JOURNAL OF SCIENCE OF HNUE Education Science, 2013, Vol 58, No 4, pp 21 33 This paper is available online at http //stdb,hnue edu \ DAY HOC GIAI QUYET VAN DE TRONG GIANG DAY PHI/ONG PHAP GIAI MOT BAI[.]
Trang 1Education Science, 2013, Vol 58, No 4, pp 21-33
This paper is available online at http://stdb,hnue.edu.\
DAY HOC GIAI QUYET VAN DE TRONG GIANG DAY
PHI/ONG PHAP GIAI MOT BAI TOAN TREN IVIAV TINH DIEN TlT
Nguyen Tan An
Khoa Cdng nglie Thdng tin, Tnfdng Dgi hoc Suphgm Hd Ndi
Tom tat Bai bao trinh bay torn luoc ve phUdng phap day hoc giai quyel vAn de, sit
phil hop ciia phUdng phap nay trong dao lao ngudn nhan lUc Cong nghe Thong tin
va Truyin thong noi chung va trong giang day ndi dung giai mot bai toan tren may tinh dien tfl ndi rieng Bai bao ciing dUa ra kich ban phac thao de day giai bai toan 'Tam Quan Hau" theo phUdng phap nay Cac kit qua thfl nghiem dlu khang dinh phUdng phap day hpc giai quyet van de la phUdng phap huy ddng dUdc tinh tich cue cua sinh vien, phu hop vdi muc tieu dot mdi phUdng phap day hoc hien nay va rit thich hdp khi giang day npi dung giai mol bai toan tren may tinh dien tfl
TUkhda: Day hoc giai quyet vSn de doi mdi phUOng phap day hoc day hpc Tin
hoc bai loan Tam Quan Hau
1 Mof dau
De doi mdi phUdng phap giang day, cac nha su pham da dUa ra r§t nhilu quan diem khac nhau, nhflng gSn nhfl tSt ca cac quan diem do dlu thdng nhat rSng trong qua trinh day hoc phai lam sao tich cflc hda hoat dpng nhan thflc cfla sinh vien (SV), biln qua trinh nhan thflc Ihu ddng cfla SV thanh qua trinh SV chii ddng xay dflng tri thflc cho ban than, biln qua trinh dao tao SV ihanh qua trinh SV tu dao tao dudi su hudng dSn cfla giang vien (GV) Lay ngudi hoc Iam trung tam la mdt thuat ngfl dfldc nhilu ngudi dung khi ndi vl ddi mdi phUdng phap day hpc
Kien thflc thupc linh vUc Cdng nghe Thdng tin va Truyin thdng (CNTT&TT) dfldc dua vao giang day rpng rai trong nha IrUdng mupn hdn r k nhilu so vdi cac ndi dung khoa hpc khac PhUdng phap giang day cae mdn thudc llnh vUc CNTT&TT cung cd nhilu diem khdng gidng vdi phUdng phap giang day cac mdn thudc cac linh vUc khoa hoc khac Trong
C N I T & I T , cd nhflng ndi dung chi thich hdp vdi nhflng each day theo kieu "ddi tay chi viec" Vi du, giang day sfl dung phkn mim, that khd kien tao hay neu vkn de khi GV
hudng din SV thuc hien mdt tac vu kieu nhU chen mot bflc anh tfl file vao van ban soan
Ngay nhan bai: 5-6-2012, Ngay chap nhan dang 16-1-2013
Trang 2thao vdi Microsoft Office Word 2007: Bifa con Iro den vi tri tniiim chen hire dnh ^ Vdo menu Insert -> Pictiue -> Chim file hlu hifc dnh can chen -> Kich ndi Imserl 'liiy nhien,
eung CO nhiing noi dung diy c h k tU duy Iham chi cd ca yeu t6 nghe thuit nhu nhung mon lien quan dfin lap Irinh
Trong diio Uio ngu6n nhan luc Cong nghe Thong lin va Truyen thong (CNTT&TT) 11,2], nhung phuong phiip giang day huy dong sU lich eiic cua ngufti hoc dac biel Ihich hop Kien thUc Irong linh vilc CN'l'I'&T'T thay doi rSI nhanh nhung ngUdi liim cong tac CN'lT&'l'l' hju hel la nhUng ngUdi niing dong Ihuc lc, siing tao vii co kha nang IU cap nhat ki6n thu'c mdi De' diio lao nhung con ngUdi nhu the, cin phai iip diing nhiing phUdng phiip day hoc tich eUe, tao difiu kien eho SV sdm duOc ren luyfin theo nhiing doi hoi dac thil ciia nghe nghifip Phuong phap day hoc giiii quyet vSn dfi (DH GQVD) lii phUdng phap day hoc tich eUe vii rat Ihich hdp khi giang day nhieu noi dung Irong dao tao nguon nhan luc CNTl'&'l-r
