Luận văn Bộ phân tích bài toán hỗ trợ cho việc giải các bài toán ở bậc phổ thông

ij)mxodday: mij= [ 1ne'unhu'phepbie'nd6i OJ lamgiamst.l'khacbi<$tdi 0 ne'ungu'(;fcl~i 1~2.2.2/Phlto'l1gphap STRIPS: Vi<$nghienCUuStanfordda du'ara phu'dngphapSTRIPS (Stanford ReseachInstitudeProblemSolver)vaonhungnam1970STRIPSda sitdl;mg phu'dngphaplogichvi tr!tU'capmQtd~motakhonggianbi~udi~ncuavand-e dudid~ngcacvi trt Tr~ngthaidu'(;fcxemlakhaini<$mcdbancuaSTRIPS.M~t khacm6iphepbi6nd6iloantittrongSTRIPSc'andu'(;femientiicacdi-euki<$nap d\lngvacachi<$ulingsankhiapdt.mgcacphepbie'nd6in'ay. Phu'dngphapSTRIPS daco nhi-eulingdl;mgtrongvi<$cxaydvngmQth<$ th6ngchu'dngtrinhdi-eukhi~nRobotvah<$n'aydingcotenSTRIPS. 1-2.3/Cae phlto'l1gphaptlm kie'm: Nhudatrlnhbay,h'auhe'tcaevand-ed-euco th~phatbi~udu'did~ng"Ti'imQt tr~ngthaiband'auhayfunmQtduC1ngdfinde'ntr~ngthaike'tthucmongmu6n". Quatrinhtoodu'C1ngdfintU'tr~ngth~ixuatphat(So)de'ntr~ngthaike'thuc (So)dath~hi<$nr5cachgiaiquy6tvand-ebaog6m: - LvachQnkhonggiantooki6mthichh(;fp. - Tie'nhanhtimki6mmQtcachcohi<$uquatrongkhonggiantimki6m. - HuydQngva sitdvngcacngu6ntri thlicco lienquanvaoquatrinhfun kie'mtilythuQCtirngmi-end6itu'(;fngCt.lth~. Khonggiantimkie'mcuamQtvand-edU(;fcgiai trenmaytinhthu'C1ngdu'(;fC bi~udi~nbdi d6 thiho~cmQtd~ngd~cbi<$tcuad6 thila cay.Khi bi~udi~nbai loandudid~ngd6thiho~ccaytadu'(;fC: - M6i dinhla mQtgiaido~ncuaquatrinhgiai (tr~ngthai) 9 LU~NVANTHACsTKHOAHQC - M5i clingla mcd9ngbie"nd6iquatrlnhtU'giaido~nnaysanggiaido~nkhac. Vi~cgiaiquye"tvftnd~duq~xemnhula vi~cfunduCJngdi ill tr~ngthaiband'au de"ntr~ngthaimongmu6nduqcbi€u di~nqua2dinhnaod6cuaciy funki6m. Vi~cc6 th€ bi€u di€n quatrlnhgiiii quye"tm9tsa lo~ivifnd~b~ngda thi nhutrenkhangnhfi'ngdii chophepcac nhatri tu~nhant~osa dlJ.ngnhi~uke"t quaclia 19thuye"tda thi ma con clingcifpcho ta phuongti~ndon gian d€ th€ hi~nslJ.'ho~tdQngcnacacky thu~tImki6mkhacnhau. MQt trongnhfi'ngtrdng~iIon nhiftkhi tamoanapdlJ.ngcacphuongphap cnatri tu~nhant~od€ giaicacbftiloancliath~I'ct6la qui mavadQphuct~pcna Unhhuang.M~tkhacdom9tsa bai loan n6ugiiii b~ngphtI'ongphaptlmki6m ngftunhienthl riftkh6 hy vQngUrnra Wi giciiva sa duCSngdi c6 th€ tang-theo hamsamll cna cacdinh.VI v~y,banchiftcnaphuongphapkhi giai quye"tcac vifnd~la giamthi€u sal~ntlmki6m. Cho d6nnaygiai quy6tvifnd~b~ngphuongphaptlmki6mlcsigiai vftnla phuongphaprift c~nthi6tvaquailtrQng. Cacthnt1J.cUmki6mbaagam: - TIm ki6m theochi~urQng(Breath - fIrst search) - TIm ki6m theochi~usan (Depth - first search) - TlDl ki6m sand~n(Depth wise search) - TlDl ki6m clJ.'cti€u h6a gia thanh(Cost minimization search) - TlDlki6m voi tri thucb6 sung(Heursisticsearch) 1-2.3.1/Phu'o'ngphapOmkie'mtheochi'eurQng: Phuongphaptlmki6mtheochi~urQnglaphuongphapki€m ITatft'ngdinh cuaclingmQtmucraimoichuy€nsangcacdinhd mucsanhon.Vi dlJ.xetcay: A A : tr~ngthaid~u B : tr~ngthaicuai B A C A E F G H ApdlJ.ngphuongphaptlmki6mtheochi~urQngvaodathitrenvan6sedi quacaedinhdathitheothut1J.'ABC D E F G 10 LuANVANTHACsTKHOAHQC Phuongphaptimkie'mtheochi~urQngdambaasetlmdu<JcWigiai(ne'u tant1;li)VInoclingcoth~suybie'nthanhki~utimkie'mvetc1;ln. 1-2.3.2/Phuongphaptimkie"mtheochi'eusau: Phuongphaptimkie'mtheochi~usanlaphuongphapthai iliacduongdftn mQtud'aude'ncu6itradckhichuy~nquaduongdftnkhac.Vi d\lxetcay: A E : tr1;lngthaicu6i B A A D E F G Apd\lngphuongphaptlmkie'mtheochi~usanVaGdathjtren,n6sediqua cacdinhcuadathjtheothunrA B D B E. Theocachtimkie'mnaythlphaidi de'nt~ndinhcu6iho~cdinhtrainhat.Trongtruongh<Jpg~pdinhcu6ithlc'anlui mQtmucvasangphaivasand611;lisangtraichode'nkhig~pdinhcu6iho~cdiOO dich.C'anl~p11;liquatrlnhnaychode'nkhitlmth~ydinhcu6icungcuathonggian funkie'm. Phuongphaptlmkie'mtheochi~usandambaaIuonIuontlmthayVItrong tntongh<Jpxaunhatn6sechuy~nsangtlmkie'mvetc1;ln. Tuynhienphuongphaptlmkie'mtheochi~usansethongthichh<Jpvdi nhii'ngtlnhhu6ngtrongd6taphaiki~mITaIDQtnhanhr~tdaichid~bie'tdinh cuan6thongphaiIa loi giai.Trongnhii'ngtraongh<Jpnhuthe'tanendung phuongphaptimkie'mtheochi~urQng. 1-2.3.3/Phuongphaptlmkie"msaud:1n: Phuongphaptlmkie'msand'anmythuQCvaogiatrimucsank dachoband'au. TaduavaodQsanhi~nt1;liD,gallchodQsanband'aumQtgiatrik duy~tcacdiOO trongph1;lmvicacdinhdQsan000honho~cb~ngD,sand6tangD=D+kvaduy~t tie'ptl;1c.Ne'utrongcaytant1;liitnhatI duCfngdi ill dinhg6cde'ndichthlvi~ctlm kie'msedungvachorake'tquala duongdi c6dQdaikhacduongdi ng~n hat khongquak - 1.Ne'utrongcaythongtant1;liduongdinhuv~ythiphuongphap chidungkhidathjIadinhhUllh1;ln.Vi d\lxetcay: LUANVANTH~CsTKHOAHOC A /B /D~ E~ A ~ L /c~ ~N 0 P A !\ Q R s T u v x y Ap d\lngphu'ongphaptimIdemsand'ankhik =2 thti't\fduy~tcacdinh la ABDECFGHQRKSTLMUVN 1-2.3.4/Phu'o'ngphaptlmkie'mcljcti€u h6agiathanh: Trongtru'CSngh<Jpmlii clingcuad6 thjdu'<Jcgall gia thanhthlhu'dngdi tim kie'mdu'<Jcxaedinhbdi vi~ccvclieuh6agiathanhdu'CSngdi. Vi d\l xetcayvagiacacclingnhu'hlnhve vat~ndinhdichla {D,H} A B Al /\2 D E G H PhuongphaptimIde'mcvctieDh6agiathanhchoke'tqualadu'CSngdiAPH. Thu~tgiainaythongtheapd\lngdu'<JCkhibailoanlId nenphti'et~pdodoihoi phiiithaom(>tseSlu'<JngWncacmil. 1-2.3.5/Phu'o'ngphaptlmkie'mvaitri thucbffsungHeuristic BeSivdinhi~ubai loanvi~curnkiemdu'CJngdi teSiu'Usedu'<Jcdinhhu'dng ~ptrunghonxungquanhdu'CSngdi teStnh~tneusad\lngcacthongtind~ctav~ btii loan.TheodinhnghlacaethongtinnaygQila Heuristic."Heuristicsdon giiinla caequi ukdanhgia cackha nangde vi~eurnIdemtie'nhanhIDeom(>t haongdung" (TTNT :cacphu'ongphapva«ngd1;1ng-B~chHu'ngKhang,HoangKiem- Nhaxu~tbanKHKT 1985) Caekythu~tHeuristicsgQilacacmyOgiai. 