'alue less than !.

double e!pdouble !"double e!pdouble !" # Compute e!ponential of !.# Compute e!ponential of !.

double fabs double ! "double fabs double ! " # Compute absolute 'alue of !.# Compute absolute 'alue of !.

double logdouble !"double logdouble !" # Compute log to the base e of !.# Compute log to the base e of !.

double log() double ! "double log() double ! " # Compute log to the base () of !.# Compute log to the base () of !.

double po* double !, double y"double po* double !, double y" # Compute ! raised to the po*er y.# Compute ! raised to the po*er y.

double s+rtdouble !"double s+rtdouble !" # Compute the s+uare root of !.# Compute the s+uare root of !.


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Function Protot(pesFunction Protot(pes

• sua""(, a function is efine *efore it is ca""e.sua""(, a function is efine *efore it is ca""e.– main() main() is t$e "ast function in t$e program.is t$e "ast function in t$e program.

– Eas( for t$e compi"er to ientif( function efinitions in aEas( for t$e compi"er to ientif( function efinitions in a

sing"e scan t$roug$ t$e fi"e.sing"e scan t$roug$ t$e fi"e.

• Qo%e'er, man( programmers prefer a top#o%n approac$,Qo%e'er, man( programmers prefer a top#o%n approac$,

%$ere t$e functions fo""o%%$ere t$e functions fo""o% main(). main().

– ust *e some %a( to te"" t$e compi"er.ust *e some %a( to te"" t$e compi"er.

– Function protot(pes are use for t$is purpose.Function protot(pes are use for t$is purpose.

• )n"( neee if function efinition comes after use.)n"( neee if function efinition comes after use.


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– Function protot(pes are usua""( %ritten at t$e *eginning ofFunction protot(pes are usua""( %ritten at t$e *eginning ofa program, a$ea of an( functions 2inc"uinga program, a$ea of an( functions 2inc"uing main()main()33..

– E-amp"es:E-amp"es:


'oi i'M 2int num*er36'oi i'M 2int num*er36

• Hote t$e semico"on at t$e en of t$e "ine.Hote t$e semico"on at t$e en of t$e "ine.

• T$e argument names can *e ifferent6 *ut it is a gooT$e argument names can *e ifferent6 *ut it is a goo

practice to use t$e same names as in t$e function efinition.practice to use t$e same names as in t$e function efinition.


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Qeaer Fi"esQeaer Fi"es

• Qeaer fi"esQeaer fi"es – Contain function protot(pes for "i*rar( functions.Contain function protot(pes for "i*rar( functions.

– ,, , etc, etc

– oa %it$:oa %it$: #include #include

– E-amp"eE-amp"e::

#include #include

• Custom $eaer fi"esCustom $eaer fi"es – Create fi"e2s3 %it$ function efinitions.Create fi"e2s3 %it$ function efinitions.

– Sa'e asSa'e asfilename.hfilename.h

2sa(3.2sa(3.

– oa in ot$er fi"es %it$oa in ot$er fi"es %it$ #include "filename.h"#include "filename.h"

– euse functions.euse functions.


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Parameter passing: *( La"ue an *( eferenceParameter passing: *( La"ue an *( eference

• se %$en in'oing functions.se %$en in'oing functions.

• Ca"" *( 'a"ueCa"" *( 'a"ue

– Passes t$ePasses t$e valuevalue of t$e argument to t$e function.of t$e argument to t$e function.

– E-ecution of t$e function oes not affect t$e origina".E-ecution of t$e function oes not affect t$e origina". – se %$en function oes not nee to moif( argument.se %$en function oes not nee to moif( argument.

• !'ois accienta" c$anges.!'ois accienta" c$anges.

• Ca"" *( referenceCa"" *( reference

– Passes t$ePasses t$e referencereference to t$e origina" argument.to t$e origina" argument. – E-ecution of t$e function ma( affect t$e origina".E-ecution of t$e function ma( affect t$e origina".

