C,C++ language for bio-medical engineering courses.pdf

203
 XO,O++ MEN IAKFO^- IQJFE^FN- WQILQMBBJELXIIWR @MELVMLF DIQ AJI- BFNJOM@- FELJEFFQJEL OIVQ_F_; WMQ^-=, EI^F_ R X^FS^-AIIH; ^CF \MJ^F LQIVW‚_ ^VQAI-O WQILQMBBJEL DIQ ^CF WO MEN ^VQAI- O++, AZ QIAFQ^-@MDIQF, QFTJ_FN-FNJ^JIE R XJt‚s tcf oiursf wcmt J `fmrefn je aftwffe 1774 ti 177< je _jr -_yfn Vejvfrsjty id Feljeffrjel men tfocei`ilyX __VF^ R, BZ A@IL-5 www.bfnj om`-jbmlf- priofssjel.a`ilspit.oibR 17=? AZ BICMBBMN-_JHMENMQ-HCME-@INCJ [email protected] 4/1</17=?

Transcript of C,C++ language for bio-medical engineering courses.pdf

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XO,O++ MEN IAKFO^-IQJFE^FN-

WQILQMBBJELXIIWR

@MELVMLF DIQ AJI-BFNJOM@-

FELJEFFQJEL

OIVQ_F_; WMQ^-=,EI^F_ RX^FS^-AIIH; ^CF \MJ^F LQIVW‚_ ^VQAI-O

WQILQMBBJEL DIQ ^CF WO MEN ^VQAI-

O++, AZ QIAFQ^-@MDIQF, QFTJ_FN-FNJ^JIE

RXJt‚s tcf oiursf wcmt J `fmrefn je aftwffe 1774 ti 177< je _jr-_yfn Vejvfrsjty id

Feljeffrjel men tfocei`ilyX __VF^ R, BZ A@IL-5 www.bfnjom`-jbmlf-

priofssjel.a`ilspit.oibR

17=? 

AZ BICMBBMN-_JHMENMQ-HCME-@INCJ

[email protected]

4/1</17=?

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 1-id-=:: 

^ma`f id Oietfets

  JE^QINVO^JIE;  ................................................................................................................................... >

Oc-=; tcf turai O prilrmbbjel fevjriebfet 8 Xstmrt cfrfR ........................................................................ 4

Djl # = .................................................................................................................................................. =4

Djl # ? .................................................................................................................................................. 16

MNNQF__-IWFQM^IQ ‐(MBWFQ_MEN_)&‒ ;- .......................................................................................... 1:

Njmlrmb X djl # > R  ............................................................................................................................... ?7

BV@^JW@F JEWV^ \J^C _JEL@F somed()8 ;-.............................................................................................. ?7

Djl # 6  .................................................................................................................................................. ?=

CI\ ^I FE^FQ ^CF TM@VF;-  ................................................................................................................. ?=

DJF@N-\JN^C _WFOJDJFQ_;- ...................................................................................................................... ?6

NJLJ^-WQFOJNJEL ^CF NFOJBM@ WIJE^;- ................................................................................................ ?4

lftocf()8 DVEO^JIE; ............................................................................................................................... ?:

OC-1 X _^MQ^ CFQFR ..................................................................................................................................... >=

TMQJMA@F_ ;- ................................................................................................................................................ >=

IWFQM^IQ‚_;- ......................................................................................................................................... >>

^CF JEOQFBFE^ MEN NFOQFBFE^ IWFQM^IQ;- ................................................................................... 66

OIBBFE^_-IWFQM^IQ_;- ..................................................................................................................... 47

QF@M^JIEM@-IWWFQM^IQ;- ..................................................................................................................... 4=

m.  QF@M^JIEM@ IWFQM^IQ_ XF]VM@-^IR X22R IWFQM^IQ‚_;- .......................................................... <7

WQFOFNFEOF, QIVEN JJ ;- ....................................................................................................................... <1

Oc-? stmrt cfrf X @IIW R ............................................................................................................................. <>

LF^OCF()8 ................................................................................................................................................ <4

IWFQM^JIE-ID-DIQ-@IIW;- ................................................................................................................... 37

litixy(o,r) DVEO^JIE;- ........................................................................................................................... 3?

OC-?; @IIW;- .......................................................................................................................................... 36

=)  DIQ @IIW;-  ..................................................................................................................................... 34

_^QVO^VQF-ID-^CF-DIQ-@IIW;- ............................................................................................................ 33

Djl # =3 ................................................................................................................................................ 3:

@IIW-FSWQF__JIE;- ................................................................................................................................ :7

EF_^FN-DIQ-@IIW;- ............................................................................................................................. =77

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?-id-=:: 

DIQ-@IIW  ...................................................................................................................................... =76

 \CJ@F-@IIW(o`mss-=);  ................................................................................................................. ==:

 \CJ@F-@IIW(o`mss-1);  ................................................................................................................ =14

_uenmy, Bmy ?, 177: ............................................................................................................................. =>4

(O@M__-=)-NFOJ_JIE_;(JD & F@F_-_^M^FBFE^_); ............................................................. =>4

_^QVO^VQF-ID-JD-_^M^FBFE^;- .......................................................................................................... =>3

IWFQM^JIE ID JD-_^M^FBFE^;- ........................................................................................................... =>:

\IQN-OIVE^JEL WQILQMB;- ............................................................................................................ =67

BV@^JW@F-_^M^FBFE^-\J^C JD-_^M^FBFE^;- ................................................................................... =61

_^QVO^VQF ID EF_^FN JD-_^M^FBFE^;- ............................................................................................. =66

Jd-F`sf _tmtfbfet;- ................................................................................................................................ =64

^CF JD-F@_F-_^M^FBFE^; ...................................................................................................................... =64

IWFQM^JIE-ID-JD-F@F_-_^M^FBFE^;- ................................................................................................. =63

OCMQMO^FQ LQMWCJO_ MEN ^CF OCFOHFQ AIMQN .............................................................................. =41

NQM\ ^\I NJMLIEM@ ;- .................................................................................................................... =44

IWFQM^JIE-ID-EF_^FN JD-F@_F _^M^FBFE^;- .................................................................................... =43

F@_F-JD _^M^FBFE^;- ............................................................................................................................ =<4

EF_^FN \CJ@F-@IIW;- .......................................................................................................................... =<3

AQFMH-_^M^FBFE^; .............................................................................................................................. =<:OC-6 XDVEO^JIE_R; ................................................................................................................................... =3=

\IQHJEL-ID-DVEO^JIE NFO@MQM^JIE;- ........................................................................................... =3>

\CM^ NI DVEO^JIE NI ;- ................................................................................................................... =3<

DVEO^JIE ^CM^ QF^VQE_ M TM@VF;- .................................................................................................. =:?

DVEO^JIE ^CM^ MOOFW^ TM@VF;- ........................................................................................................ =::

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

@jehs ti o-`melumlf tutirjm`s;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >-id-=:: 

cttp;//www1.jts.strmtc.mo.uh/oiursfs/o/tma`fidoietfets

?Y=.ctb` 

cttp;//www.op`usp`us.oib/nio/tutirjm`/ 

cttp;//www.pcysjos.nrfxf`.fnu/oiursfs/OibpYWcys/Lf

efrm`/OYamsjos/ 

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

  JE^QINVO^JIE;

\jtc tcjs aiihmen turai O++, yiu wj`` af tmhjel me fmsy

men fddfotjvf pmtc ti bmstfry id tcf O-`melumlf men tcf

maj`jty ti wrjtf WO mpp`jomtjies.

  \CZ V_F O ;

 je tcf `mst nfomnf , tcf O prilrmbbjel `melumlf cms

afoibf tcf ivfrwcf`bjel ocijof id sfrjius WO

prilrmbbfrs , wcy9 O js uejquf mbiel prilrmbbjel

`melumlfs je tcmt jt privjnfs tcm oievfejfeof id m cjlcfr

`fvf` `melumlf suoc ms AM_JO ir Wmsom`, aut mt tcf smbf

tjbf m``iws buoc o`isfr oietri` id m oibputfr –s

cmrnwmrf men pfrjpcfrm`s, ms mssfba`y `melumlf nifs .

 tcfrf mrf vfry dfw ipfrmtjies tcmt ome af pfrdirbfn ie

tcf WO je mssfba`y `melumlf, tcmt omeeit af

mooibp`jscfn usum``y dmr birf oievfet`y je O, tcjs js

priama`y tcf prjeojp`f rfmsie dir O‚s pipu`mrjty ie tcf

WO.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 6-id-=:: 

 Aut O cms itcfr mnvmetmlfs ms wf``. ^cf afttfr O

oibpj`frs ome eiw lfefrmtf mbmzjel`y dmst Oinf. ^cjs

oinf js si fddjojfet tcmt jt js idtfe njddjou`t ti prinuof

sjlejdjomet spffn jeorfmsfs ay rfwrjtjel jt je mssfba`y

`melumlf .

 O js m`si m wf`` struoturfn `melumlf; jts syetmx bmhfs jt

fmsy ti wrjtf prilrmbs tcmt mrf binu`mr men tcfrfdirf

fmsy ti uenfrstmen & bmjetmje .

 ̂ cf O `melumlf jeo`unfs bmey dfmturfs tcmt mrf

spfojdjom``y nfsjlefn ti cf`p orfmtf `mrlf ir oibp`fx

prilrmbs.

 Djem``y, O js pirtma`f; jts fmsjfr ti oievfrt m O prilrmb ti

rue ie m njddfrfet Bmocjef tcfe jt js ti oievfrt prilrmbs

wrjttfe je bist itcfr `melumlfs .

Eitf ; O `melumlf js usfn je bmey cmrnwmrf `jhf -5

 yiu sciu`n cmvf moofss ti me JAB WO, S^, M^,W_/1,ir

oibpmtja`f. ^cfsf bmocjefs usf

3733,3734,37134,37?34,ir 37>34 Bjori-priofssirs. Je

lfefrm`, mey bmocjef tcmt ome rue vfrsjie 1.7 ir `mtfr id

B_-NI_ ir WO NI_ js mppriprjmtf.

 Jt sciu`n cmvf mt `fmst 4>7h id bfbiry.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 4-id-=:: 

Oc-=; tcf turai O prilrmbbjel fevjriebfet 8 Xstmrt cfrfR

  OIBWV^FQ-@MELVMLF;

Je tcf oibputfr, tcf jestruotjie wrjttfe mooirnjel ti sft idru`f men je m spfojdjo wmy id bmeemr, tcjs sft id ru`f‚s ir

jestruotjies js om``fn oibputfr-`melumlf , dir fxmbp`f ;

O/O++,IIW,kmvm,f.t.o8

  OIBWV^FQ-WQILQMBBJEL;-

^cf sft id jestruotjies Xir ru`fsR wcjoc wj`` ljvfe ti oibputfray wcjoc tcf oibputfr ome pfrdirbfn spfojdjo tmsh wjtc tcf

cf`p id tcjs jestruotjies , men tcjs sft id jestruotjies Xir ru`fs R

om``fn ms Oibputfr prilrmbbjel .

  OCMQM_^J_^JO-ID-‐O-@MELVMLF‒; 

  Fddjojfet-`melumlf;

^cf O-`melumlf ome njrfot`y fxofss ie tcf cmrn-wmrf id m

oibputfr systfb men jt usf tcf ‐dfvfr oibbmen‒ ti oibpj`f

‐O-prilrmbbfn‒ , jts birf Fddjojfet`y ms jts oibpmrfn ti tcf

itcfr `melumlf .

 OM_F-_FE_J^JTF-@MELVMLF;

O-`melumlf js m omsf sfesjtjvf `melumlf jt bfmes tcmt jd m

ocmrmotfrX`mttfrR js wrjttfe je `iwfr omsf jt wj`` af oiesjnfr ms

njddfrfet dirb ms smbf `mttfr js wrjttfe je Vppfr omsf 8

 @JEF-_FE_J^JTF-@MELVMLF;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <-id-=:: 

^cf O-`melumlf js eit m `jef sfesjtjvf `melumlf afomusf jt

bfme tcmt , yiu ome wrjtf sfvfrm` oibbmen je smbf `jef ay

usjel ‐stmtfbfet-^frbjemtirX sfbj-oi`ie 2 stmtfbfet-

^frbjemtir 2 8 R‒. 

 WIQ^MA@F-@MELVMLF;-

^cf O-`melumlf ome af stirfn ie ief typf id oibputfr `jhf

Wfetjub-> , oibputfr systfb , aut jt m`si af stirf ie fmsj`y ie

itcfr typf id oibputfr `jhf ‐Wfetjub = ir 1 oibputfr

systfb, tcmt js jts rfqujrf `fss systfb rfqujrfbfet nurjel

fxfoutjie,

 AM_JO-DIQ O++ ;

^cf stmtfbfets , oibbmens men bftcini`iljfs wcjoc js usfn

je O `melumlf tcfy mrf m`si mvmj`ma`f je O++ , tcus `fmrejel O-

@melumlf js tcf =st

 stfp tiwmrns `fmrejel ‐O++ `melumlf‒. 

 JE^FLQM^FN-NFTF@IWBFE^-FETJQIEBFE^ XJNFR;

^cf fevjriebfet id O js om``fn ms JNF, jt js m sorffe njsp`my

fevjriebfet wjtc wjeniws men pu`` niwe bfeus, jts sjbj`mr

ms NI_ fnjtir .

Jeput sorffe dir O-`melumlf 2 JNF8

Iutput sorffe id O-`melumlf 2 NI_8

----

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 3-id-=:: 

]1)

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

Tijn bmje(vijn)

{

jet fvfet8 /* wf kust nfo`mrjel tcf vmrjma`f cfrf */

ocmr cfmt8 /* wf kust nfo`mrjel tcf vmrjma`f cfrf */

d`imt tjbf8 /* wf kust nfo`mrjel tcf vmrjma`f cfrf */

fvfet268 /* wf mssjlejel tcf vm`uf id fmoc vmrjma`f cfrf */

cfmt2 ‚o‚8 /* wf mssjlejel tcf vm`uf id fmoc vmrjma`f cfrf */ 

tjbf2 1<.168 /* wf mssjlejel tcf vm`uf id fmoc vmrjma`f cfrf */

prjetd(‐ ^cf wjeejel tjbf je cfmt %o ‐, cfmt )8 

prjetd(‐ id fvfet %n wms %.1d . ‐,fvfet, tjbf)8 

}

-----------djejscfn-cfrf----------

%o 2 sjel`f ocmrmotfr .

%s2 strjel2 bist ocmrmotfr.

%n2 sjlefn nfojbm` jetflfr.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :-id-=:: 

%d2 d`imtjel pijet (nfojbm` eitmtjie).

%f2 d`imtjel pijet (fxpiefetjm` eitmtjie ).

%l2 d`imtjel pijet (% d ir %f, wcjoc fvfr js scirtfr).

%u2ue-sjlefn nfojbm` jetflfr.

%x2 ue-sjlefn cfxm-nfojbm` jetflfr (usfs ‐m,a,o,n,f,d ‒ ). 

%i2 ue-sjlefn iotm` jetflfr.

J2prfdjx usfn wjtc %n, %u, %x, %i ti spfojdy `iel jetflfr ( dirfxmbp`f %Jn ).