12 LUANVANTHACsi KHOAHOC Ta c6 the du'ara m~ogiainhu'sau: - ChQntoclnht xftydl;1'ngcungsaochoc6 theIO<;1ibatnhungdinhkhonglien quande'nbailoan,IO<;1ibatcacdinhitc6trienvQngflAmtrendu'dngdi t6iu'U. - Sit d~mgthongtinb6 sungnhAmsa:pxe'pcacdinhtrongt~pcacdinhdin phaimd,m6i fandin IffymQtdinhtrongd6.Mu6n v~y,tadin phaidu'ara du'<;lC donaod6 choph6pxac dinhtri~nvQngcuacacdinh thu'dngdu'<;lcgQila ham danhgia(costfuntion) Cachamdanhgiadlt<;lCxftyd~tngdl1atrennhungphttdngphapkhacnhau: - Xac sufftmQtdinhnaod6flAmtrendltdngdi t6ilID. - Khoangcachhays~tkhacbi~tgiua1dinhnaod6vdi cact~pdinhdich. Vi d~l:X6tbailoanthapHaNQivdin=2 Lffyhamfo=go+ho(ho(m)thongtinn6ithemv~m6ilienh~giuamva tr<;1ngthai dich) Chiing h<;1n: -Ne'ud CQCC chu'ac6ilia naothlho=2 -Ne'udCQC c61iliatothiho=1 - Ne'ud CQCC c6 1dlanhothlho=3 - Ne'ud CQCC c62 dla,dlanhod trenilia to thiho=0 k€t quadu'<;lcchira d hinhvesau: g=2 O~J / h=2 h=3 0f=5 h=2 f=4 g=l h=2 f=5 h=O f=3 h=l f=4 13 LUANVANTHACsi KHOAHOC Thong tin Heuristicmy khong phiHIa luon luon chinhxac va dambao nhungno lamtangcelhQid~vi~ctimkie'mICfigiai,nhanhheln, t6i l1l1helnho~c ch~nch~nheln. M~tkhac,trongkhi timICfigiai cl1ngnhugiaiquye'tvin d~,connguCfi thuCfngb6sungthemhi thuccuabanthanminh.Nhii'ngtrithuciy he'tsucquari trQngVInogiuptagiambOtthCfigiandmkie'mvahuongram\lclieu.LOpth\!'c giaiHeuristichaycongQila myOgiai th~ts\!'conIOnhelnca lOpthu~tgiai Algorithms.Thu~tgiaiHeuristickhacthu~tgiaiAlgorithmsd mucdQph6d\lng vakhongphailucnaocl1ngthanhcongoHelnnii'akhongphailucnaodingfun duQcthu~tgiaiAlgorithms. " " ,., '" " , 11-l~P lU~N TIEN VA l~P lU~N lUI 11-1/ l~plu~ntie'n: L~plu~ntie'nb~tdl1uto'tr~ngthaixuitphat,thongthuCfngtaphiiixayd\!,ng mQtcaycuagiaicacchuy~ndQng(matacoth~gQila giaiICfigiai)biingcach xuitphatto'hinhth~bandl1ud~t~orag6ccuacay.T~oramuctie'pIDeocua caybiingcachtlmtit cacaclu~tmaphiatrltOCcuanophfthQpvoinutg6cvasti' d\lngphiaphaicuanod~t~oracachinhth~mOi.L~it~otie'pcacnuttie'ptheo biingcachliy m6inutduQct~orad muctrttOcvaapd\lngvaonotit cacaclu~t maphiatraicu~hl~tIa phfthQpvoi no.Tie'pl\lcnhuv~yde'nkhi naot~ora duQcmQthinhth~moiphuhQpvoitr~ngthaidich. 11-2/l~plu~nlui : L~plu~nlftixuit phatto'tr~ngthaidich.B~l~plu~nlfti trttOche'ttaphai xayd\!,ngmQtcaycuacacdaychuy~ndQngbiingcachxuitphatto'hinhth~dich d~t~orag6ccuacay.T~omuctie'ptheobiingcachtlmtit cacaclu~tmaphia phiiicuanophuhQpvoinutg6c.Sti'd\lngphiatraicuacaclu~tiy d~t~ofa cac dinhdmucthuhai.L~it~otie'pcacmuctie'ptheocuacaybhngcachliy titca cacdinhd muctruOcvatlmtit cacaclu~tmaphiaphaicualu~tiy phuhQpvoi no.Rail~isad\lngcacphiatraitu'elngungd~t~oraduQcmQtnutmOi.Tie'pl\lc nhuv~yde'nkhinaomatat~oduQcmQthinhth~moiphfthQpvoitr~ngthaiban dl1u. Vi dl)mink h{Ja: Giii satacl1ndmWi giai cuabai loansau: "Tan t~ihaykhonghai so' nguyenduelngm,nthoamand~ngthucsau: m2+(m+1)2=n4+(n + 1)4 B~kh~ngdinhco tant~ihaykhonghai so'nguyenduelngm, n thoaman d~ngthucb."enthltaphaihinhdungduQcphl1nnaothuQctinhcuahai s6m,n do. 14 LU~NVANTHACsTKHOAHOC £)i~ud6 g<;fiY dingtaphaixuiltphattiYtr~ngthaidfch,tucIas\\,tont~icuahais6 nguyenduongm,n thoad~ngthuctren. m2+(m+1)2=n4+(n +1)4 ~ 2m2+2m =2n4+4n3+ 6n2+4n ~ m2+m+ 1=(n2+n + 1)2 Dod6m2+m+Ila s6chinhphuong. M~tkhactal~ic6(m-1)2<m2+m+1<(m+1)2nenm2+m+1khong theIas6chinhphuong. VI V?ykhongthetont~ihais6m,nthoamand~ngthuctren. Vi dt:!v~bailoantinhtichphan: khonggiancacbai loancuabailoanla t?Ph<;fpcaccongthUCtrongd6c6mQts6bienthuctichphan.Tr~ngthaixuilt phatla mQtcongtht1'cql theva trongcongthuciCyco mQts6bienthuctieh phan.Tr~ngthaidfchmongmu6nla rutramQts6congthuckhongchuabien thuctichphanvatu'ongduongvdicongthucband'au.Be giaiquye'tvilnd~nay, l?plu?ntie'nbie'nd6itfchphandet~orabienthuckhongchuatichphanthlt6t honlaxuiltphattU'cacbienthuckhongchuatichphanva sii'dt:!ngcaequilAc d~ohamdethii'nh~mt~oracacbienthucc6chuatichphanband'au. Haividt:!trenconneukharov~t'amquailtrQngcuam6ilienh~gillatr~ng thaixuiltphatvatr~ngthaidfchtrongvi~cxayd\\,ngmQthuangdi t6tnhiltnh~m quye'tdinhquatrlnhtimkie'msedi IDeohuangnaokhi mah~s6phannhanh theohai huangla xilp xi nhau.Tuy nhien,ding c'anphai chuyde'ncatru'ong h<;jpkhimah~s6phannhanhtheohaihuanglakhongnhunhau. CackythU?timkie'mvftndU<;fCsii'dt:!ngph6bie'nhi~nnayvftnla timkie'm theohuongtie'n,timkie'mIDeohuanglui.TrongmQts6tru'ongh<;fpnguoitacon ph6ih<;fpcahaiphuongphap. 111-BIEUDIEN TRI TH(JC: Quatrlnhtimkie'mth\\'chillla quatrlnhchuyendQngtrencacdinhcua mQtd6thiho~caymam6idinhcuachungbiendi~nmQtdiemcuakhonggian bailOan.Honnllacacbailoanmachungtamu6ngiaiIacacbailoanngaycang phuc~pthlvilnd~biendi~ncacd6itu'<;fngcacs11ki~nclingnhucactrithuccua bailoankhongthela mQtvilnd~ddngian.G'andaymQts6ky thU?tmdidu'<;fc hlnhthanhtrongtinhQcvadatrdthanhnQidungcobancuatritu~nhant~o,d6 lacacky thU?tbiendi~n,xii'ly va quailtri tri thuctrenmaytinh.Theoquail diemcuatinhQcthltrftu~nhant~ola khoahQcv~vi~cbiendi~nva sii'dt:!ng kie'nthat.MQichudngtrlnhcuatrftu~nhant~od~uphaid11atrenmQtlU<;fCd6 bi~udi~nkie'nthucnaod6. 15 LU~NVANTHACSI KHOAHQC 111-1/Caed~ngtri thue: Tri thuctant~idudihaid~ngcdban: - Tri thacdinhht<Jng. - Tri thacdinhtinh. Cactri thacdinhlu<JngthuClngAllvdi cacHenristickhacnhau,cacky thu~tHeuristicpht~thuQcvaonhi~ucacchatlu<Jngciiacachamdanhgiala cd sdd~h;1'achQnchie'nlu<Jcdi~ukhi~n:xa ly c~nhtranhvachQnhu'dngdmkie'm phuh<Jp. Cactri thacdinhtinhdu<Jchiathanh3 lo~i: -Tri thacmota(Declarativeknowledge) -Tri thacthii~c (Proceduralknowledge) - Tri thucdi~ukhi~n(Controlknowledge) * Tri thucmotachonhungthongtinv~mQts~ki~n,hi~ntu'<Jnghayqua trlnhmathongduarathongtinv~ca'utrUcbelltrongclingnhucacphudngphap sad\mgbelltrongtrithacdo.Tri thucmotaconchophepmientam6ilienh~, cacrangbuQcgiuacacd6itu'<Jng,cacs~ki~nvacacquatrinh. * Tri thucthii~cchotanhungca'utructriiliac,ghepn6ivaSHYdi~ncactri thli'cmditUtrithacdiico.Caclo~itrithacnayt~onencdsdciiaky ngh~xaly trithac(Knowledgengineering) * Tri thacdi~ukhi~ndungd~di~ukhi~n,ph6ih<Jpnguantrithacthii~c vatrithacmatakhacnhau. VidT!-..E>6ivdiphudngphapgiiiiquye'tva'nd~nhClbi~udi~ntrongkhong giantr~ngthai. - Cactrithacmotalacacthongtinv~cung,dinh. - Cactrithacthii~clacacthii~cfimkie'm. - Cactri thtl'cdi~ukhi~nlienquande'ncacchie'nlu<Jcdi~ukhi~nd~l~a chQndinhndu<Jcthaoravahuangtimkie'mtrongthonggian. 111-2/Caephuongphapbi€u di~ntri thue: Tu'dngungvdihailo~itri thacmotavatri thtl'cthii~c,c62 lapphudng phapbi~udi~ntrithac: bi~udi~nmotavabi~udi~nthiitq.c.Caccdche'di~u khi~nseduQclangtrongbanthanca'utrUcngonngubi~udi~ntri iliac.Co th~ phanlo~inhu'san: 16 LU~NVANTHACsTKHOAHOC - Phuongphapbi€u di~ntri thll'Cmota : logic,m<;lngngii'nghla,AOV - Phltongphapbi€u di~ntri thucthilt~lC: sanxua't. -Phu'ongphapbi€u di~nh6nhqp: frame. 111-2.1/Caephuongphapbi€u di~ntri thuemofa. 