– Hot irect"( supporte in C RHot irect"( supporte in C R can be effected by using pointerscan be effected by using pointers

++C supports on"( ca"" *( 'a"ueC supports on"( ca"" *( 'a"ue


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E-amp"e:E-amp"e:anom Hum*er Generationanom Hum*er Generation

•

rand rand functionfunction – Protot(pe efine inProtot(pe efine in

– eturns OranomO num*er *et%eeneturns OranomO num*er *et%een !! anan $N&'$$N&'$

i rand();i rand();

– PseuoranomPseuoranom

– Preset seuence of OranomO num*ersPreset seuence of OranomO num*ers

• Same seuence for e'er( function ca""Same seuence for e'er( function ca""

• Sca"ingSca"ing

– To get a ranom num*er *et%eenTo get a ranom num*er *et%een ** anan nn

* + (rand() % n )* + (rand() % n ) – To simu"ate t$e ro"" of a ice:To simu"ate t$e ro"" of a ice:

* + (rand() % )* + (rand() % )


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anom Hum*er Generation: Cont.anom Hum*er Generation: Cont.

• srand srand functionfunction – Protot(pe efine inProtot(pe efine in ..

– Taes an integer see, an ranomies t$e ranomTaes an integer see, an ranomies t$e ranom

num*er generator.num*er generator.

srand (seed);srand (seed);


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1 J8 ! programming e-amp"e

= anomiing ie#ro""ing program 8J

> /inc"ue st"i*.$

/inc"ue stio.$

? int main23M 4

int i6

U unsigne see610

11 printf2 OEnter see: O 361= scanf2 OuO, &see 36

1> sran2 see 361

1 for 2 i 5 16 i 5 106 i77 3 4

1? printf2 O10 O, 1 7 2 ran23 ? 3 36

1M

1 if 2 i 55 0 3

1U printf2 O 9


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Program )utputProgram )utput

-nter seed /0 1 2 * * * 3 1

-nter seed 0

* 2 1 * * 2

-nter seed 0 * 2 1 * * 2


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/efine: acro efinition/efine: acro efinition

• Preprocessor irecti'e in t$e fo""o%ing formPreprocessor irecti'e in t$e fo""o%ing form:: /efine string1 string=/efine string1 string=

– ep"aces string1 *( string= %$ere'er it occurs *eforeep"aces string1 *( string= %$ere'er it occurs *eforecompi"ation. For e-amp"e,compi"ation. For e-amp"e,

/efine PI >.11U=?/efine PI >.11U=?


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/efine: acro efinition/efine: acro efinition


/efine PI >.11U=?/efine PI >.11U=?

main23main23

44

f"oat r5.0,area6f"oat r5.0,area6

area5PI8r8r6area5PI8r8r6

99


main23main23

44

f"oat r5.0,area6f"oat r5.0,area6

area5area5>.11U=?>.11U=?8r8r68r8r6

99


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/efine %it$ arguments/efine %it$ arguments

• #define#define statement ma( *e use %it$ arguments.statement ma( *e use %it$ arguments.

– E-amp"e:E-amp"e: /efine sr2-3 -8-/efine sr2-3 -8-

– Qo% %i"" macro su*stitution *e carrie outBQo% %i"" macro su*stitution *e carrie outB

r 5 sr2a3 7 sr2>036r 5 sr2a3 7 sr2>036 r 5 a8a 7 >08>06 r 5 a8a 7 >08>06

r 5 sr2a7*36r 5 sr2a7*36 r 5 a7*8a7*6 r 5 a7*8a7*6

– T$e macro efinition s$ou" $a'e *een %ritten as:T$e macro efinition s$ou" $a'e *een %ritten as:

/efine sr2-3 2-382-3/efine sr2-3 2-382-3

r 5 2a7*382a7*36r 5 2a7*382a7*36

-/0-/0


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ecursionecursion

• ! process *( %$ic$ a function ca""s itse"f repeate"(.! process *( %$ic$ a function ca""s itse"f repeate"(. – Eit$er irect"(.Eit$er irect"(.