------------djejscfn cfrf--------

])

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

Tijn bmje(vijn)

{

D`imt yfmr, nmys8

prjetd(‐ p`fmsf typf yiur mlf je yfmrs; ‐)8 

somed(‐%d‒,& yfmrs)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =7-id-=:: 

nmys2yfmrs*?468 /* tcf stmrX*R usfn dir bu`tjp`jomtjie je O-

`melumlf */

prjetd (‐ Pe yiu mrf %.=d nmys i`nfr Pe‒, nmys)8 

}

IV^-WV^ M^ NI_ _OQFFE;

p`fmsf typf yiur mlf je yfmrs; 1?

yiu mrf 3?:6 nmys i`nfr

p`fmsf typf yiur mlf je yfmrs;

-----------Djejscfn-cfrf-----------

] )

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

D`imt yfmrs,nmys8 /* wf nfo`mrfn vmrjma`f */

prjetd(‐ p`fmsf typf yiur mlf je yfmrs; ‐)8 

somed(‐%d‒,& yrmrs)8 

nmys2yfmrs*?468 /* cfrf wf mssjlejel tcf vm`uf */

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ==-id-=:: 

prjetd(‐Pe yiu mrf %.=d nmys i`nfrPe‒, nmys)8 

lftocf()8

}

Iut-put X ie NI_ sorffe R;

p`fmsf typf yiur mlf je yfmrs; =>

yiu mrf =6==7 nmys i`nfr

p`fmsf typf yiur mlf je yfmrs;

--------djejscfn-cfrf-----

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

jet kiy8

prjetd(‐\cmt js yiur‚s mlf ; ‐)8 

somed(‐%n‒,& kiy)8 

 kiy2=>

prjetd(‐Pe yiur mlf js %nPe‒, kiy)8 

lftocf()8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =1-id-=:: 

}

IV^-WV^;

\cmt js yiur‚s mlf ; => 

yiur mlf js =>

-----------DJEJ_CFN-CFQF----

])

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

Wrjetd(‐By embf js _jhmenfr‒)8 

Wrjetd(‐yiur embf js _jhmenfr‒ Pe)8

Wrjetd(‐ICC‒)8 

Lftoc()8

}

By embf js _jhmenfr yiur embf js _jhmenfr

ICC

--------------djejscfn-cfrf----------

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?-id-=:: 

OIBWV^FQ-@MELVMLF;-

Je tcf oibputfr, tcf jestruotjie wcjoc wj`` wrjtf mooirnjel ti

tcf spfojdjo ru`fs, tcjs ru`f js om``fn oibputfr `melumlf iro/o++, kmvm, AM_JO,

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

DVEO^JIE-NFDJEJ^JIE;

^cf ‐bmje()‒ js m amsjo dueotjie id ‐O-prilrmbbfn‒ , tcf ‐O-

prilrmbbfn‒ oiesjsts id ief ir birf dueotjies tcf ‐bmje()‒js tcf ie`y dueotjie ,, ti wcjoc jt oietri``fn , jt pmss drib

ipfrmtjel systfb nurjel tcf prilrmbbfn js fxfoutjel jt‚s

tcf =st

  dueotjie wcjoc js ‐fxfoutfn‒. 

vijn bmje(vijn) ;

^cf wirn ‐vijn‒ prfofnjel bmje ( vijn bmje( ) ) spfojdjfntcf dueotjie bmy eit rfture mey vm`uf, tcf sfoien ‐vijn‒ je

tcf pmrfetcfsjs ‐()‒ spfojdjfn tcmt tcf dueotjie tmhf ei

mrlubfets ir mey vm`uf.

NF@JBJ^FQ_ ‐{}‒; 

^cf ‐Nf`jbjtfrs‒ mrf tcf armohfts wcjoc sciws tcf

afljeejel men fen ainy id m dueotjie , ‐ tcf ipfejel armohft

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>-id-=:: 

jenjomtfn ir sciw‚s tcf stmrt id dueotjie men o`isjel armohft

jenjomtf tcf fen id dueotjie.

‐O‒-_^M^FBFE^_;-

_^M^FBFE^-^FQBJEM^IQ X 8 R ;-

M ‐ O-stmtfbfet‒ js tfrbjemtfn X ir stip R js

om``fn ‐sfbj-oi`ube X8R‒ , jt bfme usfr ome wrjtf sfvfrm`

jestruotjie je m smbf `jef ay usjel ‐sfbj-oi`ubeX8R‒ je

aftwffe tcfb.

F.l;

Tijn bmje(vijn)

{

O`rsor()8

prjetd() DVEO^JIE;

^cf oibbmen je o-`melumlf js om``fn ‐prjetd()8‒ js m dueotjie

tcmt jt omusfs , m sfetfeofs jesjnf tcf oittmtjie (‐ ‒) ti af

prjetfn ie iutput sorffe.

f.l;

prjetd(‐djrst O-prilrmb‒)8 

tcjs stmtfbfet Xprjetd()8R wj`` prjets X djrst O-prilrmb R ie tcf

NI_ sorffe X iut-put sorffe R.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =6-id-=:: 

FSFOV^JIE ID ‐O-WQILQMBBFN‒; 

Jt wj`` oiesjsts id di``iwjel twi stfps,

=. Oibpj`jel.

1. @jehjel .

=) OIBWJ@FQ IQ OIBWJ@JEL;

 M prilrmbbfn tcmt js ti af fxfoutfn je bjori-priofssir

bust af je m dirb id bmocjef-`melumlfX=/7R dirb. ̂ cf oibpj`fr wcjoc js m pmrt id JNF , wcisf trmes`mtfn tcf

siurof oinf jeti tcf meitcfr dj`fs je bmocjef `melumlf .

^cmt js ;

X =/7 R dirbs.

1) @JEHJEL IQ @JEHFQ;

^cf priofss id ‐`jehjel‒ `jehs vmrjius `maiur`y riutfjes wjtc

tcf prilrmbbfn tmhfs tcf oibpj`mr men tcf `jehfr aitc mrf

auj`n je turai-O fevjriebfet ‐JNF‒ . 

^cf tfxt fnjtir prinuofs .OXsiurofs dj`fsR ay prilrmb.bf

wcjoc oievfrtfn jeti .Iak X iakfot dj`fsR ay tcf oibpj`fr ,wcjoc js tcfe oievfrtfn jeti .fxf X fxfoutfn dj`fs R ay tcf

`jehfr.

.o X siurof dj`f R

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =4-id-=:: 

.Iak Xiakfot dj`f R

.fxf X fxfoutf ma`f dj`fs R

-----------------------djejscfn-cfrf-------

QF@M^JIE_CJW-ID-OIBWJ@FQ-MEN-@JEHFQ-IWFQM^JIE;-

Djl # =

ME FSW@IQJEL prjetd() ;-

_ibf usfdu` hfy wirn mrf mvmj`ma`f je ‐o-prilrmb‒ tcmt wirn

`jf je aftwffe oiutmtjie (‐ ‐)8 id prjetd()8 oibbmen. 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =<-id-=:: 

Fsompf _fqufeof;

Jts tcf wirns tcmt pfrdirbfn spfojm` hfy dueotjie wjtc je tcf

oiutmtjie id prjetd()8 oibbmen .

Fxmbp`f;-

Pa 2 fsompf sfqufeof ti nf`ftf .

Pe 2 efw `jef.

Pt 2 tma X 3-njljt lmp R.

P‚ 2 sjel`f quitfs . 

P‚‚ 2 niua`f quitfs. 

Fxmbp`f;

vijn bmje(vijn)

{

prjetd(‐ Fmoc Pt wmrn Pt js Pe tmaafn Pt ivfr Pt ieof‒)8 

lftoc()8

}

NI_ iut put ;

Fmoc wmrn js

tmaafn ivfr ieof

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =3-id-=:: 

-----------djejscfn-cfrf---------

vijn bmje(vijn)

{

prjetd(‐Fmoc Pt wirn Pt js Pe tmaafn Pt ivfr P‚o P‚‚m Pt ieof‒)8 

}

Iutput;

Fmoc wirn js

tmaafn ivfr –o‚ ‐m‒ ieof 

--------------djejscfn-cfrf---

?. DIQBM^ _WFOJDJFQ;-

 M dirbmttfn spfojdjfr js usfn ti oietri``fn wcmt dirbmt

js af usfn ay prjetd()8 ti prjet iut m pmrtjou`mr vmrjma`f iroiestmet .

 Men jt m`si tf`` prjetd()8 wcfrf ti put m vm`uf je m strjel X

%s R.

JBWIQ^ME^-DIQBM^-_WFOJDJOM_-MQF;

=). %o 2 sjel`f ocmrmotfr.

1). %s 2 strjel X lriup id ocmrmotfr R.

?). %n 2 Jetflfr X eubafr R.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:-id-=:: 

>). %d 2 d`imtjel pijet eubafr X Nfojbm` eubafr f.l ; 7.7= R.

Fxmbp`f;

prjetd(‐ tcjs js %o ‐,‚M‚)8 

prjetd(‐ tcjs js %s ‐, ‐Aiih‒)8 

prjetd(‐ tcjs js eubafr %n‒, 1)8 

prjetd(‐ tcjs js eubafr %d ‐,>.67)8 

----------djejscfn------

]) \rjtf m prilrmb tcmt prjet tcf sfetfeof9

Ljvfe;

M,a,o m`` mrf ocmrmotfr‚s

_i`utjie;

_iurof oinf;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

o`rsor()8 /* o`rsor()8 -5 tcjs oibbmen js usfn dir o`fme tcf

sorffe mdtfr fxfoutjel tcf prilrmb */

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 17-id-=:: 

prjetd(‐ %o,%o,%o m`` mrf ocmrmotfr ‐, –m‚,‚a‚,‚o‚)8 

lftoc()8

}

NI_ iut put ;

m,a,o m`` mrf ocmrmotfr

---djejscfn-cfrf--------

]) wcmt js tcf iutput id di``iwjel prilrmb 9

_IVQOF-OINF;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

{ o`rsor()8

prjetd(‐%s Pe %s Pe %s ‐,‒ief‒,‒twi‒,‒tcrff‒ )8 

lftoc()8

}

IV^-WV^;

ief

twi

tcrff

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 1=-id-=:: 

---------------------djejscfn-cfrf------------

]) wrjtf tcf tma`f je yiur prilrmb9

IV^-WV^;

1*=21

1*12>

1*?24

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ o`rsor()8

prjetd(‐ 1*=2%n ‐,1)8 

prjetd(‐Pe 1*12%n‒,>)8 

prjetd(‐Pe 1*?2%n‒,4)8 

lftoc()8

}

-------------djejscfn------

IQ

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 11-id-=:: 

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ o`rsor()8

prjetd(‐Pt 1*=2%n ‐,1)8

prjetd(‐Pe Pt 1*12%n‒,>)8 

prjetd(‐Pe Pt 1*?2%n‒,4)8 

lftoc()8

}

--djejscfn----------

])

NI_ IV^-WV^ ;

Fmoc wirn js

tmaafn ivfr –o‚ ‐m‒ 

ieof

_IVQOF-OINF;

#jeo`unf0stnji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 1?-id-=:: 

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ o`rsor()8

prjetd(‐Pt FmocPt wirnPt js‒)8 

prjetd(‐PePt tmaafn Pt ivfr P‚o Pt P‚‚m ‐)8 

prjetd(‐PePt ieof‒)8 

lftoc()8

}

-----------djejscfn--------

WQJE^ LQMWCJO OCMQMO^FQ;-

=. Pxnn 2 Cfxmoinf id M_OJJ .

1. Pnnn 2 iotm`oinf id M_OJJ.

^wi sompf sfqufeofs ‐Pnnn‒ men ‐Pxnn‒ mrf usfn ti prjet

M_OJJ oinf ay usjel prjetd()8 dueotjie.

Fxmbp`f;

]) wrjtf m prilrmb tcmt njsp`my aix9

Ljvfe;

Djl # 1 ;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 1>-id-=:: 

_i`utjie;

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

{ o`rsor()8

prjetd(‐PxO: PxON PxON PxAA‒Pe)8

prjetd(‐PxAM PxAM‒Pe)8

prjetd(‐PxO3 PxON PxON PxAO‒)8 

lftoc()8

}

-------------djejscfn-cfrf--------

@foturf-Nmtf ie __VF^ ; 1:/</1774

somed()8 Dueotjie;-

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 16-id-=:: 

tcf somed()8 js m jeput dueotjie tcmt tmhfs m jeput drib tcf

‐usfr‒ men smvf jt je ti tcf bfbiry `iomtjie nfdjef ay

vmrjma`f .

somed(‐%d‒,&yfmrs)8 

Njmlrmb;

Djl # ?

 Vsfr bust typf XfetfrR tcfe dueotjie wj`` njlfst wcmt

usfr cms affe typf.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 14-id-=:: 

 Jd wf usfn ie`y vmrjma`f embf tcmt js ,yfmr ,bfmes tcf

oietmje id tcf vmrjma`f yfmr tcmt js =3 .

  Jd wf usfn ‐& yfmr‒ jts bfme tcf pcysjom` mnnrfss id

bfbiry `iomtjie, rfsfrvf ay tcf vmrjma`f tcmt js =?4<

ti =4<7.

Fxmbp`f;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

D`imt yfmr,nmys8

prjetd(‐Fetfr yiur mlf je yfmrs; ‐)8 

somed(‐%d‒,&yfmr)8 

nmys2yfmrs*?468

prjet(‐yiur mlf je nmys js %d ‐, nmys)8 

}

-------djejscfn-cfrf---------

])

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 1<-id-=:: 

\rjtf m prilrmb tcmt tmhf m eubafr drib usfr men njsp`my jts

squmrf9

_i`utjie;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

jet eub=,squmrf8

prjetd(‐wrjtf m prilrmb tcmt tmhf m eubafr drib tcf usfr men

njsp`my jts squmrf‒)8 

somed(‐%n‒,& eubafr)8 

squmrf2eubafr*eubafr8

prjetd(‐^cf squmrf id %n js %n,eub,squmrf)8 

}

----djejscfn„ 

\rjtf m prilrmb tcmt tmhf m eubafr drib tcf usfr men prjet

jts tma`f9

_IVQOF-OINF;-

#jeo`unf0stnji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 13-id-=:: 

#jeo`unf0oieji.c5

Tijn bmje(vijn)

{

Jet eub8

prjetd(‐Fetfr m eubafr‒)8 

somed(‐%n‒,&eub)8 

prjetd(‐%n*=2%n‒,eub,eub*=)8 

prjetd(‐%n*12%n‒,eub,eub*1)8 

prjetd(‐%n*?2%n‒,eub,eub*?)8 

prjetd(‐%n*>2%n‒,eub,eub*>)8 

prjetd(‐%n*62%n‒,eub,eub*6)8 

prjetd(‐%n*42%n‒,eub,eub*4)8 

prjetd(‐%n*<2%n‒,eub,eub*<)8 

prjetd(‐%n*32%n‒,eub,eub*3)8 

prjetd(‐%n*:2%n‒,eub,eub*:)8 

prjetd(‐%n*=72%n‒,eub,eub*=7)8 

lftoc()8

}

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 1:-id-=:: 

-----djejscfn-

vijn bmje(vijn)

{

d`imt eub,ouaf8

prjetd(‐Fetfr mey eubafr‒)8 

somed(‐%d‒,&eub)8 

ouaf2(eub*eub*eub)+=78

prjetd(‐^cf ouaf+=7 id tcf eubafr js %d‒)8 

lftoc()8

}

------------djejscfn---

MNNQF__-IWFQM^IQ ‐(MBWFQ_MEN_)&‒ ;-

^cf ‐&‒  js m Mnnrfss ipfrmtir wcfe fvfe usfr wrjtf

‐&‒ ie prfofnjel ‐vmrjma`f‒ ‐embf‒ si jts sciwe m

pcysjom` mnnrfss id tcmt vmrjma`f je tcf bfbiry, ms

sciwe je tcf di``iwjel fxmbp`f;

Fxmbp`f ;vijn bmje(vijn)

{ jet m8

m218

prjetd(‐ vm`uf 2%n,Mnnrfss2%n‒,m,&m)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?7-id-=:: 

lftoc()8

}

Njmlrmb X djl # > R

---------meswfr-----djejscfn-----

BV@^JW@F JEWV^ \J^C _JEL@F somed()8 ;-

Bu`tjp`f jeput wjtc sjel`f somed()8 js m`si pissja`f aut jt

cmvf sibf `jbjtmtjie.

_IVQOF-OINF;-

vijn bmje(vijn)

{ jet m8

ocmr a8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?=-id-=:: 

d`imt o8

prjetd(‐ Fetfr m ocmrmotfr,jetflfr men nfojbm` ; ‐)8 

somed(‐%o %n %d‒,&m,&a,&o)8 

lftoc()8

}

_ff djl # 6

Djl # 6

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

CI\ ^I FE^FQ ^CF TM@VF;-

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?1-id-=:: 

 Jd tcf ‐dirbmttfn spfojdjfs‒ mrf sfpmrmtfn wjtc

sjel`f spmof tcfe mt tcf tjbf id fetfrjel Nmtm usfr

ome usfn ‐sjel`f spmof‒, Pt XtmaR ir fetfr Xmey wjnf

spmof ocmrmotfr.

 Jd m dirbmttfn spfojdjfrs mrf sfpmrmtfn wjtc X‐,‒

IQ ‐.‒ R mt tcf tjbf id fetfrjel Nmtm usfr sciu`n

usfn tcmt smbf ocmrmotfr itcfr wjsf tcf lmramlf

nmtm wj`` af fetfr.

