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  • 8/21/2019 C Programlama - Eemdersnotlari.com Ders Notlar 2

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    G Trl`rohnoho Cfrs

    Kltnor

    ]fvezylk vf Mosi Men`ese=?/?7.4=.=4?= ?72?6244

    www.ffhcfrskltnore.glh

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 =

    ekcfienfrekcfienfr ................................................................................................................................... =

    ksz .......................................................................................................................................... 6Uoronoknomenfgfi Cefr Ioykoinor ........................................................................................ 6

    Trl`roh Kfcer ............................................................................................................................ :Trl`rohnoho Cene Kfcer< ........................................................................................................... 0G Kosn Mer Trl`rohnoho Cenecer< .............................................................................................. 1G'cf Trl`roh Uozho... ............................................................................................................... 5

    kk kevfrsetfse ktfrkft Hfrifzekcf Trl`roh Uozho ...................................................... 5Ifkce Ufrfn Men`esoyorkzco prl`roh yozho ..................................................................... ?4UoznhTrl`roh Iot zfrekcf ontrho ...................................................................... ??

    @fkfn Trl`roh Uops .............................................................................................................. ?=Monorifk .............................................................................................................................. ?=

    Cfeifknfr vf Orethftei enfhnfr ....................................................................................... ?3Cfeifk Sokhnoho Iuronnor ................................................................................................ ?0

    Wometnfr ................................................................................................................................. ?0Cfeifk Srnfre ................................................................................................................... ?1

    Cfeifk Ocnokcrho Iuronnor ....................................................................................... ?1Onjo soyson Cfeifknfr ................................................................................................... ?1Woyson Cfeifknfr .......................................................................................................... ?5Sokhnohonor ................................................................................................................... ?5

    Orethftei jocfnfr ................................................................................................................. =4Orethftei Lpfrotrnfr ........................................................................................................... =4Hoktison ejocfnfr ................................................................................................................. =?Iornotrho nfnfre vf Hoktison Lpfrotrnfr ................................................................. =?

    Iornotrho enfnfre ....................................................................................................... =?Hoktison Lpfrotrnfr ...................................................................................................... ==

    Sr Ckhnfre .................................................................................................................. =7Ortrho vf Fisenthf lpfrotrnfre .......................................................................................... =3Hoktison Met lpfrotrnfre .................................................................................................... =6Cffr Otoho ejocfnfre .......................................................................................................... =6Ilunnu jocfnfr .................................................................................................................... =6

    @ereinfhnfre ................................................................................................................. =:Wtokcort Itpaokfyf Freeh ............................................................................................... =:

    Wtokcort @ere, Wtokcort ivf Aoto iklitonor ......................................................... =:Wtokcort @ereiJlkiseylknor ....................................................................................... =0Meehnfkcerenheinor ..................................................................................................... =5Meehnfkcerenhe@erenfr ...................................................................................................... 74Mfnnfi Meeh ckh jlkiseylknor ................................................................................... 7?Ioroitfr cezfsekek Liukup-Uoznhos ................................................................................. 7=kfhne mer toih jlkiseylknor ............................................................................................. 7=

    Ioroitfr Wkoho vf cktrhf jlkiseylknor ................................................................ 7=uk`ftg ............................................................................................................................... 77

    Trl`roh Oi vf Trl`roh OiCfkftehe .............................................................................. 73Ilhutnor vf Mnlinor ............................................................................................................. 73

    Ej-Fnsf ilhutu ...................................................................................................................... 73Fnsf ej ilhutu ................................................................................................................... 7:

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 7

    Fteiftnfr vf `ltl ilhutu ...................................................................................................... 70swetga ilhutu ...................................................................................................................... 71Ck` Ilhutnor - waenf ..................................................................................................... 34Ck` Ilhutnor - jlr .......................................................................................................... 3?Ck` Ilhutnor - cl...waenf .............................................................................................. 33

    Ck` iIlhutu - mrfoi ............................................................................................... 36Ck` cfvoh Ilhutu - glktekuf ........................................................................................ 3:Jlkiseylknor vf @fkfn Trl`roh Uops ................................................................................... 30

    Oko prl`roh mnlu (hoek) ................................................................................................... 30G prl`roh `fkfn yops ....................................................................................................... 31

    #ekgnucf Sokhnor ........................................................................................................... 31#cfjekf Sokhnor ............................................................................................................. 31Cefr mnhnfr ................................................................................................................. 31

    Sfhfnnfr ............................................................................................................................... 35Jlkiseylk porohftrfnfre aoiikco ....................................................................................... 64Cfeifknfrek ftiene lncuu mn`fnfr .................................................................................... 6?

    @fkfn Cfeifknfr ................................................................................................................ 6?fxtfrk cfeifknfr ................................................................................................................ 6=stoteg cfeifknfr .................................................................................................................. 6=rf`estfr cfeifknfr .............................................................................................................. 6=Mnli Uops ........................................................................................................................... 67ni cffr otoho ..................................................................................................................... 67zyekfnfhf (]fgurselk) ....................................................................................................... 67G cene kenfhgese .................................................................................................................. 63

    Clsyo Coaen fthf ............................................................................................................. 63Hoirl vfyo sfhmlnei somet tokhnoho ............................................................................. 66

    Cezenfr ....................................................................................................................................... 6:Ceze Kfcer< ........................................................................................................................... 6:Mer Zfitrk vfyo hotresek Sokhnokhos .......................................................................... 6:Cezenfr vf Hotresnfr zfrekcf uy`unokomenfgfi enfhnfr ...................................................... 60

    Ceze sronoho .................................................................................................................... 61Ceze efresekcf estfkenfk mer fynfr munho ......................................................................... 61Hotresek cfvreeke onho .................................................................................................... 65

    Ioroitfr cezfnfre (Cez`f) .......................................................................................................... :?Ioroitfr cezfse tokhnoho vf iunnokho ............................................................................... :?

    @stfr`fnfr-orftenfr .............................................................................................................. :3orftenfr vf Ocrfsnfr .......................................................................................................... :3

    orftenfr vf Jlkiseylk porohftrfnfre ................................................................................. ::orftenfr vf cezenfr .............................................................................................................. :0Ocrfs Orethftee ................................................................................................................... :1Ioroitfr orftenfre vf Jlkiseylknor .................................................................................. :5

    Clsyonorno en`ene enfhnfr .......................................................................................................... 0?Clsyo Srnfre vf freeh ........................................................................................................ 0?Hftek Clsyonor .................................................................................................................... 0=

    Clsyo oho enfhe ........................................................................................................... 0=Clsyocok liuho .............................................................................................................. 07Clsyoyo yozho ................................................................................................................ 07Clsyo iopoho .................................................................................................................. 07

    Clrucok Freehne Clsyonor................................................................................................. 03Clsyo oho enfhe ........................................................................................................... 03

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 3

    Clsyocok liuho .............................................................................................................. 03Clsyoyo yozho ................................................................................................................ 06Clsyo iopoho enfhnfre ................................................................................................... 06Clrucok freehne clsyonoro zfn curuhnor. .................................................................... 06

    Zfre Uopnor (strugturf) ........................................................................................................... 0:

    Sfhfn Sokhnor .................................................................................................................... 0:Zfre Uopnorkk jlkiseylknorno iunnoknhos ....................................................................... 01SypfCfj ................................................................................................................................ 05

    Aozr Jlkiseylknor ................................................................................................................... 1?Ceyo`klstei enf en`ene jlkiseylknor ........................................................................................ 1?

    vlec ossfrt(ekt ejocf)9 ........................................................................................................ 1?Cfrnfyege Mencerehnfre ............................................................................................................... 15

    #ekgnucf mencerehe ................................................................................................................. 15#cfjekf mencerehe ................................................................................................................... 15#ej...#fkcej mencerehe ............................................................................................................. 5?#frrlr vf #pro`ho mencerehnfre ............................................................................................. 5=

    Torohftrf Sokhnoho .............................................................................................................. 57G Ilcnohoco fk li yopnok aotonor ........................................................................................ 53

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 6

    kszMu cfrs kltnorkk yoznhoskco Mreok P Ifrke`aok vf Cfkkes ]etgaef esehne

    yozornork Saf G Trl`rohhek` Nok`uo`f esehne ietomkcokjoyconoknhtr. Mu ietom kk kevfrsetfse Itpaokfsekcf munomenhfkezhhikcr. Mu cfrs kltnor afh efrei lnoroi afh cf toiep ftteehjrfcot lnoroi yuiorco moase `ffk ietom rkfi lnoroi onhtr.

    Uoronoknomenfgfi Cefr Ioykoinor

    ?. Tonhf Uoykgni, Trl`rohnohoy G enf rfkeylruh, HuaohhftUlrunhoz, Wfafr Ulrunhoz

    =. Topotyo Uoykfve, G Trl`rohnoho Cene, Cr. ]ejot nifsfk

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 :

    Trl`roh Kfcer Lpfrotrk slnukcoie cffr sokcoie cffrcfk iitr. i>?=7

    ;8 Lpfrotrk slnukcoie cffr sokcoiekcfk myi yo co fetter. i;8?=7

    >8 Lpfrotrk slnukcoie cffr sokcoie cffrcfk iitr. i>8?=7

    88 ie cffr mere merekf fetter i88?=7!8 ie cffr mere merekcfk jorincr. i!8?=7

    Mu cffr iornotrho enfhnfre yo soyson cffrnfr eek yo co onjo soysontfi ioroitfrnfr eek `ffrnecer. ie onjo soyson cezfkek iornotrnhos eekmertoih jlkiseylknork iunnoknhos `frfihfitfcer. Sfi ioroitfrnfr esf'Sfi trkoi' seh`fnfre oroskco yoznrnor.

    kgfnei lnoroi th iornotrho lpfrotrnfre oyk kgfnef soaepter. Okgoitoahek fcfgfekez `eme iornotrho enfhnfrekek kgfnee orethftei

    lpfrotrnfrekiekcfk citr. Uoke iornotrho enfhekcf kgfneine lnoroivor esf orethftei enfhnfr `frfinfterener.

    Hoktison Lpfrotrnfr

    Hoktison Lpfrotrnfr mercfk jozno hoktison ejocfye mere merekf monohoieek iunnoknomenfgfi hoktison cfehnfrcer. Mu cfehnfr vf, vfyo, cfenenfhnfrekf iorni `fnfk ejocfnfrcer.

    Lp. Oinoho rkfi

    &&

    vf lpfrotr. ie Hoktison ejocfkek cf clru lnhosk `frfiterfklpfrotrcr. Uoke eie jorin hoktison ejocf oyk okco clru cfenesf fncf fcenfgfi slku yoknlnhoitocr.