111-2.1.1/Bi€u di~ntri thueAhalogich: Cosdlogichbi€u di~nb~nglogichm~nhde. Cosdtrithuc(Knowledgebase)gam2ph'an: - Cacs~iki~n: (Facts) - Caclu~t(Rules) Cacs~tki~ndltqCchobdicaclu~td~cbi~td<;lng: T~pF =(qI; q2 qk)t<;lODengia thie'tchoph'anSHYdi~ncac dinhlu~td d h ;! " "<;lugc uanPI .oo.Pn~ q Cosdtrithucbi€u di~nb~nglogichvi tri. Cosdtrithucgam2ph'an: - T~pcacs~ikit'$nF. - T~pcaclu~tR. Cacs\1kit'$nduqcchobdi 0 ~ qi (x, y, zoo..)Hi cac vi tri ph~lthUQCVaGcac h<;lngthucx, y, Zoo. TrongtruClnghqpx, y, z Hicacbie'n,ne'uchungg1{nvdi luqngtU':3thiphai thaychungbdi mQtgia tri tltqngtIlingho~cth~ts\1. Caclu~tcod<;lngPI (.) /\.oo"Pn(.) ~ q(.)dieuc'anluuy lacacbie'nthalligia trongpi & q denphaig1{nvdihiqngtU'"vdi mQi" Logicvi tr!va logichmt'$nhdecocacliu di€m san: - La ngon ngii'bi€u di~nki€u mo ta. - Co khaDangSHYdi~nvdi caccoche'quellthuQc. 17 0 ql 0 q2 0 qk LUANVANTH~CsTKHOAHOC - Kha tr~lcquail dO'ivoi ng11C1isi 'd1Jng. - Khag'angUiv~cuphap. - Co th6dungd6motacffutrucvaxii'ly dQngmohinh. - Co th6ki6mtratinhmauthuantrongcdsdtrith((c. - Tinhmoduncao. Ng1IQCl~icongc1;1logichdiibQclQmQtsO'ye'udi6m.. - M((c dQhinhth((choaquacao,danWi kho higHngfi'nghlacacvi tri khi xemxetch1ldngtrinh. -Nangsufftxii'ly thffp. - Do cactri th((cd1lQCbi6u di~nnhC1cacvi tri nendin u'uthe'sii'd1;1ngdiu trucdfi'li~uthong d1lQCthai iliactri~td6. 111-2.1~2/Bi~udi~ntri thucnhomiJ-ngngunghia. M.~mgngfi'nghlala d6 thidinhh1longmacacdinhtu'dng((ngdO'ivoicacdO'i tu'Qngho~cthai ni~mth6,concaccungphananhnhfi'ngquailh~gifi'acacdinhdo. (Tritu~nhant~o:Cacph1ldngphapva((ngd1Jng) MQtcachhinhth((c,m~ngngfi'nghlacoth6mohinhbdimQtd6thiG =(N, A)voit~odinhN vat~pcungA. T~pdinhN t1ldng((ngvoi cacdO'itu'Qng,cacthai ni~mhays1;fki~nC1;1th6. T~pcungA = {(a,b) / a,b E N) tu'dng((ngvoi cacmO'ilien h~giUacacdO'i tu'Qnga& dO'it1lCJngB. Co 2 lo~iquailh~d~cbi~t: "a lab" va"a baag6mb". Trongquailh~"a baag6mb" cacthongtincd banv~cacdO'itllQngchobdia setruy'Cnl~ichob.Nh11v~ytacod1lCJCmQtcd chelantruy~nthongtintrenm~ngngfi'nghlamythuQCvaocacmO'il enh~.Cac bi6udi~nnayco1mdi6m: - Cho phepbi6u di€in mQtcachtr1;fcquailcac S~Iki~nva cacmO'ilien h~ gifi'achung. - Tinhmodulcaotheonghlatrith((cthemvaohoanloandQcl~pvoicactri thac u. - La ngonngfi'bi6udi~nd~ngmota. - Co th6ap d~mg1 sO'cd che'SHYdi€in trenm~ng: cd che'truy~nva thua huangthongtingiii'achung. 18 LU~NVANTHACsTKHOAHOC Bi€u di~nnay cling c6 mQtsO"nhll'qcdi€m : - Khongc6phudngphapSHYdi~nchungchomQilo~im~ngngii'nghla. - Kh6 ki€m soatquatrinhc~pnh~ttri thl1'c,clandtn c6 mallthuantrongcd sdtri thl1'c. 111-2.1.3/ Bi€u di~ntri thucthutl}ccach~lu~td~n: Ngaynaytrenthtgioidaxufithi~nkhanhi~ucaechltdngtrinhIOngiaicac baitoaDtrencactanhV\l'ckhacnhaunhll'dt;1'baathaititt,thittkt h1dQng...f)~c di€mcuacacchudngtrinhnayladungl~plu~nthonghinhthl1'cdt;1'atrentrithl1'c docacchuyengiatrenti1'ngtanhvt;1'cclingcfip.Hftuhtt cacchudngtrinhn6i trend~uchl1'acactrithl1'cbi€u di~ntheoki€u :"IF -THEN" Thid~:Ntu tamgiacABC cant~iA thi B =C CacquiHlcki€u IF - THEN nhll'v~yse t~oDen1 cd sdtri thl1'cbi€u di~n theoquit~cdi~nxufit(hayh~lu~tdaD).Ta c6d~ngt6ngquatcuamQtqui~c trongh~lu~tclanla: . -Quit~cX : Ntu di~uki~n1 di~uki~nrn Thi ktt lu~n1 ktt lu~nn Tuytheornl1'cdQphl1'ct~pcuatri thl1'c,quidinhvitt cacdi~uki~nktt lu~n c6th~lam~nhd~ddngiancacvi tt;1'cfip1 kerntheodQch~ch~nvatinc~y. Ngu'oitac6th€ sad~ngquit~cclanxufittheochi~uti~nho~clui. Thi d~chocdsdtri thl1'csan: Cd sd S\l'ki~n Tl1'giacPQRS la hinhbinhh~mh. Tl1'giacc6 2 duangcheob~ngnhau. Tqpcaeluqfla .- Tl1'giacPQRSlahinhbinhhanh~ Tu giacc6cacc~pc~nhdO"isongsong(R1) Tl1'giacla hinhchii'nh~t~ Tl1'giacc64 g6cd dinhd~uvuong(R2) 19 LUANVANTHACsi KHOAHOC T(( giac PQRSlahinhbinhhanh~ T((giacco c~pq.nh d6i songsong(R3) T(( giacco c~pc<:J.nhd6i b~ngnhauva 2 du'ongcheob~ngnhau~ T(( giac la hinh chii'nh~t(Rt) T(( giac co 4 goc d dinh b~ng1 vuongva ill' giac co 2 du'ongcheob~ng nhauvaill'giacco2c~pc<:J.nhd6ib~ngnhau~ T((giacco2 trl;1cd6ix((ng(Rs) T(( giac co 1 c~pc<:J.nhd6i songsongva 2 du'ongcheoc~tnhaut<:J.itrung di~mcuam6idu'ong~ T((giacla hinhbinhhanh(R6) Giasatakyhi~u: Cdsddii'li~ulaM, N T~pcaclu~tdaDla : (R3): M ~ A (R2): B ~ D (R4):E " N ~ B (R5) :D " E " N ~ C (Rl): A~E (R6): G" H ~ A Nhu'v~yM, N daDxuattheochi€u titn sechoktt quasan: Vdi qui t~cl~plu~ntrenchi vdi 2 sl;!'ki~nM, N se daDxua'tthemcacsl;!' ki~nA, B, C, D, E. Ngu'qcl<:J.imu6nxem sl;!'ki~nD c6 daDxua'tngu'qcto'dii'ki~nnaota sa dQngquatrinhdaDxua'tlui. Theo sd d6 cay vA. - HoAc trenta tha'y2 bQsl;!' ki~ndaDraD la (M, N) va(H, G) G >v~ Ho~c E A D H B N 20 (R3) MA {A,M, NJ (Rl) AE {A,E, M, N} (R4) E"NB {A,B, E, M, N} (R2) BD {A,B, D, E, M, N} (R5) D"E"NC {A,B, C, D, E, M, N} LUANVANTH~Csi KHOAHOC Cach bi€u di€n nhCJlu~td~nc6 cac lID di€m san : -Cachbi€u di€n khaddngianvatn!cquaD: - C6 th€ SHYdi€n theocacchi6nluQckhacnhau: SHYdi€n ti6n,SHYdi€n lui, SHYdi€n h6nhQp. - Khag'angfiivdingonngurootacuangonnguLISP. - C6th€ ki€m ITatinhmallthu~ngiuacaclu~t. - Tinh modulcao,nghlala vi~cthembdt, lo(;libi) cac lu~td~nhoanloan khonganhhudngWicaclu~tkhacvacdch6suydi~n. NguQcl(;licachbi€u di~nn'ayc6mQts6h(;lnch6: - Nanglq'cxii'lythip. - Khongsii'd~ngduQCciu trucduli~u. Bi€u di€n nhCJbQbalienhQpOAV. MQtcachbi€u di€n khacla sii'd~ngbQbaB6i tu'Qng- ThuQCtinh - Ghl tri (Object- attribute- Value)d€ chi ding "B6i tu'Qng"vdi "thuQctinh" da choc6 mQt..gia tri" nao.d6. C'anphanbi~thaid6itu'Qng: d6itu'Qngtinhva d6itu'QngdQng.Cacd6i tu'QngfinhduQclu'utrongh~nhddaih(;lnvakhic'anduQcduavaobQnhdlam vi~cd€ xii'ly.NguQcl(;li,trongquatrinhlam'Yi~ckhic'ansekhdit(;locacgiatri thuQctinhciiacacd6itu'dngdQngvachungduQchtlldbQnhdtrongph~cv~.cho vi~cxii'ly ti6ptheo. Phudngphapbi€u di~nbQbalienhQpc6nhungdi€m m(;lnhsau: - Chophepbi€udi~ntn!cquaDcacd6itu'Qng. - Tinhmodultu'dngd6icao. - La ngonngubi€u di~nd(;lngmotit. -Cho phepdi~nd(;ltkhatu'CJngminhcaclu~tsuydi~n. Tuynhienphudngphapn'ayclingc6mQts6nhuQcdi€m nhunhuQcdi€m cuacachbi€u di€n theom(;lngngunghla.Ngoaira,cacquaDh~lienk6tgiuacac d6itu'Qngkhongth€ bi€u di~nmQtcachtu'CJngminh. 