Algoritmos e Lógica de Programação

  

Ajgfrhtlfs bJþghnamb Prfgralaçîf

 

 

Ajgfrhtlfsbjþghnas mbprfgralaçîf

LarnhfAparbnhmfArtbrf TaobssaNamao^nebddbr

 

 

©3015pfrBmhtfrabMhstrhcuhmfraBmunanhfoaj^.A. ]fmfsfsmhrbhtfsrbsbrvamfs.Oboeulapartbmbstapucjhnaçîfpfmbrásbrrbprfmuzhmafutraoslhthmambquajqubr lfmffupfrquajqubrfutrflbhf,bjbtrýohnffulbnãohnf,honjuhomfdftfnþpha,gravaçîffuquajqubrfutrfthpf mbshstblambarlazboalbotfbtraoslhssîfmbhodfrlaçîf,sblprèvhaautfrhzaçîf,pfrbsnrhtf,maBmhtfrab MhstrhcuhmfraBmunanhfoaj^.A.

Prbshmbotb

SfmrhgfGajhomf Thnb-PrbshmbotbAnamélhnfmbGramuaçîfbmbBmunaçîfCáshna

LárhfGehfIùohfr NfosbjefAnamélhnf

AoaJunhaIaokfvhnCarmuneh NalhjaNarmfsfSftbjja MaohbjjyOuobsAomrambOfè GrashbjbAparbnhmaJfurboçf HsacbjNrhsthoaNeagasCarcho JhmhaobNrhsthoaThvajmhohFjf ]eathaobNrhsthoa ]eathaobNrhsthoamfs^aotfs mfs^aotfsmbNarvajefS mbNarvajefShcbhrf hcbhrf Sbvhsîf]ènohna

SuyDjávhfmbFjhvbhra Bmhtfrhaj

NalhjaNarmfsfSftbjja(Mhrbtfra) JhmhaobNrhsthoaThvajmhohFjf(Gbrbotb) BjlhrNarvajefma^hjva(Nffrmboamfr) JbtìnhaCbotfPhbrfoh(Nffrmboamfra) SboataIèsshnaGajmhof(Nffrmboamfra)

MamfsHotbroanhfoahsmbNatajfgaçîfoaPucjhn MamfsHotbroanhfoahsmbNatajfgaç îfoaPucjhnaçîf(NHP) açîf(NHP)

 Artbrf,Larnhf Artbrf, LarnhfAparbnhmf Larnhf Aparbnhmf A754a Ajgfrhtlfsb Ajgfrhtlfs b bjþghnas jþghnasmb jþghnas mbprfgralaçîf mb prfgralaçîf/ prfgralaçîf / /Larnhf LarnhfAparbnhmf Larnhf Aparbnhmf Artbrf,TaobssaNamao^nebffbr.„Jfomrhoa9Bmhtfrab MhstrhcuhmfraBmunanhfoaj^.A.,3015. Mhstr hcuhmfraBmunanhfoaj^.A.,3015.  314p. 314 p.  

H^CO875-52-233-0705-2 1.Ajgfrhtlfs.3 .Prfgralaçîf.H.Ar tbrf,Lar tbrf,Larnhf nhf Aparbnhmf...HH. Aparbnhmf HH.^nebffbr, HH.^nebffbr, ^nebffbr,TaobssaNamao.HHH. TaobssaNamao.HHH. ]ìtujf. NMM400

]ealhrhsLaotfvaohNSC-5/8=81

3015 BmhtfrabMhstrhcuhmf Bmhtfrab MhstrhcuhmfraBmunanhfoaj^.A. Mhstrhcuhmf raBmunanhfoaj^.A. AvbohmaParhs,472„Pa rqubSbshmbonhajIfîfPhza rqubSbshmbonhaj IfîfPhza NBP9540=1-100”Jfomrhoa”PS b-lahj9bmhtfra.bmunanh b-lahj9 [email protected] [email protected] Eflbpagb9ettp9//www.krftfo Eflbpagb9 ettp9//www.krftfo.nfl.cr/ ettp9//www.krftfo .nfl.cr/

 

 

^ulárhf Rohmamb1|Jþghnambprfgralaçîf

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^bçîf1.1-Mbdhohçòbsmbjþghna

8

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Rohmamb3|Bjblbotfsmbajgfrhtlfs

22

^bçîf3.1-Bxbnuçîfsbqubonhajbbstruturasmbmbnhsîf

27

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^bçîf3.>-Bstruturambmamfs

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148

^bçîf=.1-Prfgralaçîfbduoçòbsnflvbtfrbs ^bçîf=.1- Prfgralaçîfbduoçòbsnflvbtfrbs

17 171 1

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15 155 5

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301 30 1

 

 

 

Pajavrasmfautfr Narfajuof! ^biacbl-vhomfàmhsnhpjhoambajgfrhtlfsbjþghnambprfgralaçîf. ^biacbl-vhomfàmhsnhpjhoambajgfrhtlfsb jþghnambprfgralaçîf. È prfvávbj qub vfné iá tboea sb mbparamf nfl ula jhoma nfostruçîf,ulbmhdìnhfdacujfsfqublahsparbnbulafcrambartb, nfostruçîf,ulbmhdìnhfdacujfsfqublahspa rbnbulafcrambartb, nbrtf6TbiafnasfmfLA^P(LusbumbArtbmb^îfPaujf),ulafcra maarquhtbtaJhoaCfCarmh.Bssafcrabonaotapbjfpjaobialbotfb aumánhablqubdfralcasbamfsfsnájnujfslhounhfsfs.]ajfcra bstásuspbosapfrquatrfnfjuoas,jhgamaspfrulavhgaqubpbrnfrrb bstásuspbosapfrquatrfnfjuoas,jhg amaspfrulavhgaqubpbrnfrrb tfmffprèmhf,tblnflfmbstaqubulvîfmbjuzhlprbss hfoaotbb ulpè-mhrbhtfmbfhtflbtrfs. Bod odhl hl,, f qub bs bsssa gra raom omb b fcr craa tb tbl l a vbr br nf nfl l ajg jgf frhtl rhtlf fs b jþghnambprfgralaçîf6Blalcfsfsnasfs(fcrassfdhsthnamasb prf prfgra gralaç laçîf îf), ), sîf sîf obn obnbss bssárh árhfs fs pja pjaobi obial albotf botfs s b ul pbo pbosal salbot botf f jþghnfparaasuanfostruçîf.AsshlnflffprfibtfmfLA^Ptbvb ul ulaa pjaot jaotaa nf nfl l tf tfm mfs fs fs sbu buss ná nájn jnu ujf jfs s para ra qub ub ne nebg bgas asssb af rbsujtamfdhoaj,ulprfgralambnflputamfrp rbsujtamfdhoaj,ulprfgralam bnflputamfrprbnhsasbrpbosamf rbnhsasbrpbosamfb b bstruturamfparaajnaoçarfsbufcibthvf,usaomfnflfhostrulbotf ajþghnambprfgralaçîfpfrlbhfmbajgfrhtlfs ajþghnambprfgralaçîfpfrl bhfmbajgfrhtlfs.. Para f su Para sunbs nbssf sf ma ma nfl nflprb prbbos bosîf îf mbs mbstb tb la latbr tbrhaj haj, , va valfs lfs mhv mhvhmh hmh--jf -jf bl bl qu quat atrf rf uo uohm hmam ambs bs, , na nama ma ul ula a nf nfl l fc fcib ibth thvf vfs s bs bspb pbnì nìdh dhnf nfs s b nf nflp lpbt btéon éonha has s qu qub b rb rbsu sujt jtal al bl bl ap aprb rbom ombr br b assh asshlh lhja jar r a jþ jþgh ghna na, , fs ajgfrhtlfsbfsbjblbotfsmbprfgralaçîf. Oa Oa pr prhl hlbh bhra ra uo uohm hmam amb, b, vf vfné né hr hrá á nf nflp lprb rbbo bomb mbr r b sb sbrá rá na napa paz z mb rbajhzarajþghnambprfgralaçîf.Jþg rbajhzarajþghnambprf gralaçîf.Jþghnabssaqubmbs hnabssaqubmbsbovfjvbrábl bovfjvbrábl vfné,ajuof,eachjhmamb vfné,ajuof, eachjhmambs smbbonfotrarsfjuçòbs mbbonfotrarsfjuçòbsparafs parafslahs lahsmhvbrsfs mhvbrsfs pr prfc fcjb jbla las. s. Ah Ahom oma a ob obst sta a uo uohm hmam amb, b, vf vfné né bs bstu tuma mará rá fs fs nf nfon onbht bhtfs fs mb ajgfrhtlfsbsuasnarantbrìsthnas. Oasbguomauohmamb,vfnéhráaoajhsarbapjhnarfsbjblbotfsmb ajgfrhtlf ajgfrh tlfs; s; taj taj apr aprbom bomhza hzamf mf f nfo nfomu muzhr zhrá á a rbs rbsfjv fjvbr br prf prfcjb cjbla las s mb anfrmfnflasnarantbrìsthnasmaprfgralaçîf. anfrmfnflasnarantbrìsthnasmaprf gralaçîf. Oauohmambtrés,vfnéhránflprbbombrbapjhnarfsnfonbhtfs mb mbprf prfgra grala laçîf çîf uth uthjhz jhzaom aomf fa ajho jhogua guagbl gbl N, N,pa para rahss hssf, f, sbr sbrá áprb prbnhs nhsf f tracajearnflabstruturambnfomhnhfoahsbmbrbpbthçîf.

 

 

Bbonbrraomf,auohmambquatrftblnflffcibthvfapjhnara

prfgralaçîfuthjhzaomf9vbtfrbs, prfgralaçî futhjhzaomf9vbtfrbs,latrhzbs,duoçòbsbrbnurshvhmamb. latrhzbs,duoçòbsbrbnurshvhmamb. Asuambmhnaçîfbsbupftbonhajsbrîfdatfrbsmbnhshvfsparanrhar prfgralasqubpfssalsfjunhfoarmhvbrsfsprfcjblasmfsbumhaamha.

Èhssf!]umfluhtfdasnhoaotb! Cfosbstumfsbcfasfrtb!