    (i;?=7) && (i>7=?)T _ T && _? ? ?

    ? 4 4

    4 ? 4

    4 4 4

    ||

    vfyo Lpfrotr ie Hoktison ejocfcfk socfgf merekek clrulnhosk `frfiterfk lpfrotrcr. Uoke eie jorin hoktison ejocfcfk

    fk oz mere clru esf fncf fcenfgfi slku clru oise aoncf slkuyoknlnhoitocr.

    (i;?=7) || (i>7=?)T _ T || _? ? ?

    ? 4 ?

    4 ? ?

    4 4 4

    !cfen lpfrotr. Mer hoktison ejocfkek hoktison cfeneke fncffcfk lpfrotrcr. ! (i;8?=7) finekcf iunnoknr vf i>?=7ejocfsekf fcffrcer.

    ! (i;8?=7)

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 =7

    Mu enfhnfrcf kgfnei slncok soocr. Afsopnoho9 clru yoco yokncffrek munukcuu okco9 ffr cffr kf yopnogok mfnernfhf eek yftfrneesf curcurunur. Mu iretfrnfr onok mer prl`roh yozhoi eek kfhnecer.rkfek mu tokh kftnfterfgfi mer ilhut ekgfnfyfneh

    Jlr ( e849 e>neh-? && (g8`ftgaor()) !8 ^k && g !8FLJ9++e) sYeX8g9

    Mu rkfitf yfke mer ioroitfr liuhocok kgf tohplk soaoco (s cez`ese)yftfrne yfr lnup lnhoc cfkftnfkhfnecer. L kfcfknf e>neh-? ilktrln eniyopnr. Ffr mu ilktrln yokn slku vfrersf coao jozno ioroitfrliuhohoncr. Zf prl`roh slkroie ochnorcok cfvoh fcfmenhfnecer.

    Mfkzfre mer fiencf g eekf liukok cffr FLJ ioroitfre lnhohoncr yocosotr slku eorfte lnhohoncr. && enfhekek kgfnee || enfhekcfkyisfiter. Mu kfcfknf e>neh-? && (g8`ftgaor()) !8 ^k && g

    !8FLJ9++etorzkcoie enfhnfrek fi poroktfznfrf eateyog munukhoz. Okgoi!8enfhekek kgfnee cffr otohocok yisfi lncuu eek poroktfznfrfeateyo vorcr.

    (g8`ftgaor()) !8 ^kenfhe estfkenfk slkugo unohohz sonor.

    ! lpfrotr hoktison clru cffreke hoktison yokno vfyo hoktsonyokn hoktison clruyo fverer.

    Sr Ckhnfre

    Ffr mer enfhcf enfkfk cffrnfrek trnfre jorin esf `fkfn mer lrtoi trfcktrnr vf ynf enfh yopnrnor. Mu ckhcf u iuronnor uy`unokr.@fkfncf ltlhotei lnoroi yopnok tfi ckh enfhe tohsoy cffrekifserne cffrf cktrnhfsecer. rkfek j + e enfhe sroskco e ifsernesoyyo fvrener. Okgoi mukuk yok sro mer ifserne cfeifk/cffr cezenfrcfekces cffre lnoroi iunnoknrso ltlhotei ckh `frfinfhfz.

    kgfneine lnoroi9 gaor vf ekt trnfre roaotnino mere mere eekcf orethfteiejocfnfrcf iunnoknomenernfr. Afr gaor ltlhotei lnoroi mer ekt cffrekf

    cktrnr. Mu mer toih ioroitfr enfhnfrekcf ekoknhoz ilnoyninorsonor. Oyrgo ioroitfr cezenfreke ektf`fr cffrf fverfk otle jlkiseylkutokhnokhtr. Ioroitfrnfr zfrekcf orethftei enfh yopok mer rkfimyi aorje ii aorjf fverhfi yo co tfrse enfhecer.

    gaor ga9ej (ga;8o && ga>8z)

    ga-87=9

    ejocfse ga eekcfie aorje ii aorj esf myi aorjf cktrr.

    Ontrho =

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 =3

    Uuiorco mer mnh vfrenfk prl`roh porosk cefr G zfnneinfreiunnoknoroi thnfei mer G Trl`roh aonekf cktrkz.

    Ontrho 7

    Uuiorco mer mnh vfrenfk prl`roh poroskcok fncf ftteekez prl`rohMyi aorjnfre ii aorjf fverfgfi fiencf lnuturukuz.

    Mu enfh OWGEE ioroitfr ihfse vf mu ihfkek zfnneekcfk ioykoinokr.OWGEE ioroitfr ihfsekcf o enf O aorjnfre oroskco 7= jori vorcr.

    Gaor vf salrt tokhnor ekt trf fvrener jnlot trnfr clumnfo fvrener.

    Ffr trnfrcfk mere clumnf esf cefre cf clumnf fvrener vf slku clumnflnoroi munukur.

    Ffr trnfrcfk mer nlk` esf cefr tr nlk`o fvrener vf slku nlk` lnoroimunukur.

    Srnfrcfk mer ukse`kfc esf cefre cf ukse`kfc trf fvrener vf slkuukse`kfc lnoroi munukur.

    Cefr curuhnorco enfkfknfr ekt trcfcer vf slku ekt lnoroi munukur.

    Wlku lnoroi moz curuhnorco co tr ckhnfre zlruknu lnoroi

    prl`roh/prl`rohg torojkcok yopnhoncr. Mu curuhco

    (tr-oc) ejocf

    tokh enf ejocf enf mfnertenfk cffrnfr estfkenfk trf cktrnrnfr. Muenfhf gost cfkener.

    Ortrho vf Fisenthf lpfrotrnfre

    G cenekcf cfeifknfrek cffreke ortrok vfyo fisentfk onnhoci eie

    lpfrotr munukur. Orttrho lpfrotr ++ enfhe yokkcoie cfeifkekcffreke mer orttrrifk fisenthf lpfrotr lnok yokkcoie cfeifkekcffreke mer fisenter. Cfeifknfrek cffrnfreke ++ lpfrotr enf orttrrz.Onnhoci cefr mer ilku esf ++ vfyo lpfrotrnfrekek afh kfi(cfeifkcfk kgf ++k) afh cf slkfi (cfeifkcfk slkro k++) lnoroiiunnoknomeneylr lnhoscr. Afr eie curuhco co kek cffre mer orttrnr. Joiot++k enfhekcf kek cffre iunnoknhocok kgf orttrnrifk9 k++ enfhekcfk cffre kgf iunnoknr. slkro ? orttrnr. Mu curuhco uku synfyfmenerez2kek cffre 6 lnhoi ioycyno

    Q8k++ enfhe slkugukco xek cffre 6 k'ek cffre esf : lnurifk

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 =6

    Q8++k enfhe slkugukco xek cffre : ke cffre esf : lnur. @rnczfrf afr eie curuhco co kek cffre oyk lnurifk xek cffrecfehfitfcer. ++ vfyo lpfrotrnfre socfgf cfeifknfrnf merneitfiunnoknomener. Uoke x8(+b)++ uy`uk mer iunnokh cfencer.

    Hoktison Met lpfrotrnfreG cenekcf mer `rup lpfrotr met czfyekcf enfh yopomenhfitfcer. Mulpfrotrnfr jnlot vf clumnf trnfre zfrekcf enfh yopohohoitocr.

    & Met czfyne ZF enfhe | Met czfyne ZFUO enfhe [ Met czfyne QL] enfhe (Cnoyok yo co) >> metnfre slno ioycr ;; metnfre soo ioycr

    & lpfrotr luknuino soyson mer cffr zfrekcf estfkenfk metnfrekhosifnfkhfseke sonor. | lpfrotr mu enfhek tfrsekek yopnhosk sonor.Mu lpfrotrnfrek && vf || enf iortrnhohos `frfinecer.

    Cffr Otoho ejocfnfre

    e8e+? finekcfie ejocfnfre G cenekcf e+8= meehekcf oknotomenerez. Muroco +8finekcf mer cffr otoho lpfrotr iunnoknhtr. iene lpfrotrnfrek

    afpsekek mu fiencf cffr otoho cfehnfre munukur. ynf ie9ejocf? lp8 ejocf= ejocfse ejocf? 8 ejocf? lp ejocf= finekcf oknotnomener.

    Ilunnu jocfnfr

    ej (o;m)z8o9

    fnsfz8m9

    ejocfse o vfyo m cffrnfrekcfk myi lnokk cffreke munok ejocfcer. Muenfhek iorn lnoroi u fiencf mer ejocf enf yozhoi hhik lnhoitocr.

    z8(o;m) < o 2 m9

    mu ejocfkek `fkfn `stfrehe u fiencfcer2

    (ILVN) < ejocf= 2 ejocf7

    Mu `stfrehcf kgfneinf ILVN hoktison ejocfse afsopnokr. Ffrhoktison lnoroi clru esf vfyo 4cok jorin mer cffr afsopnokrso ejocf=enf `stfrenfk enfhnfr9 cfensf cf ejocf7 enf `stfrenfk enfhnfr yopnr.

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 =:

    @ere i nfhnfre@ere i Ilhutnor mer Trl`rohnoho cene eek lncuio kfhnecer. kilnuok itnork iunnokg vfyo prl`rohgyo unohos `frfitee `eme

    iunnokgkk co Trl`roho vfre vfrhfse `frfifmener. Okgoi `frfitf`ere/i ehiknor G cenekek mer poros cfennfrcer. G Trl`rohnoho cenekcf@ere i enfhnfre `frfitf ilhutnor enf cfen stcel.aitpaokfsekcfmunukok jlkiseylknor enf `frfinfterener. Mu mnhcf stokcort @/itpaokfsekcf yfr onok vf G prl`rohnorkco iunnoknok jlkiseylknorcokmoasfcfgfez. Jlkiseylknor @/ enfhnfreke ilnoynino yopomenfgfitokhnoro soaepnfr. Vy`unohokk kf iocor iretei lnhosko moihoiszk thprl`rohgnor mu ruteknfre roaotnino vf ftiek mer fiencf iunnokomenernfr. Zfslk lnoroi mu jlkiseylknor tokomener fiencf tosornokhnorcr. Uokeafraok`e mer prl`rohg yozc G prl`rohk G cfrnfyegesekek munukcuu

    afraok`e mer enfteh sestfhe pnotjlrhuko toyomener.

    Mu mnhcf @/ itpaokfse eekcf yfr onok th jlkiseylknoroknotohoyogoz. Mezeh eek coao kfhnese yluk iunnoknok jlkiseylknornotokhoi vf mer G prl`rohkk enfteh sestfhe fvrf lrtohyno ftienfehekesonoyogoi iuronnorcok moasfthfiter.