• V ca""s V.V ca""s V.

– )r c(c"ica""( in a c$ain.)r c(c"ica""( in a c$ain.

• V ca""s , an ca""s V.V ca""s , an ca""s V.

• se for repetiti'e computations in %$ic$ eac$ action is statese for repetiti'e computations in %$ic$ eac$ action is state

in terms of a pre'ious resu"t.in terms of a pre'ious resu"t.

fact2n3 5 n 8 fact 2n#13fact2n3 5 n 8 fact 2n#13


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Cont.Cont.

• For a pro*"em to *e %ritten in recursi'e form, t%o conitionsFor a pro*"em to *e %ritten in recursi'e form, t%o conitionsare to *e satisfie:are to *e satisfie:

– It s$ou" *e possi*"e to e-press t$e pro*"em in recursi'eIt s$ou" *e possi*"e to e-press t$e pro*"em in recursi'e

form.form.

– T$e pro*"em statement must inc"ue a stopping conitionT$e pro*"em statement must inc"ue a stopping conition

fact2n3 5 1, if n 5 0fact2n3 5 1, if n 5 0

5 n 8 fact2n#13, if n 05 n 8 fact2n#13, if n 0


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• E-amp"es:E-amp"es:

– Factoria":Factoria":fact203 5 1fact203 5 1

fact2n3 5 n 8 fact2n#13, if n 0fact2n3 5 n 8 fact2n#13, if n 0

– GCD:GCD:gc 2m, m3 5 mgc 2m, m3 5 m

gc 2m, n3 5 gc 2mn, n3, if m ngc 2m, n3 5 gc 2mn, n3, if m n

gc 2m, n3 5 gc 2n, nm3, if m ngc 2m, n3 5 gc 2n, nm3, if m n

– Fi*onacci series 21,1,=,>,,,1>,=1,@.3Fi*onacci series 21,1,=,>,,,1>,=1,@.3fi* 203 5 1fi* 203 5 1

fi* 213 5 1fi* 213 5 1

fi* 2n3 5 fi* 2n#13 7 fi* 2n#=3, if n 1fi* 2n3 5 fi* 2n#13 7 fi* 2n#=3, if n 1


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E-amp"e 1 :: Factoria"E-amp"e 1 :: Factoria"

"ong int fact 2n3"ong int fact 2n3

int n6int n6

44

if 2n 5 5 13if 2n 5 5 13

return 2136return 2136

e"see"se

return 2n 8 fact2n#1336return 2n 8 fact2n#1336

99


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E-amp"e 1 :: Factoria" E-ecutionE-amp"e 1 :: Factoria" E-ecution

if if (( 1 1 ("1 1 ("return ("2return ("2else return ( 3else return ( 3fact)""2fact)""2

fact4"fact4"

if if 44 1 1 ("1 1 ("return ("2return ("2else return else return 4 34 3fact5"fact5""2"2 if if 55 1 1 ("1 1 ("

return ("2return ("2else return else return 5 35 3fact$"fact$""2"2 if if $$ 1 1 ("1 1 ("

return ("2return ("2else return else return $ 3$ 3

fact("fact(""2"2

11

==

??

==

long int fact n"long int fact n"

int n2int n266 if n 1 1 ("if n 1 1 ("return ("2return ("2 else return n 3else return n 3factn7(""2factn7(""2

88


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E-amp"e = :: Fi*onacci num*er E-amp"e = :: Fi*onacci num*er

• Fi*onacci num*er f2n3 can *e efine as:Fi*onacci num*er f2n3 can *e efine as: f203 5 0f203 5 0

f213 5 1f213 5 1

f2n3 5 f2n#13 7 f2n#=3, if n 1f2n3 5 f2n#13 7 f2n#=3, if n 1

– T$e successi'e Fi*onacci num*ers are:T$e successi'e Fi*onacci num*ers are:

0, 1, 1, =, >, , , 1>, =1, @..0, 1, 1, =, >, , , 1>, =1, @..