 

Rohmamb1

 

Jþghnambprfgralaçîf Nfovhtbafbstumf

Narf Na rfaju ajuof, of, hoh hohnha nhalfs lfs bss bssa a uohma uohmamb mbap aprbs rbsbota botaomf omf a vf vfné né as mbd bdho hohç hçò òbs bs mb jþ jþg ghn hnaa, fs bjbl bjblbo botf tfss du duom omal albo bota tahs hs para pr prfg fgra rala laçî çîf f b as as rb rbpr prbs bsbo bota taçò çòbs bs mf mfs s ajgf ajgfrh rhtl tlfs fs. . Qu Quao aomf mf dajalfsbljþghna,várhfspbosalbotfsofsvélàlbotb,adhoaj mbnfotas mbnfotas,f ,fofss ofssfmhaè fmhaèrfmb rfmbamfmbjþghna amfmbjþghnab bprfnb prfnbmhlbo mhlbotfs tfs ajgfrìtlhnfs.Tfnémbvbbstarsbpbrguotaomf9nflfa ajgfrìtlhnfs.Tfnémbvbbstarsbpbrgu otaomf9nflfasshl6 sshl6 Hlagho Hlag hob b vf vfné né of of hoì hoình nhf f mf mf sb sbu u mh mha9 a9 vf vfné né pr prbnh bnhsa sa anfr anfrma marr paramarhoìnhfasuastarbdas,nbrtf6Hssfèulajþghnasbguhma mbulanfomhçîf.Apþsbstarnbrtfmbqubanfrmfubmbqub f mh mha a ho hohn hnhf hfu, u, f pr prfs fssb sbgu guhl hlbo botf tf agfr agfra a è ula ula sbqu sbquéo éonha nha mb ajg ajgfrh frhtlf tlfs, s, qua quaomf omf par para a nam nama a tar tarbda bda eav eavbrá brá ula ula rft rfthoa hoa.. Pfr bxblpjf9vfnéhrásbjbvaotar bxblpjf9vfnéhrásb jbvaotar,,nfjfnarf nfjfnarfnehob nehobjf, jf,hraf hrafcaoebhr caoebhrf, f, trfn trfnar ar mb mb rf rfup upa, a, tf tfla lar r na nadè dè b sb sb pr prbp bpar arar ar pa para ra ma mar r ho hoình ìnhf fàs às tarbdas tarbda smf mf mha mha..Pbr Pbrnbc nbcb bqu qub bulajgf ulajgfrht rhtlfè lfèulnfoi ulnfoiuot uotfmb fmb hos hostru truçòb çòbs s qu qub b mbv mbvblf blfs s daz dazbr br pa para ra rba rbajhz jhzar ar ula ula açî açîf6 f6 Pfh Pfhss bo botî tîf, f, tu tumf mf hs hssf sf è lu luht htf f da dasn snhoa hoaot otb b b vfné vfné hrá hrá ap apjhjhna nar r bs bssa sass mbdhohçòbsoaprbparaçîfbprfgralaçîfmbnflputamfrbs. Luhtfcbl,aparthrmbstauohmambvfnéhránflprbbombrb sbrnapazmbrbajhzarajþghnambprfgralaçîfofsbumhaamha. Pa Para ra ta taot otf, f, va valf lfs s af af of ofss ssf f nf nfot otbx bxtf tf mb mb ap aprb rbom omhz hzag agbl bl nflaKrfVBogboearhas,ulablprbsambrboflboaárbamb bogboearhanhvhj,dalfsapfrsuaalpjaárbambatuaçîf,qub mbsbovfjvbmbsmbulshlpjbsprfibtfatèfsblprbbomhlbotfs mbsbovfjvbmbsmbulshlpjbsprfibtfatèfsblprbbom hlbotfs lahsarrfiamfs.Fsbogboebhrfsmablprbsarbajhzalmhvbrsfs nájnujfslatbláthnfsb,oalahfrhamasvbzbs,dazblusfmb najnujamfrasbpjaohjeasbjbtrýohnas. Tfné, Tfné , pf pfrt rtam amfr fr mb mb ul ul pb pbos osal albo botf tf nf nflp lput utan anhf hfoa oaj,j, df dfhh nfotratamf para dazbr partb mbstb thlb mb bogboebhrfs, pfrèl,ulalhssîfdfhmamapbjfsbugbstfrmhrbtf9nrharul pbosal pbos albo botf tf jþ jþgh ghnf nf pa para ra qu qub b fs fs bogb bogboe oebh bhrf rfs s du dutu tura ralb lbot otb b

R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb  



7

pfssalp prrfgra ral larf fsssb sbus vbrs brsfsn nu fsl laatbl t nfs. Blhssîfmamaèlhssîfqubmbvbrásbrnul Blhssîfmamaèlhssîf qubmbvbrásbrnulprhma! prhma! Of Of pr prhl hlbh bhrf rf lf lflb lbot otf, f, vfné vfné mb mbvb vbrá rá trac tracaj ajea ear r nf nfl l sbus sbus nfjbgasbogboebhrfsfusfmajþghnaparasfjuçîfmbprfcjblas, nfjbgasbogboebhrfsfusfmajþghnaparasfjuçîf mbprfcjblas, aapjhnaçîfmajþghnaofmhaamhabfranhfnìohfjþghnf. Bl sbguhma, vfné hrá aprbsbotar as mbdhohçòbs b a

 

hvarhávbhs,nfostaotbsbsbusfpbramfrbs. lpfrtãonha mfs ajgfrhtlfs, asshl nf nfl lf a uthjhzaçîf mb Para dhoajhzar a lhssîf, vfné mbhxará mb dfrla njara nf nflf lf du duon onhf hfoa oa a jhog jhogua uagb gbl l oa oatu tura raj,j, as as nara narantb ntbrì rìst sthn hnas as mf mfss djuxfgralas,psbumfnþmhgfsbapjhnarathvhmambspráthnaspara sfjuçòbsmbprfcjblasmbjþghna. Pfhscbl,atbotb-sbaf Pfhscbl,atbotb-sbafsnfonbhtfsqubsbrî snfonbhtfsqubsbrîfaprbsbotamfs faprbsbotamfs bsbiasblprbbxpjframfrmbnfoebnhlbotfs. Cfasfrtbbþthlfsbstumfs!

5  

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf

 .

 

Mbdhohçòbsmbjþghna Mhájfgfacbrtf Narfajuof, A sht shtuaç uaçîf îf-pr -prfcj fcjbla bla mbs mbsta tasbç sbçîf îf tbl tbl pf pfr r fc fcibth ibthvf vf tra tracaj cajear ear f ranhfnìohfjþghnfmbsbovfjvhmfmuraotbfmbsbovfjvhlbotfmf‚Oîf pfmbdajtar“.AKrfVBogboearhas,ulablprbsambrboflboaárba mabogboearha,anacfumbnfotratá-jf,btîfcrbvbiájebdfhmama ulalhssîf9aiumarfssbusnfjbgasbogboebhrfsabonfotrarula dfrlaqubpfssaaiumá-jfsoabxbnuçîfmfsnájnujfslatbláthnfs mbsbovfjvhmfsoaslahsmhvbrsasárbasmabogboearha.Parahssf,vfné mbvbrámbsbovf mbvbrámbsbovfjvbrnflfs jvbrnflfsbogboebhrfsfpbos bogboebhrfsfpbosalbotfjþghnf albotfjþghnfpara para fmbsbovfjvhlbotfmb sfdtwarbs sfdtwarbsparasfjuçòbsmfsnájnujfs. Nf Nflf lf pf pfotf otf mb pa parth rthma, ma, vf vfné né mbv mbvbrá brá tra traca cajea jear r f pbo pbosal salbot botf f jþghnfmfsnfjbgasbogboebhrfs.Parataj,tbrámbaiumá-jfsarbsfjvbr jþghnfmfsnfjbgasbogboebhrfs.Parataj,tbrámb aiumá-jfsarbsfjvbr fprfcjblabonfotramfblulmfssbtfrbsmablprbsa9ulrfcý tbla tbladuoçîfmb duoçîfmbblphjear blphjearlatbrhahs latbrhahsnfl nflas assbguhotb sbguhotbs snarantb narantbrìsthnas9 rìsthnas9 -Fslatbrhahslahspbsamfsoîfpfmbldhnarsfcrbfslatbrhahs lahsjbvbs. - As phjeas (P1 P1,, P3 b P>) mbvbl bl tbr of of láxhlf > dhjbh bhrras mb latbrhahs. -Fgajpîfmhspòbapboasmb>jfnahs(A,CbN)mblfvhlbotaçòbs mfslatbrhahs,fombmbvbltraoshtarbdhnarmhspfstfsofùjthlfjfnaj (N)parafprþxhlfprfnbssfmbjfg (N)parafprþxhlf prfnbssfmbjfgìsthnamablprbsa ìsthnamablprbsa.. Aprfpfsta,botîf,ènrharulalaobhrambfthlhzarftracajef mfrfcýparaqubbjbrbajhzbatarbdauthjhzaomfalbofrquaothmamb pf pfss ssìv ìvbj bj mb mb pa pass ssfs fs b, b, nf nfos osbq bqub ubot otbl blbo botb tb, , ul ul lb lbof ofr r tb tblp lpf f oa bxbnuçîfmfprfnbssf.

R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb  

Dhgura1.1|Sfcþthnfvbtfrláquhoa



8

 

A

C

N

Dfotb9 Dfotb 9 Drbbphk. Drbbphk. Mhspf Mhspfoìvb oìvbj j bl9 bl9 :aerbd0 Anbssf bl9>0 sbt.30 sbt.3017. 17.

13

R1-Jþghnambprfgralaçîf R1-Jþghnamb prfgralaçîf

 

Pfrlbhfmbssbranhfnìohffrhghofu-sbaÁjgbcrambCffjbfuÁjgbcra Cffjbaoa.Èsachmfqubbssbthpfmbájgbcraèblcasamfoajþghna choárha.Nflfasshl6Ajþgh choárha.Nflf asshl6Ajþghnachoárha asshl6Ajþgh nachoárhapfssuhmuas nachoárha pfssuhmuas rbprbsbotat rbprbsbotathvhmambs, hvhmambs,

‚dajsf“b‚vbrmambhrf“fu‚0“b‚1“. Blrbjaçîfafssbusfpbramfrbs,sîfm Blrbjaçîfafssbusfpbram frbs,sîfmbdhohmfsAOM,FSbOF bdhohmfsAOM,FSbOF], ], fusbia,B,FRbOÎF,fomb(‚B“)èanfoiuoçîf,(‚FR“),amhsiuoçîf b(OÎF),aobgaçîf. Bxpjhnaomflbjefr,vbrblfsqub9

 

- -Nfoiuoçîf(‚B“)„ Nfoiuoçîf(‚B“)„sflbotbsb sflbotbsbas asmuas muasrbprbsb rbprbsbotathvh otathvhmambsdfrbl mambsdfrbl vbrmambhras,arbspfstasbrávbrmambhra. -Mhsiuoçîf(‚FR“)„^bpbjflbofsulambsuasrbprbsbotathvhma mbs dfrvbrmambhra,arbspfstasbrávbrmambhra. - Obgaçîf (OÎF) „ Quaomf ula rbprbsbotathvhmamb dfr vbrmambhra,arbspfstasbrádajsa,bquaomfularbprbsbotathvhmamb dfrdajsa,arbspfstasbrávbrmambhra. Parabotbombrlbjefrbstajþghnavalfsaoajhsara]acbja1.19 Parabotbombrlbjefrbstajþghnavalfsaoa jhsara]acbja1.19 ]acbja1.1|]acbjaTbrmamb„‚vbrmambhrf“fu‚dajsf“ ]acbja1.1|]acbjaTbrmamb„ ‚vbrmambhrf“fu‚dajsf“ A

C

A (‚B“) C

A (‚FR“) C

OÎF A

OÎF C

Tbrmamb

Tbrmamb

Tbrmamb

Tbrmamb

Dajsf

Dajsf

Tbrmamb

Dajsf

Dajsf

Tbrmamb

Dajsf

Tbrmamb

Dajsf

Tbrmamb

Dajsf

Tbrmamb

Tbrmamb

Dajsf

Dajsf

Dajsf

Dajsf

Dajsf

Tbrmamb

Tbrmamb

Dfotb9bjacframapbjfautfr.

Agfravalfsapjhnaratacbjavbrmambusaomfoùlbrfschoárhfs, nfodfrlblfstraa]acbja1.39 ]acbja1.3|]acbjavbrmamb„‚0“fu‚1“ A

C

A (‚B“) C

A (‚FR“) C

OÎF A

OÎF C

1

1

1

1

0

0

1 0

0 1

0 0

1 1

0 1

1 0

0

0

0

0

1

1

Dfotb9bjacframapbjfautfr.

Tbrblfsagfraajgulasapjhnaçòbs Tbrblfsagfraajg ulasapjhnaçòbs,nflfhjustraa]acbja1.>9 ,nflfhjustraa]acbja1.>9 R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb  

]acbja1.>|Apjhnaçîfmatacbjavbrmamb Duoçîf

Fpbramfr

Bxblpjf

Sbsujtamf

Obgaçîf

OÎF

OÎF (4?>)

Dajsf



1>

Nfo i iu uoçîf

B

(2?1) B (7?5)

Dajsf

Mhs i iu uoçîf

FR

(5?8) F R (8  ? 5)

Tbrmambhrf

 

Dfotb9bjacframapbjfautfr.