Fetfr mey ocmrmotfr , Jetflfr men D`imtjel;

@fttfr js M

Jetflfr js 16

D`imt js 1.6

Meswfr

Fetfr m M,16 men 1.6

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

vijn bmje(vijn)

{

ocmr m8

jet a8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ??-id-=:: 

d`imt o8

prjetd(‐Fetfr m ocmrmotfr, jetflfr men d`imt‒)8 

somed(‐%o %n %d‒,&m,&a,&o)8 

prjetd(‐`ftfr js %o Pe‒,m)8 

prjetd(‐jetflfr js %n Pe‒,a)8 

prjetd(‐d`imt js %d Pe‒,o)8 

}

IV^ WV^;

Fetfr m ocmrmotfr, jetflfr men d`imt

`ftfr js M

jetflfr js 1

d`imt js 4.1

------djejscfn---

\rjtf m prilrmb ti om`ou`mtfn tcf niuaa`f id eubafr wcjoc js

fetfr ay m usfr9

_IVOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?>-id-=:: 

vijn bmje(vjin)

{ o`rsor()8

Jet eub,nuaa`f 8

prjetd(‐ wrjtf m prilrmb ti om`ou`mtfn nuaa`f id eubafr‒)8 

somed(‐%n‒,&eub)8 

nuaa`f2eub*18

prjetd(‐^cf nuaa`f id eubafr js %n‒,nuaa`f)8 

lftoc()8

}

 Y----------------djejscfn---------

\rjtf m prilrmb , je wcjoc tcf usfr ljvf jeput men cf lft cm`d

id jt.9

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ o`rsor()8

jet eub,cm`d8

prjetd(‐wjrtf m prilrmb je wcjoc usfr ljvf jeput men cf lft

cm`d id jt ‐)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?6-id-=:: 

somed(‐%n‒,&eub)8 

cm`d2eub*=/18

prjetd(cf lft cm`d id tcjs eubafr %n‒,cm`d)8 

lftoc()8

}

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

DJF@N-\JN^C _WFOJDJFQ_;-

^cf djf`n wjtc spfojdjfr js usfn ti oietri``fn tcf wjntc id

vmrjma`f wcjoc js ti af prjetfn ay tcf prjetd() dueotjie .

NJLJ^M@ WQIOFNJEL ^CF NFOJBM@ WIJE^;-

^cf njljt priofnjel tcf nfojbm` pijet nftfrbjef ciw bmeynjljt wj`` af prjetfn mdtfr tcf nfojbm` pijet X 7.=6 R je omsf id

prjetfn mey d`imtjel pijet.

f.l;

vijn bmje(vijn)

{ d`imt eub2?6.>18

prjetd(‐Eubafr js %4.1d ‐,eub)8 

lftoc()8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?4-id-=:: 

}

IV^WV^;

Eubafr js ?6.>1

-----------

NJLJ^-WQFOJNJEL ^CF NFOJBM@ WIJE^;-

 M njljt prfojnjel tcf nfojbm` pijet je tcf djf`n wjtc

spfojdjfr.

 Oietri``fn tcf wjntc id spmof, ti af usfn ti oietmje , tcfeubafr , wcfe jts prjetfn .

Fxmbp`f;

jet mlf2??8

=. prjetd(‐Mlf js %4n.‒,mlf )8 

djl # 4(m)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?<-id-=:: 

1. prjetd(‐Mlf js %>n.‒,mlf)8 

Djl # 4(a);

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?3-id-=:: 

?. prjetd(‐mlf js %->n.‒,mlf)8 

Djl # 4 {o }

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ?:-id-=:: 

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

MWW@JOM^JIE;-

Jts usfdu` wcfe usfr cmvf ti njsp`my sfqufeof id eubafr

oi`ube wjsf .

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

lftocf()8 DVEO^JIE;

 tcf ‐lftocf()8‒ dueotjie js usf ti tmhf ocmrmotfr je-put, &

smvf jt je bfbiry spmof , tcf bmje mnvmetmlf id lftocf()8

dueotjie ivfr somed()8 js tcmt ‐ lftocf()8 dueotjie nifs eit

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >7-id-=:: 

effn ti prfss ‐Fetfr X Pr R ‒ jeput ti trmesdfr tcf vm`uf ti

tcf vmrjma`f ms ‐somed()8‒ dueotjie effn. 

 ̂ cf Njs-Mnvmetmlf Id ‐lftocf()8‒ dueotjie; tcf

njsmnvmetmlf id lftocf()8 ivfr somed() js tcmt , jd usfr typf

wriel ocmrmotfr tcfe tcfrf js ei amoh spmof iptjie ms je

somed()8 dueotjie.

Fxmbp`f;

vijn bmje(vijn)

{ ocmr oc8

prjetd(‐^ypf mey ocmrmotfr ‐)8 

oc2lftocf()8

prjetd(‐Pe yiu typfn %o‒,oc)8 

lftoc()8

}

IV^WV^;

^ypf mey ocmrmotfr;^

Ziu typfn ^

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

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >=-id-=:: 

OC-1 X _^MQ^ CFQFR

TMQJMA@F_ ;-

Tmrjma`f js m spmof je bfbiry tcmt p`my tcf smbf ri`f bmey

tjbfs aut bmey oietmje m njddfrfet vm`uf fmoc tjbf .

Dir Fxmbp`f ;

^i om`ou`mtfn tcf lrmnf id njddfrfet stunfet.

^ZWF_-ID-TMQJMA@F_-MEN-AZ^F_-IOOVWJFN-AZ-TMQJMA@F_ ;-

Djl # <

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >1-id-=:: 

Djl # 3

--------

Fxmbp`f;-

vijn bmje(vijn)

{ jet eub8

eub218

prjetd(‐ ^cjs eubafr js %n‒,eub)8 

lftocf()8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >?-id-=:: 

}

IV^-WV^;

^cjs eubafr js 1

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

] ) wrjtf m prilrmb je wcjoc tcf usfr ome put tcf vm`uf id

vi`tmlf men rfsjstmeof men djen ourrfet9

_IVQOF OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ o`rsor()8 /* o`rsor()8 jts usfn ti o`fmr tcf NI_ iutput sorffe

*/

d`imt rfsjstmeof8

d`imt vi`t8

d`imt ourrfet8

prjetd(‐Fetfr tcf vm`uf id vi`tmlf men rfsjstmeof men prfss

fetfr;Pe‒)8 

somed(‐%d,%d‒,&vi`t,&rfsjstmeof)8 

ourrfet2vi`t/rfsjstmeof8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >>-id-=:: 

prjetd(‐ Pe ^cf vm`uf id ourrfet js %d Pe‒,ourrfet)8 

lftoc()8

}

IV^-WV^;

Fetfr tcf vm`uf id vi`tmlf men rfsjstmeof men prfss fetfr;

=<.6

^cf vm`uf id ourrfet js 7.<<7777

Fetfr tcf vm`uf id vi`tmlf men rfsjstmeof men prfss fetfr;

------------djejscfn----

IWFQM^IQ‚_;- 

‐Ipfrmtir‚s mrf ‐wirn‒ ir ‐sybai`s‒ tcmt omusf m prilrmb ti

ni sibftcjel wjtc vmrjma`f‚s‒. 

Fxmbp`f;

^cf mrjtcbftjo ipfrmtir (+) men (-) wcjoc omusf m prilrmb ti

mnn ir suatrmot twi eubafrs tcfrf mrf bmey njddfrfet hjens

id ipfrmtirs mrf ljvfe af`iw.

=. MJQ^CBM^JO-IWFQM^IQ_;-

^cf O-`melumlf ome usfs tcf dirf mrjtcbftjo ipfrmtirs tcmt mrf

oibbie je bist prilrmbbjel `melumlfs men tcf meitcfr ief

‐rfbmjenfr ipfrmtir‒ wcjoc js eit si oibbie. 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >6-id-=:: 

f.l

je O-prilrmb wf usfn bu`tjp`jomtjie ipfrmtir X * R ti bu`tjp`y

twi eubafr tilftcfr tcmt js ;

=. X+R Mnnjtjie.

1. X-R _uatrmotjie.

?. X*R bu`tjp`jomtjie.

>. X/R njvjsjie.

6. X%R rfbmjenfr .

^cfrf js m fxmbp`f af`iw wcfrf sfvfrm` mjrtcbmtjo ipfrmtir

mrf usfn si tcjs prilrmb wcjoc oievfrtfn tfbpfrmturf je

Dmcrfecfjt ti ofetjlrmnf.

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet dtfbp,otfbp8

prjetd(‐typf tfbpfrmturf je nflrff Dmcrfecfjt; ‐)8 

somed(‐%n‒,&dtfbp)8 

otfbp2(dtfbp-?1)*6/:8

prjetd(‐tfbpfrmturf je nflrff ofetjlrmnf js %n‒,otfbp)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >4-id-=:: 

lftoc()8

}

IV^-WV^;

typf tfbpfrmturf je nflrff Dmcrfecfjt; ?1

tfbpfrmturf je nflrff ofetjlrmnf js 7

typf tfbpfrmturf je nflrff Dmcrfecfjt; <7

tfbpfrmturf je nflrff ofetjlrmnf js 1=

typf tfbpfrmturf je nflrff Dmcrfecfjt;

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

^cf o-prilrmb effn ti usfn stmenmrn dirbu`m dir oievfrtjel

nflrff dmrfecfjt jeti nflrff ofetjlrmnf suatrmot ?1 drib

Dmcrfecfjt tfbp men bu`tjp`y tcf rfsu`t ay 6/:

X  

 R8

‐^cfrf mrf sfvfrm` tcjels ti eitf maiut tcjs stmtfbfet. Djrst

yiu wj`` sff je fq-A , wf cmvf surriuenfn sibf id tcf

ipfrmtirs , tcf * men tcf X/R , wjtc spmofs aut cmvf eit usfn

spmofs mriuen tcf bjeus sjle aut tcf oibpj`fr nifs eit omrf

wcmt fvfr yiu usfn spmofs surriuenjel yiur ipfrmtirs ir eit,

si, yiu mrf drff ti mllmelf yiur fxprfssjie ciw fvfr tcfy

`iih afst ti yiu , jd yiu ni eit `jhf tcjs wmy id spmofs mrf

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ><-id-=:: 

mrrmelf je fxmbp`f si, yiu ome mrrmelf tcfb meitcfr wmy

wcfe yiu typf je prilrmb‒. 

1. IWFQM^IQ-WQFOFNFEOF;-

Ipfrmtir je o-`melumlf cmvf tcf smbf prfofnfeof ms je

bmtcfbmtjos .

IQ

Ipfrmtir je o-`melumlf cmvf m smbf bftcin ti si`vf

bmtcfbmtjom` fqumtjies ms wf si`vfn je bmtcfbmtjos.

f.l;

X  

 R8

X  

 R8

X

 R8

X

 R8

X

 R8

?. MQJ^CBF^JO-M__JLEBFE^ IWFQM^IQ_;-

Jd yiu oibpmrf m O-prilrmb wjtc m prilrmb wjtc m sjbj`mr

purpisf wrjttfe je meitcfr `melumlf.

Fxmbp`f;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >3-id-=:: 

^itm`2titm`+eubafr8

{;. ^itm`2=7,eubafr217 }

_i, je tcf bfbiry `iomtjie id titm` afdirf fxfoutjie tcf vm`uf

id titm` js fqum` ti =7 , men tcfe wcfe wf mnn (titm`+eubafr)

tcfe jts vm`uf afoibf titm`2?7 je tcf bfbiry `iomtjie, mdtfr

fxfoutjie.

Djl # :

_i,

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf >:-id-=:: 

\f ome mpp`jfn tcjs bftcin wcjoc prinuofn sjbj`mr rfsu`t ms

je maivf ay meitcfr `melumlf tcmt js X titm`+2eubafrR.

^itm`+2eubafr

{;. ^itm`2=7,Eubafr217}

Je tcjs bfbiry `iomtjie tcf titm` vm`uf afdirf fxfoutjie , tcf

vm`uf id titm` js fqum` ti =7, men eubafr217 afdirf fxfoutjie

je bfbiry `iomtjie , tcfe wcfe wf mnn (titm`+2eubafr) ,

tcfe tcf vm`uf id titm` afoibf X titm`2?7R men p`mofn je sibf

bfbiry `iomtjie mdtfr fxfoutjie.

X  R8

X  R8

_i, aitc fq-J men jj pfrdirbfn sibf ri`f afdirf men mdtfr

fxfoutjie, je bfbiry `iomtjie men je iutput siurof.

Djl # =7

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 67-id-=:: 

^cfrf mrf sibf di``iwjel njddfrfet typfs id mrjtcbftjomssjlebfet ipfrmtirs mrf ljvfe af`iw.

(+2) Mnnjtjie mssjlebfet ipfrmtir‚s 

(-2) suastrmotjie mssjlebfet ipfrmtirs.

(*2) bu`tjp`jomtjie mssjlebfet ipfrmtirs.

(/2) njvjsjie mssjlebfet ipfrmtirs.

(%2) rfbmjenfr mssjlebfet ipfrmtirs.

Fxmbp`f;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 6=-id-=:: 

DIQ MNNJ^JIE;

_IVQOF-OINF;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet titm`278

jet oiuet2=78

prjetd(‐^itm`2%nPe‒,titm`)8 

titm`+2oiuet8

prjetd(‐titm`2%nPe‒,titm`)8 

titm`+2oiuet8

prjetd(‐titm`2%n‒,titm`)8 

lftoc()8

}

IV^WV^ ;

^itm`27

titm`2=7

^itm`217

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 61-id-=:: 

DIQ _VA_^QMO^JIE;-

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

{ jet titm`2=78

jet oiuet2>78

prjetd(‐^itm`2%nPe‒,titm`)8 

titm`-2oiuet8

prjetd(‐^itm`2%nPe‒,titm`)8 

titm`-2oiuet8

prjetd(‐^itm`2%n‒,titm`)8 

lftoc()8

}

IV^WV^;

^itm`2=7

^itm`2-?7

^itm`2-<7

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

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 6?-id-=:: 

DIQ-BV@^JW@JOM^JIE;

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet titm`2678

jet oiuet2<8

prjetd(‐^itm`2%nPe‒,titm`)8 

titm`*2oiuet8

prjetd(‐^itm`2%nPe‒,titm`)8 

titm`*2oiuet8

prjetd(‐^itm`2%n‒,titm`)8 

lftoc()8

}

IV^WV^;

^itm`267

^itm`2?67

^itm`21>67

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 6>-id-=:: 

DIQ NJTJ_JIE;-

_IVQOF-OINF;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ d`imt titm`2<?.618

jet oiuet2678

prjetd(‐^itm`2%d Pe‒,titm`)8 

titm`/2oiuet8

prjetd(‐^itm`2%d Pe‒,titm`)8 

titm`/2oiuet8

prjetd(‐^itm`2%d‒,titm`)8 

lftoc()8

}

IV^-WV^;

^itm`2<?.61

^itm`2=>.<7>

^itm`27.1:>

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 66-id-=:: 

----------djejscfn---

^CF JEOQFBFE^ MEN NFOQFBFE^ IWFQM^IQ;-

m. JEOQFBFE^ IWFQM^IQ;-

^cf O-`melumlf usfn meitcfr ipfrmtir tcmt js ‐Jeorfbfet-

Ipfrmtir‒, tcfrf mrf tcf di``iwjel prilrmb mrf ljvfe af`iw. 