• Function efinition:Function efinition:

int f 2int n3int f 2int n3

44

if 2n =3 return 2n36if 2n =3 return 2n36

e"se return 2f2n#13 7 f2n#=336e"se return 2f2n#13 7 f2n#=336

99


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Tracing E-ecutionTracing E-ecution

• Qo% man( times is t$eQo% man( times is t$e

function ca""e %$enfunction ca""e %$en

e'a"uating f23 Be'a"uating f23 B

• Inefficienc(:Inefficienc(:

– Same t$ing is computeSame t$ing is compute

se'era" times.se'era" times.

f23

f2>3 f2=3

f213f2=3 f203f213

f213 f203

ca""e U times


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Hota*"e PointHota*"e Point

• E'er( recursi'e program can a"so *e %ritten %it$out recursionE'er( recursi'e program can a"so *e %ritten %it$out recursion

• ecursion is use for programming con'enience, not forecursion is use for programming con'enience, not for

performance en$ancementperformance en$ancement

• Sometimes, if t$e function *eing compute $as a niceSometimes, if t$e function *eing compute $as a nice

recurrence form, t$en a recursi'e coe ma( *e more reaa*"erecurrence form, t$en a recursi'e coe ma( *e more reaa*"e


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E-amp"e > :: To%ers of Qanoi Pro*"emE-amp"e > :: To%ers of Qanoi Pro*"em

>

=1

LEFT CENTER RIGHT


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• T$e pro*"em statement:T$e pro*"em statement:

– Initia""( a"" t$e iss are stace on t$e EFT po"e.Initia""( a"" t$e iss are stace on t$e EFT po"e.

– euire to transfer a"" t$e iss to t$e IGQT po"e.euire to transfer a"" t$e iss to t$e IGQT po"e.• )n"( one is can *e mo'e at a time.)n"( one is can *e mo'e at a time.

• ! "arger is cannot *e p"ace on a sma""er is! "arger is cannot *e p"ace on a sma""er is..

– CEHTE po"e is use for temporar( storage of iss.CEHTE po"e is use for temporar( storage of iss.


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• ecursi'e statement of t$e genera" pro*"em of n iss.ecursi'e statement of t$e genera" pro*"em of n iss.

– Step 1:Step 1:

• o'e t$e top 2n#13 iss from EFT to CEHTE.o'e t$e top 2n#13 iss from EFT to CEHTE.

– Step =:Step =:

• o'e t$e "argest is from EFT to IGQT.o'e t$e "argest is from EFT to IGQT.

– Step >:Step >: • o'e t$e 2n#13 iss from CEHTE to IGQT.o'e t$e 2n#13 iss from CEHTE to IGQT.


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'oi transfer 2int n, c$ar from, c$ar to, c$ar temp36'oi transfer 2int n, c$ar from, c$ar to, c$ar temp36

main23main23

44

int n6 J8 Hum*er of iss 8Jint n6 J8 Hum*er of iss 8J

scanf 2+, &n36scanf 2+, &n36

transfer 2n, WX, WX, WCX36transfer 2n, WX, WX, WCX36

99

'oi transfer 2int n, c$ar from, c$ar to, c$ar temp3'oi transfer 2int n, c$ar from, c$ar to, c$ar temp3

44

if 2n 03 4if 2n 03 4

transfer 2n#1, from, temp, to36transfer 2n#1, from, temp, to36

printf 2+o'e is from c to c


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ecursion 's. Iterationecursion 's. Iteration

• epetitionepetition – Iteration: e-p"icit "oopIteration: e-p"icit "oop

– ecursion: repeate function ca""secursion: repeate function ca""s

• TerminationTermination

– Iteration: "oop conition fai"sIteration: "oop conition fai"s

– ecursion: *ase case recognieecursion: *ase case recognie

• ot$ can $a'e infinite "oopsot$ can $a'e infinite "oops

• a"ancea"ance

– C$oice *et%een performance 2iteration3 an gooC$oice *et%een performance 2iteration3 an goo

soft%are engineering 2recursion3.soft%are engineering 2recursion3.