Talfspbosaroanfostruçîfmbtrhãogujf,bparatajnfostruçîf oîfpfmblfsusarquajqubrlbmhma,fusbia,vfnémbvbfcbmbnbr àssbguhotbsnfomhçòbs9 -Oanfostruçîfmbultrhãogujfèfcrhgatþrhfqubalbmhmamb quajqubrulmfsjamfssbialbofrqubasflamaslbmhmasmfs futrfsmfhsjamfsblahfrqubfvajfracsfjutfmamhdbrboçabotrb bssaslbmhmas. Ftbstbjþghnfdhnarha9 (a:c+n)B(c:a+n)B(n:a+c)

Ajtbroathvalbotb,ftbstbpfmbrhasbr9 (a?|c-n|)B(c?|a-n|)B(n?|a-c|)

Fcs.9Dfraluthjhzamfslþmujfs(‚|...|“)paraqubasuctraçîfmfs jamfsoîfsbiaulvajfrobgathvf. AoajhsbftrhãogujfmaDhgura1.=9 Dhgura1.=|]rhãogujfrbtãogujf

c

a

n

Dfotb9bjacframapbjfautfr.

Fomb9 a. Bsnfjebr Bsnfjebrf flfmbjf. f lfmbjf.  Bsnfjebra Bsnfjebr a alftfrhzaçîf. lftfrhzaçîf. =.

Bsnfjebra a anfr. nfr. 2. Bsnfjebr Obgfnharadfrlamb dfrlambpagalbotf. dfrlamb pagalbotf. 4. Obgfnhara Paga gar. r. 7. Pa Sbthramamf mfnarrf. mf narrf. 5. Sbthrama Pfmb-sb,talcèl,nrharulajgfrhtl Pfmb-sb,talcèl ,nrharulajgfrhtlfparafsp fparafsprfnbmhlbotfsmb rfnbmhlbotfsmb drhtarulchdb9 R1-Jþghnambprfgralaçîf R1-Jþghnamb prfgralaçîf      32  

1. Pbgaradrhghmbhra,a Pbgaradrhghmbhra,anarob,ftblpbrf narob,ftblpbrfbfþjbf. narob,ftblpbrf bfþjbf. Nfjfnarftblpbrfoa tblpbrfoanarob. tblpbrfoa narob. 3. Nfjfnarf

Anbombrf fdfgf. f dfgf. >. Anbombr Nfjfnaradrhghmbhraof drhghmbhraofdfgf. drhghmbhraof dfgf. =. Nfjfnara Nfjfnarfþjbfoa þjbfoadrhghmbhra. þjbfoa drhghmbhra. 2. Nfjfnarf Aguarmarfaqubnhlbotfmf aqubnhlbotfmfþjbf. aqubnhlbotfmf þjbf. 4. Aguarmarf 7. Nfjfnara Nfjfnaranaroboa naroboadrhghmbhra. naroboa drhghmbhra. 5. Bsnfjebrf Bsnfjebrfpfotfma pfotfmanarob. pfotfma narob.

8. Sbthrar a narob ma drh hmbhra

 . Apagarf fdfgf. f dfgf. 10. Apagar

 

uaomf bsta atho hr f

Pbrn Pb rnbc bcaa qub oî oîf f bx bxhs hstb tb sflb lbot otb b ula la df dfrl rla a mb rb rbaj ajhz hzaar ul ajgfrhtlf,vfnépfmbnrharfutrasdfrlasbsbqu ajgfrhtlf,vfnépfmbnrharfutra sdfrlasbsbquéonhasparafctbrf éonhasparafctbrf lbslfrbsujtamf. Parambsnrbvbrfduonhfoalbotfmbulajgfrhtlf,vfnépfmb usarnflfcasbarbprbsbotaçîfmbduonhfoalbotfmfnflputamfr, nfodfrlblfstraaDhgura1.4. Dhgura1.4|Sbprbsbotaçîfmfduonhfoalbotfmfnflputamfr

Dfotb9bjacframapbjfautfr.

Mb anfrmf nfl bssb lfmbjf, as botramas mfs ajgfrhtlfs sî sîf f na nara rant ntbr brhz hzam amas as pb pbjf jfs s bj bjbl blbot botfs fs (m (mam amfs fs) ) a sb sbrb rbl l df dfro robn bnhm hmfs fs ho hohn hnha hajl jlbo botb tb; ; f pr prfn fnbs bssa salb lbot otf f sb sbrá rá mb mbdho dhohm hmf f pb pbja ja bx bxbn bnuç uçîf îf mas mas aç açòb òbs s sf sfcr crb b fs fs ma mamf mfs s mb mb bo botr tram ama a b sf sfcr crb b ma mamf mfs s ho hotb tbrl rlbm bmhá hárh rhfs fs gbramfsmuraotbbstabxbnuçîf,basaìmasbráasfjuçîfmfprfcjbla gbramfsmuraotbbstabxbnuçîf,bas aìmasbráasfjuçîfmfprfcjbla fuffcibthvfathoghmf. Narfajuof,nebgfuflflbotfmbbotbombrasnarantbrìsthnas ma mas slf lfmhd mhdhna hnaçòb çòbs sb bas as sua suas sap apjhn jhnaçò açòbs bsof ofmbs mbsbov bovfjv fjvhlb hlbotf otf mb mbul ul ajgfrhtlf. Tarhávbhs

Pbosarblvarhávbhsèpbosarblajgfqubpfmbsfdrbrvarhaçòbs, nbrtf6Brbajlbotbèhssflbslf!^bguomfJfpbsbGarnha(3003),ula nbrtf6Brbajlbotbèhssflbslf!^bguomfJfpbs bGarnha(3003),ula 34

R1-Jþghnambprfgralaçîf R1-Jþghnamb prfgralaçîf

 

varhávbjè uljfnajqub jfnajqubarlazboaul arlazboaulnfotbùmfbspbnìdhn nfotbùmfbspbnìdhnf f varhávbjènfoshmbr nfoshmbrama amaul oalblþrhaprhonhpa oalblþrhaprhon hpajjmf mf nfl nflpu putam tamfr. fr. F Fofl oflb bvbl vbl mf mf dat datf fmbqub mbqub bssbjfnajpfmbnfotbrvajfrbsmhdbrbotbs,a‚gfstfmfdrbgués“,hstfè, mfprfgralamfr,mfusuárhfmfprfgrala,fumfprfgralablsh.Bl futraspajavras,fsvajfrbspfmblvarharofjfnajmbarlazboalbotf, pfrhssfbssbsjfnahsrbnbcbrblfoflbmb‚varhávbhs“. Pbsquhsblahs

Ofshtbasbguhrvfnétbráafpfrtuohmambmbrbdfrçarfsbunfoebnhl Ofshtbasbguhrvfnétbráa fpfrtuohmambmbrbdfrçarfsbunfoebnhlbotf fpfrtuohmambmbrbdfrçarfsbunfoebnhl botf sfcrb sfcr b aj ajgf gfrh rhttlfs. s. PBS PBSBHSA BHSA, , Ao Aoa a Pa Pauj uja. a. F qub è ajgfrhtlf. 3008.

Mhspfoìvbj Mhspf oìvbj bl9 :ettps9//ww :ettps9//www.tb w.tbnluomf nluomf.nfl. .nfl.cr/prf cr/prfgralan gralanaf/30 af/3053-f 53-f-qub-b-a gfr lf-. l ?. nbssfbl9 fu . .

 

Pa Para ra dh dhxa xar r f aprb aprbom omhz hzam amf f sfcr sfcrb b varh varháv ávbh bhs s b nfos nfosta taot otbs bs as assh shst sta a f vì vìmb mbf f mh mhsp spfo foìvb ìvbjj bl bl9 9 :ett :ettps ps9/ 9//w /www ww.y .yfu futu tucb cb.n .nfl fl/w /wat atne ne6v 6v0,33),(30).

R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb  

Tarhávbhsmf smfthpfjhtbraj thpfjhtbraj Tarhávbhsmf

^îf varhávbhs qub arlazboal jbtras, oùlbrfs b sìlcfjfs bsp bspbnh bnhahs ahs.. ^î ^îf f nea neala lamfs mfs mb nar narant antbrb brbs s fu, fu, bl hog hogjés jés, , str strhog hog.. Pfr bxblpjf9(Larnhf,Karhoa>5,3017). Tarhávbhsmf Tarhávbh smfthpfjþghnf smf thpfjþghnf

^îfvarhávbhsqubpfmblassulhrulvajfrvbrmambhrffudajsf, pfrbxblpjf9FNarjfstbldhjef6^hlfuOîf. ANarfjèbogboebhra6TbrmambhrffuDajsf. Tarhávbhsmf Tarhávbh smfthpfnfostaotb smf thpfnfostaotb

   37

^bguomfLaozaof(3000),ulanfostaotbpfmbsbrmbdhohmapfr tu faqu fqub  xffubst vb ,fusb a,vfn atr u ulva frpara aqubjavarhávbjbbjaoîfsfdrbajtbraçîfmuraotbnbrtfprfnbmhlbotf. aqubjavarhávbjbbjaoîfsfdrbajtbraçîfmu raotbnbrtfprfnbmhlbotf.

 

PfmblfsnhtarnflfbxblpjffvajfrmbPh,1=,fpbrnbotua Pfmblfsnhtarnflfbxblpjffvajf rmbPh,1=,fpbrnbotuajj mbmbsnfotfmfHO^^,>) <  > b jbvamf a > (>>)

ram(x)

Samhnhaçîf

lfm

Sbstf m a m hvhsîf

10 l  fm > rbsujta b l 1

Mhv

Qufnhbotb m a m  hvhsîf

12 m hv 2 rbsujta b l >

X + x, 7 + 5 

( )

ram(32)ª

*, /, mhv b lfm

=ª  

+b„

 

Dfotb9DfrcbjjfobbBcbrspanebr(3000, Dfotb9DfrcbjjfobbBcbrspane br(3000,p.30). p.30).

Quaomffsfpbramfrbsbsthvbrblmbotrfmalbslaprhfrhmamb, vfné vf né mb mbvb vbrá rá ho hohn hnha har r a sf sfju juçî çîf f ma ma bx bxpr prbs bssî sîf f ma ma bs bsqu qubr brma ma pa para ra a mhrbhta,pfrbxblpjf9 10+=„5 1=„5 4 ]u ]umf mf cbl cbl at atè è aq aquh uh6 6 Ag Agfr fra a vf vfné né va vahh nf nfoe oebn bnbr br fs fs fp fpbra bramf mfrb rbss jþghnfsbrbjanhfoahs. Fpbramfrbsjþghnfs

Na Narf rf ajuo ajuof, f, oa oa pr prhl hlbh bhra ra sb sbçî çîf f mb mbst sta a uo uohm hmam amb b tr trac acaj ajea ealf lfs s a jþghnacffjbaoa.^bguhomfbstblbslfranhfnìohf,vfnéuthjhzaráfs fpbramfrbsjþghnfspararbprbsbotarshtuaçòbsquboî fsîftratávbhs pfrfpbramfrbsarhtlèt pfrfpbramfrbs arhtlèthnfs;vbia hnfs;vbiaoa]acbja oa]acbja1.8fs 1.8fsfpbramfrbs fpbramfrbsjþghnfs uthjhzamfsofsajgfrhtlfs. ]acbja1.8|Fpbramfrbsjþghnfs Fpbramfrbs

Fpbramfrbs

Oîf

Obgaçîf

B

Nfo i iu uoçîf

FR

Mhs i iu uoçîf

Dfotb9amaptamamb9Dfrcbjjf Dfotb9amaptamamb9DfrcbjjfobbBcbrspane obbBcbrspanebr(3000). br(3000).