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet eub278

prjetd(‐Eubafr2%nPe ‐,eub)8 

prjetd(‐Eubafr2%nPe‒,eub++)8 

prjetd(‐Eubafr2%n‒,eub)8 

lftoc()8

}

IV^WV^;

Eubafr27

Eubafr27

Eubafr2=

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 64-id-=:: 

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

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet eub2=>8

prjetd(‐Eubafr2%nPe‒,eub)8 

prjetd (‐Eubafr2%nPe‒,eub++)8 

prjetd(‐Eubafr2%nPe‒,eub++)8 

prjetd(‐Eubafr2%nPe‒,eub++)8 /* eub2=<(je bfbiry)*/ 

prjetd(‐Eubafr2%nPe‒,++eub)8 /*eub2=3(je bfbiry men

njsp`my iutput*/

prjetd(‐Eubafr2%nPe‒,++eub)8 /*eub2=3+=(=:)(je bfbiry

men njsp`my iutput*/

prjetd(‐Eubafr2%nPe‒, eub++)8 /*eub2=:+=(17)(je

bfbiryX17R men njsp`myX=:R iutput*/

prjetd(‐Eubafr2%nPe‒, eub)8 /* eub217 (je njsp`my) */ 

lftoc()8

}

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 6<-id-=:: 

IV^-WV^;

Eubafr2=>

Eubafr2=>

Eubafr2=6

Eubafr2=4

Eubafr2=3

Eubafr2=:

Eubafr2=:

Eubafr217

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

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

{ jet eub2118

prjetd(‐ Eubafr2%nPe‒,eub)8 /*eub211*/ 

prjetd(‐Eubafr2%nPe‒,eub++)8/*eub211+=21?, eub21? je

bfbiry , men je njsp`my js 11 */

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 63-id-=:: 

prjetd(‐Eubafr2%nPe‒, eub--)8 P*eub21?-=211, 11je

bfbiry men 1? je njsp`my*P

prjetd(‐Eubafr2%nPe‒, ++eub)8 P*eub211+=21?, 1? jebfbiry men m`si 1? je njsp`my *P

prjetd(‐Eubafr2%nPe‒,eub+=)8 P*eub21?+=21>, 1> je

njsp`my *P

prjetd(‐ Eubafr2%nPe‒,--eub)8P*eub21>-=21?, 1? je

bfbiry men m`si je njsp`my*P

prjetd(‐Eubafr2%nPe‒,eub+=)8P*eub21?+=21>,1> je njsp`my

ut eit je bfbiry *P

prjetd(‐Eubafr2%nPe‒, eub-=)8P*eub21?-=211, 11je njsp`my

men 1? je bfbiry*P

prjetd(‐ Eubafr2%nPe‒,--eub)8P*eub21?-=211 , 11 jebfbiry men m`si je njsp`my*P

prjetd(‐Eubafr2%nPe‒,eub)8P*eub211,11je bfbiry men

m`si je njsp`my*P

prjetd(‐Eubafr2%nPe‒,++eub)8P*eub211+=21?, 1? je

bfbiry men m`si je njsp`my*P

prjetd(‐Eubafr2%nPe‒,eub)8P*eub21?, 1?je njsp`my *P

lftoc()8

}

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 6:-id-=:: 

IV^-WV^;

Eitf;^ry ay yiur sf`d.

-----djejscfn----------

NFOQFBFE^;

_IVQOF-OINF;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

jet eub2-=38

prjetd(‐Eubafr2%nPe‒,eub)8P* eub2-=3*P

prjetd(‐Eubafr2%nPe‒,eub--)8P*eub2-=3-=2-=:,-=: je

bfbiry aut -=3 je njsp`my*P

prjetd(‐Eubafr2%nPe‒,--eub)8P*eub2-=:-=2-17,-17 je

bfbiry men m`si je njsp`my *P

prjetd(‐ Eubaf2%nPe‒,eub-=)8 P*eub2-17-=2-1= , -1= je

njsp`my aut eit je bfbiry *P

prjetd(‐Eubafr2%nPe‒, eub)8P*eub2-17*P

IV^-WV^;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 47-id-=:: 

-=3

-=3

-17

-1=

-17

---------------djejscfn cfrf-----

OIBBFE^_-IWFQM^IQ_;-^cf oibbfets X /* */ R , js cf`pdu` ti usfn jt m`wmys usfn je

tcf siurof oinf dj`f, tcf bmje purpisf id ‐oibbfets‒ js tcf

prilrmbbfr ome wrjttfe mey tcjel maiut jts prilrmb mey

fxp`jemtjie rf`mtfn ti lujn ir iwe smttjsdjomtjie wcjoc mrf

wrjttfe jesjnf X /* mey tcjel maiut prilrmb */ R men tcjs

oibbfets js vjsja`f dir m prilrmbbfr aut ue vjsja`f dir tcfoibpj`fr,

\f ome m`si usfn oibbfet ay jenjomtfn tcf nfmotjvmtfn

stmtfbfet dir nfaulljel { rfbivjel frrir} je prilrmb.

Fxmbp`f;

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 4=-id-=:: 

vijn bmje(vijn)

{jet yfmr,nmys8 /* jetflfr vmrjma`f */

prjetd(‐ Fetfr mlf je yfmrs‒)8 /* prjet yiur mlf*/ 

somed(‐%d‒,&yfmrs)8 /* tmhf jeput*/ 

nmys2yfmrs*?468

prjetd(‐yiu mrf %d nmys i`n‒, nmys)8 /* njsp`my iutput */ 

lftoc()8

}

---------

QF@M^JIEM@-IWWFQM^IQ;-

Je tcf efxt twi ocmptfr wf wj`` af nfm`jel wjtc `iips men

nfojsjie, tcfsf oiestruots rfqujrf tcf prilrmb ti msh qufstjiemaiut tcf rf`mtjiescjp aftwffe twi vmrjma`fs.

Qf`mtjiem` ipfrmtir mrf viomau`mry tcf prilrmb usfs ti msh

qufstjies maiut vmrjma`fs .

‐^cf usfr kust typfn fqum` ti men tcfe m spmof tcfe m

ocmrmotfr ‐ tcmt js sciwe je af`iw djl # ==; 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 41-id-=:: 

FSMBW@F; ^cjs prilrmb js om``fn `fss tcme.o ;

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet mlf8

mlf2=68

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 4?-id-=:: 

prjetd(‐Js mlf `fss tcfe 1=9%nPe‒, mlf 0 1=)8 

mlf2?78

prjetd(‐Js mlf `fss tcfe 1=9 %n Pe‒, mlf01=)8 

}

IV^-WV^;

Js mlf `fss tcfe 1=9 =

Js mlf `fss tcfe 1=9 7

------

‐Je tcjs prilrmb maivf tcf prjetd() stmtfbfet tmhfs tcf wci`f

fxprfssjie‒ 

Mlf 01=

^cf vm`uf id ‐mlf‒ nfpfen ie tcf vm`uf id ‐mlf‒ wcjoc mrf

mssjlefn mt maivf prjetd() dueotjie.

^cf fvfry vm`uf nfpfen ie vm`uf tcf vmrjma`f mlf tcmt js

\cfe mlf js =6 X mlf2=68R , /* wcjoc js `fss tcfe 1=*/

^cme

Wrjetd(‐Js mlf `fss tcme 1=9 %nPe ‐, mlf 01=)8 

^cfe tcjs stmtfbfet mlf 2=68 je wcjoc mlf js `fss tcme 1=

tcjs stmtfbfet js truf,si,

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 4>-id-=:: 

^cfe ,

Jt prjet iut ‐=‒  jetflfr, tcjs bfme tcmt , tcf maivf

stmtfbfet tcmt js mlf01= js truf , si o-`melumlf sciws =jetflfr tcmt js stmtfbfet js truf , ir +6 vi`t, sff je af`iw djl

# =1 ,

1. \cfe mlf js ?7, X mlf2?7R

mlf2?78/* wcjoc js lrfmtfr tcfe 1=*/ , tcfe

prjetd(‐Js mlf `fss tcme 1= 9 %n Pe ‐, mlf 0 1= )8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 46-id-=:: 

tcfe je tcjs stmtfbfet wcfrf X mlf2 ?78 R je wcjoc mlf js

lrfmtfr tcfe 1= tcjs stmtfbfet js dm`sf.

^cfe jt prjet 7 jetflfr , tcjs bfme tcmt , tcf maivfstmtfbfet tcmt js mlf 0 1= js dm`sf afomusf mlf 2 ?78

_i, o-`melumlf , sciws 7 jetflfr tcmt js stmtfbfet js dm`sf ir

7 vi`t , 7 jetflfr ,

Je o-`melumlf ;

^ruf;

Je tcf O-`melumlf tcf truf js rfprfsfetfn ay tcf jetflfr =

ir 6 vi`ts ir stmtfbfet js truf.

Dm`sf;-

Je tcf o-`melumlf tcf Dm`sf js rfprfsfet ay tcf jetflfr X7 R ,

ir 7-vi`t, X zfri jetflfr, ir zfri-vi`tR, ir tcf stmtfbfet js

dm`sf.

M`si,

JE _IBF I^CFQ @MELVMLF;-

^cfrf mrf sibf itcfr `melumlf suoc ms ‐Wmsom`‒, truf men

dm`sf vm`uf mrf prfsfetfn ay m spfojm` vmrjma`f typf om``fn

Aii`fme.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 44-id-=:: 

^CF QF@M^JIEM@ IWFQM^IQ JE O-@MELVMLF @IIH BVOC

@JHF ^CI_F JE I^CFQ @MELVMLF ^CFQF MQF _JS ID ^CFB

;-

0 @fss tcme

5 Lrfmtfr tcme

02 @fss ir fqum` ti

52 Lrfmtfr tcme ir fqum` ti

22 Fqum` ti

!2 Eit fqum` ti

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

NJMLQMB; DJL # =>

Jd mlf 2=68

tcfe

Djl # => (m)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 4<-id-=:: 

Djl # => (a) iut ‟put siurof;-

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 43-id-=:: 

1. Njmlrmb X djl # =6 R

JEWV^-_IVQOF;-

Djl # =6 (m)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 4:-id-=:: 

Iut-Wut siurof ;

Djl # =6 (a)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <7-id-=:: 

-----------

m. QF@M^JIEM@ IWFQM^IQ_ XF]VM@-^IR X22R IWFQM^IQ‚_;-

Je tcf ‐rf`mtjiem`-Ipfrmtir‒ wf usfn meitcfr tcjel js tcmt

‐fqum` ti‒ wcjoc js rfprfsfetfn ay twi fqum` sjles. ^cmt js . 

X 22 fqum` ti R

Aut wf ni m sjbp`f bjstmhf js tcmt js wf usum``y put sjel`f

‐fqum` ti‒ sjle tcmt js wriel dir rf`mtjiem` ipfrmtirs . 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <=-id-=:: 

Aut tcf oibpj`fr nifs eit eitjof ms me frrir, wcfe wf put

sjel`f ‐fqum`-ti‒ sjle tcmt js wcjoc js wriel dir rf`mtjiem`

ipfrmtirs .

_i, wcfe wf usjel fqum` ti X 22R ipfrmtir (sibf tjbf om``fn

‐Fqum`-fqum`‒ Ipfrmtirs). 

DIQ FSMBW@F ;

Jeput-siurof;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

Tijn bmje(vijn)

{ jet spffn 2 <68

prjetd(‐Js spffn fqum` ti 669 %nPe‒,spffn2266)8 

spffn2668

prjetd(‐Js spffn fqum` ti 669%nPe‒, spffn2266)8 

lftoc()8

}

IV^-WV^ ;

Js spffn fqum` ti 669 7

Js spffn fqum` ti 669 =

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <1-id-=:: 

---------djejscfn„ 

]) \cfe O-`melumlf lfefrmtfn fjtcfr dm`sf X7R ir truf X=R

vm`uf 9

Meswfr;

Me jetfrfstjel pijet ti eitjof maiut truf men dm`sf vm`uf js

tcmt , m`tcisf o-`melumlf wj̀ ` lfefrmtfn m = wcfe jt iasfrvfn

tcmt tcf stmtfbfet js truf.

M`si o-`melumlf wj`` lfefrmtfn m 7 wcfe jt iasfrvfn tcmt tcfstmtfbfet js dm`sf.

‐J wj`` rfoilejzf mey eie-zfri vm`uf ms truf . tcmt js tcfrf mrf m

`it id jetflfrs tcmt o-`melumlf tcjehs id ms truf , aut ie`y ief-

7- jt tcjehs id ms dm`sf, wf wj`` bmhf usf id tcjs dmot je `fttfr

prilrmbs.

------------djejscfn-----------

WQFOFNFEOF, QIVEN JJ ;-

] ) \cmt wj`` af prjetfn iut jd yiu fxfoutf tcf di``iwjel

prilrmb9

{;. Qfbfbafr tcmt ^ruf js tcf jetflfr X=R ir 6 vi`t X stmtfbfet

js rjlctR , wcfe dm`sf js tcf jetflfr X7R ir 7 vi`t Xir stmtfbfet js

dm`sfR}

^cfsf vm`ufs ome af usfn kust `jhf mey itcfr jetflfr vm`ufs ms

sciwe af`iw9

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <?-id-=:: 

Fxmbp`f;

JEWV^-_IVQOF OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

prjetd(‐Meswfr js %n‒, 1+= 0 > )8 

lftoc()8

}

------------- jd yiu tcjeh ‐Meswfr js =‒ si yiu rjlct , je tcjs djrst

1+= js fvm`umtfn ti yjf`n ? , tcmt js 1+=2? , tcfe tcjs oibpmrfn

wjtc >, jts `fss tcfe >, X ?0> R , si tcfe fxprfssjie afoibfstruf ir stmtfbfet js truf tcmt js =.

IV^WV^;

Meswfr js =

^cjs bfme tcf stmtfbfet js truf.

------djejscfn-cfrf----------

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <>-id-=:: 

vijn bmje(vijn)

{ o`rsor()8

prjetd(‐Meswfr js %n‒, 1+=0>)8 

prjetd(‐Pe meswfr js %n‒, (=01)+>)8 

lftoc()8

}

IV^WV^;

Meswfr js =

Meswfr js 6

------------djejscfn-----------

Oc-? stmrt cfrf X @IIW R

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet j 8

dir(j2=8j0==8j++)

{

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <6-id-=:: 

prjetd(‐ 1*%n2%n Pe‒,j,j*1)8 

}

lftoc()8

}

IV^WV^;

1*=21

1*12>

..

.

.

1*=7217

----DCJEJ_CFN„ 

DIQ-@IIW;-

Jeput-siurof-oinf;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet m8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <4-id-=:: 

dir(m2=8m0=?8m++)

{

prjetd(‐1*%n2%n Pe‒,m,m*1)8

}

dir(m2=8m0=?8m++)

{

prjetd(‐ Pe ?*%n2%n‒,m,m*?)8 

}

lftoc()8

}

IV^WV^;

^MA@F ID 1 VW ^I =1

^MA@F ID ? VW ^I =1

----DJEJ_CFN---

LF^OCF()8

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vjin bmje(vijn)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <<-id-=:: 

{ ocmr e8

prjetd(‐ Fetfr tcf =st

 oc id yiur embf; ‒)8 

e2lftocf()8

prjetd(‐Pe Cf``iw Br. %o ‐, e )8 

lftoc()8

}

IV^-WV^;

Fetfr tcf =st

 oc id yiur embf; _

Cf``iw Br. _

Fetfr tcf =st

 oc id yiur embf;

------djejscfn-----------

\rjtf m prilrmb tcmt tmhf m eubafr drib tcf usfr men njsp`my

jts tma`f usjel Dir `iip9

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet m,j8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <3-id-=:: 

prjetd(‐Jesfrt mey eubafr ti lft tcf tma`f id jt‒)8 

somed(‐%n‒,&m)8 

dir(j2=,j02=7,j++)

{

prjetd(‐ %n*%n2%n ‒,m,j,j*m)8 

}

lftoc()8

}

IV^-WV^;

--------------djejscn-----

] wrjtf m prilrmb tcmt tmhf m eubafr drib tcf usfr men

njsp`my jts tma`f up ti =6 tjbfs ay usjel Dir @iip9

ME_\FQ;

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet m,s,p8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf <:-id-=:: 

dir(m2=8m02=68m++)

{

prjetd(‐Fetfr m eubafr id yiur ocijof ;‒)8 

somed(‐%n‒,&s)8 

p2s*m8

prjetd(‐%n*%n2%n‒,s,m,p)8 

prjetd(‐Pe‒)8 

}

lftoc()8

}

------------djejscfn-----------

] ) \rjtf m prilrmb tcmt njsp`my tcf di``iwjel sfrjfs usjel dir

‐dir-`iip‒ 9 

X

   R8

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 37-id-=:: 

vijn bmje(vijn)

{ jet j,k8

dir(j2=8j02<8j++)

{ k217+(1*j)8

prjetd(‐%n/%n ‐,j,k)8 

}

lftoc()8

}

-----------------djejscfn-cfrf------------

IWFQM^JIE-ID-DIQ-@IIW;-

Djrst id m`` tcf jejtjm`jzf fxprfssjie js fxpfotfn tcfe tcf tfxt

oienjtjie js fxmbjefn.

 Jd tcf tfst oienjtjie js dm`sf ti afjel tcfe tcf ainy id

`iip js eit af fxfoutfn mt m`` .

 Jd tcf tfst oienjtjie js truf , tcfe ainy id `iip js

fxfoutfn men tcfe tcf di``iwjel tcmt tcf jeorfbfet

fxprfssjie js fxfoutfn.