    Wtokcort Itpaokfyf Freeh

    Wtokcort @/ lrtohko hrogoot fcfk th G prl`roh ioykoi ilcnorkco

    oocoie sotr munukhoncr2

    #ekgnucf >stcel.a;

    Mu sotr mer G prl`rohkk fk monorkco yfr onr. stcel.a clsyos eekcf@/ itpaokfse torojkcok iunnoknok mer toih hoirlnor vf cfeifknfrtokhnokhtr. >; eorftnfreke itpaokf ockk ftrojkco iunnokhoy eorftnfreke iunnokhoyo tfrgea fcfrez. ki cfrnfyegeyf, mu itpaokfclsyoskk sestfh torojkcok tokhnokok ekgnucf inosrkcf (moniclsyonorkk munukcuu inosrcf) lncuuku mfnerthfi estfrez. Ffr

    eorftnfre iunnoknh lnsoyc mu itpaokf clsyos inosrk eekcfceroknohko `fnfgfiter.

    Wtokcort @ere, Wtokcort i vf Aoto iklitonor

    Mer G Trl`rohkco lnuok cffrnfr stokcort lnoroi firoko yoznr. Mumerehf stokcort i merehe cfker (Wtokcort Lutput stclut).

    Mer G Trl`rohkco `erenfgfi cffrnfr stokcort lnoroi inovyfcfk liukur. Mumerehf stokcort `ere merehe cfker (Wtokcort Ekput stcek).

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 =0

    Mer G Trl`rohkco lnuok aotonor stokcort lnoroi firoko yoznr. Mu merehfstokcort aoto merehe cfker (Wtokcort Frrlr stcfrr).

    Mer `ere i jlkiseylku iunnoknckco mu jlkiseylkuk zfnneekf `rfstokcort @ere vfyo Wtokcort i lrtohkcok cffr enfteehekcf

    munukunur.

    Wtokcort @ere i Jlkiseylknor

    Fk moset `ere yktfhe tfi mer ioroitfrek stokcort `ere merehekcfkliukhoscr. `ftgaor() jlkiseylku `ere merehekcf srocoie cefr ioroitfreckcrr. Merli enfteh sestfhe lrtohkco G prl`rohnoho cenetfrhekoncfk/inovyfcfk cffr liuyogoko moio mer clsyocok ioroitfrnfreliuyomener. Ffr mer prl`rohco `ftgaor() jlkiseylku iunnoknh esf ufiencf yoznok mer ilhut sotr

    prl` >`eresclsyose

    prl` ockcoie prl`rohk firok yfrekf `eresclsyose ocn clsyocok `ercenfreliuyogoitr. Muroco > eorfte `ercekek yknfkcerencee vf cefr mer clyokk`erce clsyos lncuuku oknotr. Ffr mu fiencfie mer prl`roho vfrenfrmoio mer prl`rohcok `fnfgfi esf mlru (pepf |) enfhe yopnoroi slrukaonnfcenfmener. ynf ie2

    mosioprl` | prl`

    ilhut sotr eie prl`roh co ontrr vf mosioprl` ockcoie prl`rohkitsk prl` ockcoie prl`roho `erce lnoroi ylnnor.

    Mer `ere clsyoskco clsyo slku lnukgo `ftgaor jlkiseylku FLJ cffrekeckcrr. FLJ cffre Wtokcort Itpaokf eekcf ? lnoroi tokhnokhtr.Okgoi prl`rohco FLJ tokh iunnoknhos tokomenernei oskcok coaouy`ukcur.

    i enfhe eek putgaor( g ) jlkiseylkuku iunnokomenerez. Mu jlkiseylku tfi

    mer ioroitfre stokcort i merehekf yozogoitr. i ioroitfrnfre ;eorfte enf yknfkcerenfmener. rkfek2

    prl` ; geiesclsyose

    finekcfie ilhut sotrkco prl` esehne prl`rohk its tfrhekonfyoznogoko geiesclsyose esehne clsyoyo yoznogoitr. Ffr mu prl`rohkits moio mer prl`roho `kcfrenfgfisf mlru eorfte iunnoknomener.

    Mukuk aoregekcf clsyonor zfrekcf Liuho/Uozho yopok ilhutnor enfrcfieilkunorhzco fnf onkp rkfinfkfgfiter. Mu ilhutnor co eie joriniotf`lrecf ekgfnfhfi ae cf yokn lnhoso `frfi.

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    gaor g9...g8`ftgaor()9

    Meehekcf `stfrenfmenfgfi fiencf yoznok ilhutuhuz stokcort `eremerehekcfk mer ioroitfr liur. Uoco

    gaor g9...

    g8`ftg(stcek)9finekcf iunnoknck `rfmenersekez.

    gaor g9.../* Sfi ioroitfr yozor */

    putg(g,stclut)9

    putgaor(g)9 finekcf yoznr vf g enf ejocf fcenfk tfi ioroitfre stokcorti merehekcfk yozor.

    rkfi ?

    Oocoie Trl`roh Inovyfcfk `erenfk aorjnfre firoko szfrfi yozhoitocr.ynf ie inovyfcfk `erenfk aorjnfrcfk o aorjeke firoko yozhohoitocr vfmu enfhe fktfr tuuko mosnkgoyo iocor cfvoh ftterhfitfcer.

    #ekgnucf >stcel.a;

    hoek(){

    gaor g9waenf((g8`ftgaor())!8'^k')

    ej (g!8'o') putgaor(g)9prektj("^k")9

    }

    Mer li prl`roh tfi mer `ere ioykokcok liur vf tfi mer i klitoskomu men`enfre yozor. Mu ohono co `ftgaor, putgaor vfyo prektj `eme @/jlkiseylknor iunnoknr.

    rkfi =

    Oocoie rkfi inovyfcfk `erenfk ioroitfrnfre ii aorjf fverfrfifiroko yozok mer prl`rohcr.

    #ekgnucf >stcel.a;

    hoek(){ekt g9

    waenf((g8`ftgaor()) !8 FLJ)

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    putgaor(esuppfr( g ) < tlnlwfr( g ) 2 g)9}

    Mu rkfitfie esuppfr vf tlnlwfr hoirlnor stcel.a itpaokfsekcftokhnokh lnok jlkiseylknorcr. Mu jlkiseylknorcok esuppfr ifkcesekf

    `kcfrenfk ioroitfrek myi aorj lnhos curuhukco clru cffr yoknlnhos curuhukco yokn cffr ckcrr. Slnlwfr jlkiseylku esfifkcesekf `kcfrenfk ioroitfre ii aorjf fverer.

    Meehnfkcerenhe inor

    stfkenfk cffrnfrek uy`uk fiencf vf uy`uk yfrnfrcf `rkfmenhfse eekMeehnfkcerenhe i Ilhutu iunnoknomener.

    prektj("Meeh Sokhnor vf Womet

    ejocfnfr"Y,Cfeifk?Y,Cfeifk=...XX)

    finekcf iunnoknok ilhut mu oho eek slk cfrfgf uy`ukcur. MuJlkiseylk Womet ejocfnfrek vf cfeifknfrek mfnernfkhe meeh tokhnorko`rf firoko yoznhosk sonor. Meeh tokhnor vf Womet ejocf cfceehioroitfr cezesekcf eie jorin trcf men`e munukur. Muknor klrhon ioroitfrnfrenf ejocf fcenfk ejocfnfr vf g eek mer oknoh toyok ckh ejocfnfre. Muckh ejocfnfre estfkenfk mer cfeifkek porohftrf lnoroi yoznh esfestfkenfk mer meehcf firoko yoznhosk sonor.

    prektj("Hfraomo %s u okco Aovo %c sgoinkco^k", oc, aovo)9

    Mu cfyeh Hfraomo Oahft u okco Aovo =7 sgoinkco`eme merejocfye firoko yozogoitr. Mu sotrco yfr onok vf % enf monoyp mercktrhf ioroitfre enf metfk ejocf ckh yopok meeh tokhcr. %eorfte enf cktrhf ioroitfre oroskco yfr onok mnhcf u ioroitfrnfrmunukomener2

    - eorfte 2 yoznogoi ejocfkek slno yokoi yoznhosk sonoyogoitr. Woyson mer cffr 2 yoznogoi ejocfkek firokco io mosohoini onoko

    sogok mfnernfyfk soyson mer cffrcer. Ffr ejocf mfnernfkfk yfrfsohoyogoiso sln torojtok irpnogoitr. . eorfte 2 onok ifsernesoyson onokcok oyrok klito.

    n eorfte 2 Meeh tokhkk uzuk lnup lnhock vfrfk mer tokhnoyg .

    Meehnfkcerhf tokhnor yo co cktrhf ioroitfrnfre eek oocoietomnlco yfr onok tokhnor iunnoknhoitocr.

    Meeh Sokh

    cIorni lnoroi `fnfk cfeifkek cffreke soy lnoroi firoko

    yozor.l Iorni lnoroi `fnfk cfeifkek cffreke 1'nei soy lnoroi firoko

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    yozor.

    xIorni lnoroi `fnfk cfeifkek cffreke ?:'ni soy lnoroi firokoyozor.

    uIorni lnoroi `fnfk cfeifkek cffreke eorftsez mer cffr

    lnoroi firoko yozor.

    gIorni lnoroi `fnfk cfeifkek cffreke tfi mer ioroitfr lnoroifiroko yozor.

    sIorni lnoroi `fnfk cfeifkek cffreke mer ioroitfr cezfselnoroi firoko yozor. Mu ioroitfr cezfse cezf slku oknohko `fnfkkunn ioroitfre munukukgoyo iocor yoznr.

    f Iorni lnoroi `fnfk cfeifkek cffreke menehsfn `stfrehcfiesoy lnoroi firoko yozor.

    j

    Iorni lnoroi `fnfk cfeifkek cffreke ifserne soy lnoroi

    firoko yozor.@ %f vfyo %jcfk iso lnokk iunnokhosk sonor

    Ffr % eorftekcfk slkro iunnoknok eorft cktrhf ioroitfre cfen esfvf klrhon mer ioroitfr lnoroi % eorfte iunnoknogoiso %% finekcfiunnoknhoncr

    Iunnoknok zfn Ioroitfrnfr

    ^k Ufke Wotr Ioroitfre

    ^t SOM Ioroitfre

    ^^ ^ Ioroitfre^" " (Srkoi) Ioroitfre

    Meehnfkcerenhe @erenfr

    stfkenfk Cffr vf ejocfnfrek men`esoyoro `erenhfseke sonor. Iunnokh lnoroiprektj enf oyk ortnor sonor. Zf men`esoyoro `ere yk enf onr.

    sgokj("Meeh Sokhnor"Y,Cfeifk?Y,Cfeifk=...XX)

    finekcf iunnoknr. sgokj stokcort `ere merehekcfk ioroitfrnfre liur vfvfrceekez meeh tokhnorko `rf liukok ioroitfrnfre ylruhnor vfcffrnfre en`ene cfeifknfrf yfrnfterer. Okgoi ceiiot fcenhfnecer ie Cfeifklnoroi ejocf fcenfk cfeifknfrek ocrfsnfre mu jlkiseylko `kcfrenhfnecer.Muroco cfeifknfre afr mere meeh tokhnor enf mfnernfkfk tokhnoro merfmerrthfi zlrukcocr. prektj'cf `rnfk th meeh tokhnoygnor sgokj eekcf `ffrnecer. Cfeifknfr esf ocrfsnfre enf vfrenhfnecer. Ffr cfeifk mosetcfeifk esf mu ocrfs cffre "&" lpfrotr enf munukhoncr. Ffr cfeifk

    ioroitfr cezfse `eme mer cfeifk esf socfgf cfeifk ock vfrhfi yftfrnelnogoitr.