R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb  

Agfravbiaatacbjavbrmambmfsfpbramfrbsjþghnfs9 ]acbja1.10|]acbjavbrmamb A

C

A (‚B“) C

A (‚FR“) C

OÎF A

OÎF C

Tbrmamb

Tbrmamb

Tbrmamb

Tbrmamb

Dajsf

Dajsf

Tbrmamb

Dajsf

Dajsf

Tbrmamb

Dajsf

Tbrmamb

Dajsf

Tbrmamb

Dajsf

Tbrmamb

Tbrmamb

Dajsf

Dajsf

Dajsf

Dajsf

Dajsf

Tbrmamb

Tbrmamb

Dfotb9bjacframapbjfautfr.

Tbiafbxblpjfasbguhr9 ^bftbrrbofdfrpjaof bmbotrfmbulnfomflìohf,nfostrufa mbotrfmbulnfomflìohf,nfostrufanasa. nasa.

   38

A br uo uota taè è9 9Qu Quao aomf mfv vfu fun nfo fost stru ruhr hra ana nasa sa66 ^flbotbsbftbrrbofdfrpjaof bmbotrfmbulnfomflìohf. Agfra9 ^bftbrrbofdfrpjaof fumbotrfmbulnfomflìohf,nfostruf anasa. Bagfra6Quaomfvfnénfostrþhanasa6 Blalcfsfsnasfs,sbftbrrbofdfrpjaofvfnénfostrþhanasa fusbdfrmbotrfmbulnfomflìohf.

 

Fpbramfrbsrbjanhfoahs

^bguomf Dfrcbjjfob b Bcbrs rsp panebr (3000), fs fpbramfrbs rbjanhfoahssîfuthjhzamfsoarbajhzaçîfmbnflparaçîfbotrbvajfrbs mf mf lb lbsl slf f thpf thpf pr prhl hlht hthv hvf, f, fu fu sb sbia ia, , pf pfmb mbl l sbr sbr rbp rbprb rbsb sbot otam amfs fs pf pfrr varhávbhs,nfostaotbsbatèlbslfblbxprbssòbsarhtlèthnas varhávbhs,nfostaotbsbatèlbslfbl bxprbssòbsarhtlèthnas.. Tbiaoa]acbja1.11fsfpbramfrbsrbjanhfoahs. ]acbja1.11|Fpbramfrbsrbjanhfoahs ]acbja1.11| Fpbramfrbsrbjanhfoahs Fpbramfrbs

Duoçîf

Bxblpjfs

<

Hguaj

A:2, x:y 

?<

Lahfr fu hgu aj

x?. >. Bl Bl tb tbrn rnbh bhrf rf,, fs fs fp fpbra bramf mfrb rbs s rbj rbjan anhf hfoa oahs hs,, qu qub b fc fcbm bmbn bnbl bl af afss paréotbsbsb,oaauséonhambssbs,afpbraçîfèrbajhzamama bsqubrmaparaamhrbhta; =. B bl bl quartf tf,, fs fpbramfrbs bs jþghnfs, qub fcbmbnbl afs paréotbsbsb,oaauséonhambssbs,afpbraçîfèrbajhzamama bsqubrmaparaamhrbhta. Dhqu Dhqubl bl at atbo botf tfs s pa para ra bs bssa sas s rb rbgr gras as cá cásh shna nas, s, pf pfhs hs bj bjas as sb sbrî rîf f mb graombvajhap graombvajhaparaasfjuçîf araasfjuçîfmfsprfcjbla mfsprfcjblas. s.

Atrhcuhçîf

Atrh At rhcu cuhç hçîf îf pf pfmb mb sb sbr r ut uthjhjhz hzam ama a bl bl aj ajgf gfrh rhtl tlfs fs pa para ra mb mbtb tbrl rlho hoar ar ulvajfraulavarhávbjfuatèlbslfparaulabxprbssîf,bè rbprbsbotamapfrulasbta( A   ←7



 ←

).

^hgohdhnaqub Atblfvajfr 7(fu Arbnbcbfvajfr 7).Hlpfrtaotb! Asvarhávbhsmbvblsbrmflbslfthpfmfvajfrasbratrhcuìmf,fu sbia,ulavarhávbjmfthpfhotbhrfs sbia,ulava rhávbjmfthpfhotbhrfsþrbnbcbulvajfrmf þrbnbcbulvajfrmfthpfhotbhrf. thpfhotbhrf. R1-Jþghnambprfgralaçîf prfgralaçîf      >1 R1-Jþghnamb  

Nflbotárhfs

Blajguosnas Blajguosnasfs,vfnépf fs,vfnépfmbnrharnflbotárhfs(bxpjhna mbnrharnflbotárhfs(bxpjhnaçòbs)oas çòbs)oas jhoeasmb jhoeas mbnfla nflaomfs omfs mfsajgfrh mfsajgfrhtlfs tlfs uthjh uthjhzaomf zaomf (//), (//), jblcraomf jblcraomf qub fqubbsthvbroadrbotbmas‚//“oîfsbráhotbrprbtamfpbjfajgfrhtlf. Botramabsaìma

Pfmblfsmbsnrbvbrfssbguhotbsnflaomfsmbbotramabs Pfmblfsmbsnrbvbrfssbguhotbsnfl aomfsmbbotramabsaìma9 aìma9 Nfla Nf laom omf f ‚bsnrbva“ „ uthjh thjhza zamf mf para ra lfstra trar ajg jgf f oa oa tb tbja ja mf nflputamfr,nfoebnhmfnflfnfl nflputamf r,nfoebnhmfnflfnflaomfmbsaìm aomfmbsaìma. a. Nflao Nf laomf mf ‚jbha“ „ ut uthjhjhz hzam amf f para para ar arla lazb zboa oar r fs fs ma mamf mfs s mb mb ul ulaa varhávbj,talcèlnfoebnhmfnflfnflaomfmbbotrama varhávbj,talcèlnfoebnhmfnflfnf laomfmbbotrama.. Luhtfcbl,agfraqubvfnénfoebnbasmbdhohçòbsbapjhnaçòbs

paraasvarhávbhs,nfostaotbsbfpbramfrbs,valfstracajearajguos ajgfrhtlfsoasuabstruturasbqubonhaj. Jblcraomf qub a bstrutura sbqubonhaj mb ul ajgfrhtlf nfrrbspfombàdfrlajhobarmbbxbnuçîf. Nfoebçaagfraabstruturamfajgfrhtlf9

 

Hoìnhf//hoìnhfm Hoìnhf//hoìnhfmfajgfrhtlf fajgfrhtlffupartb fupartbmbcjfnf mbcjfnf Tar//mbnjaraçîfmasvarhávbhs. .... ....//nfotbùmfmfajgfrhtlf. .... .... dhl.//dhoajhzafajgfrhtlf. Tbia Tb ia f aj ajgf gfrht rhtlf lf a sb sbgu guhr hr, , qu qub b na najn jnuj uja a a lè lèmh mha a ar arht htlè lèth thna na mf mfss ajuofsmam ajuofsmamhsnhpjhoambajgfrhtl hsnhpjhoambajgfrhtlfbjþghnambprfg fbjþghnambprfgralaçîf. ralaçîf. hoìnhf9//hoình //hoìnhfmf //hoình fmfajgfrhtlf fmf ajgfrhtlf 1. hoìnhf9 rbaj9ofta1,ofta3,vajfrVmaVlèmha;// 3,vajfrVmaVlèmha;//varhávbhsmfth 3,vajfrVmaVlèmha;// varhávbhsmfthpfrbaj. varhávbhsmfth pfrbaj. 3. rbaj9ofta1,ofta >. narantbrb9oflb; narantbrb9oflb;//varhávbj //varhávbjmfthpf //varhávbj mfthpfnarantbrb. mfthpf narantbrb. =. bs bsnr nrbv bva9 a9 (‚ (‚Mh Mhgh ghtb tb f of oflb lb mf mf aj ajuo uof“ f“); ); nf nfla laom omf fmb mb sa saìm ìma, a, f

nfotbùmfmftbxtfsahráoatbjamfnflputamfr. jbha ha9 9 (o (ofl flb) b); ; // // sb sbrá rá ar arla lazb zboa oamf mf f nf nfot otbù bùmf mf ma ma va varh rháv ávbj bj 2. jb

>3

R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb

 

‚oflb“oalblþrhamfnflputamfr. 4.bsnrbva9(‚MhghtbaPrhlbhraOfta“);//nflaomfmbsaìma,f

nfotbùmfmftbxtfsahráoatbjamfnflputamfr. jbha ha9 9 (o (oft fta a 1); 1); // // sb sbrá rá ar arla lazb zboa oamf mf f nfot nfotbù bùmf mf ma ma va varh rháv ávbj bj 7. jb "ofta1"oalblþrhamfnflputamfr. bsnrbv rbva9 a9 (‚M (‚Mhgh hghtb tba a^bg ^bguom uoma aOft Ofta“) a“); ;// // nflaom nflaomf fmb mbsa saìma ìma, ,f f 5. bsn nfotbùmfmftbxtfsahráoatbjamfnflputamfr. jbha ha9 9 (o (oft fta a 3) 3); ; // // sb sbrá rá ar arla lazb zboa oamf mf f nfot nfotbù bùmf mf ma ma va varh rháv ávbj bj 8. jb ‚ofta3“oalblþrhamfnflputamfr. TajfrV frVma maVlè Vlèmha mha   ← (ofta 1 + ofta 3) / 3 // obstb nasf è 10. Taj atrhcuìmffrbsujtamfmabxprbssîf atrhcuìmff rbsujtamfmabxprbssîf ‚(ofta1 ‚(ofta1+ofta +ofta3)/ +ofta 3)/3 3)/ 3 ‚ paraavarhávbj‚lèmha“

11. Bsnrbva9 (‚A lèm ha mf ajuof è9“; vajfrVmaVlèmha); //

obs b nasf a rasb ‚  l a f a uof 9“ sa r  oa b a f nflputam nflpu tamfr frb b f frbs rbsujt ujtam amf f arl arlazb azboam oamf foa oava varhá rhávbj vbj ‚lè ‚lèmha mha““ sbráaprbsbotamfjfgfàdrbotbmadrasb.

 

13. dhl.

Tbiaagfranf Tbiaagfranflfdhnafajgfrhtlf lfdhnafajgfrhtlfsblfsnflbotárhf sblfsnflbotárhfs9 s9 hoìnhf; rbaj9ofta1,ofta3,vajfrVmaVlèmha; narantbrb9oflb; bsnrbva9(‚Mhghtbfoflbmfajuof“); jbha9(oflb); bsnrbva9(‚MhghtbaPrhlbhraOfta“); jbha9(ofta1); bsnrbva9(‚Mhghtba^bguomaOfta“); jbha9(ofta3); vajfrVmaVlèmha (ofta (ofta1 1+ 1+ +ofta ofta3) ofta 3)/ 3) /3; /3; Bsnrbva9(‚Alèmhamfajuofè9“;vajfrVmaVlèmha); dhl.

R1-Jþghnambprfgralaçîf prfgralaçîf      >> R1-Jþghnamb  

Sbdjhta Quaomfdfrmbdhohrulavarhávbj, nuhmamfoa nuhmamfoaeframa eframasuahmbothdhnaçîf! suahmbothdhnaçîf!  Jblcr blcrbb-sb sb9 9 vf vfné né oî oîf f pfmb pfmb ho hohn hnha har r ul ula a va varh rháv ávbj bj nf nfl l na nara rant ntbr brbs bs bspbnhahs(è,ç,î,&,%,#,@,*,-,botrbfutrfs)bxnbtf‚V“( Rombrjhob).).