111-2.1.4/Bi€u di~ntri thucb!ingFrame B€ ciu truch6amQtluQngtri thacldn.Murskydaduara mQthinhm~u Frame.Framethl1Cchit la s,!t6ngquath6aciu trUcbanghitrongPascalho~c danhsachbanth€ tTongLISP vatu'dngt1!nhuciu trucd6itu'QngtrongC++,t~n 21 LU~NVANTH~CsTKHOAHQC d~lllgdll'~cacu'udi~mcliacac1u~Hdftnvavi tri, clIngnhll'm~ngngfi'nghla.MQt Framedll'~Ct~onen fir mQtt~ph~pcae tru'ongterminal.Trong m6i tnl'ong termina1labi~udi6ncilamQtdangky co th~(nhll'mota lo~i,di~uki~nvamall saochocacdangky do t~oramQtsl1ke'th~phcjp1y) "Cach~chuyengiau'encdsdFramegall, thiVl]GUSvaNUDGE" TTNT : Cacphll'dngphapangdl;lngB~chHu'ngKhang-HoangKie'm-Nha xuatbanKHKT - 1989 Cachbi~udi6nFramechotanhfi'ngll'ndi~msan: - Bap ll'ngcacyell diu bi~udi6ntri thac. - Cho phep ngu'oisirdl]ngkha t~l'do khi bi~udi6n tri iliac. - Framekhongchidu'~cdungd~motatri iliac,macondu'~cdungd~th~ hi~ncacthu~ttoanSHYdftn. - Framet~ndl;lngdll'~Cnhfi'ngthe'm~nhcuabi~udi6nthutl;lcvamota. - Quatdnhxa 1ytrenFramedQcl~ptheonghlathilake'thongtinkhong nhathie'tphaitu'antl1. Benc~nhdo-FrameclIngcomQtvaih~nche'. -Quani;ingn~d6ivdi ngll'oisadl;lngthongthu'ong. - Vi~cgiau'icuacacU'll'ongterminalcotl).~gallquavi~cthvchi~ncacthu tl;lclamchovi~cthun~pvac~pnh~tri thactrdnenphact~pvalamkhanang m~mcleophuh~pvdi nhfi'ngthayddicilamoi tru'ongngoaigiamxu6ng. . -Calltruccllah~FramechophepmotacacCalltrucdi~ukhi~nxa1y: thll tl;le.Mi;itkhaeCalltrueFrameehophepd~ngbi~udi6ncaeddnvi Calltrucdi~u khi~nvacaeddnvi CalltrUedfi'li~u,nene'anphaisadl;lngcaebi~nphapkha diuky.Vi the'matHnhtrvequailtrongphu'dngphapbi~udi6n. - Khi bai toantrd nen phaet~phdn, vi~emo ta va di~ukhi~ntrongh~ Framesephaet~pnhi~utrongcaephu'dngphapbi~udi6nthll tl;lckhoa. , f l 22 LUANVANTHACsi KHOAHOC So d'cae phuong phap biiu dieD Bi~udi~ntri thl1e B"' / /eu~ ~ Bi~udi~nthd~le ~ BQbalienhqp +- M~ngng~og7"\n suilt Frame 811gi6ngnhaugiiiacaephuongphapbiiu dieD Caelu~tSHYdanlogicconhi~udi~mgi6ngnhausovoicaelu~tsanxua't. Caedi~uki~ntronglu~tsanxua'trongnhi~utru'onghqpco th~quiv~ d~ngphcitbi~usii'dl;1ngvin'rhaym~nhd~. Caephu'dngphapbi~udi~ntrithl1ecoth~xemnhu'Him~nhngangnhauv~ khiinangmotad6inl'<;fng,caes11ki~nvamQtph'ancaem6iquailh~gifi'acaed6i tu'<Jng.Tuynhienphll'dngphapm~ngngii'nghlacokhanangbi~udi~nei~lien ke'tgiii'acaed6itu'qngphongphunha't.Tu goedQxii'ly thdtl;1e,a'utrueframe vaeaesloteoloi gQithdtl;1ecokhanangxii'ly m~nhdneaehtie'pe~nlu~tdan. 23 H san Logich Mc;mgfigii' GAV Frame Lo:;ti xua't nghla S11kin S11kin Mnh d vi trt Nut BQOAV Slot Tinh eha't S11kin Lut Quanh Lut Quanh d6itu'qng Quan h Sanxua't SHYdan Quanh Cantra gifi'a ca.e d6itu'qng LUANVANTHACsi KHOAHOC 111-2.2/ Cdche'I~plu~nv6;ibi€u di~ntri thuc : Cac nhalogichdachira C.<icphu'ongphaplu~nchuy€u san: - Phu'ongphapSHYdi~n. - Phuongphapquydi~n. - Phuongphapquin~p. PhuongphapSHYdi~nduQcdungphcSbi€n trongcac tu'duychinhxacva ch~tche,haikieuSHYdi~nquellthuQcla modusponensva modustollens.Hai cachSHYdi~ntrongquatrinhl~plu~nthu'ongdungSHYdi~nti€n valui.Ph6ihQp caccachSHYdi~nti€n valui sechocacky thu~tSHYdi~nthichhQpchocacva'n d-eCl}the. . . Phu'ongphapquin~plaphu'ongphapl~plu~ndi tUcachit$ntu'QngriengIe dekhaiquatthanhquihl~tc6HnhphcSbi€n. Kieuquin~pmaconnguoisii'd\lllg clingra'tdad~ngvaphlJthuQcnhi-eutrithlic.DosirdlJngquin~pmatrithlicloai ngu'oim6ingaydu'Qctangleura'tnhi-eu. M~tkhactri tut$con nguoicon c6 nhungkha nangra'td~cbit$td6 la kha nangbienva SHYlu~nbiingphepSHYdi~n. Trien vQngciia cac chuangtrinh"thongminh" phlJ thuQcnhi-euvao kha nangv~ndlJngnguontri tut$n6i tren. Nhi~unha tin hQcchodng diem ma'uch6tde may c6 thebien duQcslJ' tu'ongtlJ'(nhU'conngu'oi)la vit$cbiendi~nthongtinv~cacd6i tU'Qngdin sosanh dltdid~ngtit$nIQi.Thi dlJ dltdid~ngcacFramebaogammQtt~phQpchliacac giatri thuQcHnhnaod6cuad6i tuQng. DI nhien,ke cachod€n nayvit$cxay d\tngcaccoch€ SHYlu~nchocacht$ tri tut$nhant~ov~nla bai loankh6,d~cbit$tvit$cxay dlJ'ngcoch€ quyn~pcho caeht$ehuyengiavftnconIa va'nd~nailgiai. Ngoai fa, cachltdngnghienClmv-eht$ehuyengia clingdangc6 nhi-euthu hUtvi doclingchlnhlacac nghienell'uv-echltongtrinhhUllich, tit$nIQidapling duQcvit$cgiai quy€t nhi-eunhudiu th\tct€ matrudchic chU'agiaiquy€t dU'Qe. VI- H~CHUYEN CIA: Ht$chuyengia la nhungchltdngtrinhbi€t bAtehU'ocac cachling xii'eiia caechuyengia.Chungdungnhungthongtin dongltoisii'dlJngCHUgca'pdedua rayki€n v-emQtchud-enaodo. (HepbertSchildt- L~phlnhC chohi tut$nhan~o- Nhaxua'tband~ihQc- 1991) 24 LUANVANTH~CsTKHOAHOC Nhu' v~y,h~ chuyen gia co th~df;itnhi~udiu hoi d~phong va'nnglioi sa dl)ngcho d€n khi co th~nh~nbi€t dli<;lCdoi tu'<;lngphil h<;lpvoi nQi dung ITa loi cua ngu'oisadl~ng. M6i h~chuyengiaco2 bQph~nHicdsdtri tht1'cvacdch€ l~plu~n. IV-1/ Cd SO'tri thU'c: "Cd sd tri tht1'cHi mQtcd sd dil li~u cht1'anhilng thong tin df;ictIling clIng voi cac quy titcv~mQtchu d~nha'tdinh nao da'y" (HepbertSchildt- L~ptdnhC chotritu~nhflll410- Nhaxua'tband~ih9C-1991) Cd sd tri tht1'cbaa g6m mQth~lu~tphan anh hi~ubi€t va linh nghi~mcua cac chuyen gia trongmQtUinhv~l'chyp xac dinhva mQtt~ph<;lpcac sl)'ki~nlien quail d€n cac Hnhhuong dll'<;lcxem xet dll'<;lCcoi nhli dil li~uva chu y€u do nglioi sadl)ng clIng ca'p. Cha'thl'<;lngcliamQth~chuyengiaphl)thuQcra'tnhi~uvaocha'tlli<;lngcua cdsd tri tht1'c.Cd sd tri tht1'csemotacacdoi t:tl'<;lngva moi quailh~giila chung, motacacgiai phapkhacnhautrongcacHnhhuongCl)th~vango~il~,cacrang buQcuaquy€t dinh.Nhl(v~y,tacoth~xemcdsdtritht1'cladaubsachcacdoi t:tl'<;lngclIngcacqui titcvacacthuQctinhcolien quail. VI- 2/ Cdch~I~plu~n: "Cd ch€ l~plu~nHi chll'dngtrinhmo phongcachl~plu~nclia connglioi, Chl(dngtrinhn'ayco kha nanghQcki€n tht1'chuyengia ca'utrucva khai iliac . chungd~t~onencacl~plu~n1:1)'dQng". "Nhli v~ycd ch€ suylu~nHimQtbQph~nclia h~chuyengiaco vai tro sa d~mgthongtindll'<;lCrungca'pd~Hmra doitli<;lng". Hai lu~tlogichhinhtht1'cdll'<;lcsa d~mgtrongmQih~chuyengia Himodus pollensvamodustollens. Hai phll'dngphapcd band~xiiy dl)'ngcd ch€ SHYlu~nHi l~plu~nti€n va lui,hof;icca2 hll'ong. - Phll'dngphapl~plu~nti€n : Phll'dngphapl~plu~nti€n doi khi condli<;lcgQila phlidngphaptruy~ndil li~uva cd ch€ l~plu~nsirdl)ngthongtingiongnhli connglioisadl)ng~~ntheo ID(;lnglogichVA-HOAC d~ti€n d€n k€t thuc,WcHimtoi doi t1i<;lng.N€u cdch€ SHYlu~nkhongHmtha'ydoi t:tl'<;lngbangthongtinhi~ncothinoseyellc'authem cacthuQctinhxacdinhdoi t:tl'<;lngamthanhdliOngd§n d€n doi t1i<;lng.Cachduy nha'td~ti€p c~nd€n doi t1i<;lngHithoamanta'tcacacqui titccuadoi t1i<;lngdo. 