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    rkfi 7

    Mu Trl`roh inovyfcfk jorin zfnneinfrf soaep cffrnfr liuyup jorinzfnneinfr enf firoko yozhoitocr.

    #ekgnucf >stcel.a;#ekgnucf >strek`.a;

    hoek(){gaor ejocfY?44X9ekt i,uzuknui9jnlot ifser9gaor gfvop9

    prektj("Oc, Wgoini, c?, ifser, gfvop cffrnfreke`erekez

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    Ioroitfr cezfsekek Liukup-Uoznhos

    Mozfk tfi mer ioroitfr vfyo tfi mer ifnehf cfen cf Fktfr tuukomosnkgoyo iocor yo co sotr slku eorfteke munukgoyo iocor th

    yoznoknork liukhos `frfifmener. Mu kfcfknf u jlkiseylknor iunnokhoiyfrekcf lnogoitr.

    gaor ocY74X9...`fts(oc)9//Mer ioroitfr cezfseke inovyfcfk liur

    puts(oc)9//Mer ioroitfr cezfseke firoko yozor

    rkfi 3

    Mu rkfi'tf Inovyfcfk `erenfk mer ioroitfr cezfsekek tfrse munukoroi firoko

    yoznhoitocr.

    #ekgnucf >stcel.a;#ekgnucf >strek`.a;

    hoek(){gaor ejocfY?44X9ekt i,uzuknui9

    puts("jocfkeze @erekez^k")9`fts(ejocf)9uzuknui8strnfk(ejocf)9

    jlr(i8uzuknui-?9i;849i--)

    putgaor(ejocfYiX)9

    putgaor('^k')9}

    kfhne mer toih jlkiseylknor

    stcel.a itpaokfse eekcf iunnokn lnomenfgfi mer toih jlkiseylknormunukur.

    Ioroitfr Wkoho vf cktrhf jlkiseylknor

    esonpao( g ) g ioroitfr men`ese toylrso 4cok jorin mer cffr cfensf 4ckcrr.

    esuppfr( g ) g ioroitfre myi aorj esf 4cok jorin mer cffr cfensf 4ckcrr

    esnlwfr( g ) g ioroitfre ii aorj esf 4cok jorin mer cffr cfensf 4

    ckcrr

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    esce`et( g ) g roioh men`ese toylrso 4cok jorin mer cffr cfensf 4ckcrr.

    esspogf( g ) g mlnui men`ese toylrso 4cok jorin mer cffr cfensfckcrr.

    Sluppfr ( g ) g ioroitfreke myi aorjf fverer.

    Slnlwfr ( g ) g ioroitfreke ii aorjf fverer.

    uk`ftg

    stokcort `ere lrtohkcok vfyo afraok`e mer clsyocok liukhu ioroitfre`fre l lrtoho yozok jlkiseylkcur.

    uk`ftg(g, clsyoesorftgese)9

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    Trl`roh Oi vf Trl`roh OiCfkftehe

    G Trl`rohnorkco Trl`roh sotrnor cefr prl`rohnoho cennfrekcf lncuu`eme yuiorcok ooyo egro fcenernfr. Afr ilhut slkukco 9 (kliton ver`n)ioroitfre munukur. Mnli yopn mer cencer vf mu monohco cfeifknfrtokhnokcinor mnli efresekcf ftienecernfr. Mercfk jozno ilhutnor {...}seh`fnfre oroskco fnf onkoroi fi mer ilhuthu eme mnlinokomener. Mfniecoao kgf toktkz ilhutnor muroco coao oyrktn mer fiencfekgfnfhfyf onogoz.

    Ilhutnor vf Mnlinor

    G Cenekcf Kliton ver`n ilhut slknokcrho mfnertfgecer.

    x849e++9

    prektj(.....)9

    yuiorcoie afr mer 9 ilhutuk metteeke vf cefr ilhuto `fenceekesfhmlnezf fcfr. Ilhutnor mnlinohoi eek {...} ihf poroktfznfreiunnoknhoitocr. Mu poroktfznfr oroskco yoznok ilhutnor io tokf lnursolnsuk tfi mer ilhuthu `eme on`nokr. ej, fnsf, jlr, waenf `eme ilhutnork

    afhfk pfekcfk 9 iunnoknhoz. Oyrgo mer mnlu meterfk } eorftekekpfekcfk cf kliton ver`n ilkunhoz. Mu co zhnfhfcf estfkenfkishnork iopon mer iutu ehe `eme `stfrenhfseke sonor.

    Ej-Fnsf ilhutu

    Ioror vfrhfye sonoyok Ilhut'tur. Sfhfn Uops

    ej (hoktison\ejocf)

    Ilhut-?9

    fnsf

    Ilhut-=9

    Mu yopco fnsf ish sfehneiter. Uoke iunnoknhoso co lnur. Ilhutukonhos u fiencf ezoa fcenfmener2

    kgfneinf hoktison ejocf afsopnokr vf mer cffr munukur. Mu cffr 4 aoregekcf mer cffr esf (yoke hoktison ejocf clru esf)

    Ilhut-? enf `stfrenfk ilhut uy`unokr

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    Mu cffr 4 esf (yoke hoktison ejocf yokn esf) fnsf'cfk slkroieilhut-= enf `stfrenfk ilhut uy`unokr.

    Ffr fnsf ish yli esf vf cffr 4 esf Ilhut-? uy`unokhocok 9'cfkslkroie ilhutnorcok cfvoh fcener.

    @frfitf ej ilhutu mer soyson cfeifkek cffreke ilktrln fceylrso mertoih isonthonor iunnokhoi hhikcr. rkfek9

    ej (cfeifk !84) ejocfse yfrekfej (cfesifk) yoznomener. Okgoi tfrgeafk merekge yoznok coao oknonr vfonno`fnhe lnokcr.

    Mu yopco Ilhut-? vfyo Ilhut-= enf `stfrenfk yfrnfrcf mercfk joznoilhut uy`unokhoi zlrukco esf mu ilhutnor ihf poroktfznfre efresekfonkp tfi ilhuthu `eme `stfrenfmener.

    Mu yopco fnsf ish sfehnei lncuu eek e ef ej yozhnorkco slruknornoiornoomenersekez. zfnneinf mer ej ilhutukuk fnsf thgfse yli esf mfnersezneilrtoyo ior. Mu curuhco fnsf slk ejf oetter. Coao clrusu ejnfr etfk coclru iopotnr. ynf ie2

    ej (k;4)ej (o;m)

    z8o9fnsf

    z8m9

    ilhut tlpnunuukco fnsf ilhutu eiekge srocoie ej ilhutuko oetter. Coaooknonomener lnsuk ceyf ilhutnork yozh sroskco `erekte iktnoro ceiiotfcenheter. Ffr oknotnhoi estfkfk mu cfen cf moio mer sro eceysf ihfporoktfznfre iunnoknomenerce.

    ej (k;4) {ej (o;m)

    z8o9}

    fnsfz8m9

    moz curuhnorco mu mfnersezneinfr aotonoro coae kfcfk lnomener. ynf ie

    ej (k;4)jlr(e849 e>k9 e++)

    ej (sYeX;4) {prektj(....)9rfturk(e)9

    }

    fnsf /* Uoknjocf */prektj(k kf`otej lnohoz ^k)9

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    G Trl`rohnoho Cfrs Kltnor

    1/?7.4=.=4?= ?:2?5244 7:

    @erekte iktnork ilkuhuko `rf yoptkz enf cfrnfyegekek oknoc jorinlnogoitr. Cfrnfyege eiekge ej ilhutukuk fnsf ilhutuku yozckz sokogoivf ilcu muko `rf rftfgfiter.Mynfgf prl`rohkzco gecce hoktison meraoto yoph lnursukuz. Mu tr mer aotoy oyinohoi lncuio zlrcur.

    rkfi 6

    Mu rkfitf inovyfcfk `erenfk eie soyson cffr iornotrnylr, myilnokcok ii lnok iornylr vf slku firoko yoznylr.

    #ekgnucf >stcel.a;#ekgnucf >strek`.a;

    hoek(){ekt o,m9

    prektj("O eek mer cffr `erekez

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    Ilhutnork slkukcoie fnsf cfehe ilunnorcok aemerekek `frfinffhfhfsecuruhukco egro fcener. Mozfk ilunnorcok aemerekek clru lnhoccuruhnorco yopnogoi cfeei mer ilhut munukhoyomener. Mu curuhco musotrnor (fk slk fnsf sotr) yoznohoyomener. Mozfk cf mu curuh enf osnoiornonhoyogoiso ehioksz curuhu `rfmenhfi eek yoznomener.

    Fteiftnfr vf `ltl ilhutu

    G eek ae tfrgea fcenhfyfk mer ilhut lnok mu ilhut prl`roh oik merklitocok cefr mer klitoyo yknfkcerer. G Trl`rohnoho cene li ftiene mnliyopn mer cencer. @n Ck` Ilhutnor, Jlkiseylkfn yop vf aotto aoregeitpaokfnfr lnuturup muknor prl`roho monoho enfhekcfk clnoy mynfmer ilhuto ifsekneinf eateyo munukhohoitocr. Aotto lksuz prl`rohyozhokk Gcf li ilnoy lncuuku synfyfmenerez.

    Uekf cf fsie Trl`rohnoho oniokninor lnoknor eek mu ilhut iunnoknomenermer ilhut lnoroi G cene efresekcf vorcr.

    fteift2.......`ltl fteift9

    finekcf iunnoknhoitocr. kgfneinf `ltl ilhutu enf sopnogoi vfyo

    connoknogoi ilkuho mer oc vfrener. Mu ilkuh eek vfrenfgfi oc cfeifkesehnfkcerhf iuronnorkcoie `eme ocnokcrnomener. Mu oc (2 -eie klito ststf) sfhmln toiep fthfnecer. Ck` lnuturhoi eek tfrgea fcenhfsf cfmfnie iunnoknhos `frfifgfi merio klito synfkfmener. ynf ie2

    ef mercfk jozno ck` lnok mer yopco fk c ck`yf unohoi eek...