Pbosaomfobssarbgra,quajadfrlanfrrbtaparambdhohrulavarhávbj blulajgfrhtlf6

Parabonbrrarbstasbçîfmfjhvrf,valfshovbrtbrfsvajfrbsmb muasvarhávbhsblulajgfrhtlf. Hoìnhf9 Hotbhrf9A,C,HOTBS]B;//mbdhobasvarhávbhs bsnrbva(‚ajgfrhtlfhovbrtbrvajfrbs“);//lfstraradrasboa

tbja,nflaomfmbsaìma  ;  r u  paraavar vb  C   ←300;//Atrhcuh300paraavarhávbjC HOTBS]B   ←A;//atrhcuhfvajfrmavarhávbjAparaavarhávbj HOTBS]B A   ←C;//atrhcuhfv C;//atrhcuhfvajfrmavarhá ajfrmavarhávbjCparavarháv vbjCparavarhávbjA bjA

 

←

C   ←HOTBS]B;//atrhcuhfvajfrmavarháv HOTBS]B;//atrhcuhfvajfrmavarhávbjHOTBS]B bjHOTBS]Bparaa paraa varhávbjC bsnrbva("FvajfrmbAagfraè9",A);//Lfstraroa bsnrbva("FvajfrmbAagfraè9",A); //Lfstraroatbjafofvf tbjafofvf vajfrmavarhávbjA bsnrbva("FvajfrmbCagfraè9",C);//Lfstraroatbjafofvf vajfrmavarhávbjC dhl. Bxblpjhdhnaomf

Tbiaagfraulajgfrhtlfqubrbajhzafnájnujfmbulasaìmambmamfs9 AjgfrhtlfsaìmaVmbVmamfs Tar prbVuoht,prbVtft9rbaj quaot9hotbhrf Hoìnhf

>=

R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb

 

prbVuoht95

R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb

 

^bçîf1.> Sbprbsbotaçòbsmbajgfrhtlfs Mhájfgfacbrtf Na Narf rf aju ajuof, of, nebg nebgal alfs fs à tbr tbrnbhr nbhra a sbç sbçîf îf mbs mbsta ta uohma uohmamb. mb. Ofs Ofssf sf pr prho honh nhp paj nf nfl lprf rfl lhs hsssf è qub vf vfné né nf nfoe oebç bçaa as na nara rant ntbr brìs ìsth thna nass mb ul ula a jho jhogu guag agbl bl oat oatura uraj, j, f mbs mbsbov bovfjv fjvhlb hlbotf otf mfs mfs mha mhagra grala las s mb cjfnfs(djuxfgrala cjfnfs(djuxfgralas)basapjhnaçòbsblpsbumf s)basapjhnaçòbsblpsbumfnþmhgfs. nþmhgfs. Pfhscbl,pbosbqubvfnémbnhmhunfostruhrulanasabprbnhsfu lfstrarparafarquhtbtffqubvfnépbosfunflfana sahmbajoasua nfo nfonbpç nbpçîf, îf,b bbsta bstasbrh sbrha aa ajho jhoguagb guagbl loatu oaturaj. raj.F Farqu arqu arquhtbtfmbsboefuas htbtfmbsboefuas

narantbrìsthnasmasuanasab,obssbnasf,trata sbmbuldjuxfgrala fuatèlbslfmbulpsbumfnþmhgf.Apþsbssbsprfnbmhlbotfs,a nasasbrhanfostruìma,bsbrharbajhzama nasasbrhanfostruìm a,bsbrharbajhzamaaprfgrala aprfgralaçîf. çîf. Sbsgataomffnfotbxtfmbaprbomhzagblmasbçîfaotbrhfr,f sbu sbu gbs gbstfr tfr bst bstá á luh luhtf tf sat sathsd hsdbht bhtf f nfl nfl f sbu sbu mbs mbsblp blpboe boef f pbr pbraot aotb b

 

sbusnfjbgasbogboebhrfs,bbstáluhtfnjarfqubfpbosalbotf nflputanhfoajpbrlbhaabquhpb. Agfra è f lflbotf mb vfné né aprbsbotar afs sbus nfjbgas as as mhdb mhdbrb rbot otbs bs df dfrl rlas as mb mb bs bstr trut utur urar ar as as hmbh hmbhas as mbot mbotrf rf mf mf nf nfot otbx bxtf tf nf nflp lput utan anhf hfoa oaj,j, fu fu sb sbia ia, , na nara rant ntbr brhz hzar ar a ut uthjhjhz hzaç açîf îf ma ma jhog jhogua uagb gbl l oaturaj,nrharbapjhnarfdjuxfgralabfspsbumfnþmhgfsb,pfrdhl, rbajhzarathvhmambsparasfjuçòbsmbprfcjblasjþghnfs. ^bg bgu uho hom mf bs bsssa jhjhoe oeaa mb mb pbo bosa sal lbo botf tf,, vfné né pr prf fpýs afs fs sbu buss nfjb nf jbg gas bo bog gbo boeb ebhr hrf fs qub ub bs bsnr nrbv bvbs bsssbl bl,, bl bl jhjhog ogu uagbl bl oa oatu tura raj,j, djuxfgralasbpsbumfnþmhgfs,fnájnujfmadþrlujaqubnfovbrtba tblpbraturabl tblpbraturablgrausnbotìgram grausnbotìgramfspara fsparagrausDaerboebht.A grausDaerboebht.Adþrluja dþrluja    8  ⋂n + 140   D < ,fomb‚D“èatblpbraturabl parabssanfovbrsîfè9

2

Daerboebhtb‚n“èatblpbraturablnbotìgramfs. ^bia nr ^bia nrha hath thvf vf b tb tbot otb b mb mbsb sbov ovfj fjvb vbr r bs bssa sa at athv hvhm hmam amb b nf nfl l a la lahf hfrr njarbzapfssìvbj. Cfasfrtbbcfosbstumfs! R1-Jþghnambprfgralaçîf prfgralaçîf      >8 R1-Jþghnamb  

Oîfpfmbdajtar Narf juof of,, ne lfss à ùjthl jthlaa sbç îf mbs ta uoh mamb mb. . Atè rf aju nebg bgaalf bçîf bsta ohm tè f prbsbotblflbotf,vfnébstumfuajþghnambprfgralaçîfbfs duomalbot fsmb duomalbotfs mbajgfrhtlfs,agfra ajgfrhtlfs,agfrahrblfsbstumar hrblfsbstumaras asrbprbsb rbprbsbotaçòbs otaçòbs masjhoguagbosqubsbrvhrîfmbcasbparadutura masjhoguagbos qubsbrvhrîfmbcasbparaduturasprfgralaçòbs sprfgralaçòbs.. Oasbguomasbçîfmbstauohmambmbboshof,vfnémbsbovfjvbu eachjhmambsparaanrhaçîfmbajgfrhtlfs,botbombuasap jhnaçòbsmb varhávbhs,atrhcuhçòbsbfpbramfrbs,bnflbçfuatbrulpbosalbotf bstruturamfparaassfjuçòbsmbprfcjblas bstruturamfparaassfju çòbsmbprfcjblas.Pfhscbl,ag .Pfhscbl,agfravalfs fravalfs nfoebnbrasrbprbsbotaçòbsqubbovfjvblasjhoguagbos. Jhoguagbloaturaj

^bguomf^aotfs(3001),ajhoguagbloaturaj,oambdhohçîfgbraj, èuladfrlambnfluohnaçîfbotrbaspbssfasmbmhvbrsasjìoguas, pf pfmb mbom omf f sb sbr r da daja jama ma, , bs bsnrh nrhta ta, , gb gbst sthn hnuj ujam ama, a, bo botr trb b fu futr tras as df dfrl rlas as mb

nfluohnaçîf.Ajhoguagbloaturajtblulagraombnfotrhcuhçîf      , pf pfmb mb mh mhrb rbnh nhfo foar ar mb mb df dfrl rla a shlp shlpjb jbs s b bd bdhn hnhb hbot otb b as as mb mbsn snrh rhçò çòbs bs mf mfss prfcjblasbsuassfjuçòbs.

 

Pararbdfrçarfsnfonbhtfsmbjhoguagbloaturaj,valfstflar nfl nflf f bxbl bxblpjf pjf a fp fpbra braçîf çîf mb mfh mfhs s va vajfr jfrbs bs uth uthjhza jhzaomf omf fs qu quatr atrfs fs fpbramfrbscáshnfsmalatbláthna.  F pr prfc fcjb jbla la è f sb sbgu guho hotb tb9 9 f us usuá uárh rhf f mbvb mbvbrá rá bo botr trar ar nf nfl l mfhs mfhs vajfrbs,bfnflputamfrrbtfroaráfrbsujtamfnflnamaulamas fpbraçòbsarhtlèthnas(sfla,suctraçî fpbraçòbsarhtlèthnas (sfla,suctraçîf,lujthpjhnaçîfbmhvhsî f,lujthpjhnaçîfbmhvhsîf). f). Ta Talf lfs s já! já! Bx Bxhs hstb tbl l vá várh rhas as df dfrl rlas as mb mb bs bstr trut utur urar ar bs bssb sb pr prfc fcjb jbla la.. Tbiaasbguhrulamaslaobhra Tbiaasbguhru lamaslaobhrasparaqubbjbpf sparaqubbjbpfssasbrrbajhzamf ssasbrrbajhzamf99 1. Hoìnhf. 3. Botrarnflfprhlbhrfvajfr. >. Botrarnflfsbguomfvajfr. =. Sbajhzarasflauthjhzaomffprhlbhrfvajfrlahsfsbguomf. 2. Sbajhzarasuctraçîfuthjhzaomffprhlbhrfvajfrlbofsfsbguomf. 4. Sbaj Sbajhzar hzara alujt lujthpjh hpjhnaç naçîf îfuthj uthjhzao hzaomf mff fprhl prhlbhr bhrf fvajf vajfr rvbzb vbzbs sf f fsbguomf. sbguomf. =0

R1-Jþghnambprfgralaçîf prfgralaçîf R1-Jþghnamb

 

Sbajhz jhzar ara a mhv mhvhsî hsîf f uth uthjhz jhzaom aomf f f prh prhlbh lbhrf rfva vajfr jfr mhv mhvhmh hmhmf mfpbj pbjf f 7. Sba sbguomf. Lfstraroatbjaf tbjafrbsujtamfma tbjaf rbsujtamfmasfla. rbsujtamfma sfla. 5. Lfstraroa 8. Lfstraroatbjafrbsujtamfmasuctraçîf. 10.. Lfstraroatbjafrbsujtamfmalujthpjhnaçîf. 10 11.. Lfstraroatbjafrbsujtamfmamhvhsîf. 11 13.. Dhl. 13

]raosnrbvbrajhoguagbloaturajbljhoguagblnflputanhfoaj obnbsshtambulprèvhfbotbomhlbotf,qubpfstbrhfrlbotbpfmbrá sfdrbrtraosdfrlaçòbsbldfrlambajgfrhtlfs,mhagralambcjfnfs bpsbumfnþmhgfs. Luhtfcbl,agfravalfsbstumarfduonhfoalbotfmfsmhagralas Luhtfcbl,agfravalfsbstumarfduonhfoalbotfmfsmhag ralas mbcjfnfs. Mhagralambcjfnfs(Djuxfgrala)

^bguom omf f Laoz ozaaof (3 (30 012), pfmblfs narantbr brhhzar mhag hagrala

mb cjfnfs nflf ul nfoiuotf mb sìlcfjfs grádhnfs bl qub nama ul mbssbs sìlcfjfs rb rbsbota a òbs bs bnìdhnas a sbrbl bx bxbn bnut utam amas as pb pbjf jf nf nflp lput utam amfr fr. . Ta Tajb jb jblc jblcra rar r qu qub b f mh mhag agra rala la mb cjfnfsfudjuxfgralambtbrlhoaajhoeambranhfnìohfuthjhzamapbjf

 

prfgralamfrpararbsfjvbrprfcjblas.Afbsnrbvbruldjuxfgrala, f pr prfg fgra rala lamf mfr r mb mbvb vb bs bsta tar r nh nhbo botb tb mb mb qu qub b fs fs sìlc sìlcfj fjfs fs ut uthjhjhz hzam amfs fs mbvbl mbvb l bs bsta tar r bl bl ea earl rlfo foha ha b sb sbr r mb mb dá dánh nhjj bo botb tbom omhl hlbo botf tf. . Pa Para ra qu qub b fsmhagr fsmhagralas alasmb mbcjfn cjfnfstboeal fstboealnbrtanfbréonha, nbrtanfbréonha,fs fssbus sbussìlcfjf sìlcfjfss dfral pamrfohzamfs pbjf dfr jf AO^H (Hosthtutf tf Ofrtbb-A Albrhnaof mb Pamrfohzaçîf). Tbiaagfraambdhohçîfmfsprhonhpahssìlcfjfsuthjhzamfsblul mhagralambcjfnfsfudjuxfgrala9 Quamrf1.1| Quamrf1.1|Mbsnrhçîfbshgohdhnamfsmb Mbsnrhçîfbshgohdhnamfsmbsìlcfjfsof sìlcfjfsof sìlcfjfsofmhagralambcjfnfs mhagralambcjfnfs ^ìlcfjf

 

^hgohdhnamf

 

Mbsnrhçîf

]brlhoaj

Sbprbsbotafhoìnhffufdhl mbuldjuxfjþghnf.Blajguos nasfsmbdhoblassuc-rfthoas.