 ̂ cjs js wcy tcf =st Eubafr js prjetfn iut ay prilrmb, X

fxmbp`f = R js 7 eit =,

 Wrjetfn tmhjel p`mof afdirf oiuet js jeorfbfetfn ay X++R

ipfrmtirs .

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 3=-id-=:: 

 Djem``y tcf `iip rf-oyo`fs, men tcf tfxt fxprfssjie ,

fxmbjefn mlmje jt wj`` oietjeuius , uetj` tfxt fxprfssjie

js dm`sf.

Fxmbp`f =;

vijn bmje(vijn)

{

Jet oiuet8

dir(oiuet278oiuet02=78oiuet++)

{

prjetd(‐%nPe‒,oiuet)8 

}

lftoc()8

}

IV^-WV^;

7

=

1

?

>

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 3?-id-=:: 

Oiuet27 , titm`27

Oiuet2=, titm`2=

Oiuet21, titm`2?

.

.

.

Oiuet2: , titm`2>6

-------------djejscfn---

litixy(o,r) DVEO^JIE;-

jts usfn ti oietri``fn tcf oursfr pisjtjie ie tcf sorffe XNI_

sorffe R;

Fxmbp`f ;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet j8

dir(j2178j02>78j++)

{

litixy(j,6)8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 3>-id-=:: 

prjetd(‐ NA ‐ )8 

}

lftoc()8

}

IV^-WV^; X djl # =4 R

----djejscfn-----

FSMBW@F ;

#jeo`unf0stnji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 36-id-=:: 

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet j , k 8

dir(j2178j02>78j++)

{

litixy(j,6)8

prjetd(‐Pe NA‒)8 

}

dir(k2<78k02378k++)

{

litixy(k,17)8

prjetd(‐PeNA‒)8 

}

lftoc()8

}

------------djejscfn-----------

OC-?; @IIW;-

^cf `iip cms tcf maj`jty ti pfrdirbfn m sft id jestruotjie ,

bmey tjbfs.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 34-id-=:: 

Jts usfn dir rfpfmtjel sibf pirtjie id prilrmb fjtcfr

=. _pfojdjo eubafr id tjbf .

1. Ir uetj` pmrtjou`mr oienjtjie cms affe smtjsdjfn.

^cfrf mrf tcrff typfs id @IIWs;-

=. Dir `iip X jts usfn dir djxfn eubafr id tjbfs R.

1. \cj`f-@iip X wf usfn wcj`f `iip ti rf fxfoutf m prilrmb

aut wf nieit heiw ciw bmey tjbfs wf fxfoutfn tcjs

prilrmbR

?. Ni \cj`f @iip X ir Ni-@iipR.

=) DIQ @IIW;-

Jts idtfe tcf spfojdjo omsf je prilrmbbjel , tcmt yiu wmet ti

ni sibf tcjel wjtc m djxfn eubafr id tjbf.

MNTME^MLF ID DIQ-@IIW;-

^cf mnvmetmlf id dir-`iip js tcmt ;

=. Jd yiu wmet ti om`ou`mtfn tcf pmyocfohs dir =17 fbp`iyfs

je mey irlmejzmtjie, yiu sciu`n ti om`ou`mtfn wjtc tcf

cf`p id ‐Dir-@iip‒ ay djxfn eubafr id tjbf. 1. Jd yiu mrf tii curry, si yiu sciu`n om`ou`mtfn tcf squmrf

id fmoc jetflfr dirb =-ti-67 , je tcf irnfr id , tcfe yiu

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 3<-id-=:: 

usfn dir-`iip , ti flt tcf squmrf vm`uf id fmoc jetflfrs

dirb =-ti-67,

Fxmbp`f ;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

jet oiuet8

dir(oiuet278oiuet0=78oiuet++)

{

prjetd(‐oiuet2%nPe‒,oiuet)8 

}

lftoc()8

}

IV^ WV^;-

Oiuet27

Oiuet2=

.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 33-id-=:: 

.

Oiuet2:

--------djejscfn----------

_^QVO^VQF-ID-^CF-DIQ-@IIW;-

^cf wmy id di``iwjel pmttfre‚s, je wcjoc tcf hfy wirn ‐dir‒

p`mys me jbpirtmet ri`f je tcf ‐Dir-@iip‒ , tcjs hfy-wirn XdirR

Vsfn ti nrjvf tcf dir `iip fxprfssjie, tcmt js X

(oiuet2=8oiuet0=78oiuet++)R jts om``fn ms @iip fxprfssjie;

Eiw

^cf ci`f ‐Dir-@iip-Fxprfssjie‒ njvjnfn ay tcf sfbjoi`ieX8R

jeti tcrff sfpmrmtfn jenjvjnum` fxprfssjie, wcjoc mrf ljvfe

af`iw, (oiuet2=8oiuet0=78oiuet++)

=. Jejtjm`jzf Fxprfssjie X oiuet2= R.

1. ̂ fst-Fxprfssjie X oiuet0=7 R.

?. Jeorfbfet XIr Nforfbfet R Fxprfssjie X Oiuet++ (ir

Oiuet--)R.

Fxprfssjie Embf Wurpisf= Oiuet27 Jejtjm`jzf

fxprfssjie

Jts usfn dir jejtjm`jzfn `iip

fxprfssjie /* dir mssjlejel

vm`uf id ‐oiuet‒ vmrjma`f*/ 

1 Oiuet0=7 ^fst- Dir tfst ̀ iip vmrjma`f /* dir

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :7-id-=:: 

@IIW-FSWQF__JIE;-

^cfrf mrf tcrff typfs id `iip fxprfssjie.

=. JEJ^JM@J[F-FSWQF__JIE;-m. ^cf djrst fxprfssjie js tcf jejtjm`jzf fxprfssjie (oiuet27)

,mdtfr wrjttfe tcjs fxprfssjie wf p`mofn m sfbj-oi`ie X 8 R

tcjs fxprfssjie js usfn ti jejtjm`jzf tcf ‐oiuet‒ vmrjma`fs ir

jts usfn ti mssjlejel tcf vm`uf id vmrjma`f ‐oiuet‒ ms ‐7‒ X

oiuet27R je jts bfbiry `iomtjie.

a. ̂ cjs jejtjm`jzfn fxprfssjie X oiuet27R js m`wmys fxfoutfn mssiie ms tcf `iip X ir oibpj`frR fetfrfn je tcjs jejtjm`jzf

fxprfssjie.

o. \f ome mssjlejel jejtjm`jzf fxprfssjie wjtc mey eubafr `ft,

suppisf ( oiuet2= ) je tcjs maivf omsf tcf vmrjma`f ‐oiuet‒

js fqum` ti ‐=‒ . 

n. 

Aut jd js eit efofssmry , tcf dir-`iip ome af prjetfn iut aystmrtfn wjtc ms X oiuet2= R, je tcf iutput siurof.

f. Aut jts m`si af pissja`f tcmt , jt sciu`n af prjetfn iut

vmrjma`f oiuet ms fqum` ti 1 X oiuet21 R ir X oiuet2 -= R jts

nfpfen upie tcf jeorfbfet ir nforfbfet fxprfssjie.

1. ^F_^-FSWQF__JIE;

m. ^cf sfoien fxprfssjie js tcf ‐tfst fxprfssjie‒ ( oiuet0=7), tcjs tfst fxprfssjie usfn ti tfst X ocfohR tcf omrjma`f

‐oiuet‒ je fmoc tjbf vjm tcf `iip , fjtcfr vmrjma`f ‐oiuet‒

js ‐`fss tcme X0 R‒ jetflfr =7 ir eit tcmt js X oiuet0=7 R. 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :=-id-=:: 

a. Je tcjs tfst fxprfssjie wcfrf Xoiuet0=7 R tcjs fxprfssjie js

usfn tcf mey rf`mtjiem` ipfrmtirs, aut je Xoiuet0=7 R, tfst

fxprfssjie , jt usfn ‐`fss tcfe X0R‒ rf`mtjiem` ipfrmtir. 

o. _uppisf, jd tcf tfst fxprfssjie js truf tcmt js ; wcfe

vmrjma`f ‐Oiuet‒ js `fss tcme =7 je tcjs tfst fxprfssjie

Xoiuet0=7R, tcf ainy id `iip wj`` af fxfoutfn mlmje men

mlmje , tj`` tcfe tcjs tfst fxprfssjie wj`` afoibf dm`sf,

afomusf tcf rfmsie id tcjs dm`sf tfst fxprfssjie stmtfbfet

js tcmt vmrjma`f oiuet js fqum` ir lrfmtfr tcme =7, tcmt js

Xoiuet=7 , ir ,oiuet !0 =7R.

?. JEOQFBFE^/NFOQFBFE^-FSWQF__JIE;-

m. ^cf tcjrn fxprfssjie js tcf jeorfbfet fxprfssjie, tcmt js

Xoiuet++R tcjs jeorfbfet fxprfssjie js usfn dir jeorfbfet

X ir jeorfmsf R tcf vm`uf id vmrjma`f ‐oiuet‒ ay mnnjel ief

jetflfr fmoc tjbf , mdtfr , wcfe `iip wj`` fxfoutfn , jt

jeorfmsf ay mnnjel je tcf jejtjm`jzf vm`uf id vmrjma`f

‐oiuet‒ wjtc jetflfr X=R. Ie fmoc ture id tcf `iip oyo`f.  

a. M`si tcf tcjrn fxprfssjie js tcf nforfbfet fxprfssjie, tcmt

js X oiuet-- R tcjs nforfbfet fxprfssjie js usfn dir

nforfbfet X ir nforfmsf R tcf vm`uf id vmrjma`f ‐oiuet‒

ay suatrmotjel ief jetflfr fmoc tjbf , mdtfr , wcfe ̀ iip

wj`` fxfoutfn , jt nforfmsf ay suatrmotjel je tcf jejtjm`jzf

vm`uf id vmrjma`f ‐oiuet‒ wjtc jetflfr X=R. Ie fmoc ture id

tcf `iip oyo`f.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :1-id-=:: 

------------djejscfn----------

@MA # 4 IE __VF^ JE AJI-BFNJOM@ OIBWV^JEL ;

]) \rjtf m prilrmb tcmt prinuof tcf siuen id njddfrfet

drfqufeoy9

_IVQOF-OINF;

#jeo`unf0nis.c5

vijn bmje(vijn)

{

jet j 8

dir(j2=:168j52?778j-216)

{

siuen(j)8 /* drfqufeoy j2=:16-?77 */

nf`my(67)8 /* nf`my id 67 bjori sfoien */

ei siuen()8 /* jts omusf ti stip siuen*/

}

}

IV^-WV^ X M^ NI_ _OQFFE R;

Ziu cfmrn tcf _IVEN id njddfrfet drfqufeojfs drib tcf

jetfrem` spfmhfr id yiur oibputfr .

-------------djejscfn--------

@ma 6

Iakfotjvf

\rjtf m prilrmb tcmt njsp`my M_OJJ oinf tma`f ie iut-put

sorffe9

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :?-id-=:: 

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet j 8

dir( j2=8 j021648j++)

{

prjetd(‐%n2%o‒,j,j)8 

}

lftoc()8

}

IV^-WV^;

-------djejscfn-----------

] ) wrjtf m prilrmb tcmt njsp`my tcf di``iwjel ljvfe

iutput ay usjel efstfn dir @iip9 _ff djl # =: , af`iw.

Ljvfe djl # =: ;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :>-id-=:: 

_I@V^JIE;

Djl # ?<

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :6-id-=:: 

^cf djl # ?< , sciw tcf afst njmlrmb ti uenfrstmen tcf dueotjieid o-`melumlf , ms yiu ome sff tcf njrfotjie id x men y irnjemtf

bivjel drib tip `fdt oirefr X wcfrf x2=, men y2= R ti mnkmofet

pisjtjie , `jhf y-irnjemtf bivf drib tip `fdt oirefr id NI_

iutput sorffe ti tcf aittib `fdt oirefr id tcf NI_ iutput

sorffe, sjbj`mr`y tcf x-irnjemtf bivf drib tip-`fdt oirefr X

wcfrf aitc irnjemtf mrf = , x2=, men y2= R id tcf NI_ iutputsorffe ti tcf tip-Qjlct oirefr id tcf NI_ iutput sorffe.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :4-id-=:: 

_i , jd yiu uenfrstmen tcf bfocmejsb id maivf pijet tcfe tcf

o-`melumlf afoibf buoc fmsy dir yiu je tfrbs id mem`ysjs

pijet id vjfw .

Eiw wf wrjtf m rfqujrfn prilrmb id ljvfe djlurf # ?< wcjoc js

je dious dir mem`ysjs tcf prilrmb.

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

jet x,y8

dir(y2=8y02==8y++)

{ dir(x2=8x02y8x++)

{ prjetd(‐PxNA‒)8 

} prjetd(‐Pe‒)8 

} lftoc()8

}

-------------------------djejscfn-------------

] wrjtf m Wrilrmb wcjoc njsp`my tcf di``iwjel ljvfe iutput9

Ljvfe;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :<-id-=:: 

Djl # ?3

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet x,y8

dir(y2=8y02:8y++)

{

dir(x2=8x02(=7-y)8x++)

{ prjetd(‐PxNA‒)8 

}

prjetd(‐Pe‒)8 

}

------------djejscfn-------------

] om`ou`mtf tcf sjbp`f jetfrfst dir ? sft id p,e men r 9

Vsjel dirbu`m;

Ljvfe

X

 R8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf :3-id-=:: 

_I@V^JIE;

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmjb(vijn)

{ jet p,e,r,om`8 /* om`ou`mtfn id sjbp`f jetrfst dir ? sft id p,e men

r */

d`imt ej8

dir(om`2=8om`02?8om`++)

{ prjetd(‐Fetfr tcf vm`uf id p,e men r ; ‐)8 

somed(‐%n %n %n‒, &p,&e,&r)8 

ej2p*e*r/=778

prjetd(‐Pe ^cf vm`uf id Qupfjsf2 Qs. %d‒, ej)8 

}

lftoc()8

}

IV^WV^ _IVQOF-OINF;

Fetfr tcf vm`uf id p,e men r ; 1 > 1

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ::-id-=:: 

^cf vm`uf id Qupfjsf2 Qs.(=4/=772 9 )

-----------

Djl # 11

------djejscfn-cfrf----------

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =77-id-=:: 

EF_^FN-DIQ-@IIW;-

Jd wf cmvf ti jbp`fbfet m prilrmb je wcjoc riw men oi`ubes

id iut put sorffe aitc mrf jevi`vfn ir ocmelf nurjel

fxfoutjie dir suoc typf id tmsh wf usfn Efstfn Dir `iip X `iip

jesjnf tcf meitcfr `iipR.

Fxmbp`f

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet oi`,riw8

dir(riw2=8riw02=78riw++)

{ dir (oi`2=8oi`02=78oi`++)

{ prjetd(‐%n‒,oi`*riw)8

} prjetd(‐Pe‒)8 

} lftoc()8

}

IV^-WV^ ;

= 1 ? …….=7 

1 > 4 ………17 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =7=-id-=:: 

?

>

6

4

<

3

:

=7 17 ?7 ………………….=77 

--------DJEJ_CFN---

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =7?-id-=:: 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =7>-id-=:: 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =76-id-=:: 

DIQ-@IIW

]) Vsjel tcf Lftocf()8 oibbmens je yiur prilrmb9 

si`; 

_IVQOF OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ocmr s8 

prjetd("Fetfr tcf djrst ocmrmotfr id yiur embf; ")8 

s2lftocf()8 

prjetd("Pe cf``iw Br. %o",s)8 

lftoc()8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =74-id-=:: 

IV^-WV^; 

Fetfr tcf djrst ocmrmotfr id yiur embf; M  

cf``iw Br. M  

 YYYYYYYYYYYYYY(DJEJ_CFN)YYYYYYYYYYYYYYYYYYY

 YYYY 

]VF_^JIE) wrjtf m prilrmb tcmt tmhf m eubafr drib tcf

usfr & njsp`my jts tma`f ay usjel "DIQ-@IIW"9 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

#jeo`unf0(nis.c)5 

 vijn bmje(vijn) 

{o`rsor()8jet s8 

prjetd("Fetfr m Eubafr dir usjel jts ms m tma`f; ")8 

prjetd("Pe")8 

somed("%n",&s)8 

dir(j2=8j02=18j++) 

{prjetd("%n*%n2%n",s,j,s*j)8 

nf`my(67)8 

}lftoc()8 

IV^-WV^; 

Fetfr m Eubafr dir usjel jts ms m tma`f; ? 

?*=2? 