    Aoto oyinoho ohogyno lnuturunogoi yopnorco iunnokhoi eek...

    Rlruknu lnhoso co mer `rup soykk eekcf orockz muncuukuzco mu

    curuhu oknotomenhfi eek...Ontrho :

    Inovyfcfk 4-Wjr `erenekgfyf iocor `erenfk mer `rup soykk iorfnfrekeklrtonohosk munogoi prl`roh eek G Trl`rohnoho cene enf `fneterekez.

    Ontrho 0

    Inovyfcfk `erenfgfi eie Tlzetej toh soykk LMFM (Lrtoi Mnfknfrek FkMy)eke munogoi G Trl`rohk`fneterekez. rkfek fnehezcf 7:63 vf

    ?7:6 cffrnfre lnsuk. Mu cffrnfrek LMFMe u fiencf munukhoitocr.

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    7:63 / ?7:6 Ionok 5=3?7:6 / 5=3 Ionok 33?5=3 / 33? Ionok 3=33? / 3= Ionok =?3= / =? Ionok 4

    Mu enfh srosk vf yekfnfhf zfnneinfreke iunnokoroi eie soykk LMFMekemunukuz. Mu rkfitf LMFM =? cffrecer.

    Ontrho 1

    Inovyfcf `erenfk ifserne mer soyy o/m finekcf rosylkfn lnoroi ejocf fcepfiroko yozomenfgfi prl`roh g enf `fneterekez. rkfek inovyfcfk `erenfgfilnok 4.6 cffre eek ?/= cffreke firoko yozhoncr.

    swetga ilhutuWwetga Ilhutu mercfk jozno cffrcfk sfeh yophoi eek iunnoknomenfgfizfn ioror vfrhf ilhutucur. ef jozno soyco ej..fnsf ilhutukuiunnokhoy `frfiterfk curuhnorco iunnoknomenfgfi ftiene mer ioror vfrhforogcr.

    swetga(ejocf){gosf somet\cffr?2 YIlhut?9Xgosf somet\cffr=2 YIlhut=9X

    gosf somet\cffr72 YIlhut79Xgosf somet\cffr32 YIlhut39Xgosf somet\cffr62 YIlhut69X......gosf somet\cffrK2 YIlhutK9Xcfjount2 YIlhut9X}

    rkfi :

    Oocoie prl`roh mer ejocf eekcfie roiohnor, mlnuinor vf cefr

    ioroitfrnfre soyok mer prl`rohcr.

    #ekgnucf >stcel.a;ekt g,e,kwaetf,kltafr,kce`etY?4X9

    hoek(){kwaetf 8 kltafr 8 49jlr (e849 e>?49e++)

    kce`etYeX849waenf ((g8`ftg(stcek)) !8 FLJ )

    swetga ( g ){gosf 4 2

    gosf ? 2gosf = 2

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    1/?7.4=.=4?= ?:2?5244 75

    gosf 7 2gosf 3 2gosf 6 2gosf : 2gosf 0 2

    gosf 1 2gosf 5 2kce`etYg-4X++9

    mrfoigosf 2gosf ^k2gosf ^t 2

    kwaetf++9mrfoi9

    cfjount 2kltafr++9

    mrfoi9}

    prektj(ce`ets 8 )9jlr (e849e>?49e++)prektj( %c,kce`etYeX)9

    prektj(^kwaetf spogf 8 %c, ltafr 8%c^k,kwaetf,kltafr)9}

    Mu ilhut ejocf enf mfnertenfk tohsoy ejocfye afsopnor. Uuiorcoie rkfi mug ioroitfrecer. Wlkroskco mu afsopnokok cffr gosf enf mfnertenhe lnok

    cffrnfrcfk merekf fet he ceyf ilktrln fcfr. Ffr fet lnok mer gosfejocfsekf rostnorso lkuk iorskcoie vf cefr ontkcoie ilhutnor egro fcfr.Ffr muroco mfnne mer ish ilhutnork uy`unokhos mer ishkkuy`unokhohos estfkeylrso swetga cfehekcfk mrfoi ilhutuyno inr.Ffr mu gosf cffrnfrekcfk aemere fncfie cffrf fet cfensf cfjount enf`stfrenfk ilhut uy`unokr.

    Afr gosf cfehekek yokkco mer ilhut munukhoi zlrukco lnhoc `ememercfk jozno ilhutu {...} ejocfnfre orosko yozhocok co iunnokomenersekez.Okgoi mu curuhco ilhutnork uy`unohoskk methfseke estfceekez yfrf

    mrfoi ilhutuku ilyhoy ukuthohokz `frfifgfi.

    mrfoi ilhutu swetga mnlukcok afhfk ihokz sonoyok mer ilhuttur.Afr mer gosf fteift `eme covrokc eek mere iorskcoie enfh`frfinfterenceitfk slkro cefrnfrekcfk cfvoh fcfr. Cfvoh fcenhfhfsekesonohoi ohogyno mrfoi vfyo rfturk cfehnfre enf murocok inhos`frfier. Coao slkro `rfgfehez zfrf mrfoi ilhutu waenf, jlr, clck`nfrekcfk cf inhosk sonor.

    Mu gosf cfehnfrekcfk cfvoh fcep `ecenhfse ior`ooyo yln oogoi `eme

    `rksf cf mozfk lnuhnu slkunor lnomener. ynf ie mercfk jozno fynfhe tfi

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    1/?7.4=.=4?= ?:2?5244 34

    mer gosf sotrkco iunnokhokz hhik lnomenhfitfcer. Zfyo mercfk joznogosf sotr eek oyk sotrnork ontrnhosk sonohoitocr.

    ye prl`rohnoho rkfinfre eek slk gosf sotrkcok slkro co mrfoi ilhutuiunnokhoi `frfifmener. Hoktison lnoroi `frfisez `rksf cf mu coao slkro

    muroyo finfkfgfi yfke gosf sotrnorko yoknnino connokhoy fk`fnnfyfgfimf hoktison aotonork lnuuhuku ozontogoitr.

    Ontrho 5

    Inovyfcfk `erenfk eie soy vf mer lpfrotrf `rf enfh yopp slkugu firokoyozok mer G Trl`roh `fneterekez.

    Ontrho ?4

    Inovyfcfk `erenfgfi lnok oy vf yn men`esekf `rf oyk io `k fiteekemunogoi G Trl`rohk `fneterekez.

    Ck` Ilhutnor - waenf

    Mer ilun sonokkgoyo iocor moz ilhutnork tfiror fcenhfseke sonoyokck` ilhutucur. Mu Ck` ilhutukuk zkcf socfgf ilun skohomunukhoitocr. Cffr orttrho vfyo eni cffr otoho `eme `frfine lnomenfgficefr enfhnfr oyrgo mfnertenhfnecer.

    waenf(ilun){

    ilhut?9ilhut=9......

    }

    finekcf iunnoknr vf ilun clru lncuu srfgf ilhutnork uy`unokhosksonor. Ilun enf mfnertenfk ejocf hoktison mer ejocf lnup clru lncuusrfgf ilhut?, ilhut= vm ilhutnork tfiror tfiror uy`unokhosk sonor.So ie ilun yokn lnukgoyo iocor. Ilun yokn lnurso vfyo soyson lnoroi 4cffreke torso prl`roh oi ck` ilhutukcok slkroie ilhuttokcfvoh fcfr.

    rkfi 0

    Oocoie rkfitf Jemlkfgge cezeseke mer K cffrekf iocor firoko yozokprl`roh waenf ilhutu iunnoknoroi yoznhtr.

    #ekgnucf >stcel.a;ekt o,m,g9

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    ekt k9hoek(){

    prektj(k cffreke inovyfcfk `erekez)9sgokj(%c,&k)9

    o8?9m8?9prektj(%c^k%c^k,o,m)9g8o+m9waenf(g>8k){prektj(%c^k,g)9o8m9

    m8g9g8o+m9

    }}

    Ontrho ??

    Wjr 4 `erenekgfyf iocor inovyfcfk `erenfk th cffrnfrek lrtonohoskmunup firoko yozok G prl`rohk `fneterekez.

    Ontrho ?=

    t849waenf(t>?4){prektj(%c^k,t)9

    t++9} finekcfie mer ejocfye jlr ilhutu enf yozhoyo onkz.

    Ck` Ilhutnor - jlr

    G Trl`rohnoho cene efresekcf slk cfrfgf `n mer ck` ilhutucur. Mfnnemer ilun sonokkgoyo iocor ltlhotei lnoroi ortok cffrnfrnf ck`lnuturhoy sonor.

    jlr(ejocf?9ejocf=9ejocf7){

    ilhut?9ilhut=9......}

    finekcf iunnoknr.

    Mu ilhut waenf enf oocoie `eme ejocf fcenfmener

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    1/?7.4=.=4?= ?:2?5244 3=

    ejocf?9

    waenf(ejocf=){ilhut?9ilhut=9

    ejocf79}

    Sfikei lnoroi ejocf lnoroi tokhnokh ejocfnfrcfk ejocf? vf ejocf7orethftei ejocfnfre oknotr. jocf= esf hoktison mer iornotrho ejocfsecer.Mu ejocfcfk afr aok`e mere yoznhocok pos `fenfmener. Okgoi mucuruhco menf kliton ver`nnfr yfrnfrekcf ionhoncr.ffr ejocf? vf ejocf7yoznhozso vf aotto ejocf= jlr ilhutu eekf yfrnfterenhfzsf lrtoyo iokilhut clrucur. ynf ie

    jlr(99){...

    }

    finekcf yoznok ilhut mer slksuz ck`y oknotr. Mu tr mer ck`cfkmrfoi vfyo rfturk `eme mer ilhutno inogo iomun fcener.

    Muroco cfeifk enf mfnertenfk eni ish tfi mer cffr oitorho ejocfse yfrekfver`nnfrnf oyrnhoi surfte enf mercfk jozno cffr oitorho ejocfsekemorkcromener. Mu ish mer eni cffr oitorho ejocfse lnup ck`uy`unokhoyo monohocok kgf egro fcener.

    iekge ishco iunnoknok ilun ck`kk slknokho ilunucur. Mu ilunclru lncuu srfgf ck` yekfnfker.