25 LUANVANTHACsTKHOAHQC DodocdcheSHYlu~ntienxuitphattirthongtinband'aud~huangWid6ituqng thichlingvaithongtindo. Oia sLY,ngu'oitaxay d\ingh~chuyengiav(shinhhQccocdsdtri thucnhu sau: Vai cdsdtrithucduqcxaydl!ngnhliv~ytacoth~l~psdd6th~hi~ncach SHYlu~nCliaphudngphapl~plu~nliendend6itUqnghinhvuongnhuhinhve sailday.H~th6ng.l~plu~ndfftienhanhxaydl;1'ngmQtcaytUg6cdenla. 4 c?nh I 4goc I 2 cf;ipc?nhd6i biingnhau C 2duongcheo biingnhau I 2duongcheo vuonggoc I Hinhvuong Phlidngphapl~plu~nllii L~plu~nlui Hiphudngphapngliqcvdi phudngphapl~plu~ntienxua'tphat tUgiathietd6i tUqngvayell c'authemthongtind~khiingdinhhayphudinhno. L~plu~nlui doikhi duqcgQila truy(snd6i tUqng,vi hQchuyengiaxua't phathI'd6itliqngva sandotimcachki~mchungno.Oia sa,apd\mgquatrinh l~plu~nllii VaGcdsdtrithuchinhhQcnentrentacosdd6th~hi~nphudngphap l~plu~nllii de'nd6ihiqnghinhvuong. 26 BQituqng Quitc ThuQctinh Tugiac co 4c?nh,4 goc Tugiac co 2duC1ngcheo ffinhbinhhanh co caccf;ipc?nhd6ibiingnhau ffinhbinhhanh la tUgiac . ffinhvuong co 2duongcheovuonggoc ffinhthai co 4c?nhnhau ffinhchfi'nht co 1gocddinhvuong ffinhchfi'nht co 2duongcheobiingnhau LU~NVANTHACsTKHOAHOC Hlnhvuong Hinh chi! nh~t /~ - 2 dttongcMo vu6ngg6c Hinh hinh hanh /~ 2 Mi!ng cheohAngnhan Tu giac I co2 c(;lnhd6ib~ngnhau 4 c(;lnh 4 goc 2 dttongcheo IV-3/ Ca'utruedCi'li~uehomo hlnh I~plu~nlui Giii sitcaclu~tdftntrongcdsdt\ithucd~ucod(;lng: If bie'n1=gia tri 1 bie'n2=giatri 2 AND AND bie'nn=giatri n Then bie'n=giatri * Bie'nti~nd~Ia cacbie'nchi xu~thic$ntrongph'anIF cuacaclu~tdftn (khongxu~thic$ntrongph'anTHEN cuab~tky lu~tdftnnao) * Bie'nke'tlu~n: lacacbie'ntrongph'anTHEN cuacaclu~tdftn. * Bie'nmc$nhd~:cacbie'ncoxu~thic$ntrongph'anIF cuacaclu~tdftn. IV- 4/ Caeea'utruedCi'li~u: IV-4.1/Oanhsaehke'tlu~n: (CONCLUTION LIST) La danhsacht~tcacacke'tlu~ncoth€ co.Theogiasittrenkichthttdcua caedanhsaehke'tlu~nb~ngs6lu~tdftntrongedsdtrithue. M6i ph'antittrongdanhsaehke'tlu~ngam2ph'an: - s6lu~tdftnvatenbie'nke'tlu~neiialu~tdftndo 27 Lu.~NVANTH~CsTKHOAHOC CONCLUTION =RECORD rule_number:interger; varname:string; end; CONCLUTION _LISt: alTay[1..N] ofconc1ution IV- 4.2/ Oanh sachcaeti'end'e: (VARIABLE LIST) Dogiatricuacaebie'nm~nhd~c6th~xacdinhdu'<;1Cb~ngeachhoingu'oi sadl;!ngnentac6diutrUedfi'li~usail: VARIABLE =record var_name: string; instantiated:boonlean; value: string; end; Trangd6 : var_name: tenbie'n instatiated: (chobie'tgia tri cuabie'ndil du'<;1Cxacdinhchu'a?) value: giatri cuabie'n(chidungkhi bie'ndil du'<;1cxacdinh. (instatiated=true) IV- 4.3/ Oanhsachbie'nm~nhd'e: (CLAUSEVARIABLE LIST) La danhsachcaebie'ntrongphiinIF cuacaelu~td~n. M6i lu~td~nchic6t6idamm~nhd~trongphiinIF, tae6th~dungmilng IDQtchi~ud~hilldanhsachbie'n. M6i lu~tsedu'<;1CdanhriengIDvi tri d~chll'acaebie'nm~nhd~cualu~td6. Ne'ulu~tc6 it hdnmbie'nm~nhd~thlcaevi ill thirasebo tr6ng. Ca'utruedfi'li~unayt6nbQnhdnhu'ngti~nchovi~ctinhloan. Vi dl;!:Ta c6th~bie'ttenbie'nm~nhd~thll'j cualu~td~ni chinhla phiintd' thll'ID* (i - 1)+j cuadanhsachbie'nm~nhd~. (Ne'ulu~td~ndu'<;1Cdanhs6la bQis6cua10)thlcongthll'cla : m*(i/l0-1)+j 28 LU~NVANTHAC8TKHOAHQC IV-4.4/ Ngan xe'pke'tlu~n (CONCLUTION STACK) Bay Hidiu truedu li~utrungtamd~di~ukhi~nquatrlnhl~plu~nlui. M6i ph'antd'euanganxe'pgam2 phftn: stack- item: record; ruler_number: interger; clause_number: interger; end; Thu~tloanl~plu~nlui trenCAD TRUe nCfLI:e;udii chira : . Bade 1 : Binh nghTake'tlu~n . Bade 2 : TIm trong daub saehke't lu~ntri1ngten vdi ke'tlu~ndu'qedinh nghTa. +Ne'utim tha'yd~tlu~t d6 vao ngan xe'p,baa gam s6lu~t va (1) d~di~nta s6m~nhd~. . +Ne'ukh6ng tlm tha'ythl tra Wi kh6ng tim tha'y. .Bade3 : Xaedinhcaebie'nm~nhd~eualu~t. . Bu'<k4 : Ne'umQttrongnhungbie'nm~nhd~kh6ngxaedinhthlhoi ngaoi dungd~nh~pgiatrio . Bade5 : Ne'umQttrongnhungbie'nm~nhd~la bie'nke'tlu~nthl d~ts6 eualu~tehuake'tlu~nd6vaodinhnganxe'pke'tlu~nva trdl~ibade3. . Bade 6 : Ne'u th~hi~nd dinh ngan xe'pke'tlu~nkh6ng thoa ea'utrUeIF THEN eualu~td6thlloC;lith~hi~nfa khoi dinheuanganxe'pva t1mkie'mtrong daubsaehke'tlu~nmQtke'tlu~ntrungtenvdike'tlu~ndaqedinhnghTa. . Bade7 : Ne'utimtha'ytrdlC;libade3. . Bu'de8 : Ne'ukh6ngconke'tlu~nnaotrennganxe'pke'tlu~nvdi tend6 thllu~traded6lasai. Ne'ukh6nge6lu~traded6th1baavdingaoidunglakh6ngtlmtha'y. Ne'ue6lu~traded6thltrdlC;libu'de6. . Bade9 : Ne'ulu~td dinhnganxe'pdaqexaedinhxongthllo~in6khoi nganxe'p. Ne'ue6bie'nke'tlu~nkhaed daditangs6m~nhd~vaoehom~nhd~conlC;li quaytrdngaqclC;libu'de3. 29 LUANVANTH~CSI KHOAHOC Ntu khang c6 bitn ktt lu~n nao aduoi chungta c6 th~tnllCfi diu hoi. Ngu'Cfidungsenh~ndu'qcktt qua. IY-51 Cach ho~tdQng-cuamQtdun vi chuangtrlnh (DYCT) Trongphftnnaychungta senghienCUlll£;Linganngu l~ptrinhd~timhi~u mQts6 mahinh ho£;LtdQngcua donvi chu'angtrinhd~lam ti€n d€ chovi~cd€ xufftcachho£;LtdQngmoichomahinh l~plu~nlui. Ngl(CfitaphanIO£;Linganngul~ptdnhthanh3 nh6mchinh: a/ Ngonngil finh (FORTRAN, COBOL) : bQnho dl(qCcffpphattn(ockhi chuangtrinhdl(qCtht1chi~n,khangchophepgQid~quy. bl NgonngildT!atrennganxe'p(ALGOL 60 ..) : bQnho duqccffpphatkhi chuangtrinhduqcth~(chi~ntheonguyent~cLIFO. c/ NgonngildQng: (LISP, SNOBOL 4, APL, PROLOG) : khangth~doan trl(OCbQnhodl(qCcffpphatlucnaotranglucch£;LYchuangtrinh.. Chungtasequantamdtn cachho£;LtdQngcuamQtBVCT cuanh6mngan ngud~(atrenngans~pxtp d~maphongchoCTDL cuaIDahinhl~plu~nlui. Nhungdotdnht~(phattinhciiacacnh6mngannguchoHendftulienchungtase xemxetcachh<?