?*124 

?*=72?7 

 YYYYYYYYYYYYYYY(djejscfn-cfrf)YYYYYYYYYYYYYYYY-

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =7<-id-=:: 

]) \rjtf m prilrmb tcmt tmhf m eubafr drib usfr &

njsp`my jts tma`f up ti =6 tjbfs ay usjel dir-`iip9 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

#jeo`unf0(nis.c)5 

 vijn bmje(vijn) 

{jet s,j,h8 

dir(s2=8s02=68s++) 

{prjetd("Fetfr m eubafr id yiur ocijof;")8 

somed("%n",& j)8 

h2s*j8litixy(>7,=1)8 

prjetd("%n*%n2%nPe",j,s,h)8 

nf`my(6:)8 

}lftoc()8 

 YYYYYYYYYYYYYYYYY(djejscfn)YYYYYYYYYYYYYYYYYY 

]) \rjtf m prilrmb tcmt njsp`my M_OJJ OINF tma`f ie iut-put sorffe9

  _IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =73-id-=:: 

#jeo`unf0(nis.c)5 

 vijn bmje(vijn)

{jet j8

dir(j2=8j021648j++) 

{prjetd("%n2%o",j,j)8 

nf`my(67)8 

}lftoc()8 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =7:-id-=:: 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

#jeo`unf0(nis.c)5 

 vijn bmje(vijn) 

{jet j8 

dir(j2=8j02=18j++) 

{litixy(=,j)8prjetd("*******")8 

dir(j2=18j021>8j++) 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ===-id-=:: 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ jet o,r8 

dir(r2=8r02=78r++) 

{

dir(o2=8o02=78o++) 

prjetd("%n",o*r)8 

nf`my(67)8 

} prjetd("Pe")8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ==1-id-=:: 

lftoc()8 

IV^-WV^; 

J^_ LJTF ^CF ^MA@F IE ^CF _OQFFE DQIB (= ^I =7)8 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) \rjtf m prilrmb tcmt dj``s tcf sorffe ay

oi`iur(lrmpcjo)9 

_I@V^JIE; 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ==>-id-=:: 

lftoc()8 

IV^-WV^; 

^CF I/W _OQFFE DJ@@_ AZ LQMWCJO8 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) \rjtf m prilrmb wcjoc omusf ti njsp`my tcf tma`f id tcf

usfr nfdjef mey sjel`f eubafr VW^I =69 

si`utjie; 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ==6-id-=:: 

 vijn bmje(vijn) 

{jet s,j,h8 

prjetd("Fetfr mey EI. ;")8 

somed("%n",& j)8 

dir(s2=8s02=68s++) 

{ h2s*j8 

prjetd("%n*%n2%n Pe",j,s,h)8 

nf`my(67)8 

} lftoc()8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ==4-id-=:: 

IV^-WV^; 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

 YYY 

])

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ jet s,j,h8 

dir(s2=8s02=68s++) 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ==<-id-=:: 

{prjetd("fetfr mey Ei;")8 

somed("%n",& j)8 

h2s*j8 prjetd("%n*%n2%n Pe",j,s,h)8 

nf`my(6:)8 

lftoc()8 

IV^-WV^; 

Fetfr mey Ei; =1 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ==3-id-=:: 

=1*=2=1 

Fetfr mey Ei;=6 

=6*12?7 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

#jeo`unf0(nis.c)5 

 vijn bmje(vijn) 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf ==:-id-=:: 

{ jet oiuet21,j8 

dir(j2=8j0=78j++) 

{prjetd("oiuet2%n Pe",oiuet*j)8 

nf`my(67)8 

}lftoc()8 

IV^-WV^; 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

 \CJ@F-@IIW(o`mss-=);

tcf maivf djl sciw tcf ipfrmtjie id \cj`f-`iip;  

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =17-id-=:: 

jet oiuet2i,titm`278 /*JEJ^JM@J[FN-FSWQF__JIE*/ 

 wcj`f(oiuet0=7)/*tfst-fxprfssjie*/ 

{ titm`2titm`+oiuet8prjetd("oiuet2%n,titm`2%n

Pe",oiuet++,titm`)8 /*AINZ ID @IIW */ 

} lftoc()8 

IV^-WV^; 

 YYYYYYYYYYYYYYYYYYYYYYYYY 

]) wrjtf m prilrmb tcmt tmhfs j/p drib tcf usfr & prjet tcf

tma`f id tcmt eubafr 9 (usjel \cj`f-`iip)9 _IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ jet s,j27,h8 

prjetd("fetfr tcf vm`uf id tcmt eubafr ti usfn je tma`f;")8 

somed("%n",& h)8 /*lftocf()822sjv*/

 wcj`f(j02=6) /* wcj`f(j !2 'Pr') wcfrf 25 Pr2fetfr */{ s2h*j8 

prjetd(" %n*%n2%n Pe ",h,j,s,j++)8 

lftoc()8 

IV^-WV^; 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

  IWFQM^JIE-ID-\CJ@F-@IIW;  

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =1=-id-=:: 

 vijn bmje(vijn) 

{ jet j2=8 

 wcj`f(j0==) 

{ prjetd("sjh")8 

j++8 

lftoc()8 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) \rjtf m prilrmb tcmt prjets m `jef id * ie tcf oirefr's id

sorffe ay usjel tcf wcj`f-`iip9 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

#jeo`unf0(nis.c)5 

 vijn bmje(vijn) 

o`rsor()8 jet s2=8 

 wcj`f(s0237) 

{litixy(s,=)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =1>-id-=:: 

ocmelf tcf ljvfe vm`uf id j/p ay frfsjel tcf prfvjius`y

ljvfe j/p ,

 aut tcf lftocf()8 oibbmens cms tcf vmrjfty je jt ms siie

 wf fetfr m vm`uf je jt tcfe jts wj`` smvf (stirfn) je jt8 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) wrjtf m prilrmb wcjoc msh ay tcf usfr mey sfetfeof

tcfe jts ljvf tcf titm` mbiuet id ocmrmotfr je tcmt sfetmeof

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ o`rsor()8 jet oiuet278 

prjetd("typf m sfetmeof Pe")8 

 wcj`f(lftocf() !2 'Pr') /* tfst-fxprfssjie */ 

{ oiuet++8 

}prjetd("tcjs sfetfeof cmvf %n ocmrmotfr",oiuet)8 

lftoc()8 

IV^-WV^; 

^ypf m sfetmeof

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =16-id-=:: 

Omt 

tcjs sfetmeof cmvf ? ocmrmotfr 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

 \CJ@F-@IIW; 

VE-FSOFW^FN-OIENJ^JIE;  

_IVQOF-OINF; 

 vijn bmje(vijn) 

{ jet sjh278 

prjetd("^ypf mey tcjel;Pe")8 

 wcj`f(lftocf() !2 'Pr' ) 

{ sjh++8 

}prjetd("Pe ocmrmotfr oiuet js %n ", sjh)8 

}lftoc()8 

IV^-WV^; 

^ypf mey tcjel; 

=,1,?,>,6,4,<,3,:  

^ypf mey tcjel; 

ocmrmotfr oiuet js : 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =1<-id-=:: 

si`utjie; 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ jet m,s2=8 /*jet m,s2=,h*/ 

prjetd("Fetfr mey eubafr;")8 

somed("%n",& m)8 

 wcj`f(s02=6) 

{ /* h2s*m8 */ 

prjetd("Pe %n*%n2%n",m,s,s*m)8 /* prjetd("Pe

%n*%n2%n",m,s++,h)8*/ 

s++8 /* jts eit efofssmry dir meitcfr */ 

lftoc()8 

IV^-WV^; 

Fetfr mey eubafr;1 

1*=21 

1*12> 

1*?24 

1*=62?7 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

]) \rjtf m prilrmb tcmt tmhf m j/p drib tcf usfr id mey

pcmrmsf(sfetmeof) , & om`ou`mtfn tcf eubafr id fmoc

ocmrmotfr wirn wcjoc oietmjefn ay tcf pcmrmsf 9 usfn

 wcj`f-`iip9 

si`utjie; 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =13-id-=:: 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 #jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ jet oiuet278 /* jejtjm`jzmtjie id `iip-vmrjma`f */ 

prjetd("typf je m pcmrmsf;Pe")8 

 wcj`f(lftocf() !2 'Pr' ) 

oiuet++8 /* tcjs sfbjoi`ie tfrbjemtfn `iip */ 

prjetd("Pe ocmrmotfr oiuet js %n ",oiuet)8 

lftoc()8 } 

IV^-WV^; 

^ypf je m pcmrmsf; 

 kice 

ocmrmotfr oiuet js > 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

NJDDFQFEOF A/\ somed() & lftocf() js tcmt tcf somed()

tmhf ocmrmotfr,jetflfr, d`imt , aut ---5lftocf() tmhf ie`yocmrmotfr ms j/p8 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

 YYYYYYYYY 

VE-FSWFO^FN-OIENJ^JIE;  

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =1:-id-=:: 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ ocmr oc8 

 wcj`f(oc !2 'Pr' ) 

{ ocmr oc8 

prjetd("Fetfr m ocmrmotfr ;Pe")8 

oc2lftocf()8 

prjetd("Pe tcf oinf id %o js %n",oc,oc)8 

} lftoc()8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?7-id-=:: 

IV^-WV^; 

Fetfr m ocmrmotfr; 

 M  

tcf oinf id M js 46 

Fetfr m ocmrmotfr; 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) \rjtf m prilrmb tcmt msh m sfetmeof drib tcf usfr &

tf``s ei id ocmrmotfr wcjoc oietmjes je sfetmeof9 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?=-id-=:: 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ jet oiuet278ocmr oc8 

prjetd("\rjtf m sfetmeof;Pe")8 

 wcj`f(lftocf() !2 'Pr' ) 

{ oiuet++8 

} prjetd("Pe ^cf sfetmeof oietmje %n ocmrmotfr",oiuet)8 

lftoc()8 

IV^-WV^; 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?1-id-=:: 

 \rjtf m sfetmeof; 

OM^ 

^cf sfetmeof oietmje ? ocmrmotfr 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

 Y 

]) \rjtf m prilrmb tcmt msh m ocmrmotfr drib tcf usfr &

tf``s wcftcfr tcf ocmrmotfr js truf ir eit9 usfn Efstfn

 wcj`f-`iip9 

si`utjie; 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =??-id-=:: 

 vijn bmje(vijn) 

{ jet s8 ocmr oc8 

dir(s2=8s0?8s++) 

{ prjetd("Pe Fetfr mey ocmrmotfr drib m ti f;")8 

prjetd("Pe")8 

 wcj`f((oc2lftocf()) !2 'n') 

{ prjetd("Pe _irry,^cjs '%o' js wriel",oc)8 

prjetd("Pe ^ry Mlmje")8 

prjetd("Pe Zfs jts rjlct")8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?6-id-=:: 

 a 

sirry,tcjs 'a' js wriel 

^ry mlmje 

sirry,tcjs 'o' js wriel 

^ry mlmje 

 yfs jts rjlct 

Fetfr mey ocmrmotfr drib m ti f; 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?4-id-=:: 

 yfs jts rjlct 

Lmbf Ivfr 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) \rjtf m prilrmb wcjoc tmhfs mey eubafr drib usfr &

njsp`my jts dmotirjm`, usjel wcj`f-`iip9 

si`utjie; 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ jet j8 jet h2=8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?<-id-=:: 

prjetd(" Fetfr mey Ei. dir djen jts dmotirjm`;Pe")8 

somed("%n",& j)8 

 wcj`f(j57) 

{ h2h*j--8 

} prjetd("Pe dmotirjm` id %n js %n",j,h)8 

lftoc()8 

IV^-WV^; 

Fetfr mey E7. dir djen jts dmotirjm`; 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?3-id-=:: 

dmotirjm` id ? js 4 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

]) \rjtf m prilrmb wcjoc tmhfs birf tcfe = eubafr

(maiut 6-tjbfs) drib usfr, & njsp`my fmoc id tcjs Eubafrdmotirjm` 9 usjel Efstfn-wcj`f-`iip9 

si`utjie; 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =?:-id-=:: 

{ jet s,j,h,m8s278 

 wcj`f(s06) 

{prjetd("Pe Fetfr m Ei. dir;Pe")8 

somed("%n",& j)8 

h2=8m2j8 

 wcj`f(j57) 

{ h2h*j--8 

prjetd("Pe tcf dmotirjm` id %n js %n.",m,h)8 

s++8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>7-id-=:: 

lftoc()8 

IV^-WV^; 

Fetfr m Ei. dir; 

tcf dmotirjm` id > js 1>. 

Fetfr m Ei. dir; 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYY- 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>=-id-=:: 

]) \rjtf m prilrmb tcmt tf``s ciw bmey ocmrmotfr aPw 1

ocmrmotfr's uetj`` usfr fxjts9 

_IVQOF-OINF8 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ ocmr oc=,oc18 

 wcj`f(oc= !2 'Pr' ) 

{ prjetd("^ypf =tc ocmrmotfr;Pe")8 

oc=2lftocf()8 

prjetd("Pe ^ypf 1tc ocmrmotfr;Pe")8 

oc12lftocf()8 

prjetd("Pe tcfrf mrf %n ocmrmotfr aPw aitc ocmrmotfr.",

(oc1-oc=)-=)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>1-id-=:: 

lftoc()8 

IV^-WV^; 

^ypf =tc ocmrmotfr; 

^ypf 1tc ocmrmotfr; 

 a 

tcfrf mrf 7 ocmrmotfr aPw aitc ocmrmotfr. 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

 YYYYYY 

NI-\CJ@F-@IIW-(O@M__-=)

--5 Maivf djlurf sciw tcf ipfrmtjie id "ni-wcj`f-`iip"8 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

 YYYYYYYYYY 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>?-id-=:: 

]) \rjtf m prilrmb wcjoc tmhf m ocmrmotfr drib tcf usfr

& tf`` wcmt fvfr jts truf ir eit usfn "ni-wcj`f-`iip"9 

si`utjie; 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

{ocmr oc8 

ni 

{

prjetd("PePe ^ypf je m ocmrmotfr drib 'm' ti 'f' ;Pe")8 

 wcj`f((oc2lftocf()) !2 'o') 

prjetd("Pe sirry, %o js jeoirrfot. Pe ",oc)8 

prjetd("^ry mlmje.Pe")8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>>-id-=:: 

prjetd("Pe ^cmt js jt! Pe")8 

prjetd("Pe p`my-mlmje9 (^ypf 'y') ir ti fxjst (^ypf 'o');Pe")8 

 wcj`f(lftocf() 22 'y')8 

prjetd("Pe ^cmehs dir p`myjel!Pe")8 

lftoc()8 

IV^-WV^; 

^ypf je m ocmrmotfr drib 'm' ti 'f'; 

 a 

sirry,a js jeoirrfot. 

^ry mlmje. 

^cmt js jt! 

p`my mlmje9(^ypf 'y') ir ti fxjst(^ypf 'e'); 

 y  

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>6-id-=:: 

^ypf je m ocmrmotfr drib 'm' ti 'f'; 

sirry, n js jeoirrfot. 

^ry mlmje. 