    Wlk Ishco iunnoknok cffr oitorho cfehnfre oronorkco ver`nmunukhoi ilunu enf mercfk jozno lnomener. Mu ish esf ck` eekcfieilhutnork afr uy`unokhoskcok slkro egro fcenfk enfhnfrcer. luknuinocffr ortrok ejocfnfrcer.

    jlr(x849x>?49x++){

    prektj("Wrocoie Woy %c^k",x)9}

    rkfe Wjrcok 5'o iocor soynor firoko ont onto yozok mer prl`rohpooscr.

    Ogomo kfrfcf waenf kfrfcf jlr ilhutnork iunnokhonyh< Ffrcfeifknfrf eni cffr otoho ejocfnfre yli esf vf ck`kk io cfjouy`unokogo aoiikco soyson kft mer tokh synfkfheylrso iunnokgcovroknorko mon mer ilun enf ejocf fcenfmeneylrso waenf ilhutu uy`ukmer ilhuttur. Ffr eni cffr otoho ejocfnfre vor vf ck`kk onhosilkusukco soyson mer toih cffrnfr ejocf fceneylrso jlr ilhutu coaouy`uk mer ilhuttur. ki jlr ilhutu `frfi eni cffr otohonork

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    `frfisf cf ilunu eni sotr zfrekcf `stfrcee eek coao ilnoy oknonr vfcfrne tlpnu lnoroi iorhzco curuylr. Mu co ck` ilhutuhuzukhfrifzenfhfseke vf prl`rohk ilktrlnkk ilnoynohosk sonor.

    rkfi 1

    Mu rkfitf inovyfcfk `erenfk mer K cffrekek joitryfne jlr ilhutuiunnoknoroi afsopnokhtr.

    #ekgnucf>stcel.a;ekt j,k,x9

    hoek(){prektj(k cffreke `erekez)9sgokj(%c,&k)9jlr(j8?,x8?9x>8k9x++) j*8x9

    prektj(Joitryfn8%c^k,j)9}

    Mu rkfitf osnkco joitryfne afsopnoyok ifseh socfgf jlr ilhutukukyozn lncuu sotrcr.

    rkfi 5

    Inovyfcfk `erenfgfi Q cffrekcf K cffrekf iocor th clon soynorfiroko nestfnfyfk G Trl`rohk `fneterekez.

    #ekgnucf>stcel.a;ekt x,k,i9

    hoek(){prektj(Q cffreke `erekez)9sgokj(%c,&x)9

    prektj(K cffreke `erekez)9sgokj(%c,&k)9jlr(i8x9i>8k9i++) prektj(%c^k,i)9

    }

    Ontrho ?7

    Ontrho : rkfeke `ltl ilhutu iunnokhocok waenf vfyo jlr enf yfkecfkyozkz

    Ontrho ?3

    Ontrho 0 rkfeke `ltl ilhutu iunnokhocok waenf vfyo jlr enf yfkecfkyozkz

    Ontrho ?6

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    Wocfgf tlpnoh vf iorho iunnokoroi eie soyy orpok vf slkugu firokoyozok G Trl`rohk `fneterekez.

    Ontrho ?:

    Wocfgf tlpnoh vf iorho iunnokoroi eie soyy mnfrfi mnh vf ionokmunok vf slkugu firoko yozok G Trl`rohk `fneterekez.

    Ontrho ?0

    Inovyfcfk `erenfgfi =4 soykk tfi lnoknork oyr ejt lnoknork oyr tlpnoypslkugu firoko yozok mer G prl`roh `fneterekez.

    Ontrho ?1

    J(x)8 8

    k

    x x?

    =? finekcf tokhnokh mer jlkiseylkco `erenfk k cffre eek

    slkugu afsopnoyok vf firoko yozok G prl`rohk `fneterekez. Trl`rohyozorifk ifsekneinf `ltl ilhutu iunnokhoykz.

    Ontrho ?5

    Inovyfcfk `erenfk mer toh soykk th toh mnfknfreke munup firokonestfnfyfk mer G Trl`roh `fneterekez.

    Ontrho =4jlr (x8?,j8?9x>?49x++) j*8x9finekcfie prl`roh porosk waenf ilhutuku iunnokoroi yozkz

    Ontrho =?

    Gls(x)8!:!3!=

    ?:3=

    xxx

    + finekcf tokhnokh mer onh eek inovyfcfk

    `erenfgfi mer x cffrekf `rf eni ?4 tfreh eek slkugu afsopnoyp firoko

    yozogoi G prl`rohk `fneterekez. s onho enfhe eek hota.aitpaokfsekcfie plw jlkiseylkuku iunnokkz.

    Ck` Ilhutnor - cl...waenf

    waenf vf jlr ilhutnorkco ck` slknokho ilunu ck`kk fk mokcoskokr. Okgoi mu kg ck` ilhutu lnok cl ilhutu ck` slknokhoilunuku ck` slkukco skor. Mu kfcfknf vf ck` ilhutukuk `fkfn`rkkcfk clnoy ck` ilhutu eekcfie ilhutnor fk oz mer ifz egrofcenernfr.

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    cl{ilhut?9ilhut=9.......

    }waenf (ilun)9

    kgfneine lnoroi ilhutnor egro fcener slkro ilun skokr. Clru esf ilhutnortfiror uy`unokr yoke osnkco ck` ilhutnor tfiror egro fcener. Ffr ejocfyokn lnhuso ck` slk munur.

    Soahek fcfmenfgfekez `eme cl ilhutu jlr vf waenf ilhutuko `rf lncuiooz iunnoknok mer ilhuttur. Okgoi tome ie moz curuhnorco lncuio ftiene merck` ilhutucur.

    rkfi ?4

    Oocoie rkfe ekgfnfyfneh. Mu rkfitf iunnokg inovyfcfk 4 enf ?44oroskco mer soy `erhfyf zlrnokylr. Paenf enf yoznh lnok ilun ekgfnfhfsotrko ceiiot fcekez. Ffr x>4 vfyo x;?44 esf ck` eekcfie ilhuttfiror fceneylr. ki mu estfhfceehez mer curuh. Osn estfkfk iunnokgkk`ffrne mer vezf kltu `erfmenhfsecer.

    #ekgnucf >stcel.a;ekt x9

    hoek(){cl {prektj(4 enf ?44 oroskcoie vezf kltuku `erekez)9sgokj(%c, &x)9

    }waenf(x>4 || x;?44)9}

    yuiorcoie cl...waenf mnlu inovyfcfk `erenfgfi cffrek 4...?44 oronkcolnhosk zlrnor. Zf mu oronito cfensf tfiror cffr `erenhfseke sonor.

    Ck` i Ilhutu - mrfoiKlrhon lnoroi mer ck` ilunco lnuok curuho `rf slknokr vfyo cfvohfcfr. Ck`kk mo vf slkuku mfnernfyfk ejocf vfyo ihf poroktfznfrekf`rf ck` ee vf c oyrnh curuhcocr. Ffr mer ck`cfk afraok`e merokco iho eateyog lnuurso mu ilhut iunnoknomener. Mu ilhut egrofcenceitfk slkro ck`kk slkuku mfnertfk klitocok slkroie eni ilhuttokprl`roh oi cfvoh fcfr.

    mrfoi9

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    1/?7.4=.=4?= ?:2?5244 3:

    finekcf Iunnoknr. Mu ilhut fk etfie ck`cfk ihoy sonor.

    rkfi ??

    #ekgnucf >stcel.a;

    ekt e9hoek(){

    e849waenf (?){

    ej(e ;?44) mrfoi9prektj(%c^k,e)9e++9

    }}

    Ck` cfvoh Ilhutu - glktekufMrfoi ilhutu torzkco mer ilhuttur. Mer ck`cf mu ilhutuk munukcuuklitocok tfyf ilhutnork iunnoknhohosk sonor. Lkuk yfrekf ck`moko ckp lrocok prl`roh oik cfvoh ftterhfye sonor.

    glktekuf9

    finekcf Iunnoknr.

    Sh ck` ilhutnorkco iunnoknomenerifk mrfoicfk jorin lnoroi swetgailhutu enf iunnoknohoz. Ck`cfie mer slkroie etfrosylkuk yopnhosksonor. rkfi lnoroi2

    rkfi ?=

    Oocoie rkfi e cffre ejt lnok curuhnor eek ck` mokcok cfvohfcenhfseke sonor. Uoke firoko socfgf tfi soynork yoznhosk sonor.

    #ekgnucf >stcel.a;ekt e9

    hoek(){e849waenf (e > ?44){

    ej(e % = 88 4) glktekuf9prektj(%c^k,e)9e++9

    }}

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    Jlkiseylknor vf @fkfn Trl`rohUops

    Jlkiseylknor myi prl`rohnor ii poronoro mnfk `rfvnfrcer. Oyrgocoao kgf eksoknork rfthe lnomenfgfinfre zhnfre sezek tfiror motokifjfthfhfkeze sonornor. n`ene jlkiseylknor `fkfnneinf cftoynor `eznfr.Rotfk mu cftoynork prl`rohg torojkcok menekhfsekek mer oknoh ylitur.

    G jlkiseylk iunnokhk vfrehne vf ilnoy iunnokhn mer fiencf tosornohtr.@fkfnneinf G prl`rohnor ii jlkiseylknorcok lnuhutur. Mu oroco mer Gprl`roh mer yoco coao jozno ioykoi clsyoskcok lnuomener. Mu ioykoiclsyonor oyr oyr cfrnfkhe vf merneitf yinfkeylr lnomenfgfe `eme afpmerneitf cf monokh lnomener.

    Osnkco G prl`rohnoho cene enf yoznok th prl`rohnor mer `rupjlkiseylkcok emorftter. Aotto G cenekek ilhutnorkcok aore li iunnokn meryk jlkiseylk tokhnor sz ilkusucur. Mfnie cf G ceneke `n inokyopnorcok mere cf mu jlkiseylk tokhnoho vf jlkiseylknor estfkenfkyfrnfrcf iunnokhocr.

    Mer li prl`rohco itpaokfnfrek eekcf yfr onok jlkiseylknoriunnokhkzcr. `ftg, putg, sek, gls vm. jlkiseylknor muknorcokcr. Mumnhcf mez coao li mu jlkiseylknor iunnokhoitokso muknor

    tokhnohoy rfkfgfez. Mu fiencf ifkcekezf oet prl`roh itpaokfnfrelnuturomener vf mu prl`roh poronork mer yfrcfk moio mer yfrftoyomenersekez.