£;LtdQngclIamQtDVCT clianh6mnganngutInh. * Ngonngil finh : SefluqIlgciiacaca nhodungchocacbitn Cl;lCbQla cef dinhn6 duqccffpphattronglucbiendichchuangtrinhvakhangthayd6itrong sueftquatrinhth~(chi~nDVCT. M6i DVCT dl(qCbiendichrCfir£;Lcva tliangungvoi 1BANG KfCH HOAT, vi~cthitt l~pbangghikichho£;Ltduqcchidinhtruockhi tht1chi~nvi tht bitn Cl;lC bQ se duqcma truocthCfidi~mch£;LYchuangtrinh va thCfigian sefngciia bitn dl(qCkeo dai trangthCfigianthlrChi~nloanbQChl(angtrinh. - Bang ghikich ho£;Ltcho cac bitn an loan ;! ? '" DIEM TRO VE GJ DVCT (1) DVCT (2) Bangghikich ho£;LtBVCT (1) BIEN Ct}CBQ Bangma(C) Bangkfchho~t(D) * NgonngildT!atrennganxtp: cacnganngudlratrennganxtp c6 cffutrUc kh6i,cffutrucnayki~mtratamanhhl(angcuabitn vaChl(angtrinhthanhBhang BVCT. 30 LUANVANTHACsTKHOAHOC Hai DVCT bfttky ho~cla roi nhauho~cla i6ng nhau. Ba d~ctru'ngcho ngon ngfi'dt1atren siipxe'pla : . ChophepgQid~quycacDVCT Di€u nayc6nghla la sO'Instances(instancesla sO'bangkichho~tdoihai choDVCT d mQtthaidi€m bfttky) c6 th€ khongdu'<Jcquye'tdinhtru'dcthaigian th\1chi~n. 0 m6idftnracuaDVCT, mQtbangkich ho~tmdi phai du'<JcphanbO'vdi bangsaocuabie'nC\ICbQmditht1Chi~n. . Chftpnh~nnhfi'ngcftutrucdfi'li~udQng. . Cho phep ngu'oil~ptrinhmd dO'itu'<Jngdfi'li~ud di€m tt)yy trongsuO't chu'angtrinh. Cancii'vao: - Thoi giansO'ngciiabie'n. - Moi tru'ongthamchie'uchomQth€ hi~ncuaDVCT. Ngu'oitachiangonngfi'lo~inaythanh4 lo~i: +Lo~i1 : sO'ch6din thie'tchomQtbie'nla c6dinh : (cftpphattInh) + Lo~i 2 : sO'ch6 din thie'tcho mQtbie'nchi du'<Jcxac dinhkhi thi hanh chu'angtrinhc6chii'abie'nd6. +Lo~i3 : sO'ch6din thie'theoyell diu cuamQtbangkich ho~tsekhong dtt<Jcbie'tkhi DVCT bi kich ho~tnhu'ngsedu'<JcftpphatdQngkhiCalll~nht~o l~pmdibi truyxuftt. +Lo~i4 :KhimQth€ hi~ncllaDVCT c6th~truyxufttde'nmoitru'ongngoai. DO'ivdi lo~ingonngfi'mabangghikich ho~tvdi chi€u daibie'ttrUdc,tInh khi bangghikichho~tdu'<Jct6chii'c. ? ? '" D~ACHI TRd VE Contratrade'nbangghi kichho~tdffgQin6. Con tra trendu'<JcgQila lien ke'tdQng.T~ph<Jpcac con tra t~othanhh~ thO'nglien ke'tdQng. 31 LU~NVANTH~Csi KHOAHOC Vidt:t: DVCT AgQiB DVCT B gQiC Khi C trdv~B thibangghikichho~tcuaC sedu'<;jcgiaiph6ng. Khi B trdv~A thibangghikichho~tcuaB sedu'<;jcgiaiph6ng. Ngu'aitadungthem2controh6tr<;jchocontroip. Controthli I la FREE thu'angd~td vi tri c6hi~ulyc ke'tl;1ctrongDATA MEMORY. ControthliII laCURRENTd~td vi tribangghikichho~thi~nthai. Free I Current I C'anphaihill ycdche'l~plu~nvatachbi~tvdicdsdtriiliac.Cdche'fir la 1 quitrlnhv~nhanhchungchonhi~ucdsdtrithlickhacnhaud€ t~onennhungh~ chuyengiakhacnhau.Cdcfiunaychophepthie'tl~pcach~chuyengiadamt:tc lieukhongc'anl~ptrinhl~i. Hdnnua,mQtd~ctru'ngcdbanv~hanhvi thongminhcuahechuyengiala khananggiaithichdu'<;jccacsurdi€n cuaminhtrencondu'angdi de'nke'tlu~n v~khanangITaWicacdiuhoikhacnhaudongu'aisadl;lngd~tfa. v- cAc UNG DUNG CUA HE CHUYEN GIA vA TRI TUE NHAN TAO ",' "', ~ '" ,.. TRONGTHIET KECAC PHAN MEM D~NG HQCTOAN. Nhunglingdl~ngcllakhoahQctinhQcdii lamthayd6ikhaloandi~n,kha sansAcde'nnhi~unganhkhoahQc,trongd6c6khoahQcgiaodl;lCn6ichungva d~yhQCn6irieng.Banchfitcuaquatrinhd~yhQclaquatrinhbie'nd6ithongtin, trongquatrlnhbie'nd6id6th'ayla ngu'aichud~o,conhQcsinhla ngu'aichu 32 LU~NVANTH~Csi KHOAHOC dQng.D~th~tsvHinguoichud~o,nguoith'aygiaophiiibie'tachacdi'€ukhi~n quatrlnhlacdQngqual~igiuath'ayva11"0,giuatrovatrithacd~giuphQcsinh chlldQngtlmdU<;lekie'nthll'c~di.MQttrongnhungDangh!ctachacdola Dang Ivctachacthongtingiiingd~y,baag"Omcachbi~udi~nthongtin,bi~udi~ntri thacclingnhu'phanchiatrithacthanhcacdonvi nhasaochom6ilienke'tgiua cactri thacla khoahQc,la nh§tqUailvaphuh<;lp.CacnQidungdoc6nhung di~mr§t ti~mc~n,r§t tu'ongd"OngvdicacnQidungvaphuongphapcuatri tu~ nhant~o.Hi~uquiicuavi~capd\lngtd tu~nhant~odU<;lcDangleDmQtbudcVI nhii'ngtri thacloanhQCthu'ongdu'<;lcphcitbi~udu'did~ngcacm~nhd'€ "ne'u... thl"choducactrithacdoladinhly phatbi~ududid~ng1dinhnghla,1dinhly haymQtbailoanti~uhQCblobthu'ong.Cacquyuk duoid~ng"ne'u thl"se t~onenmQtquitik dfinxu§t.H~quit~cdfinxu§tcungvdi cacdinhlu~tbi~u di€n sechophepth~hi~ndU<;lccacd6itU<;lngcualoanhQCvam6iquailh~giua chungdudid~ngcackyhi~u.Di'€ud~cbi~tbonQuala cacd6itu'<;lng§y coth~ dU<;lcxii'ly b~ngcacphuongphaptritu~nhant~odadaycongnghiencau.Ph'an m'€md~yhQcloandvatrennhii'ngthanht11Ucuatritu~nhant~oconchophep lu'ul~i"di€n bie'n"cuaquatrlnhSHYlu~ngiupchohQcsinhn~mvungboncac conduongdide'nke'tquii,t~odi'€uki~nd~sosanhvdinhungeaehgiiii,nhftng hudngSHYlu~nkhacnhau,tUd6t~oti'€nd'€ cho1hudngdi t6tnh§t,1hudng sangt~otrongtuonglai. Nguoitaclingc6th~apd\lngphuongphapnaytrongvi~cnghiencU'ugiao d\lcd~t~oDencac"bQd"Ongh'€"d~yhQClIen maynnh,"h"Osogiiii toan"... v- 1/ Bi~udi~ntri thuctminhQc: Thongthu'ongkhi changminhmQtdinhly haygiiii 1bai loan,connguoi khongnhii'ngphiiin~mvungcactinhch§t,cacdinhly c6lienquailmaconphiii hlnhdungdu<;lcvi tri,cachudnggiiiiquye'ttrongtUngkhonggianngii'ciinhhay noikhacbonladin n~mvii'nglu<;lcd'€ changminhtronghlnhhQcEuclidenguoi tadungIU<;lCd'€d~chidfinvi~curncachchangminh,lu<;lcd'€naylIdDenmQtbQ ph~nkhongth~thie'ud6ivdivi~cphattri~nmQtdinhly. GELERNTERdake't h<;lpcaccachchangminhdinhly tronghlnhhQcEuclidevoi cacquailsatcon nguoikhisii'd\lngcaeIU<;ltd"OlIend~t~orachuongtrlnhchangminhcacdinhly khathanhcongoGelernterdagQichuongtrlnhlamayhlobhQc. ChuongtrlnhcuaGelernterla 1vi d\l cuasvth~hi~nthanhcongcoche' giiiibailoand1;talIenvi~cbi~udi~ncacd6itu'<;lnghlnhhQcthanhcacvi trirai dvavaocacliend'€ va logichvi trid~changminhcacdinhly hlnhhQc.MQt trongcacml~Cdichcualacgiiikhithie'tke'mayhlnhhQCla lamchomayduara dU<;lCsvtu'ongthichvdi cachchangminhcuaconnguoi.D~thvchi~ndu<;lCco ehe'giiii bai toaDcaelien d'€ trongmayhlnhhQccuaGelernterdadu<;lechia thanh3ldp. 33 LuANVANTHAcsTKHOAHOC Cac tien d~lien ktt cac di~mvdi cac khai ni~mnhu': Bo~nth~ng,du'ongthAng,caeg6c,cactamgiac. Vi d~tiend~cactamgiacdu'<;fCmatanhu'san: Ntu A, B la 2 di~mphanbi~t. Ntu B, C Hi2 di~mphanbi~t. Ntu C, Ala 2 di~mphanbi~t. Ntu A, B, C la cacdi~mkhangth~nghang Thl A, B, C la tamgiac. Chungdu'<;fChlnhthlich6anhu'san: PHAN_BIET (A, B) PHAN_BIET (B, C) PHAN_BIET (C, A) KHONG_THANG_HANG (A, B, C) TAMGIAC (A, B, C) Cac tiend~th~hi~ntinhd6i xlingcuacacdo~nth~ng. Ntu do~nth~ngAB b~ngdo~nth~ngCD thl do~nAB b~ngdo~nDC va chungdu'<;fCdinhnghianhu'san: . DOAN (A, B) =DOAN (C, D) DOAN (C, D) =DOAN (D, C) Cac tiend~th~hi~ns11b~ngnhaugifi'acacg6cvacacdo~nthiing,s11b~ng nhau cua cac tam giac, s11song song gifi'a cac do~n th~ng ... Cac c~nhtu'dngling b~ngnhaudu'<;fCth~hi~nnhu'san : Tam giac (A, B, C) b~ngtamgiac (D, E, F) DOAN(A,B)=DOAN(D,~ DOAN (B, C) =DOAN (E, F) Va hai tamgiac la b~ngnhauntu chungc6 mQtc~nhva 2 g6ckt tu'dng ungb~ngnhau. GOC (A, B, C) =GOC (D, E, F) va 34 LU~NVANTHACsi KHOAHOC GOC (C, A, B) =GOC (F, D, E) va DOAN (B, C) =DOAN (E, F) TAMGIAC (A, B, C) =TAMGIAC (D, E, F) S\1'phan chia cac lien d<3thanh 3 ldp nhu tren la ra"tquantrQngcho vi~c sa dl;1ngcac luQcd6 d€ bi€u thi cach chang minh. Chiing h(;ln,sa d~ngcac lien d<3 va sll hlnh thac h6a cac dinh 1:9c6 th€ dua fa cach chang minh tlf dQngdinh 1:9 hlnh hQc "BuC1ngphan giac trong mQtg6c luau cach d<3uhai C(;lnhcua g6c a'y". Sll hlnh thac h6a ciia cac giii dinh nay duQcth€ hi~ndudi cac m~nhd<3Ia : DOAN (A, D) la PHAN_GIAC_GOC (B, A, C) DOAN (D, B) DOAN (A, B) DOAN (D, C) DOAN (A, C) DOAN (D, B) =DOAN (D, C) Cay timkie"mduQCminhhQanhusau: DOAN (D, B) =DOAN (D, C) / 7C(B, A, 0) = TAM GIA~ GOC (B, A, D) =GOC (D, A, C) / DOAN (A, B) =DOAN (A, C) DOAN (A, D) la PHAN_GIAC_GOC (B, A, C) 35 LUANVANTHACsTKHOAHOC v- 2/ Giai baitoan: Ap d~lllgVaGhinhhQCkh6nggiantacocelsdtri thucnhusan: Cach xiiy dung motdinhIf [t~pcacm~nhd~giathitt]~ M~nhd~ktt lu~n.D~ngC1;lth~: M~nhd~1(.)& [M~nhd~2 (.)] & [M~nhd~3 (.)] ~ M~nhd~(.) 36 Mnh d M6 ta Ba diSmthng hangA, B, C THANG_HANG (ABC) TrungdiSmM cuadon thng AB TRUNG_DIEM (MAB) Don thng AB DOAN (AB) Don AB =Don CD BANG_DOAN (AB CD) Duongtrungtn;(cd cuadon AB TRUNGTRUC (dAB) Tamgi:k ABC TAMGIAC (ABC) Tamgiacdin ti A TAMGIACCAN (AABC) TU'giacABCD TUGIAC (ABCD). IDnhblnhhanhABCD HINHBINHHANH (ABCD) IDnh thaiABCD HINHTHOI (ABCD) IDnhchfi'nht ABCD HINHCHUNHA T (ABCD) IDnhvuongABCD HINHVUONG (ABCD) Mt phng ABC MAT (ABC) DiSm M E don AB DIEMTRENDOAN (MAB) DiSmX E duongthng d DIEMTRENDUONG (Xd) DiSm X flAmtIeDduongtrollc DIEMTRENTRON (Xc) Don AB E mt phng CDE DOANTRENMA T (ABCDE) Duongth&ngaflAmtrenmt phng ABC DUONGTRENMA T (aABC) Giao diSmI cua2 don AB, CD DOANGIAODOAN (IAB.CD) Giao diSmI cua2 duongthng d, e DUONGGIAODUONG (Ide) Giao diSmI cuadon AB voi mt CDE DOANGIAOMA T (IABCDE) WANVANTHACsTKHOAHOC cae m~nhd~trong [ 1co th~co ho~cthong tUy theo s61uQngm~nhd~gia thie'tcua dinh ly. He th6ngdinh IVdungtrongchddngtrinh: (78) * Mot s6tinh chd'"tcuahlnhphdng: 1.DIEMTHUOCDOAN(IAB) & BANGNHAU(AIBI) =>TRUNGDIEM(IAB) 2. HINHBINHHANH(ABCD) & DOANGIAODOAN(IACBD) => TRUNGDIEM(IAC) 3.TRUNGDIEM(EAB) & DIEMTHUOCDOAN(FAC) & DOANSSONGDOAN(EFBC) =>TRUNGDIEM(FAC) 4.BANGNHAU(ABAC)=>TAMGIACCAN(ABC) 5.TRUNGDIEM(IBC) & DOANVGOCDOAN(AIBC) =>TAMGIACCAN(ABC) 6.DOANSSONGDOAN(ABCD) & DOANSSONGDOAN(ADBC) => HINHB INHHANH(AB CD) 7.TRUNGDIEM(IAC) & TRUNGDIEM(IBD) =>HINHBINHHANH(ABCD) 8.DOANSSONGDOAN(ABCD)& BANGNHAU(ABCD)=> HINHBINHHANH(ABCD) 9.HINHBINHHANH(ABCD)& BANGNHAU(ABBC)=>HINHTHOI(ABCD) 10.HINHBINHHANH(ABCD) & DOANVGOCDOAN(ACBD) => HINHTHOI(ABCD) 11.HINHBINHHANH(ABCD) & DOANVGOCDOAN(ABCD) => HINHCHUNHA T(ABCD) 12.HINHBINHHANH(ABCD) & BANGNHAU(ACBD) => HINHCHUNHA T(ABCD) * Hai doanthdngbAngnhau: 13.TRUNGDIEM(IAB)=>BANGNHAU(AIBI) 14.BANGNHAU(ABCD) & BANGNHAU(CDEF) =>BANGNHAU(ABEF) 15.TAMGIACCAN(ABC) =>BANGNHAU(ABAC) 16.HINHBINHHANH(ABCD) =>BANGNHAU(ABCD) 37 LU~NVANTHACsTKHOAHOC 17.HINHTHOI(ABCD) =>BANGNHAU(ABBC) 18.HINHCHUNHAT(ABCD) =>BANGNHAU(ACBD) 19.MATSSONGMAT(ABCDEF) & DOANSSONGDOAN(ADBE) => BANGNHAU(ADBE) * Badiim th~nghang: 18.DOANVGOCMAT(ABCDE) & DOANVGOCDOAN(ABFG) & DIEMNGOAIMA T(FCDE) =>DOANSSONGMAT(FGCDE) 19.DOANSSONGMAT(ABCDE) & DOANSSONGDOAN(ABFG) & DIEMNGOAIMA T(FCDE) =>DOANSSONGMAT(FGCDE) * Hai matph~ngsongsong: 20.DOANSSONGDOAN(ABDE) & DOANSSONGDOAN(ACDF) & . DIEMNGOAIMAT(ADEF) =>MATSSONGMAT(ABCDEF) 21.MAT(ABC) & DOANSSONGMAT(ABDEF) & DOANSSONGMAT(ACDEF) =>MATSSONGMAT(ABCDEF) 22.MATSSONGMAT(ABCDEF) & MATSSONGMAT(ABCGHI) & DIEMNGOAIMAT(GDEF) =>MATSSONGMAT(DEFGHI) 23.MATVGOCDOAN(ABCMN) & MATVGOCDOAN(DEFMN) & DIEMNGOAIMAT(DABC) =>MATSSONGMAT(ABCDEF) * Vu6nggoc: * Hai doanth~ngvu6nggocvdinhau: 24.DOANVGOCDOAN(ABCD)& DOANSSONGDOAN(ABEF)=> DO ANV GOC DO AN (AB EF) 25.HINHCHUNHAT(ABCD)=>DOANVGOCDOAN(ABBC) 26. HINHTHOI(ABCD) =>DOANVGOCDOAN(ACBD) 27.DOANVGOCMAT(SAABC) =>DOANVGOCDOAN(SAAB) 28.DOANVGOCMAT(ABCDE) & DOANTHUOCMAT(MNCDE) => DOANVGOCDOAN(ABMN) 38 LU~NVANTHACsi KHOAHOC *Doan th~ngvuong g6c vOimat ph~ng: 29.DOANVGOCDOAN(ABCD) & DOANVGOCDOAN(ABCE) ~ DOANVGOCMA T(ABCDE) 30.DOANVGOCMAT(MNABC) &MATSSONGMAT(ABCDEF) ~ DOANVGOCMA T(MNDEF) 31.MATVGOCMAT(ABCDEF) & MATVGOCMAT(ABCGHI) & MATGIAOMAT(MNDEFGHI)~ DOANVGOCMAT(MNABC) *Dinh If 3 ddongvuongg6c: 32.DOANVGOCMAT(SAABC) & DOANVGOCDOAN(ABBC) ~ DOANVGOCDOAN(SBBC) * Hai matph~ngvuongg6c: 33.DOANVGOCMAT(MNABC) & DOANTHUOCMAT(MNDEF) ~ MA TVGOCMA T(ABCDEF) 34.MA TVGOCMA T(ABCDEF) & MA TSSONGMAT(ABCGHI) ~ MA TVGOCMA T(GHIDEF) 39 LU~NVANTHACsi KHOAHOC 40 fact hI . fact h2 GT fact h3 fact hk Kl fact heI.. H~ CSTT GI factList GI RuleList A ? HOAT DONG CUA MOTOR. . Ri ---+ CAY L()I Glib Rj WANVANTHACsTKHOAHOC MQt sO"tac gia con ling dl~ngm~ngngii' nghla d€ giai 1 sO"cac b~LitoaD. M~ng ngii'nghla Hi d6 thi dinh hu'angma cac dinh tu'ongling vai cac dO"itu'<Jng ho~ckhai ni~mCl~th€ con cac cung phan anh nhii'ngquaDh~giua cac dinh d6. Vi dl}m~ngngii'nghla bi€u di~ntri thac hlnh hQcnhu' Bu'angcheo /,nh chii'nh~t / la b~ngnhau Blnh vuong ~~p Tfl}CdO"ixling Bu'angtrOll v- 3/ M~ngtinhtoan : # MQt trongnhii'ngm~ngngii'nghlangu'aita quaDtamd6nm~ngtinhloan. M~ngHnhtoaDHimQtm~ngngii'nghlachliacacbi6nva cacquaDh~co th€ cai d~tva sadl~ngchovi~ctinhloan.M~ngtinhloanla 1ki€u dli li~utrUutu'<Jngc6 khaDangxayd1f~gcachamdungchovi~ct6ngh<Jpthanhcacchu'angtrlnh. Vi dl.l: Quanh~f giii'asO"do 3 g6ctrongA, B, C cuatamgiacABC du'<Jc chobdi h~thlic : A"" /C CD B/ f : A +B +C = 180(donvi dQ) N6u gQiM la t~pcacbi6n. F la t~pcacquaDh~ Thl M(f) vai f E F du'<JcgQila t~pcacbi6nc6 lien h~trongquaDh~f. M(f) eM Cho m~ngtmhloan(M, F). Gia sac6 1t~pbi6nA e Mdffdu'<Jcxac~inhva B la t~pbi6nbfttky trongM. Cacvftndt3d~tfa la : - C6 th€ xacdinht~pB tUA nhacacquaDh~F ? - QuamnhHnhloantUA d6nB n6uB xacdinh. 