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Qo% are function ca""s imp"ementeBQo% are function ca""s imp"ementeB

• T$e fo""o%ing app"ies in genera", %it$ minor 'ariations t$at areT$e fo""o%ing app"ies in genera", %it$ minor 'ariations t$at are

imp"ementation epenent.imp"ementation epenent.

– T$e s(stem maintains a stac in memor(.T$e s(stem maintains a stac in memor(.

• Stac is a "ast#in first#out structure.Stac is a "ast#in first#out structure.

• T%o operations on stac, pus$ an pop.T%o operations on stac, pus$ an pop.

– A$ene'er t$ere is a function ca"", t$e acti'ation recor getsA$ene'er t$ere is a function ca"", t$e acti'ation recor gets

pus$e into t$e stac.pus$e into t$e stac.

• !cti'ation recor consists of t$e return aress in t$e ca""ing!cti'ation recor consists of t$e return aress in t$e ca""ing

program, t$e return 'a"ue from t$e function, an t$e "oca"program, t$e return 'a"ue from t$e function, an t$e "oca"'aria*"es insie t$e function.'aria*"es insie t$e function.


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main23

4 @@..

- 5 gc 2a, *36

@@..

9

int gc 2int -, int (3

4

@@..

@@..

return 2resu"t36

9

eturn !r

eturn La"ue

oca"

Laria*"es

!"#$! %&'' A"!$ %&'' A"!$ $!$*

+ T A C ,

A%-.&-#*

$!%#$/


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main23

4

@@..

- 5 ncr 2a, *36

@@..9

int ncr 2int n, int r3

4

return 2fact2n3J fact2r3Jfact2n#r336

9

L1, L1, !1

!"#$! %&'' C&'' "&% *%$ $!$*

int fact 2int n34

@@@

return 2resu"t36

9

> times

L1, L1, !1

"&% $!$*

L1, L1, !1

L=, L=, !=

C&'' *%$

> times


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A$at $appens for recursi'e ca""sBA$at $appens for recursi'e ca""sB

• A$at %e $a'e seen @.A$at %e $a'e seen @.

– !cti'ation recor gets pus$e into t$e stac %$en a function!cti'ation recor gets pus$e into t$e stac %$en a function

ca"" is mae.ca"" is mae.

– !cti'ation recor is poppe off t$e stac %$en t$e function!cti'ation recor is poppe off t$e stac %$en t$e function

returns.returns.

• In recursion, a function ca""s itse"f.In recursion, a function ca""s itse"f.

– Se'era" function ca""s going on, %it$ none of t$e functionSe'era" function ca""s going on, %it$ none of t$e function

ca""s returning *ac.ca""s returning *ac.

• !cti'ation recors are pus$e onto t$e stac continuous"(.!cti'ation recors are pus$e onto t$e stac continuous"(.

• arge stac space reuire.arge stac space reuire.


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– !cti'ation recors eep popping off, %$en t$e termination!cti'ation recors eep popping off, %$en t$e termination

conition of recursion is reac$e.conition of recursion is reac$e.

• Ae s$a"" i""ustrate t$e process *( an e-amp"e of computingAe s$a"" i""ustrate t$e process *( an e-amp"e of computing

factoria".factoria".