Botramalaouaj

Mbtbrlhoaabotramalaouaj mfsmamfs,gbrajlbotbatravès mbultbnjamf.

R1-Jþghnambprfgralaçîf prfgralaçîf      =1 R1-Jþghnamb  

^ìlcfjf

 

^hgohdhnamf

 

Mbsnrhçîf

Prfnbssalbotf

Sbprbsbotaabxbnuçîfmb açòbsmbprfnbssalbotf.

Bxhchçîf

Lfstrafrbsujtamfmbula açîf,gbrajlbotbatravèsma tbjambulnflputamfr.

Mbnhsîf

Sbprbsbotafsmbsvhfs nfomhnhfoahsoasfpbraçòbs mbtflamambmbnhsîfbjaçfs nfomhnhfoahspararbpbthçîf mbajguostrbnefsmf prfgrala.

Prbparaçîf

Prfnbssfprbmbdhohmf

Sbprbsbotaabxbnuçîfmb uljaçfhonfomhnhfoajqub pbrlhtbalfmhdhnaçîfmb hostruçòbsmfjaçf. Mbdhobulgrupfmb fpbraçòbsrbjanhfoamas aulasuc-rfthoa. Sbprbsbotapfotfsmb nfobxòbsbotrbtrbnefsmb

Nfobntfr  

Jhoea

prfgralas,qubpfmblsbr apfotamfsparafutraspartbs mfmhagralambcjfnf. Sbprbsbotafsvìonujfs bxhstbotbsbotrbfssìlcfjfs mbulmhagralambcjfnfs.

Dfotb9Amaptamfmb9Laozaof(3012).

A part parthr hr mf mf lf lflb lbot otf f qu qub b df dfr r ut uthjhjhz hzao aomf mf fs fs sì sìlc lcfj fjfs fs nf nfl l as hostruçòb hostru çòbs smbj mbjbs, bs, vf vfné névah vah ap aprbo rbombo mbomf mf b mbs mbsbov bovfjv fjvbom bomf fnam nama avbz vbz lahsajþghnambjbsblrbjaçîfafs lahsajþghna mbjbsblrbjaçîfafsprfcjblas. prfcjblas. Sbdjhta ^bguomf^fuza(3011),fsprfdhsshfoahsmaárbambBxatasdazblusfmb ^bguomf^fuza(3011),fsprfdhss hfoahsmaárbambBxatasdazblusfmb djuxfgralasmbvhmf djuxfgralasmbvhmfàsuadalhj àsuadalhjharhmambnflmhagralas harhmambnflmhagralasbsqubláthnfs, bsqubláthnfs, nfljhoguagbllatbláthna,cblnflfnflasbxprbssòbsgrádhnas. Hs Hssf sf fn fnfr frrb rb pfr pfr na naus usa a mf mf ap apbj bjf f vh vhsu suaj aj qub qub fs fs djux djuxfg fgra rala las s té tél l oa dfrlaçîfmbssbsprfdhsshfoahs.

Bvfné,nflfvébssarbjaçîfmfsdjuxfgralasnflasuaárbambatuaçîf6 djuxfgralasnflasuaárbambatuaçîf6

=3

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf

 

Talfs djuxfg la qu mb mf Talf s rb rbaj ajhz hzar ar ul ul djux fgra rala qub b rbs rbsfj fjva va f ná nájn jnuj ujf f mb mfhs hs vajfrbsbxhchomfsuasf vajfrbsbxhchomfsuasfla,suctraçîf la,suctraçîf,lujthpjhnaçîfbmhvhsîf ,lujthpjhnaçîfbmhvhsîf.. Paraullbjefrbotbomhlbotfmfdjuxfgrala,anflpaoebfs nflbotárhfsmbbxbnuçîfparanamasìlcfjf. Mhagrala1.1|Nájnujfmbmfhsvajfrbs Fsìlcfjftbrlhoajmbuhoìnhfaf mhagralambcjfnfs.

Hoìnhf

Fsìlcfjfmbprfnbssalbotfmbdhohuas varhávbhsqubsbrîfuthjhzamasofmhagralambcjfnfs9vajfr1,vajfr3,sfla,suct, lujthbmhvh.

vajfr1,vajfr3, sfla,suct, lujth,mhvh

Fsìlcfjfbxhchçîf Fsìlcfjfbxhchçîflfstraoa lfstraoatbjafqub tbjafqub fusuárhfmbvbdazbr.

Mhghtarf vajfr1

Fsìlcfjfmbbotramalaouajjhcbrapara fusuárhfbotrarnflfprhlbhrfvajfr.

Jbrfvajfr1

Fsìlcfjfbxhchçîflfstraoatbjaf

Mhghtarf

qubfusuárhfmbvbdazbr. qubfusuárhfmbvb dazbr.

vajfr3

Fsìlcfjfmbbotramalaouajjhcbrapara fusuárhfbotrarnflfsbguomfvajfr. fusuárhfbotrarnflfsbg uomfvajfr.

Jbrfvajfr3

Fsìlcfjfmbprfnbssalbotfèrbajhzamf nflasatrhcuhçòbsfsvajfrbsnajnujamfs parasuasrbspbnthvasvarhávbhs.

sfla vajfr1 vajfr1+ +vajfr3 +vajfr3 suct vajfr1 vajfr1- - -vajfr3 vajfr3 lujth vajfr1 vajfr1* * *vajfr3 vajfr3 mhvh vajfr1 vajfr1/ /vajfr3 /vajfr3

Fsìlcfjfmbbxhchçîflfstraoatbjaf rbsujtamfmbnamavajfrnajnujamf.

Asflaè9sfla Asuctraçîfè9suct Alujthpjhnaçîfè9lujth Amhvhsîfè9mhvh

 

Dhoajhzafprfgrala.

Dhl

Dfotb9Bjacframfpbjfautfr.

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf      =>  

Asshlhjb

Ta Tajb jb fcsb fcsbrv rvar ar aj ajgu guos os pf pfot otfs fs mb mb at atbo boçî çîf f para para a nf nfos ostr truç uçîf îf mb mb ul djuxfgrala9 1. Bstaratbotfafsoìvbhs. 3. Fdjuxfgralambvb Fdjuxfgralambvbnflbçarmbnhl nflbçarmbnhlaparacahxf nflbçarmbnhl aparacahxfbmabsqubrma aparacahxf bmabsqubrmapara bmabsqubrma para

amhrbhta.

>. Nu Nuhm hmam amf f pa para ra oîf oîf nr nruz uzar ar as as jhjhoe oeas as, , pr prho honh nhpa pajl jlbo botb tb as as jhjhoe oeas as mb

djuxfsmbmamfs.

Paradhoajhzarfsmhagralasmbcjfnfs(djuxfgrala),valfsnrhar ulashtuaçîfuthjhzaomfulafpbraçîfjþghnablqubadhoajhmambè botrarnflulasboeaofshstbla. Mhagrala1.3|Mhagralambcjfnfsnflusfmbmbnhsîf Hoìnhf

Mhghtarasboea  

^boea

D

^boeafut.3017. Futrfsfdtwarbluhtfuthjhzamfèf‚Mha“.Tfnépfmb Futrfsfdtwarbluhtfuthj hzamfèf‚Mha“.Tfnépfmbdazbrfmfwojfampbjf hzamfèf‚Mha“.Tfnépfmb dazbrfmfwojfampbjf jhok9mhspfoìvbjbl9:ettp9//mha-hostajjbr.mb/?.Anbssfbl93> jhok9mhspfoìvbjbl9:ettp9//mha-hos tajjbr.mb/?.Anbssfbl93>fut.3017. tajjbr.mb/?.Anbssfbl93> fut.3017. Psbumfnþmhgf

^b ^bgu guom omf f Ag Aguh uhja jar r (3 (301 011), 1), f ps psbu bumf mfnþ nþmh mhgf gf è nf nfos oshm hmbr bram amf f ul ulaa dbrraalbo dbrr bota ta qub pfmb aux uxhjhjha har r a prf rfg gra rala laçî çîf f. Pf Pfm mb sbr br bs bsnr nrht htf f bl pa bl paja javr vras as sh shlh lhja jarb rbs s af af ho hogj gjés és fu fu af af pf pfrt rtug ugué ués s pa para ra da danh nhjhjhta tar r a hotbrprbtaçîfbfmbsbovfjvhlbotfmbulprfgrala. Pfm Pfmblf blfs s nar narant antbrh brhzar zar fs fs ajg ajgfrh frhtlf tlfs s nfl nflf f ul ps psbum bumfnþ fnþmhg mhgf. f. Bxhstblvárhasdfrlasmbrbprbsbotarul Bxhstblvárhasdfrlas mbrbprbsbotarulpsbumfnþmhgf,las mbrbprbsbotarul psbumfnþmhgf,las flahs hlpfrtaotbèqubbjbaprbsbotbasfjuçîfmfp hlpfrtaotbèqubbjbaprbsbotba sfjuçîfmfprfcjblaprfpf rfcjblaprfpfstf. stf. Tbiaagfrafpsbumfnþmhgf(pfrtugfj)pararbsfjvbrfprfcjbla masfpbraçòbsarhtlèthnasnhtamasaotbrhfrlbotb9

 

1. 3.

najnujfVfpbramfrbs; var;

>. =. 2. 4. 7. 5. 8. 10. 11. 13.

vajfr1,vajfr3, vajfr3,sfla, sfla,suct, sfla, suct,lujth, suct, lujth,mhvh9 lujth, mhvh9rbaj; mhvh9 rbaj; Hvajfr1, oìnhf; vajfr3, bsnrbva(‚Mhghtb bsnrbva (‚Mhghtbf (‚Mhghtb fvajfr f vajfr1“); vajfr 1“); jbhavajfr1; jbha vajfr1; bsnrbva(‚Mhghtb bsnrbva (‚Mhghtbvajfr (‚Mhghtb vajfr3“); vajfr 3“); jbhavajfr3; jbha vajfr3; sfla ←vajfr1+vajfr3; suct ←vajfr1-vajfr3; lujth ←vajfr1*vajfr3; mhvh ←vajfr1/vajfr3;

1>. 1=. 12. 14. 17.

bsnrbva(‚a bsnrbva (‚asfla (‚a sflaè9“, sfla è9“,sfla); è9“, sfla); bsnrbva(‚a bsnrbva (‚asuctraçîf (‚a suctraçîfè9“, suctraçîf è9“,suct); è9“, suct); bsnrbva(‚a bsnrbva (‚alujthpjhnaçîf (‚a lujthpjhnaçîfè9“, lujthpjhnaçîf è9“,lujth); è9“, lujth); bsnrbva(‚a bsnrbva (‚amhvhsîf (‚a mhvhsîfè9“, mhvhsîf è9“,mhvh); è9“, mhvh); Dhl.