^cmt js jt! 

p`my mlmje9(typf 'y') ir ti fxjst (^ypf 'e'); 

^cmehs dir p`myjel! 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

 YYY 

]) 

_IVQOF-OINF; 

#jeo`unf0(stnji.c)5 

#jeo`unf0(oieji.c)5 

 vijn bmje(vijn) 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>4-id-=:: 

o`rsor()8 ocmr oc=,oc18 

 wcj`f(oc= !2 'Pr') { 

prjetd("Pe ̂ ypf =st ocmrmotfr;Pe")8 

oc=2lftocf()8 

prjetd("Pe ^ypf 1tc ocmrmotfr;Pe")8 

oc12lftocf()8 

prjetd("Pe ^cf M_OJJ-oinf id oc=2%o js %n",oc=,oc=)8 

prjetd("Pe ^cf M_OJJ-oinf id oc12%o js %n",oc1,oc1)8 

prjetd("Pe ^cfrf mrf %n ocmrmotfr a/w aitcocmrmotfr",(oc1-oc=)-=)8 

lftoc()8 

IV^-WV^; 

^ypf =st ocmrmotfr; 

^ypf 1tc ocmrmotfr;  a 

^cf M_OJJ-oinf id oc=2m js 1>:?7 

^cf M_OJJ-oinf id oc12a js 1>:?7 

^cfrf mrf 7 ocmrmotfr a/w aitc ocmrmotfr 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

 Y 

_uenmy, Bmy ?, 177:

(O@M__-=)-NFOJ_JIE_;(JD & F@F_-_^M^FBFE^_);

  NFOJ_JIE_; 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =><-id-=:: 

--5 ^cf "o-`melumlf" cms > bmkir nfojsjie bmhjel

struoturf8 

=.  Jd-stmtfbfet8 

1.  Jd-f`fs-stmtfbfets8  

?.  F`fs-stmtfbfets8  

>.  F`fs-Jd-stmtfbfets8  

6.  _wjtoc-stmtfbfets8  

=.  JD-_^M^FBFE^_; 

---5^cf struoturf id Jd-stmtfbfets js mpprixjbmtf`y

sjbj``mr ti wcj`f-stmtfbfet,aut dueotjie id aitcstmtfbfets mrf njddfrfet wjtc fmoc itcfr, 

tcf njddfrfeof je a/w aitc jd-stmtfbfets & wcj`f-

stmtfbfets mrf ms di``iwjel8 

(j-f) 

=.)---5Je wcj`f-stmtfbfets, tcf ainy wj`` af fxfoutfn mlmje

& mlmje uetj`` tcf oienjtjie je wcj`f-`iip tfst-fxprfssjie afoibf's dm`sf8 

1.)----5Ie tcf itcfr cmen , Jd-stmtfbfet,je tcf Jd-

stmtfbfets, tcf ainy wj`` af fxfoutfn ie`y mt ieof afomusf

jts nifs eit cmvf jeorfbfet-fxprfssjie8 

 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY 

])

_IVQOF-OINF; 

 vijn bmje(vijn) 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>3-id-=:: 

{ocmr oc8 

prjetd("Pe ^ypf "y" dir fxfoutfn;Pe")8 

oc2lftocf()8 

jd(oc22'y') 

{prjetd("Pe yiu typfn y.")8 

lftoc()8 

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

_^QVO^VQF-ID-JD-_^M^FBFE^;-Djl # 1>

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =>:-id-=:: 

IWFQM^JIE ID JD-_^M^FBFE^;-DJL # 16

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =67-id-=:: 

----

\IQN-OIVE^JEL WQILQMB;-

FSMBW@F;-

\rjtf m prilrmb tcmt eit oiuet ie`y tcf eubafr id ocmrmotfr

aut jt m`si oiuetfn tcf eubafr id wirn wcjoc `jf je tcf pcmrmsf

typfn ay usfr9 Jt tmhfs jeput m pcmrmsf ay usfr men oiuet

eubafr id ocmrmotfr men wirn oietmjejel je tcf pcmrmsf 9

Vsfn jd stmtfbfet9

_IVQOF OINF;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =6=-id-=:: 

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet oiuetocmr278

jet oiuetwirn278

ocmr ocm8

prjetd(‐^ypf m pcmrmsf af`iw; Pe‒)8 

wcj`f(ocm2lftocf() !2 –Pr‚ ) 

{oiuetocmr++8

jd(ocm22 ) /* (ocm22 ) 2 nifs oc js fqum` ti spmof */

{ oiuetwirn++8

}

}

prjetd(‐Pe ocmrmotfr oiuet js %n‒,oiuetocmr)8 

prjetd(‐Pe wirn oiuet js %n‒,oiuetwirn+=)8

lftoc()8

}

IV^-WV^;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =61-id-=:: 

^ypf m pcmrmsf af`iw;

Omt men nil

Ocmrmotfr oiuet js ==

\irn oiuet js ?

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

Je tcf maivf fxmbp`f wf heiw tcmt ciw tcjs fxmbp`f ome

om`ou`mtfn tcf eubafr id ocmrmotfr js prfsfetje tcf ljvfe wirn

, aut , ciw jt om`ou`mtfn tcf eubafr id wirn je m pcmrmsf si,

mssubf tcmt jt om`ou`mtfn tcf eubafr id wirn je m pcmrmsf ay

om`ou`mtfn tcf spmof aftwffe tcf fmoc wirn je tcf pcmrmsf men

wf mssubf tcmt wf mnnfn (* ief birf spmof je tcjs pcmrmsf mt

tcf stmrtjel pijet id tcf pcmrmsf si, jt om`ou`mtfn wirn je tcf

pcmrmsf ay om`ou`mtjel tcf spmof aftwffe fmoc wirn men m`si

mnnjel ief spmof mt tcf stmrtjel pijet id tcf pcmrmsf tcmt js X

Omt men nils R

---------------djejscfn-----------

BV@^JW@F-_^M^FBFE^-\J^C JD-_^M^FBFE^;-

\f ome wrjtf sjel`f stmtfbfet je tcf ainy id ‐jd -stmtfbfet‒

ay tfrbjemtfn jt ay sfbjoi`ie, wf m`si usfn bu`tjp`f stmtfbfet

wjtc je tcf ainy id jd-stmtfbfet ay usjel tcf armofs X {} R ti

feo`isfn tcf oibpiuen stmtfbfets je tcf ainy id tcf `iip

tcmt js ;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =6?-id-=:: 

Fxmbp`f-1;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ocmr oc8

prjetd(‐Fetfr mey ocmrmotfr ;Pe ‐)8 

oc2lftocf()8

jd(oc22‚y‚) 

{ prjetd(‐Pe yiutypfn y. ‐)8 

prjetd(‐Pe Eit sibf itcfr `mttfr. ‐)8 

}

lftoc()8

}

IV^-WV^;

Fetfr mey ocmrmotfr;

Z

Ziu ^ypfn y.

Eit sibf itcfr `mttfr.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =6>-id-=:: 

-----------djejscfn--------

^cf maivf fxmbp`f #1 wj`` m`si af wrjttfe je tcjs wmy tcmt js

vijn bmje(vijn)

{ ocmr oc8

prjetd(‐fetfr mey ocmrmotfr;Pe‒)8 

jd(lftocf()22‚y‚) 

{prjetd(‐Pe yiu typfn y. ‐)8 

prjetd(‐Pe Eit sibf itcfr `mttfr.‒)8 

} lftoc()8

}

IV^WV^;

------------DJEJ_CFN--------

Efstfn Jd-_tmtfbfet;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{

o`rsor()8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =66-id-=:: 

prjetd(‐^ypf mey pcmrmsf ti fxjt ir typf –ei‚ ti fxfoutfn jt; ‐)8 

jd(lftocf()22 –e‚ ) 

{

jd(lftocf()22 –i‚ ) 

{

prjetd(‐Pe yiu typf –ei‚. ‐)8 

}

}

lftoc()8

}

IV^-WV^;

^ypf mey pcmrmsf ti fxjt ir typf –ei‚ men –ei‚ ti fxfoutfn jt; ei

Ziu typf –ei‚ 

-----------djejscfn----------

_^QVO^VQF ID EF_^FN JD-_^M^FBFE^;-

Djl # 14

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =64-id-=:: 

----------djejscfn----------

Jd-F`sf _tmtfbfet;-

^CF JD-F@_F-_^M^FBFE^;

Ms wf sff je tcf sjel`f jd-stmtfbfet, si m sjel`f jd-stmtfbfet wj``

fxfoutfn m sjel`f stmtfbfet id m oibpiuen X lriupR

stmtfbfets wjtc je tcf ainy id sjel`f jd-stmtfbfet,

Aut , jd-stmtfbfet ni eit ni eitcjel wcfe ‐^fst-fxprfssjie‒

wj`` af afoibf dm`sf. ,

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =6<-id-=:: 

^cfrf js mey pissjaj`jty ay wcjoc wf ome fxfoutf m lriup id

stmtfbfet jd wcfe ‐^fst-Fxprfssjie‒je tcf jd -stmtfbfet

fxprfssjie js eit truf9

Zfs, tcfrf js m pissjaj`jty ay wcjoc wf ome fxfoutfn m lriup id

stmtfbfets.

^cmt js F`sf-stmtfbfets;

\f dirbfn jd-f`sf stmtfbfet ti oibajef aitc tilftcfr .

FSMBW@F-ID-JD-F@F_ _^M^FBFE^;-

vijn bmje(vijn)

{ ocmr oc8

prjetd(‐^ypf m ocmrmotfr ; Pe ‐)8 

oc2lftocf()8

jd(oc22 –y‚ ) 

{ prjetd(‐Pe yiu typfn y.‒)8 

}

f`sf

{ prjetd(‐Pe yiu njn eit typfn –y‚. ‐)8 

}lftoc()8

}

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =63-id-=:: 

IV^-WV^;-

^ypf m ocmrmotfr;

y

Ziu typfn y.

^ypf m ocmrmotfr;

e

yiu njn eit typfs –y‚ 

--------------------djejscfn-----------

IWFQM^JIE-ID-JD-F@F_-_^M^FBFE^;-

Djl # 1<

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =6:-id-=:: 

Djl # 13

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =47-id-=:: 

---djejscfn----

] wrjtf m prilrmb wcjoc nrmw di``iwjel iut put je djl # 1:9

Djl # 1:

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =4=-id-=:: 

_IVQOF OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet x,y8

dir(y2=8y0:8y++)

{ dir(x2=8x0:8x++)

{jd(x22y)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =41-id-=:: 

prjetd(‐PxNA‒)8} 

f`sf

{prjetd(‐PxAI‒)8 

} prjetd(‐Pe‒)8 lftoc()8 

}

-----------DJEJ_CFN-CFQF-------------

OCMQMO^FQ LQMWCJO_ MEN ^CF OCFOHFQ AIMQN] wrjtf m prilrmb wcjoc sciws m ocfohfr airn ie

bieiocribf sorffe , usfn jd-f`fs stmtfbfet9

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{jet x,y8

dir(y2=8y02=78y++) /* stfppjel niwe*/

{ dir(x2=8x02=78x++) /*stfppjel moriss*/

{ jd((x+y)%1227)

{prjetd(‐PxNAPxNA‒)8 

}f`sf

{prjetd(‐ ‐)8 /* twi spmof ocmrmotfr */ 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =4?-id-=:: 

}

} prjetd(‐Pe‒)8 

} lftoc()8

}

IV^-WV^;

_ff djl# ?7

---------djejscfn----

]

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =4>-id-=:: 

vijn bmje(vijn)

{jet x,y8

dir(y2=8y0:8y++) /*stfppjel niwe m`iel y-mxjs*/

{ dir(x2=8x0:8x++)/* stfpjel moriss m`iel x-mxjs*/

{ jd((x+y)%1 !27) /*prjet inn eubafr*/

{prjetd(‐PxNAPxNA‒)8 

}f`sf

{prjetd(‐ ‐)8 

}

}prjetd(‐Pe‒)8 

}

lftoc()8

}

IV^WV^;

DJL # ?= MEN ?1

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =46-id-=:: 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =44-id-=:: 

------------djejscfn----------

NQM\ ^\I NJMLIEM@ ;-

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet x,y8

dir(y278y021>8y++)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =4<-id-=:: 

{ dir(x278x021>8x++)

{ jd(x22y)

{prjetd(‐PxNA‒)8 

}f`sf

{prjetd(‐PxAI‒)8 

}

}prjetd(‐Pe‒)8 

}

dir(y21>8y5278y--)

{ dir(x2=8x021>8x++)

{ jd(x22y)

{prjetd(‐PxNA‒)8 

}f`sf

{prjetd(‐PxAI‒)8 

}

}prjetd(‐Pe‒)8 

}

}

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =43-id-=:: 

Djl # ??

\f lft twi njmliem` `jhf je djl # ?? `jhf m oriss scmpf.

-----------djejscfn--------

IWFQM^JIE-ID-EF_^FN JD-F@_F _^M^FBFE^;-

Djl # ?6

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =4:-id-=:: 

------------djejscfn----

\CJOC JD LF^_ ^CF F@_F;-

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet tfbp8

prjetd(‐W`fmsf typf tfbp;‐)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =<=-id-=:: 

#jeo`unf0oieji.c5

vijn bmje(vijn)

{jet tfbp8

prjetd(‐p`fmsf typf je tfbp;‒)8 

somed(‐%n‒,&tfbp)8 

jd(tfbp037)

jd(tfbp547)

prjetd(‐Pe Ejof nmy!‒)8 

f`sf

prjetd(‐surf js scj``y!‒)8 

f`sfd(surf js cit!‒)8 

lftoc()8

}

IV^WV^;

W`fmsf typf je tfbpfrmturf;41

Ejof nmy!

-----------djejscfn----------------

#jeo`unf0stnji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =<1-id-=:: 

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet tfbp8

prjetd(‐typf je tfbp;Pe‒)8 

somed(‐%n),&tfbp)8 

jd(tfbp037)

{ jd(tfbp547)

prjetd(‐ejof nmy! ‐)8 

}

f`sf

prjetd(‐surf js cit‒)8 

lftoc()8

}

IV^-WV^;

typf je tfbp;

31

surf js cit

-------------djejscfn-----

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =<?-id-=:: 

] ) _IVQOF OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{jet x,y8

dir(y2=8y01>8y++)

{dir(x2=8x01>8x++)

{jd(x22y || x221>-y)

{prjetd(‐PxNA‒)8 

}

F`sf

{prjetd(‐PxAI‒)8 

}

} prjetd(‐Pe‒)8 

}lftoc()8

}

IV^-WV^;

Djl # ?4

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =<6-id-=:: 

Jet njljtoiuet278

Ocmr oc8

Wrjetd(‐typf m pcmrmsf;Pe‒)8 

\cj`f((oc2lftocf())!2 –Pr‚ ) /* –Pr‚ 25 Fetfr */ 

{ocmroiuet++8

Jd(oc5>< && oc063 )

{ njljtoiuet++8

}

}prjetd(‐Pe ocmrmotfr oiuet js %n.‒,ocmroiuet)8 

Wrjetd(‐Pe njljt oiuet js %n‒, njljtoiuet)8 

Lftoc()8

}

IV^-WV^;

^ypf m pcmrmsf;

Cf lit 46 bmrhs iut idd =77 bmrhs.

Ocmrmotfr oiuet js ?>.

Njljt oiuet js 6.

------------djejscfn--------

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =<4-id-=:: 

F@_F-JD _^M^FBFE^;-

] wrjtf m prilrmb Xm om`ou`mtirR wcjoc pfrdirbfn diur

dueotjie om`ou`mtjie9

_I@V^JIE;-

_IVQOF-OINF;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{d`imt eub=2=.7,eub12=.78

ocmr ip8

wcj`f( !(eub=227.7 && eub1227.7))

{prjetd(‐^ypf eubafr,ipfrmtir,eubafrPe‒)8 

somed(‐%d,%o,%d‒,&eub=,&ip,&eub1)8 

jd(ip22 –+‚)

prjetd(‐Pe eub=+eub12%d‒,eub=+eub1)8 

f`sf

jd(ip22 –-–) 

prjetd(‐Pe 2%d‒,eub=-eub1)8

f`sf

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =<3-id-=:: 

2=777777.777777

-----------------djejscfn--------

EF_^FN \CJ@F-@IIW;-

]) wrjtf m prilrmb wcjoc tmhf m eubafr ay tcf usfr men prjet

jts dmotirjm` men jt wj`` af fxfoutfn ay wcfe tcf usfr prfss mey

hfy 9 usfn efstfn wcj`f `iip9

_IVQOF-OINF;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn bmje(vijn)

{ jet J,h2=8ocmroc8

\cj`f(oc!2 –a –) 

{prjetd(‐Fetfr m eubafr ir m ocmrmotfr ; ‐)8 

_omed(‐%n,%o‒,&J,&oc)8 

\cj`f(j !27 ||oc!2‚a‚) 

{h2h*j--8

Rprjetd(‐dmotirjm` js %n‒,h)8 

}prjetd(‐lmbf-Ivfr‒)8 lftoc()8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =37-id-=:: 

---------djejscfn-----------

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn twiaffp(vijn)8

vijn bmje(vijn)

{ twiaffp()8

prjetd(‐Fetfr m ocmrmotfr ;‒)8 

lftocf()8 /* wmjt dir hfy prfss*/

twiaffp()8

lftoc()8

}vijn twi affp(vijn)

{`iel k8

prjetd(‐Px<‒)8/*affp*/ 

dir(k2=8k02=77778k++)

prjetd(‐Px<‒)8 

}

----------djejscfn------

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =3=-id-=:: 

OC-6 XDVEO^JIE_R;

EI^F; sibf pfrofet tcfiry ie dueotjie drib oc-6 mrf cfrf.