– !cti'ation recor "oos "ie:!cti'ation recor "oos "ie:

eturn !r

eturn La"ue

oca"

Laria*"es


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E-amp"e:: main23 ca""s fact2>3E-amp"e:: main23 ca""s fact2>3

int fact 2n3

int n6

4

if 2n 5 5 03

return 2136

e"se

return 2n 8 fact2n#1336

9

main23

4

int n6

n 5 >6

printf 2+


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Do ourse"f Do ourse"f

• Trace t$e acti'ation recors for t$e fo""o%ing 'ersion of Fi*onacciTrace t$e acti'ation recors for t$e fo""o%ing 'ersion of Fi*onacci

seuence.seuence.

#include #include int f (int n)int f (int n)44

int a, ;int a, ; if (n < 1) return (n);if (n < 1) return (n); else 4else 4 a f(n5*);a f(n5*); f(n51); f(n51); return (a+); 6return (a+); 666

main() 4 main() 4 printf(7Fi(2) is %d 8n9, f(2)); printf(7Fi(2) is %d 8n9, f(2));66

eturn !r

2eit$er main,

or V, or 3

eturn La"ue

oca"

Laria*"es2n, a, *3

&-*


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Storage C"ass of Laria*"esStorage C"ass of Laria*"es


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A$at is Storage C"assBA$at is Storage C"assB

•It refers to t$e permanence of a 'aria*"e, an itsIt refers to t$e permanence of a 'aria*"e, an its scopescope %it$in a%it$in aprogram.program.

• Four storage c"ass specifications in C:Four storage c"ass specifications in C:

– !utomatic!utomatic:: autoauto

– E-terna"E-terna" :: e:terne:tern – StaticStatic :: staticstatic

– egisteregister :: registerregister


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!utomatic Laria*"es!utomatic Laria*"es

•T$ese are a"%a(s ec"are %it$in a function an are "oca" to t$eT$ese are a"%a(s ec"are %it$in a function an are "oca" to t$efunction in %$ic$ t$e( are ec"are.function in %$ic$ t$e( are ec"are.

– Scope is confine to t$at function.Scope is confine to t$at function.

• T$is is t$e efau"t storage c"ass specification.T$is is t$e efau"t storage c"ass specification.

– !"" 'aria*"es are consiere as!"" 'aria*"es are consiere as autoauto un"ess e-p"icit"(un"ess e-p"icit"(specifie ot$er%ise.specifie ot$er%ise.

– T$e e(%orT$e e(%or autoauto is optiona".is optiona".

– !n automatic 'aria*"e oes not retain its 'a"ue once contro" is!n automatic 'aria*"e oes not retain its 'a"ue once contro" is

transferre out of its efining function.transferre out of its efining function.


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#include #include

int factorial(int m)int factorial(int m)

44

auto int i;auto int i;

auto int temp*;auto int temp*;

for (i*; i


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Static Laria*"esStatic Laria*"es

• Static 'aria*"es are efine %it$in ini'iua" functions an $a'eStatic 'aria*"es are efine %it$in ini'iua" functions an $a'et$e same scope as automatic 'aria*"es.t$e same scope as automatic 'aria*"es.

• n"ie automatic 'aria*"es, static 'aria*"es retain t$eir 'a"uesn"ie automatic 'aria*"es, static 'aria*"es retain t$eir 'a"ues

t$roug$out t$e "ife of t$e program.t$roug$out t$e "ife of t$e program.

– If a function is e-ite an re#entere at a "ater time, t$e staticIf a function is e-ite an re#entere at a "ater time, t$e static'aria*"es efine %it$in t$at function %i"" retain t$eir pre'ious'aria*"es efine %it$in t$at function %i"" retain t$eir pre'ious

'a"ues.'a"ues.

– Initia" 'a"ues can *e inc"ue in t$e static 'aria*"e ec"aration.Initia" 'a"ues can *e inc"ue in t$e static 'aria*"e ec"aration.