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf      =2  

Tbiafsnflbotárhfsmbssbajgfrhtlf9 Jh Jhoe oea a 19 19 ‚n ‚náj ájnu nujf jfVf Vfpb pbra ramf mfrb rbs“ s“ bs bssb sb è f of oflb lb rb rbsb sbrv rvam amf f pa para ra hmbothdhnarfajgfrhtlf. Jhoea39‚Tar“shoajhzafhoìnhfmasvarhávbhs. Jhoea Jhoe a >9 >9 ^î ^îf f fs fs of oflb lbs s ma mamf mfs s pa para ra as as va varh rháv ávbhs bhs (v (vaj ajfr fr1, 1, va vajf jfr3 r3,, sfla,suct,lujth,mhvh);obstajhoeatalcèlsîfmbdhohmfsfsthpfs mbvarhávbhs(rbaj). Jhoea=9hohnhafsprfnbmhlbotfsmfsajg Jhoea=9hohnhafsprf nbmhlbotfsmfsajgfrhtlfs(hoìnhf). frhtlfs(hoìnhf). Jhoea29‚bsnrbva“èulnflaomfmbsaìmabhomhnafqubvahsbr lfstramf lfstramfoatbjamf oatbjamfnflputamf nflputamfr.Gbrajlbotbfnfotbù r.Gbrajlbotbfnfotbùmfmftbxtf mfmftbxtf dhnabotrbaspas(‚Mhghtbvajfr1“). Jhoe Jhoea a 49 49 ‚j ‚jbh bha“ a“ è ul ul nf nfla laom omf f mb mb bo botr tram ama, a, f va vajf jfr r mh mhgh ghta tamf mf è arlazboamfoavarhávbj(vajfr1). Jhoea79‚bsnrbva“èulnflaomfmbsaìmabhomhnafqubvahsbr lfstramf lfstramfoatbjamf oatbjamfnflputamf nflputamfr.Gbrajlbotbfnfotbù r.Gbrajlbotbfnfotbùmfmftbxtf mfmftbxtf dhnabotrbaspas(‚Mhghtbvajfr3“). Jhoe Jhoea a 59 59 ‚j ‚jbh bha“ a“ è ul ul nf nfla laom omf f mb mb bo botr tram ama, a, f va vajf jfr r mh mhgh ghta tamf mf è arlazboamfoavarhávbj(vajfr3). Jhoea89Aamhçîfmasvarhávbhsvajfr1bvajfr3èatrhcuìmapara

varhávbjsfla(sfla ←vajfr1+vajfr3).  

Jhoea109Asuctraçîfmasvarhávbhsvajfr1bvajfr3èatrhcuìmapara Jhoea109Asuctraçîfmasvarhávbhsvaj fr1bvajfr3èatrhcuìmapara varhávbjsuct(suct ←vajfr1„vajfr3). Jhoea119Alujthpjhnaçîfmasvarhávbhsvajfr1bvajfr3èatrhcuìma paravarhávbjlujth(lujth ←vajfr1*vajfr3). Jho Jhoea139 ea139A Amhv mhvhsî hsîf fmas mas va varhá rhávbh vbhs sva vajfr jfr1 1b bva vajfr jfr3 3è èatr atrhcu hcuìma ìma pa para ra varhávbjmhvh(mhvh ←vajfr1/vajfr3). Jhoe Jh oea a 1> 1>9 9 Bs Bsnrb nrbva va oa oa tb tbja ja f qu qub b bs bstá tá bo botr trb b as aspa pas s (‚ (‚a a sf sfla la è9 è9“, “, sfla)bfvajfrqubbstáarlazboamfoavarhávbjsfla.Pbrnbcaqub avarhávbjènfjfnamadframasaspas,paraqubbjasbiarbprbsbotama pbjfsbuvajfrnfrrbspfombotb. Jhoea1=9Bsnrbvaoatbjafqubbstábotrbas pas(‚asuctraçîfè9“, suct)bfvajfrqubbstáarlazboamfoavarhávbjsuct.Pbrnbcaqub avarhávbjènfjfnamadframasaspas,paraqubbjasbiarbprbsbotama pbjfsbuvajfrnfrrbspfombotb. Jhoea129Bsnrbvaoatbjafqubbstá Jhoea129Bsnrbvaoatbjaf qubbstábotrbaspas(‚a botrbaspas(‚alujthpjhnaçîf lujthpjhnaçîf è9“, lujth) b f vajfr qub bstá arlazboamf oa varhávbj lujth. =4

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf

 

Pbrnbcaqubavarhávbjènfjfnamadframasaspas,paraqubbjasbia rbprbsbotamapbjfsbuvajfrnfrrbspfombotb. Jhoea149Bsnrbvaoatbjafqubbstábotrbaspas(‚amhvhsîfè9“, mhvh)bfvajfrqubbstáarlazboamfoavarhávbjmhvh.Pbrnbcaquba varhávbjènfjfnamadframasaspas,paraqubbjasbiarbprbsbotama pbjfsbuvajfrnfrrbspfombotb. Jhoea179Bonbrrbfajgfrhtlfnflapajavra‚dhl“bfpfotfdhoaj. Quaomfofsrbdbrhlfsafusfmbpsbumfnþmhg Quaomfofsrbdbrhlfsafusfmbp sbumfnþmhgfsblajgfrhtlf fsblajgfrhtlfss mfthpfpfrtugfj,shgohdhnaqubbssbmbvbsbrbsnrhtfmbdfrlaqub futraspbssfaspfssalbotbombrmblaobhralahsdfrlaj,fusbia, fsnfonbhtfsmbvbldhnarnjarfsbblulajhoguagblanbssìvbjpara fsnfonbhtfsmbvbldhnarnjarfsbblulajhoguag blanbssìvbjpara qublhráhotbrprbtarfajgfrhtlf. È hlpfrt Èhlp frtaot aotb b bst bstar aratb atbotf otf pa para raajg ajgul ulas asrbg rbgras ras cá cáshn shnas as qu quaom aomf f uthjhzarpsbumfnþmhgfs9 •Bsnfjebruloflb. • •Av Avaj Av ajha har r as as va varh rháv ávbh bhs, s, m ar ar at atboç boçîf îf afs sbu s thp thpfs b às suas narantbrìsthnas. • •Mbs Mbsnrbv Mbs nrbvbr br mb dfr dfrla la nja njara ra f qub sb rá arl arlazb azboam oamf f b sb a s varhávbhsmbsthoamasabssahodfrlaçîfbstîfnfrrbtas.

• •Tbrhdhnarsbashostruçòbsdazblsbothmfbsbtélulasbquéonha Tbrhdhnarsbashostruçòbsdazblsbothmfbsbtélulasbquéonha jþghna.  

•Avajharfrbsujtamfb,quaomfpbrthobotb,lfstraroatbja. •Avajharfrbsujtamfb,quaom fpbrthobotb,lfstraroatbja. •Dhoajhzarfajgfrhtlf. Bxblpjhdhnaomf

Tbia ul ajgfrhtlf qub najnuja a árba mf nìrnujf usaomf ul psbumf psbu mfnþ nþmh mhgf gf bspbn bspbnìd ìdhn hnf f para para sbr sbr bxbn bxbnut utamf amf of of sfdt sfdtwa warb rb Ths Thsua uajg jg (sfdtwarbqubbxbnutafsnflaomfsmfs ajgfrhtlfs). ajgfrhtlf"árbamfnìrnujf" var árba,p1,rahf9rbaj hoìnhf //^bçîfmbNflaomfs Bsnrbva("mhghtbfrahfmfnìrnujf")

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf      =7  

Jbha(rahf) p1:->.1= árba:-(p1*(rahf_3)) bsnrbva("Aárbamfnìrnujfè9",árba) dhlajgfrhtlf Pbrnbcaqubfs Pbrnbca qubfsparãl parãlbtrfs btrfsuthjhzam uthjhzamfstalcèl fstalcèlsîfnfoshmbramf sîfnfoshmbramfsul sul ajgfrhtlfmfthpfpfrtuguésbstruturamf,fusbia,mbdánhjbotbomhlbotf bhotbrprbtaçîf. ^f ^fdt dtwa warb rb mh mhsp spfo foìv ìvbj bj bl bl9 9 :e :ett ttp9/ p9//v /vhs hsua uajg jg>. >.nf nfl. l.cr cr/?. /?. Anbs Anbssf sf bl9 bl9 3>fut.3017.

Paracèos! uohmambmbstbjhvrf,nfothoub jhvrf,nfothoub Paracèos! Tfnétbrlhofua Tfnétbrlhofuaprhlbhr prhlbhra auohmambmbstb bstumaomfbprathnaomf.Cfasfrtbbatèaprþxhlauohma bstumaomfbprathnaomf.Cfasf rtbbatèaprþxhlauohmamb! mb!

^bllbmfmbbrrar Ne b g f u  f  l f l b o t f  m b  p r a t h n a r  f  n f o t b ù m f  b s t u m a m f . Jblcrb-sb9 vfnédfhbjfgham Jblcrb-sb9 vfnédfhbjfghamfpbjfsbu fpbjfsbumbsbl mbsblpboef pboef bsbu bsbugbst gbstfr fr bspbraqubvfnénfjfqubmbdfrlanfovhonbotbasapjhnaçòbsma

jhogu jho guag agbl bl oat oatura uraj, j, mf mfs s mha mhagra gralas las mb cjf cjfnfs nfs (dj (djuxf uxfgra gralas las) ) b mf us f  b  p s b u f n gf s . A sua ua lhs hsssîf è mbl blf fos ostr traar afs sbu buss nf nfjb jbg gas as bo bog gbo boeb ebhr hrf fs a ap apjhjhna naçî çîf f bl bl jho jhogu guag agbl bl oa oatu tura raj,j, djux djuxfg fgra rala las s b ps psbu bumf mfnþ nþmh mhgf gfs, s, f ná nájn jnuj ujf f ma ma dþ dþrl rluj uja a qu qub b nf nfov ovbr brtb tb ul ula a tb tblp lpbr brat atur ura a bl bl gr grau auss nbotìgramfsparagrausDaerboebht.Adþrlujaparabssanfovbrsîfè9

 

   8  ⋂ n + 140 D < 2

,blqub‚D“èatblpbraturablDaerboebhtb‚n“èa

tblpbraturablnbotìgramfs. Prhlbhrf, vfné mbvb bsnrbvbr bl jhoguagbl oaturaj f duonhfoalbotfmadþrlujaqubnfovbrtbgrausnbotìgramfsparagraus Daerboebht.Parahssf,frgaohzbfsbupbosalbotfmbdfrlabstruturaj bdfrlaj,lasjblcrb-sb,obltfmfsfsbogboebhrfstbrîfflbslf pbosalbotf, pbosalbotf,fhlpfrtaotbè fhlpfrtaotbènebgaràsf nebgaràsfjuçîfmf juçîfmfprfcjbla. prfcjbla. Oanfostruçîfmfdjuxfgralavajbrbsgatarasmhnasnhtamasof ‚Oîfpfmbdajtar“9

=5

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf

 