    Oko prl`roh mnlu (hoek)

    Mu iocor jlkiseylk efresekcf uku mfnerthfi `frfier2 Osnkco Gprl`rohkk oko mnlu co mer jlkiseylk tokhcr. Uoke hoek ceyfocnokcrnok mer jlkiseylkcur. Afr Trl`rohco hutnoio munukhos `frfierokgoi porohftrf onhoi zlrukco cfencer vf cffr ckcrhfi zlrukco co

    cfencer.tokhnor.......

    hoek(){....../* Trl`roh enf en`ene oko `ereejocfnfre muroyoyoznogoitr.*/......}

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    G prl`roh `fkfn yops

    #ekgnucf tokhnor#cfjekf tokhnor@nlmon cfeifk tokhnorjlkiseylk\oc(){......./*Jlkiseylk tokh muroyo*/.......}/* Mu prl`rohco iunnoknomenfgfi th jlkiseylk tokhnor */

    hoek(){....../* Trl`roh enf en`ene oko `ereejocfnfre muroyoyoznogoitr.*/......}

    #ekgnucf Sokhnor

    Trl`rohco iunnoknogoi aorege yo co kgfcfk tokhnokh jlkiseylknorkmunukcuu itpaokfkek tokhnokc ejocfnfrcer.

    Mu geks itpaokf stcel.a, strek`.a, glkel.a tehf.a vm. Itpaokfnfr lnupmu itpaokfnfrek afrmere mer enfh `rumu mfnernfyfk jlkiseylknork meroroco munukcuu clsyonorcr.

    Mu itpaokfnfr, kgfcfk tokhnokh itpaokfnfr (Trl`rohnoho cene`fneteregenfre torojkcok) lnomenfgfe `eme, sezek lnuturcuukuz meritpaokfnfr cf lnomener.

    #cfjekf Sokhnor

    Mer Trl`roh efresekcf iunnokhoi estfyfmenfgfekez somet ejocfnfretokhnohoi eek iunnoknok szgitr. Afhfk eni ishco yfr onr.

    Cefr mnhnfr

    Sh prl`roh efresekcf iunnoknogoi cfeifknfr hoek mnlukcok kgftokhnokhoncr. Mu fiencf tokhnockz cfeifknfr @nlmon lnurnor vfth prl`roh efresekcf tokhn aonf `fnernfr.

    Coao slkro jlkiseylknor tokhnokr. Mu jlkiseylknork tokhnokhos merslkroie mnhcf fnf onkhtr.

    Oko Trl`roh mnluku tokhnokhos vf ilcnorkk yoznhos enf prl`roh

    tohohnokh lnur. osnkco hoek()ceyf ocnokcrnok mu mnli klrhon merjlkiseylk tokhkco lncuu `eme tokhnokr. Okgoi oc zfncer vf

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    cfeterenfhfz vfyo cfeei ohonor eek iunnoknohoz. Oyrgo mer Gprl`roh ontrnhoyo monokckco eni lnoroi mu mnli uy`unokr. Cefrjlkiseylknor vfyo prl`roh poronor murocok ornr vfyo murocok egrofcenernfr. Mu oknohco zfn mer jlkiseylkcur. hoek() jlkiseylku. Ffrontrnrifk porohftrf enf iunnoknok mer prl`roh lnoroi ontrnrso ()'nfr

    oroskco `fnfk ejocfnfr l prl`rohk porohftrfnfrecer.

    Sfhfnnfr

    Trl`roh mermerekcfk mohsz mer ish jlkiseylk tokhnorkcok lnuur.Jlkiseylknor oroskco aomfrnfhf, porohftrfnfr vf jlkiseylknorkckcrc cffrnfr enf `frfinfer. Mozfk cf mu cffr troksjfre aoregecfeifknfr enf `frfinfer.

    Jlkiseylknor ioykoi ilcco afraok`e mer sroco yoznomener. Aotto ioykoiilc mercfk jozno clsyoyo mnkfmener. kfhne lnok jlkiseylknorkmnkhfhfsecer.

    ]fturk cfehe jlkiseylkcok cffr ckcrhfye sonoyok vf ornc yfrfcffre ckcrfk cfehcer. ]fturk cfeheke afraok`e mer ejocf eznfyfmener.

    rfturk (ejocf)9

    orok jlkiseylk ckfk cffre ceiiotf onhoho aususukco sfrmfstter.Jlkiseylkco rfturk yokko cffr yozhoi co zlruknu cfencer mu curuhco

    orok jlkiseylko cffr ckcrnhfz.

    Jlkiseylk, ornc klitoyo cffr yo co aezhft ckcrfk prl`rohporos lnoroi tokhnokomener. Iunnokh ohog mer enfhek li si tfirorfcenhfsekcfk clnoy poiftnfkhfseke sonohoi vf iunnokh okkco socfgfmu poiftek ock iunnokhoitr. Mu yktfh enf oyk ee yopok mer prl`rohporos li cfjo yoznogoko mer cfjo yoznp li yfrcf iunnokhosukunhu lnur.

    Mu yktfhnf yopson prl`rohnor `fneterfmenersekez. G cene enf fk protei

    prl`roh yozhokk ylnu jlkiseylknorcok `ffr. zfnneinf li yluk vfiorhoi prl`rohnork yoznhoskco afh yozh ilnoynotrhoi afh cfoknonrn orttrhoi eek jlkiseylk iunnokh slk cfrfgf ecfoncer. Oyrgoslruknor zhnfrifk jlkiseylkfn iovrohnorno zhnfhfi slrukuk ilnoyzhnfkfmenhfsekf kfcfk lnogoitr.

    Mer Jlkiseylk tokh `fkfn lnoroi oocoie yopyo soaepter.

    Yjlkiseylkuk trX jlkiseylkuk\oce(YT?Y,T=..XX)Ycfesifktr T?9cf`esifktr T=9

    ................X{

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    1/?7.4=.=4?= ?:2?5244 64

    Jlkiseylko oet cfeifknfr vf tokhnorJlkiseylko oet yopnogoi enfhnfr vf ilhutnorYrfturk cffrX9}

    Mu tokhco jlkiseylk ffr mer cffr ckcrhylr esf jlkiseylkuk\trcfkenfk ish ml lnomenfgfe `eme ffr jlkiseylk porohftrf onhylr esf T?,T= `eme ejocfnfrf eateyo munukhohoitocr.

    Ffr jlkiseylk cffr ckcrhylr esf fk slkcoie rfturk cffrejocfsekf`frfi ylitur. muroco cffrcfkenfk ejocf jlkiseylkuk ckcrfgfe cffresfhmlnezf fcfr.

    Ffr jlkiseylkuk porohftrfnfre yli esf mu porohftrfnfrek tr tokhyopnhoz. Muroco tokhnokok mu porohftrfnfr socfgf jlkiseylk efresekcf

    iunnoknomener.Torohftrf2 Mer jlkiseylkco jorin cffrnfr eek jorin slkunor fncffthfheze sonoyok vf jlkiseylko `kcfrenfk cffrnfrf vfrenfk occr.

    Jlkiseylk porohftrfnfre aoiikco

    u oko iocor `rchz jlkiseylknor porohftrfnfre cffrnfornhnorc. Mu yktfhf gonn my vonuf cfker vf ornok jlkiseylk thporohftrfnfr eek cffre onr vf zfn yfrfn mer cfeifkf ilpyosk

    lnuturur. Mu enfhcf l cfeifkek ocrfse iunnoknhoz. Mu enfhcfk cf mujlkiseylkuk mu cfeifkek cffreke cfeterfhfyfgfe `eme mer slku ior.Afr jlkiseylk mu tep cfeifknfre vf ifkce yfrfnekcf tokhnokhcfeifknfre socfgf ifkce efresekcf cfeterfmener.

    Mer Jlkiseylk porohftrfse lnoroi mer cezekek oc iunnoknckco mu cezekek`ere ocrfse jlkiseylko enftener. Cezekek th cffrnfre jlkiseylkoilpyonokhoz. Jlkiseylk cezekek fnfhoknork ekces cffrnfre enf horejfte enfroaotnino cfeterfmener. Murocok u slku iornomener cezenfr rfjfrokscffre enf yoke ocrfs enf jlkiseylko enftenernfr. Wlkroie ilkunorhzco

    eorftenfrek iunnokhkk oknotnhos enf mu ilku coao kft lnoroioinokogoitr.

    Mu oroco cfeifk soyco porohftrf onok jlkiseylknor plrtotej lnoroiyozhokk mer ylnu hoonfsfj munukhuylr. Mu kfcfknf cf cfeifk soycocffrnfrcfk fk myk vfyo fk ik munomenfgfi jlkiseylkuyozhoi Gcf yozhoi li co ilnoy lnhoso frfi.

    Ontrho ==

    Ifkcesekf `kcfrenfk o vf m `eme eie cfeifkek efresekcfie cffrnfre

    fverfk swop ockco mer jlkiseylk tokhnoykz. Mu tokhk prl`roh eekcfkosn iunnoknogok `stfrekez.

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    1/?7.4=.=4?= ?:2?5244 6?

    Ontrho =7

    Ifkcesekf `kcfrenfk mer tohsoy cezeseke sronoyoroi oroko `freckcrfk jlkiseylku G cene enf `fneterekez.

    Cfeifknfrek ftiene lncuu mn`fnfrG Mnli yopn mer prl`rohnoho cenecer. Mu kfcfknf cfeifknfr osnkcotokhnokcinor mnli efresekcf iunnoknomenernfr. Mer moio mnli efresekcf lcfeifk tokhsz iomun fcener. Mer cfeifkek mer mnli efresekcf tokhnokptokhnokhoc cfrnfhf oohoskco oknonomener. Ffr Wyktox Frrlraotos enf iornonp ukcfjekfc voreomnf `eme aotonor onkylrso cfeifktokhnokhoh vfyo yokn mnlinorco mu cfeifk iunnoknhoyo onnylrcfhfiter.

    Mu tokhnoro `rf "Afr cfeifk socfgf tokhnokc jlkiseylkefresekcf iunnoknomener"cfhfiter. Okgoi @nlmon lnoroi tokhnokhcfeifknfrekez vor esf mu cfeifk th jlkiseylknorkz efresekcfiunnoknomener.

    @fkfn Cfeifknfr

    G Trl`roh mer `rup aorege kfskfcfk lnuur. Muknor mozfk cfeifknfrmozfk cf jlkiseylknorcr. Mer jlkiseylkuk eekcf tokhnokok cfeifknfr

    yfrfn cfeifk lnoroi ocnokcrnrnor. Moz curuhnorco muknoro coaenecfeifk cf cfkfmener. Jlkiseylknork ckco tokhnokok cfeifknfr@fkfn cfeifknfr lnup mozfk cf aorege cfeifk lnoroi ocnokcrnrnor.