41 LuANVANTHACsTKHOAHOC - Cac di~uki~nb6 sungde co th~xac dinh du<;jcB tirA. Bai toaDxacdinhB tirA trenm~ng(M, F) vi6tdu<;jcdltdid~ngA ~ B Ngu'oitadungkhai ni~mbaodongcuat~ph<;jplam 1 trongnhfi'ngphu'dng ti~nde giiii quy6tbai toaDU"en.Bao dongcuat~ph<;jpA ky hi~ula duQcxem nhula sl1mdr(}ngt6idaCllaA U"enmohlnh(M, F) A chinhla t~pconIOnnhfitthu(}cM saochobai toaDA --7B giiii duQc.Va tacodinhIy sau: " Tren m(}tm~ngtinhtoaD(M, F) bai toaDA ~ B la giiii duQckhi B c A V~Wigiiii cuabaitoaD: Ta codinhnghiasau: Cho D = {fI, f2,...,fd la day quaDh~clia m~ngtinhtoaD(M, F). A eM. Ta noi dayquaDh~D la apd\lngduQctrenA khi va chikhi taco thelfinIUQtap d~lDgduQccacquaDh~ft. fz, fkxufitphattUgiii thi6tA... N6u d~tAo=A, Al =AoU M(fI) Ak = Ak U M(fk) vaky hi~uAk=D(A) thlD la Wigiiii cliabai toaDA ~ D(A) D(A) la s~l'mdr(}ngcuat~pA nhoapd\lngdayquaDh~D Ta co m~nhd~sau: Day quaDh~D la loi giiii cuabai toaDA ~ B khi va chikhi D apdl~ngduQcu"enA vaD(A) ::::>B Be tlm m(}tWi giiii t6t hon tir loi giiii erabi6t ta co the xem xet til'dinh Iy sau: Cho D = {fI,f2, , fIll}la m(}tWi giiii cuabai toaDA ~ B lingvdi m6ii =1 m d~tDi = {fI, f2, , fi},Do=O.Ta xfiydl1ng1hQcacdayconSIll'Sm-I, ... Sz,SI cuadaynhuD nhusau: Sm= {fIll} N6u Dm-Ila Iloi giiii N6uDm-Ithong la Iloi giiii Sm=0 Si =Si+I N6u Di-I U Si+Ila 11oigiiii N6uDi-IU Si+Ithongla Iloi giiiiSi= {fi} U Si+I "ifi=m - I, m - 2, ,2, 1 Khi do taco (I) Sm C Sm+IC C Sz C SI (2) Di-I u Si la 1loi giiii d6ivdibai toaDA ~ B i =m, ...,2, 1 42 LUANVANTHACsTKHOAHQC (3) Ne'u Si 13.1 day con th~tst!cua Si thi Di-l u Si kh6ng phai 13.1 Wi giai cuabai tmlnA ~ B'v'i (4) SI 13.Wi giait6tnhatcuabai toanA ~ B Ngu'oi ta c6 th€ phat tri€n m~ngtlnh toan thanh m~ngcac d6i tu'Qngtlnh toan. Trong m~ngcac d6i tuQngtinh toan m6i 1 d6i tu'QngduQcthay the'bdi 1 m~ngtinhtoan tu'dngling gQi 13.m~ngcon hay con gQi la 1 d6i tu'Qngtlnh toan. Quan h~f giua cac bie'nClIa d6i tu'Qngtinh toan la 1 quail h~giua cac d6i tu'Qng d6. Nhu the'm~ngcac d6i tu'Qngtlnh toan baa gam m9t t~pcac d6i tu'Qngtinh toan. 0 ={Ol,O2,03, , On} va 1t~pcacquailh~giuacacd6i tu'QngF ={fl Fm} f)~tM(fi) =t~pcacbie'nc6 lien quailvdi nhaubdi quailh~fi M(F) = U Mf(D M(O) =U M(Oi) M(OD la t~pcacbie'nc6 lienquailde'nd6i tu'QngOi) M la t~phQpcac bie'nduQcxem xet trenm~ngk€ ca cacbie'nthuQct~p M(fi) Mi =M (1M (00 i= 1,2,...,m Vi d\l chobai toanti€u hQcsau: Bie'tchi'eucaoh cuatamgiacADE va 3 c~nh a, b, c cuatamgiacABC. Tinh di~ntichhinhthangBCED. Bai toanc6d~ngcua1m~ngcacd6i tu'Qngtlnhtoanbaagam: 1/ B6n d6i tu'Qng: 01 : Tam giac ABC O2 : Tam giac AOE 03 : Tam giac BEC 04 : Tam giac BCD 43 LuANVANTHACsTKHOAHQC Os : Hinh thang BCDE M6i tamgiaee6caebie'na,b, e,h, s 2/ Quan h«$giii'acaedo'itu'c;lng fl : 01s=Olb * Ole f2 : 01h =OlS * 2 : 01a f3 : 03h =Olh -02h f4 : 03S =01a * 03h f5 : 03b=03S * 2 :Ole f6: O2b=Olb - 03b fl : 03 S=04S f8 : 04 e=04S * 2 : 01b f9 : O2e=Ole - 04e fl 0 : O2S=O2e * O2b :2 flI :.OsS=OlS - 02S Trongvi d1;lnaytae6 : M(fl) ={OlS , Olb , Ole} M(f6) ={02b , Olb , Olb } M(f2)={Olh, OlS , Ola} M(fl) ={03S, 04S} M(f3) ={03h,Olh, 02h} M(f8) ={O4e, 04S, Olb } M(f4) ={03S, Ola , 03h} M(f9) ={Oze,01e , 04e } M(f5) ={03S, Ola , 03h} M(flO) ={OsS, OlS , O2S } Caid~tm~ngtinhroan: Vi«$eaid~tm~ngtinhroand11atrenn~ntangeuavi«$eaid~t~phc;lp.Vi«$e eaid~t~phc;lphiiiehophepvi«$eth11ehi«$ncaepheproantrent~phc;lPd6.f)~ eaid~t~phc;lpX talamnhu'san: -Ghinh~ncaeph'antii'x ellaX trongmQtdanhsaeh,m6iph'ane6chiso' xaedinh. -A c X sedu'c;lebi~udi~nbflngmQtdaybit,m6ibittu'dnglingvdimQtso' thlit11haylingvdiph'antd'xeX d~ghinh~nph'antd'x e6thuQet~pconA haykhong.Kihi«$ubittu'dngllngvdi so'thli111i ( lingvdimQtph'antd'x) trong 44 WANVANTHACsi KHOAHOC daybitAla A(i),taco th€ quiudcding A(i)=l khi xEA, A(i)=O khi x ~A, IDeo cachnhuthe't~pr6ngsedu<;fCbi€u di~nbdi daybit O,t~pX du<;fCbi€u di~nbdi daybit 1,t~ph<;fpchicomQtph'antii'd'autiendu<;fcbi€u di€n bdi daybit d'autien 1£1vacacbitconl(;lila O. -Cac pheptinhgiao,hQi,hi<$uliiy cacph'anbusetu'dngl1ngvdi cac thao tac trencacbit -Phepki~mtraIDQtph'antii'co s6thl1nrla i co thuQc~p h<;fpA haykhong tu'dngl1ngvdi vi<$cxacdinhxembit i cuadaybitA la O.hay1. - Vi<$cthembotra ph'antll'co s6 thl1nr i tUt~ph<;fpA tll'dngl1'ngvi<$cgall chobiti trongdaybitA la 0 hay 1. D€ cai d~tm(;lngtinh toan chung ta du'ara cach ghi nh~nd'aydu thongtin c'ancho vi<$cXll'1)1v~t~ph<;fpcac bie'n,t~ph<;fpcac quail h<$. Do'i vdi cac bie'nta c'anqUail1)1chung IDeocac bie'nsan: n: s6bie'n trongm(;lng. s:danhsachcacbie'n. x: danhsachcacbie'nghinh~ngia tri Cllatl"Yngbie'ntrongm(;lngtinhtoan Do'ivdi cacquailh<$,tac'ancocacbie'ntrongcai d~tnhusan: m: so'quailh<$ pf danhsachghinh~ntinhd6ixl1ngcuabie'n. Mf danhsachcact~pbie'ntu'dngl1ngcuacacquailh<$. rfdanhsachcach(;lngcuaquail h<$d6ixl1ng vf danhsachcacbie'nphl;1thuQc. expf:danhsachcacbi~uthl1cuacacquail h<$. flamerdanhsachcactenhaycachgQicuavungquailh<$. Lu~tbie'nd6icacd6i tu<;fngtinhtoan Trongquatrinhv~ndl;1ngcackie'nthl1cv~d6i tu'<;fngd~giiHquye'tde'ncac b~litoanlien quail,nguoi ta con v~nd1;lllgcac quy lu~tbie'nd6i giii'acacdo'i tu'<;fng.Cac quy lu~tbie'nd6i baahammQts6 dinh1)1hay quy tftcthuongdung cho vi<$chl1ngminh.Chungchophepbie'nd6i hay thaythe'mQts6 do'itu'Qng tinhtoanclingvdi mQts6quailh<$(hayIDQtm(;lngcacd6i tu'Qngtinhtoan)thanh mQtd6i tu'Qngkhacmatri thl1cv~nogiupchovi<$ctinhtoandu<;fcd€ dang. Vi d1;ltaco t~plu~tbie'nd6i lien quailde'ntamgiacnhu: 45 LUANVANTHACsi KHOAHOC - L 1 : Tam giac c6 hai q.nh b~ngnhauHi tamgiac din. - L2: Tamgiacc62 g6cb~ngnhaula tamgiacdin. - L3: Tamgiacc6du'(jngcaovadu'C1ngtrungtuye'ntu'dnglingb~ngnhau la tamgiacdin. - L4: Tam giac c6 du'C1ngcao va phan giac tu'dngti'ngb~ngnhaula tam giac can. - L5: Tam giac c6 trungtuye'nva phan giac tu'dngti'ngb~ngnhaula tam giac can. - L6: Tam ghic c6 mQtg6c vuong la tamgiac vuong. - L 7 : Tam giac c6 blnh phu'dngmQtc~nhb~ngt5ngblnh phu'dngcuahai c~nhkia la tamgiac vuong. - L8: Tamgiacc6mQtg6cvuongvahaic~nhkt3g6cvuongb~ngnhaula tamgiacvuongcan. - L9: Tamgiacvuongc6hai c~nhkt3g6cvuongb~ngnhaula tamgiac vuongcan. - LID: Tamgiaccanc6g6cd dinhla g6cvuongla tamgiacvuongcan. - LII: Tamgiacc6bac~nhb~ngnhaula tamgiacdt3u. - LI2: Tamgiacc6bag6cbhngnhauHitamgiacdt3u. - LI3: Tamgiaccanc6mQtg6cb~ng;latamgiacdt3u. 46