Bstaratbotf atbotfafs atbotf afsoìvbhs afs oìvbhsof oìvbhs ofdjuxfgrala. of djuxfgrala. 1. Bstar Fdjuxfgralambvbnflbçar mbvbnflbçarmbnhla mbvbnflbçar mbnhlaparacahxf mbnhla paracahxfbma paracahxf bmabsqubrma bma bsqubrma 3. Fdjuxfgrala paramhrbhta. Nuhmamfparaoîfnruzar oîfnruzarasjhoeas, oîfnruzar asjhoeas,prhonhpajlbotbas asjhoeas, prhonhpajlbotbasjhoeasmb prhonhpajlbotbas jhoeasmb >. Nuhmamfpara djuxfsmbmamfs. Dhoajhzb bssa athvhmamb bsnrbvbomf a nfovbrsîf mb graus nbotìg nbotìgramf ramfspara sparagrau grausDaerboebhtbl sDaerboebhtblpsbu psbumfnþ mfnþmhgf mhgf..Ass Asshlnflf hlnflf ofdjuxfgrala,asdfrlasmbpbosalbotfpfmblsfdrbrajtbraçòbs, lasfhlpfrtaotbèfrbsujtamfbajþghnaparasua lasfhlpfrtaotbèfrbsujtamfbajþg hnaparasuasfjuçîf. sfjuçîf. Nacblasmhnas9 • Bsnfjebr Bsnfjebrul uloflb ul oflbpara oflb paraf para fajgfrhtlf. f ajgfrhtlf. • Avaj ajha har r as va varh rháávbh bhss, mar atb tboç oçîîf afs fs sbu buss thpfs b às suas narantbrìsthnas. • Mb Mbsn snrb rbvb vbr r mb mb df dfrl rla a njar njara a f qub qub sb sbrá rá ar arla lazb zboa oamf mf b sb as varhávbhsmbsthoamasabssahodfrlaçîfbstîfnfrrbtas. • Tbrhdhnar sb as hostruçòbs dazbl sbothmf b sb tél ula sbquéonhajþghna. • Avajharf Avajharfrbsujtamfb, rbsujtamfb,quaomfpbrthobotb, rbsujtamfb, quaomfpbrthobotb,lfstrar quaomfpbrthobotb, lfstraroa lfstrar oatbja. oa tbja. • Dhoajhzar f ajgfrhtlf.

 Dhoajhzar Dhoajhzarf fajgfrhtlf. f ajgfrhtlf. Cfasfrtbbcfosbstumfs!

 

Avaoçaomfoapráthna ]hpfsmbtrhãogujfs„nfoshmbraomfsbus ãogujfshotbrofs Mbsnrhçîfmashtuaçîf-prfcjbla

Tfnédfhmbshgoamfparaaiumarulmbpartalbotfmablprbsa Uhs&Yh a bonfotrar fs ãogujfs hotbrofs mfs trhãogujfs qub nfrrbs nfrr bsp pfom fombl bl a ajg jgu uos os thp thpfs mb pbç bçaas. Pf Pfr r lbhf bhf mas lb lbm mhm hmaas bonf bonfotr otrama amas, s, vf vfné némbv mbvbrá brá ap apfot fotar arf fthp thpf fmf mf trh trhãog ãogujf ujf..A Ablp blprbs rbsaa prbnhsa qub vfné né passb bl dfrl rlaa mb jhoguagbl bl oatura rajj bssb prfnbmhlb prfnbm hlbotf otf..Tbi Tbia aoaDhgur oaDhgura a1.1 1.12 2fs fs thp thpfsmb fsmbtrh trhãog ãogujf ujfs sb bas as su suas as rbprbsbotaçòbsblrbjaçîfafsãogujfs.

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf      =8  

Dhgura1.12|]hpfsmbtrhãogujfsnjasshdhnamfspfrãogujfshotbrofs Dhgura1.12|]hpfsmb trhãogujfsnjasshdhnamfspfrãogujfshotbrofs

Dfotb9bjacframfpbjfautfr.

Sbsfjuçîfmashtuaçîf-prf Sbsfjuçîfmashtuaçîf-prf shtuaçîf-prfcjbla cjbla

Bljhoguagbloa Bljhoguagbloaturaj,pfmbrhas turaj,pfmbrhasbrbsnrhtamasbguhotbdfrl brbsnrhtamasbguhotbdfrla9 a9 Hoình nhf. f. 1. Hoì 3. ^fjhnhtarabotramamf ^fjhnhtarabotramamfprhlbhrfãogujf(TarhávbjaogA). prhlbhrfãogujf(TarhávbjaogA). ^fjhnhtarabotramamfsbguomfãogujf(TarhávbjaogC). sbguomfãogujf(TarhávbjaogC). >. ^fjhnhtarabotramamf =. ^fjhnhtarabotramamftbrnbhrfãogujf(TarhávbjaogN).

Tbrhdhnarsbassflasmfsãogujfshotbrofssflal150graus mfsãogujfshotbrofssflal150graus 2. Tbrhdhnarsbassflas (aogA+aogC+aogN.^bguomfAguhjar(3011),fpsbumfnþmhgfènfoshmbramfuladbrralbota

qubpfmbauxhjharaprfgralaçîf.Pfmbsbrbsnrhtfblpajavrasshlhjarbsaf hogjésfuafpfrtugués,paradanhjhtarahotbrprbtaçîfmbajgfrhtlfsbasshl nrharpfsshchjhmambsparanfostruçîfmbprfgralas nflputanhfoahs.

23

R1-Jþghnamb R1-Jþghnambprfgralaçîf prfgralaçîf

 

Aoajhsbadajeaoftrbnefmfpsbumfnþmhgfasbguhrbasshoajbaajtbroathva qubnfrrbspfombàdfrlanfrrbtaoabxbnuçîf9 ajgfrhtlf"NajnujarfHLN"; var; oflb9narantbrb; pbsf,hln,ajtura9rbaj; Hoìnhf bsnrbva("Bsnrbvafoflb"); jbha(oflb); bsnrbva(Bsnrbvafpbsf"); jbha(pbsf); bsnrbva("Bsnrbvaaajtura"); jbha(ajtura); hln-Nfonbhtfsmbprfgralaçîf mbprfgralaçîf R>-Nfonbhtfs

 

]botbfutraslaobhrasmbnrharfprfgrala,daçatbstbsbprathqub fláxhlfpfssìvbj.

Avaoçaomfoapráthna Adfrça Mbsnrhçîfmashtuaçîf-prfcjbla

Blulmbcatbnflsbusalhgfsbogboebhrfs,vfnédfhmbsa dhamf a rb rbssfjv jvbr br atr traavès ès mf ná nájn jnu ujf jf ma df dfrç rçaa b mbpfhs hs prf rfg gra rala lar r bl JhoguagblNasbguhotbshtuaçîf9 Hl Hlag agho hob b ul ula a pj pjan ana a mb mb nhlb nhlbot otf f sf sfcr crb b ul ula a pjat pjatad adfr frla la pj pjao aoaa fombsbráobnbssárhfnajnujaradfrçaofrlajulaoafutra.Ahmbha mfnájnujfèoîfmbhxarqubffcibtfsþjhmfsbiaatravbssamfpfr futrfs.Tbiaqubadfrçamagravhmambblpurraapjanaparacahxf,af lbslftblpfblqubadfrçaofrlajv lbslftblpfblquba dfrçaofrlajvahnfotrabja. ahnfotrabja. P Pararbajhzarbssbsnájnujfs,vfnépfmbrá Pararbajhzarbssbs ararbajhzarbssbsnájnujfs,vfnépfmbráusara usarasbguhotbdþrluja9 sbguhotbdþrluja9 O-Nfonbhtfsmbprfgralaçîf R>-Nfonbhtfsmbprfgralaçîf      138  

snaod("%d", &l); prhotd("Mhghtbagravhmamb9Zo"); &

snaod("%d", g); o0

R>-Nfonbhtfsmbprfgralaçîf mbprfgralaçîf R>-Nfonbhtfs

 

Aoajhsbfprfgralaacahxfbrbspfomaaajtbroathvaqubnfrrbspfombaf vajfrparapbq. hotlaho() { hotp,q;  p-Nfonbhtfsmbprfgralaçîf mbprfgralaçîf R>-Nfonbhtfs

 

Agfra,vbiaashotaxbpararbaj hzaçîfmarbpbthçîfnfltbstbofdhoaj9 Agfra,vbiaashotaxbpararbajhzaçîfmarbpbthçîfnfltbstbofdhoaj9 mf { nflaomfs; } wehjb(nfomhçîf); Bxblpjf19Prfgralaqubnajnujaalbtragblquamramambul tbrrbofusaomfftbstbofdhoajparanrharafpçîf tbrrbofusao mfftbstbofdhoajparanrharafpçîf mbmhght mbmhghtarofvfs arofvfs vajfrbssblsahrmfprfgrala. #honjumb:stmhf.e? laho(){ djfatlbtragbl1,lbtragbl3,rbsujtamf; hotrbsp; lbtragbl1).^uauthjhzaçîf èvastambvhmfàdanhjhmambbljbrbbsnrbvbrmamfsbàvbjfnhmambnflqub asfpbraçòbssîfrbajhzamas. 185

R=-Apjhnaçòbsmbprfgralaçîf

 

Aoajhsbasassbrçòbsasbguhrbarbjaçîfprf Aoajhsbasassbrçòbsasbguhrba rbjaçîfprfpfstabotrbbjas. pfstabotrbbjas. H„Latrh H „Latrhz zè èul ulabstrut abstrutura ura mbmamfs mbmamfs uth uthjhz jhzama ama par paraarlaz aarlazboa boar rmam mamfsbl fsbl dfrl df rla a mb ta tacb cbja ja, , fu fu sbia sbia, , mhstr mhstrhc hcuì uìmf mfs s bl bl jh jhoe oeas as b nf nfju juoa oas, s, b ul ula a ma mass narantbrìsthnasmbssabstruturambmamfsè narantbrìsthnasmbssabstrutura mbmamfsèsbrmhoãlhna sbrmhoãlhna.. PFSQRB HH HH „ A napanhmamb ma latrh trhz prbnhsa sa sbr hodf dfrrlama of lflbotf ma mbnjaraçîfmavarhávbj,sbomfobnbssárhfhodfrlarmfhsvajfrbs,ulpara rbprbsbotarfìomhnbmajhoeabfutrfpara rbprbsbotarfìomhnbmanfjuoa. a)AsassbrçòbsHbHHsîfprfpfshçòbsvbrmambhras,baHHèulaiusthdhnathva nfrrbtamaH.

c)AsassbrçòbsHbHHsîfprfpfshçòbsvbrmambhras,lasaHHoîfèula iusthdhnathvanfrrbtamaH. n)AassbrçîfHèulaprfpfshçîfvbrmambhra,baHHèulaprfpfshçîfdajsa. m)AassbrçîfHèulaprfpfshçîfdajsa,baHHèula m)AassbrçîfHèula prfpfshçîfdajsa,baHHèulaprfpfshçîfvbrmambhra. prfpfshçîfdajsa,baHHèula prfpfshçîfvbrmambhra. b)AsassbrçòbsHbHHsîfprfpfshçòbsdajsas. 3. Quaomfuthjhza-sbulasfjuçîfnfllatrhzbsèprbnhsftbrnjarbza

      .       nfjuoahohnhal-sbblzbrf,pfrtaotfaprhlbhrapfshçîfasbrfnupama èjhoea0„nfjuoa0.

 

Nfos Nfoshmbrbfprfgral hmbrbfprfgralaacahxf aacahxfb bbsnfj bsnfjeaafpçîf eaafpçîfqubnfotèlfqubsbrá qubnfotèlfqubsbrá hlprbssfoajhoea11. 1.

#honjumb:stmhf.e?

3.

vfhm vfh ml laho aho(){ aho(){

>.

djfatt l djfa latrhz atrhz[3\[ atrhz[3\[3\; 3\;

=. 2.

hott h, ho h,i,  i,rb rbsu sujt jtam amf f