    @fkfn cfeifknfr th jlkiseylknor torojkcok freenfmener lncuukcokjlkiseylk porohftrfnfrekf vf cffr ckcrhf hfiokezhosko ontfrkotejlnoroi iunnoknomener. Mer jlkiseylk `fkfnneinf `fkfn lnoroi tokhnokhafraok`e mer cfeifkf ock okhoi surfteynf frefmener.

    Ffr jlkiseylknor oroskco lrtoi iunnoknogoi cfeifknfr li esf uzukporohftrf nestfnfre yfrekf `fkfn cfeifk tokhnohonor coao ftienelnogoitr. Okgoi mu co jlkiseylkuk plrtotejneeke vf prl`roh yopsilkusukco cokin mfnertfgfiter. Mu fiencf jlkiseylknor oroskco merli vfre mo munukogoitr.

    @fkfn cfeifknfrek iunnoknhoskk tfhfn kfcfknfrekcfk mere cf cfeifkcffrnfrekek sjrnokhosk sonohoitr.

    @fkfn lnoroi tokhnokh mer cfeifk th cefr jlkiseylknorco tokhnlnogo `eme prl`rohk onhoskk mettee oko iocorco mfnnfitf tutunurnor.Aonmuie mer jlkiseylkuk eekcf tokhnokh yfrfn cfeifkekez esf

    jlkiseylko `erceekezcf mfnnff onkr vf jlkiseylkcok ikgoyo iocor

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    mfnnfitf ionr. Mu kfcfknf eie yo co coao jozno jlkiseylk vfrenfrepoynoogoiso mu vfrenfrek `fkfn cfeifknfr enf poynonhos hhikcr.

    fxtfrk cfeifknfr

    Ffr mer prl`roh mercfk jozno clsyo zfrekcf tokhnokhso vf mozcfeifknfr th clsyonorco iunnoknomenhfi vf freenfmenhfi esteylrnorso mucfeifknfr fxtfrk lnoroi tokhnokrnor. rkfek hoek jlkiseylkukuklncuu mer prl`roh mnlukco `fkfn cfeifknfr czfyekcf

    ekt ionfh9 finekcf mer tokh yoph lnsokz vf cefr mer prl`rohclsyoskcok mu cfeifke iunnokhoi estfsfkez l clsyoco u fiencftokhnohokz `frfifgfiter.

    fxtfrk ekt ionfh9

    mu fiencf mu cfeifkek mu clsyo eekcf cfen cefr mer clsyo eekcftokhnokh lncuuku vf mer eneie eekcf lncuuku `rfmenersekez.

    stoteg cfeifknfr

    stoteg tokh fxtfrk `eme mer cfeifkekezf zfn mer sjot iotok cfehcer.

    Wtoteg cfeifknfr `fkfn tokhnokomenceinfre `eme yfrfn cf tokhnokomenernfr.Ufrfn lnoroi tokhnokok mer stoteg cfeifk socfgf l jlkiseylk eekcfiunnoknomener vf cefr jlkiseylknorco tokkhoz okgoi cefr yfrfncfeifknfrcfk jorin lnoroi cfeifk jlkiseylk metehekcf mfnnfitfkotnhoz. Aotto efresekcfie cffr coae stotei lnoroi ilrukur. Jlkiseylkukslkroie tfiror ornhoskco eekcfie cffr iunnoknr. Mu co u oknoho`fner2 yfrfn stoteg mer cfeifk zfn oho iong mfnnfi soaonor lnuturur.

    Mu fiencf tokhnokhoi estfkfk mer cfeifk eek kkf stoteg ejocfsekeilyokz yftfrne lnogoitr.

    stoteg ekt i9

    stoteg gaor mujY?=1X `eme.

    rf`estfr cfeifknfr

    rf`estfr tokh enf vfrenfk mer cfeifk prl`roh torojkcok sioiunnoknogoitr oknohko `fner. Ffr hhik lnurso mu cfeifknfrmen`esoyork yozhonorko (rf`estfr) yfrnfterener. Mu soyfcf mu prl`rohnorafh azn afh cf coao ii lnurnor. ]f`estfr tokh enf yopnok mercfeifk tokhnoho sotr u fiencfcer2

    rf`estfr ekt x9

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    rf`estfr gaor aorj9

    Vy`unohoco rf`estfr cfeifknfre enf en`ene lnoroi mer toih istnohonormunukogoitr. Mu istnohonor clkokhcok ioykoinokoko istnohonorcr.Mer jlkiseylkuk eekcf socfgf merio tokf cfeifk rf`estfr lnoroi

    oyornokomener. Oyrgo th trnfrek rf`estfr lnomenhfse hhik cfencer.Vy`uk lnhoyok tokhnor eek rf`estfr ejocfse iunnoknso menf cfrnfyegetorojkcok `rnhfz. Oyrgo mu istnohonor hoiekocok hoiekoyocfefmenfgfiter.

    Mnli Uops

    G Tosgon, TN/E vf on`lncf lncuu `eme e ef mnlinork tokhnokomenceeyopco mer cen cfencer. G cenekcf th jlkiseylknor oyk czfycftokhnokrnor vf e ef lnohoznor. Okgoi mu torz mer tokh cfeifknfr eeksz ilkusucur. Uoke cfeifknfr e ef mnlinorco tokhnokomenernfr. Zf mumnlinor ihf poroktfze enf mfnernfker. Ffr mer mnli eekcf tokhnokok mercfeifk vor esf l cfeifk l mnluk slkuko iocor `ffrnecer. Mer cfeifkmer mnli eekcf tokhnokh esf vf mer st mnlito co tokhn esf onttoie mnlo`erenceekcf yfke tokh `ffrne lnur cefr tokh mu mnli metekgfyf iocormfinftener.

    ni cffr otoho

    Mu mnh tokhnockz cfeifknfrf kosn eni cffr otoyomenfgfekeze vfyoeni cffr otohozsokz kfnfrek vorsoynogok oknotr.

    fxtfrk vf stoteg cfeifknfr sezek torojkzcok oyrgo mer tokh yopnhocesf 4 cffre enf ltlhotei lnoroi monornor. ]f`estfr vf cefr cfeifknfrcfeni cffr otoh enfhe yopnhoc esf cfeifkek cffre rost `fnf mer cffrlnur.

    Moset cfeifknfrf tokhnokcinor okco eni cffr otohos yopomenersekez.]f`estfr cfeifknfr vf klrhon cfeifknfrf eni cffr otokrifk somet lnhozlruknunuu munukhohoitocr. Sokhn cffrnfrnf lnuhu lnok afraok`emer ejocf cf cffr otoho eek iunnoknomener.

    zyekfnfhf (]fgurselk)

    G jlkiseylknor zyekfne lnoroi iunnoknomenernfr. Uoke mer G jlkiseylkuifkceke clrucok yo co clnoyn lnoroi oromener. Fk inosei rkfinfrekcfkmere joitreyfn afsopnoho lnoroi `stfrenfmener. ki joitryfn tokh`frfe u fiencf oknotnomenhfitfcer

    rkfi ?7

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    K!8K*(K-?)! Mu enfh k ? lnukgoyo iocor cfvoh fcfgfi fiencf onomener.K mer lncuukco joitryfn cffre zotfk ? lnogoitr.

    #ekgnucf >stcel.a;

    ekt joi(ekt k){ej (k88?) rfturk ?9fnsf rfturk k*joi(k-?) 9

    }

    hoek(){ekt k9

    prektj(Joitryfne afsopnokogoi cffre `erekez)9sgokj(%c,&k)9

    prektj(K cffrekek joitryfke8%c^k,joi(k))9

    }

    Mu prl`rohco k cffre joitryfne afsopnokhoi zfrf joi jlkiseylkuko`kcfreneylr. Okgoi joi jlkiseylku co ifkceseke tfiror ororoi joitryfneafsopnohoyo ontk `rfmenersekez.

    Ontrho =3

    Inovyfcfk `erenfk afraok`e mer toh soykk eienei soy sestfhekcfieiornk firoko yozomenfgfi jlkiseylku zyekfne lnoroi tokhnoykz.

    G cene kenfhgese

    G cene cenek zfnneinfreke `fkenfthfi eek mer toih cfehnfr iunnokr. Muknorokenfhge ilhutnor cfker.

    Clsyo Coaen fthf

    Mer toih jlkiseylknork prltltep tokhnork vf cfjekf enf yopnh mer toihtokhnor prl`roho coaen fcfmenhfi eek ekgnucf ockcoie ilhuttur.

    #ekgnucf clsyo

    finekcf iunnoknr vf oc clsyo lnok clsyokk eekcfie th men`enfre muprl`roho coaen fcfr. Afhfk afhfk afr G prl`rohkco ? yoco mfnie =sotr mu fiencfie tokhnor `rhfi hhikcr. Myi prl`rohnorco mfnnemer toih tokhnor th yorchg clsyonorco `rfmenhfi eek ekgnucf enftokhnoh lnomenfgfekez `fkfn mer tokh clsyosk th clsyonoro coaenfcfrfi tokhnork lrtoink `oroktenfhe lnomenersekez.

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    Hoirl vfyo sfhmlnei somet tokhnoho

    #cfjekf FZFS ?

    finekcfie mer tokh fk moset sfhmlnei somet soyy tokhnor. Mu tokh enf

    prl`rohhzco iunnoknhoi zfrf FZFS ockco sfhmlnei mer somettokhnoh lnuruz. Cfrnfyege prl`roh cfrnfrifk cfjekf ejocfse yokkcotokhnoh lnomenfgfekez somete prl`rohco yfrnfterer vf l ejocf yfrekfsomete ilyoroi prl`rohk cfrnfkhfseke sonor.

    Mu ortnor ontkco u fiencf yopomenfgfekez tokhnorco en`ene onhkyopnhosk sonornor.

    #cfjekf iorf(x) x * x

    finekcfie tokh prl`roh cfrnfkekgf iorf(x) yfrekf x*x ilkhosksonoyogoitr.

    Ontrho =6

    Ifkcesekf `kcfrenfk k cffre eek j(x)88

    k

    x

    x

    ?

    jlkiseylkuku afsopnoyp

    oroko ckcrfk jlkiseylku G cene enf yozkz.

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    CezenfrMozfk moset cfeifknfr mer toih slruknork znhfse eek yftfrnelnhoznor. rkfek eie hotresek tlpnohk munomenfgfi mer prl`roh moset

    cfeifknfr enf yoznohoz. Uo co mer ceze cffr zfrekcf sronohoyopomenfgfi prl`roh, mer ceze soy efresekcf estfkenfk cffre munomenfgfiprl`roh yekf moset cfeifknfr enf yoznohoz.

    Mu tep prl`rohnor eek aotto mer li mfkzfre prl`roh eek ceze vfyo hotrestokhnor yopomenhfkez `frfihfitfcer.

    Ceze Kfcer