• Ai"" *e initia"ie on"( once.Ai"" *e initia"ie on"( once.• !n e-amp"e of using static 'aria*"e:!n e-amp"e of using static 'aria*"e:

– Count num*er of times a function is ca""e.Count num*er of times a function is ca""e.


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#include #include

int factorial (int n)int factorial (int n)

44

static int count!;static int count!;

count++;count++;

printf (7n%d, count%d 8n9, n, count); printf (7n%d, count%d 8n9, n, count);

if (n !) return *;if (n !) return *;

else return (n factorial(n5*));else return (n factorial(n5*));

66

main() main()44

int i;int i;

printf (7=alue is %d 8n9, factorial(i)); printf (7=alue is %d 8n9, factorial(i));

66

EV!PE 1


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• Program output:Program output: n, count*n, count*

n, count1n, count1

n2, count3n2, count3


n1, countn1, count

n*, countn*, count

n!, count0n!, count0

=alue is 01! =alue is 01!


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#include #include

int fi (int n)int fi (int n)

44

static int count!;static int count!;

count++;count++;


if (n < 1) return n;if (n < 1) return n;

else return (fi(n5*) + fi(n51));else return (fi(n5*) + fi(n51));

66

main() main()44

int i2;int i2;

printf (7=alue is %d 8n9, fi(i)); printf (7=alue is %d 8n9, fi(i));

66

EV!PE =


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• Program output:Program output: n2, count*n2, count* n3, count1n3, count1


n*, count2n*, count2

n!, countn!, count

n*, countn*, count


n*, count/n*, count/

n!, countn!, count =alue is 3 ?!,*,*,1,3,,/,@.A =alue is 3 ?!,*,*,1,3,,/,@.A

f23

f2>3 f2=3

f213f2=3 f203f213

f213 f203


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egister Laria*"esegister Laria*"es

• T$ese 'aria*"es are store in $ig$#spee registers %it$in t$e CP.T$ese 'aria*"es are store in $ig$#spee registers %it$in t$e CP.

– Common"( use 'aria*"es ma( *e ec"are as registerCommon"( use 'aria*"es ma( *e ec"are as register

'aria*"es.'aria*"es.

– esu"ts in increase in e-ecution spee.esu"ts in increase in e-ecution spee.

– T$e a""ocation is one *( t$e compi"er.T$e a""ocation is one *( t$e compi"er.


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E-terna" Laria*"esE-terna" Laria*"es

• T$e( are not confine to sing"e functions.T$e( are not confine to sing"e functions.

• T$eir scope e-tens from t$e point of efinition t$roug$ t$eT$eir scope e-tens from t$e point of efinition t$roug$ t$e

remainer of t$e program.remainer of t$e program.

– T$e( ma( span more t$an one functions.T$e( ma( span more t$an one functions.

– !"so ca""e g"o*a" 'aria*"es!"so ca""e g"o*a" 'aria*"es..

• !"ternate %a( of ec"aring g"o*a" 'aria*"es.!"ternate %a( of ec"aring g"o*a" 'aria*"es.

– Dec"are t$em outsie t$e function, at t$e *eginningDec"are t$em outsie t$e function, at t$e *eginning..


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#include #include

int count!; B CDE$D =$G$D- Bint count!; B CDE$D =$G$D- B

int factorial (int n)int factorial (int n)

44

count++;count++;


if (n !) return *;if (n !) return *;

else return (n factorial(n5*));else return (n factorial(n5*));

66

main() 4 main() 4

int i;int i;

printf (7=alue is %d 8n9, factorial(i)); printf (7=alue is %d 8n9, factorial(i));

printf (7Hount is %d 8n9, count); printf (7Hount is %d 8n9, count);

66


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• Program output:Program output: n, count*n, count* n, count1n, count1



n1, countn1, count

n*, countn*, count

n!, count0n!, count0

=alue is 01! =alue is 01!

Hount is 0Hount is 0

Documents

Lec-4 C Programming