_JBW@F-DVEO^JIE;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

#jeo`unf0nis.c5

Tijn `jef(vijn)8 /* dueotjie prititypf*/

Tijn bmje(vijn) /* bmje Dueotjie */

{

@jef()8 /*om`` ti dueotjie*/

Wrjetd(‐PxNA ^j^V_ MENQIEJOV_ Px NA Pe‒)8 

@jef()8 /*om`` ti dueotjie*/

nf`my(67)8 /* nf`my dir tjbf jetfrvm` */

lftoc()8

}

Tijn `jef(vijn)/* ei sfbj-oi`ie cfrf , ^o-omusf , nfdjejtjie*/

{ jetk8

Dir(k2=8k02178k++)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =31-id-=:: 

{ prjetd(‐PxNA‒)8 

Wrjetd(‐Pe‒)8 

}

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

‐^cf bmje dueotjie js m`wmys fxfoutfn djrst jd fjtcfr wf p`mofn

itcfr dueotjie tcmt js X vijn `jef(vijn)R afdirf tcf bmje()

dueotjie, aut bmje() dueotjie js m`wmys fxfoutfn djrst‒

Je tcjs fxmbp`f tcf X bmje()R dueotjie ‐om``s‒ tcf dueotjie `jef().

{ om``s bfme tcf ^o-omusf ti af fxfoutfn} ti nrmw tcf twi `jefs

id aix , bmje ()8

Om``s `jef() dueotjie twjof tjbfs.

^cfrf mrf ie`y tcrff prilrmb f`fbfet wcjoc jevi`vfn dir usjel

m dueotjie . tcmtjs

=. Dueotjie Writitypf X Dueotjie Nfo`mrmtjieR;-

1. Om``jel tcf dueotjie /* ti fxfoutfs m dueotjie*/ .

?. ^cf Dueotjie Nfdjejtjie /* jts dueotjie jtsf`d*/

=) DVEO^JIE WQI^I^ZWF XDVEO^JIE NFO@MQM^JIE_R;-

\f heiw tcmt wf usfn je iur fxmbp`f ‐`jef() dueotjie‒ wfheiw tcmt tcf bmje() dueotjie m` m`wmys fxfoutfn mt djrst jd

wcfe fvfr wf p`mofn `jef() dueotjie afdirf ir mdtfr tcf bmje()

dueotjie.

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =3>-id-=:: 

^cf `jef() dueotjie je iur fxmbp`f js nfo`mrfn je m sjbj`mr wmy mt

tcf afljeejel id m prilrmb tcmt js ‐vijn `jef(vijn)8‒ afdirf jts

om``fn dir fxfoutf.

\IQHJEL-ID-DVEO^JIE NFO@MQM^JIE;-

Djl # >7

^cf dueotjie nfo`mrmtjie tf``s oibpj`fr tcf embf id tcf

dueotjie tcmt js `jef(), tcf nmtm typf id tcf dueotjie rftures X jd

meyR men tcf eubafr men nmtm typfs id tcf dueotjie‚s tmhfs

mrlubfets X jd mey R ,

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =36-id-=:: 

djl # >=

Eitjof tcmt tcf prititypf js wrjttfe afdirf tcf bmje() dueotjie

tcjs motjie omusf tcf prititypf dueotjie wj`` af vjsja`f ti m`` tcf

dueotjies je m dj`f. (je tcf siurof oinf).

M prititypf nfo`mrfs m dueotjie

M dueotjie m`` fxfoutfs m dueotjie

M dueotjie nfdjejtjie js tcf dueotjie jtsf`d.

_IVEN FSMBW@F;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =34-id-=:: 

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn twiaffp(vijn)8

vijn bmje(vijn)

{twi affp()8

prjetd(‐^ypf mey ocmrmotfr; ‐)8 

lftocf()8

twiaffp()8

lftoc()8

}

vijn twiaffp(vijn)

{`iel k8

prjetd(‐Px<‒)8 

dir(k2=8k02=777778k++)

prjetd(‐Px<‒)8 

}

------------DJEJ_CFN--------

DVEO^JIE;

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =3<-id-=:: 

\CM^ NI DVEO^JIE NI ;-

^cf dueotjie ome usfn ti mvijn ti cjnf tcf smbf rfpftjtjie id

oinf mlmje men mlmje je tcf smbf prilrmb.

]) wrjtf m prilrmb je wcjoc put aix mriuen tcf tfxt . 9

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn `jef(vijn)8 /* prititypf dir `jef()*/

vijn bmje(vijn)/*bmje dueotjie*/

{ `jef()8 /* om`` ti dueotjie */

prjetd(‐PxNA tjtus Menrijous PxNA Pe‒)8 

`jef()8

lftoc()8

} /* dueotjie nfdjejtjie*/

vijn `jef(vijn)/*dueotjie nfo`mrmtjie*/

{ jet s8

dir(s2=8s02178s++)

{prjetd(‐PxNA‒)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =33-id-=:: 

}

Wrjetd(‐PxNA‒)8 

}prjetd(‐Pe‒)8

}

IV^-WV^ ;-

Djl # >1

--------------djejscfn-----------

_IVEN FSMBW@F ;-

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =3:-id-=:: 

]) wrjtf m prilrmb wcjoc pfrdirbfn twi affpsfpfrmtf`y ay m

scirt jetfrvm`9

_IVQOF-OINF;

/* Px< js tcf M_OJJ oinf dir Af`` */

Tijn twi affp(vijn)8

Tijn bmje(vijn)

{twiaffp()8 /* dueotjie om``jel */

Wrjetd(‐^ypf m ocmrmotfr ; ‐)8 

Lftocf()8

/* wmjt dir hfy prfss*/

^wiaffp()8 /*dueotjie om``*/

Lftoc()8

}vijn twiaffp(vijn)}

{`iel k8 /* `iel js jetflfr */

Wrjetd (‐Px<‒)8 /*=st

  affp*/

Dir(k2=8k0=77778k++) /* nf`my*/

8 /* eu`` stmtfbfet*/

Wrjetd(‐Px<‒)8/*1en

 affp */

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:7-id-=:: 

IV^WV^

twi affp ay scirt jetfrvm`,

-----------DJEJ_CFN-----

] wrjtf m prilrmb tcmt prjets tcf di``iwjel iutput uefn

dueotjie9

Njmlrmb;-

Djl # >?

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:=-id-=:: 

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

Tijn `jef(vijn)8

Tijn bmje(vijn)

{ `jef()8

Wrjetd(‐Pe Aji-bfnjom`Pe‒)8 

@jef()8

lftoc()8

} /* Dueotjie nfdjejtjie js ljvfe af`iw*/

Tijn `jef(vijn) /*dueotjie nfo`mrmtjie*/

{ jet k8

Dir(‐k2=8k02178k++) 

{prjetd(‐PxNA‒)8 

}

}

----------djejscfn---------

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:1-id-=:: 

]) wrjtf m prilrmb tcmt prjets tcf di``iwjel iutput9 Vsjel

dueotjie9

Ljvfe njmlrmb;- djl # >>

_IVQOF-OINF;-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

vijn `jefi(vijn)8 /*prititypf dir `jefi() */

vijn bmje(vijn)

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:?-id-=:: 

{`jefi()8 /*dueotjie om``jel*/

Wrjetd(‐Pe PxNA Aji-Bfnjom` PxNAPe‒)8 

@jefi()8/*dueotjie om``jel */

Lftoc:78

}

/* dueotjie nfdjejtjie js ljvfe af`iw */

Tijn `jefi(vijn)

{jet s8

Dir(s2=8s02178s++)

{prjetd(‐PxNA‒)8} 

}

------------djejscfn-----------

DVEO^JIE ^CM^ QF^VQE_ M TM@VF;-

 Je tcjs omsf , je wcjoc tcf dueotjie tcmt rftures m vm`uf ,

tcf lfefrm` tcfmb id tcjs js tcmt , .

 Je tcjs typf id dueotjie wcfe yiu om`` ,wcfe tcf ‐dueotjie

om``jel‒ js sjbj`mr ti tcmt wcfe m pfrsie wcisf wmet tifxmbjef tcf tjbf ay tcf tf`fpcief , si, cf djrst njm`f m

eubafr , tcmt js WC# Ei ; SSSS-SSS, tcfe ie itcfr sjnf tcf

oibputfr X ir m pfrsieR wcisf mrf mssjlejel dir tcmt kia

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:>-id-=:: 

ti tf`` yiu tcf fxmot tjbf tcfe , si tcmt oibputfr tf`` yiu

tcmt tjbf wjtc iut tmhjel mey jedirbmtjie drib yiu tcmt ,

 Je tcjs sjbj`mr`y wmy ms wf kust mem`ysjs X`iihR tcf ljvfe

af`iw dueotjie fxmbp`fs ms wcfe tcf vijn bmje(vijn) X

bmje()8 R dueotjie wj`` af fxfoutfn m`wmys =st

 tcfe jt omusf

ti fxfoutfn tcf om``jel dueotjie X om`` ti dueotjieR

 .wcfe tcjs Xom`` ti dueotjie R wj`` af fxfoutfn tcfe jt omusf

ti fxfoutfn tcf X dueotjie nfdjejtjieR wcjoc js m`rfmny jtsf`d

dueotjie ,

 \cfe ‐om`` ti dueotjie‒ om`` tcf ‐dueotjie nfdjejtjie‒ tcfe

tcjs dueotjie nfdjejtjie oietmjes m ofrtmje pfmof id

jedirbmtjie wcjoc wj`` af priofss, Xbmtcfbmtjom``y ir

sibf itcfr bftcinR , tcfe tcjs rfsu`t id tcmt trmesdfr wj``

af rfturefn ti wcfrf tcf dueotjie wj`` om``fn mt ‐Om`` ti

tcf dueotjie‒. 

 FSMBW@F;

ocmr sbm`` `fttfr (vijn)8

vijn bmje(vijn)

{ocmr oc8

Wrjetd(‐Fetfr mey m ompmojtm` `fttfr; ‐)8 

Oc2sbm```fttfr()8 /* om` ti dueotjie*/

Wrjetd(‐Pe je sbm`` `fttfr jts –%o‚ ‐,oc)8 

Lftoc()8

}

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:6-id-=:: 

Ocmr sbm`` `fttfr (vijn)

{ocmr m,a8

m2lftocf()8

a2m+?18 /*(m+?1) bmhfs m ompjtm` `fttfr jeti m sbm``

`fttfr*/

rfture(a)8/*jt‚s tcf rfture ipfrmtir `jhf nf`my(67)8*/ 

}

IV^-WV^;

Fetfr mey m ompjtm` `fttfr;M

Je sbm`` `fttfr jts –m‚ . 

--------djejscfn---

] wrjtf m prilrmb tcmt oievfrtfn mey ‐ompjtm` `fttfr‒

wcjoc wj`` af tmhfe drib tcf jeput ay usfr jeti jts ‐sbm``-

`fttfr‒9 

_IVQOF-OINF-

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

Ocmr sbm`` `fttfr(vijn)8

Tijn bmje (vijn)

{ocmr oc8

Wrjetd(‐Fetfr mey m ompjtm` `fttfr;Pe ‐)8 

Oc2sbm```fttfr:78

Wrjetd(‐Pe Je sbm```fttfr jts –%o‚ .‒,oc)8 

Lftoc()8

}

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:4-id-=:: 

ocmr sbm```fttfr(vijn)

{ocmr m,a8

m2lftocf()8

a2m+?18 /* (m+?1) tcjs dirb bmhfs ompjtm` `fttfr jeti sbm``

`fttfr */

rfture(a)8

}

IV^-WV^;

Fetfr mey m ompjtm` `fttfr;

A

Je sbm`` `fttfr jts –a‚. 

------------djejscfn---------

{;. Jd wf mnn ?1 je mey uppfr omsf `fttfr ,si jts oievfrtfn

jeti jts `iwfr omsf9}

]) wrjtf m prilrmb tcmt oievfrt mey sbm`` `ftfr wcjoc wj``

af tmhfe drib usfr ms m jeput men oievfrtfn jt jeti

‐Ompjtm`-`fttfr‒9 

_IVQOF-OINF;

#jeo`unf0stnji.c5

#jeo`unf0oieji.c5

Ocmr sbm```fttfr(vijn)8/*prititypf*/

Tijn bmje(vijn)

{ocmr oc8

Wrjetd(‐Fetfr mey sbm`` `fttfr ; Pe ‐)8 

Oc2sbm```fttfr()8 /*om`` ti dueotjie */

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:<-id-=:: 

prjetd(‐Pe je ompjtm` `fttfr js –%o‚ .‒,oc)8 

lftoc()8

}

Ocmr sbm```fttfr(vijn)

{ocmr m,a8

m2lftocf()8

a2m-?18 /* (m-?1) tcjs bmhf mey `iwfr omsf `fttfr jeti tcf uppfr

omsf `ftfr ir jt oievfrtfn mey sbm`` `fttfr jeti ompjtm` `fttfr*/

rfture(a)8

}

IV^-WV^

Fetfr mey sbm```fttfr;

m

je ompjtm``fttfr js –M‚ . 

------djejscfn------------

] wrjtf m prilrmb wcjoc tmhfs sibf eubfrjom` vm`uf ay tcf

usfr men om`ou`mtfn men ljvf jts om`ou`mtfn vm`uf je iutput;9

_IVQOF-OINF;

#jeo`unf0stnji.c5

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =:3-id-=:: 

#jeo`unf0oieji.c5

Tijn om`ou`mtir(jet,ocmr,jet)8

Tijn bmje(vijn)

{ jet eub=,eub18 ocmr ip8

Wrjetd(‐Fetfr;=st

 eubafr , ipfrmtir, 1en

 eubafr ; ‐)8 

_omed(‐%n,%o,%n‒,&eub=,&ip,&eub1)8 

Om`ou`mtir(eub=,ip,eub1)8

Lftoc()8

}

Tijn om`ou`mtir(jet x,ocmr ip,jet y)

{swjtoc(ip)

{

Omsf –+‚; 

Wrjetd(‐Pe sub js 2%n‒, x+y)8

Arfmh8

Omsf –-–; 

Wrjetd(‐sub js 2%n‒,x-y)8

arfmh8

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf =::-id-=:: 

omsf –*‚;

prjetd(‐prinuot js 2 %n‒,x*y)8 

arfmh8

omsf –/‚ ; 

prjetd(‐ njvjsjie js 2%n‒,x/y)8 

arfmh8

nfdmu`t;

prjetd(‐Veheiwe ipfrmtir ; ‐)8 

}} IV^-WV^;

Fetfr; =st

 eubafr,ipfrmtir,1en

 Eubafr id yiur ocijof ; 1+?

_ub js 2 6

------------djejscfn--------

DVEO^JIE ^CM^ MOOFW^ TM@VF;-

^cf mey dueotjie mt moofpt men ms wf`` ms rfture vm`uf js om``fn

m ‐dueotjie tcmt moofpt men rftures vm`uf‒ 

Djl # >6

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 177-id-=:: 

Fxmbp`f;

Jet lrfmtfr(jet,jet)8

Tijn bmje(vijn)

{ jet eub=,eub1,eub?8

Wrjetd(‐Fetfr =st

 men 1en

 vm`uf ; ‐)8 

_omed(‐%n,%n‒,&eub=,&efb1)8 

Jd(eub=22eub1)

{prjetd(‐Aitc mrf fqum`‒)8 

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

X A J I - B F N J O M @ - F E L J E F F Q J E L L V J N F . J E O A Z _ J H M E N M Q @ I N C J R Wmlf 17=-id-=:: 

}f`sf

{eub?2lrfmtfr(eub=,eub1)8

/* je maivf tcf pmrt je yf``iw js rfture men tcf pmrt je `jlct

lrffe mrf moofptfn*/

Wrjetd(‐Lrfmtfr mwmy `jef js %n‒,eub?)8 

Lftoc()8

}

Jet lrfmtfr(jet m,jet a)

{

Jd(m5a)

{rfture (m)8

}

F`sf

{rfture(a)8

}

}

-----------djejscfn-------------

-----oc= ti oc-6 je o-`melumlf , ie aji-bfnjom` feljeffrjel

Djejscfn-cfrf-----------

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XO,O++ MEN IAKFO^-IQJFE^FN-WQILQMBBJELXIIWR @MELVMLF DIQ AJI-BFNJOM@-FELJEFFQJEL

OIVQ_F_; WMQ^-=, EI^F_ R

SBVCMBBMN-_JHMENMQ-HCME-@INCJ

I\EFQ ID BZ WFQ_IEM@ VEJTFQ_J^Z EI^F_. ^cursnmy, Kuef 1<, 17=?