Bill bao nay trinh bay viec ap dung phuong phap DH GQVD Irong giang day each giiii mot bai loan trfin may tinh dien tti (computer, sau day la goi chung la may linh), mot noi dung c6t loi trong moi chUdng trinh dao tao CNT'I'&'IT
2 Noi dung nghien ciiu
2,1 PhUdng phap DH GQVD
2.1.1 Khai niem
DH GQVD [1,4,6] lit phUOng phap day hpc, theo do, GV dat ra cho SV mot hay mot he th6ng v5n dfi nhiin thiic, dUa SV viio tinh huong cd viin dfi, tti dd hudng diin, dieu khien SV giai quyfit vin de, giup SV chii dong Irong hoc tap de niim duoc noi dung bai hoc va thoat khoi tinh hudng co vin de
DH GQVD phu hdp vdi tinh than ctia li thuyfit nhan thiic, phii hdp vdi quan difim liy ngucii hpc lam trung tiim
Mot each tu nhicn, thong qua cac vin dfi duoc diil ra, dUdc hudng dSn giai quyfil noi lifip nhau, phuong phap niiy ludn kich hoat linh tich cUc hoc lap eiia SV, do vay khi sti dung phuong phap nay mol each phu hop se cuon hiit diroc SV viio biii giang va gay hieu qua nhan thitc eao
PhUdng phap niiy dae bifit thich hdp vdi giang day dai hoc hay giang day 0 cac trudng chuyen nghiep, bdi kha nang giiip SV ren luyfin phong each lam viec tich cUc, sang tao, sdm hinh thanh thdi quen tim toi, nghifin ciiu
2.1.2 Nliirng chii y khi ap dung phKOng p h a p day hoc giai quyet van d i
- Van de dua ra phai p h i hdp vdi thdi difi'm, hoan canh va dac biet phai phii hpp vdi doi tUdng sinh vien, dam bao dua SV vao tinh hudng cd vin de Dat van de qua kho hay qua dfi deu khong thfi' dua SV vao tinh huong co van de Mtfc do thanh cong cua phuong phap nay phu thuoc rat nhifiu vao nghe Ihuat dai vin de va d i n dSt giai quyfit vin de cua
GV Mudn thiinh cong, GV phai nam chic kifin thiic, phai hieu SV Vi Ihfi, c i n g mpt giao
Trang 3an, khi day d cac 16p khac nhau se dfldc neu van de theo nhflng each thflc va mflc dp khac nhau
- Sau khi dat vin de, viec hfldng din SV trong qua trinh giai quylt vin dB phai rat
linh hoat Kip thdi khuyin khich nhflng hfldng di dung va khuyin khich nhflng giai phap tdt ddng thdi udn nan nhflng giai phap khdng hop li hoac khong sal vdi muc dich ma GV
dang hudng qua trinh nhan thflc cua SV dat tdi PhSn lom lit, he thdng hda kiln thflc tflng phan hay loan bai phai co dong, ngan gpn, neu dfldc giai phap giai quylt van dl dang
\\\ckn lim
- Chu y quan li Ihdi gian va lien irinh gid giang cho tdt Trong khudn kho Ihdi gian cua mot bai day neu each neu v4n dl khdng dUdc chuan bi ki, nlu hudng dSn thao luan hoac nhan xel nhflng giai phap ma SV dfla ra con lan man, vice long ket khdng trpng tam trong diem, , dl Iam cho bai giang thieu thdi gian, khdng dat kit qua mong muon
- Nen phdi hdp phfldng phap nay vdi cac phUdng phap giang day khac Khdng nen
ap dung ddn dieu mol phUdng phap Trong mdi bai day nen cd mot phUdng phap chu dao
va nhilu phfldng phap khac bd trd
2,2 Day hoc giai quyet van de rat thich hop khi giang day each giai mot bai toan tren may tfnh
2.2.1 Ba! toan
Trfldc tien, cin ndi rang trong Tin hgc cd nhflng bai toan khdng the giai tren may tinh theo each Ihdng thudng Tinh giai dupc va khdng giai dudc la mpt ndi dung quan trpng trong Li thuylt Tinh loan Mdn Tri tue nhan tao da cung d p nhilu chien lUdc tim kiem ldi giai [3] 6 day chung ta cbi xet nhflng bai toan dudc phat bieu chinh vdi md hinh nhu sau:
Cho Cdi vdo (Input); Cho Cdi ra (Output); Cho nhflng thao tac cd the dfldc sfl dung trong qua trinh bien ddi tfl Cdi vdo thanh Cdi ra
Yeu cku: Tim Cdi ra
Nhflng thao tac co the dupc sfl dung trong qua trinh biln ddi Ifl Cdi vdo thanh Cdi
ra ndi chung khdng dfldc phat bieu tfldng minh khi cho bai toan de giang day hoac kiem
tra kiln thflc cua SV Khi dd ta ngam hieu rang, dd la cac phUdng phap tinh toan, cac cdng thflc, cac dinh li, ma SV 6 trinh dd hien tai phai biet va cd the ap dung dfldc Cac bai toan vflPt khdi trinh dp nay cd khi bi gpi la "dSu bai sai" Sai d day cd nghia la sai so vdi pham vi kiln thflc cua ngfldi dudc giao bai tap, Vi de giai bai toan, SV phai ap dung ca cac kiln thflc chua dUdc hpc Luu y rang, dlu bai la cau hdi, ma cau hoi thi khdng nhan
gia tri dung/sai
Vl the, nhilu tai lieu chi viit rdng: Mo hinh mdt bai toan gdm: Cho Cdi vdo, Cdi
ra Yeu clu: Ttf Cdi vdo tim Cdi rai
Trang 42.2.2 Giai bai loan tren may tinh
Ciiiii mpt bai loan Iren may linh cd nghia la ngUdi giai phai lim Irong cac thao lac
ma minh bill nhflng thao i;ie cin thiel s^p xep cac Ihao lac do theo mol trinh tfl thflc hien
nhll dinh de sao cho sau mol sd hflu han bfldc tfl Cdi vdo ta cd Cdi ra
Chfla hel tiep dd ngfldi giai phai viel day cac Ihao lac do bang mol ngdn ngfl lap trinh de may hieu dfldc, nham muc dich cudi ciing la "giao" cho may Ihflc hien viec tfl
Cdi vdo lim Cdi ra Neu "giao" xong, ngfldi dung chi cin nap vao Cdi vdo, may linh se dfla ra Cai ra IUdng flng Day chinh la bfldc vicl chUdng irinh
Dc "giao" eho may linh giai bai loan vii hoan thien phin mem giai bai loan, ndi
chung ein ihuc hien 5 bfldc sau:
Budc I Xdc dinh bdi todn: Xac dinh bai loan'd day chinh la vice xac dinh ro Cdi vdo Cdi ra
Budi 2 Lua chgn huac ihiet ke gidi ihugt Thudng khi thill ke hoac chon giai thual,
ngUdi giai ddng thdi phai nghi ngay den viec td chflc dfl lieu
Budc 3 Vtei cliuung liinh: BUdc nay chinh la budc ngfldi giai eai dat giai thual cung
eau true dfl lieu xac dinh 0 budc tren Dd chinh la vice viel chUdng trinh sao cho cd the
"giao" cho may thuc hien viec giai bai loan,
Budc 4 Kieh tint vd hieu chinh chuong ttinh: Da\ la bUdc kiem thfl Neu chfldng
trinh cdn ldi, phai sfla het Idi
Budc 5 Viet tdl lieu Tai lieu phai md ta chi tilt bai loan, thuat loan, chUdng Irinh,
hfldng dan sfl dung , Tai lieu rlt cd ich va cin ihiel cho ngfldi sfl dung chfldng trinh va nhflng ngudi quan tam nham hieu, khai thac lot va bao Iri, nang d p chUdng trinh
Cac budc tren cd the lap di lap Iai nhieu ian cho din khi tam dat yeu cau Vi thi, ta thay, vdi mdi chudng trinh ihudng cd cac phien ban khae nhau Phien ban sau la cai tiln ciia phien ban trfldc
Trong 5 bUdc ke tren, hai budc- Bifdc 2 Tim kiem hogc thiet kc gidt ihudt va Bifdc
3 Viet ehuung uinh la hai bfldc khd nhll va cflng quan Irong nhll TVii nhien d l ihflc hien dUdc hai bfldc nay, SV phai qua dfldc Budc I Tim lueu/xdc dinh hdi tudn
Trong khuon khd ciia bin bao, chung ta chi ban din giang day ba budc nay 2.2.3 PhUdng phap DH (JQVD rat Ihich hdp khi gianj; day giai mot bai toan tren
may ti'nh
Giang day Budc 7, tim hieu/xac dinh bai loan, thong thudng GV dung phUdng phap
thuyet trinh, giang giai can ke, thdng nhll nhflng khai mem, nhflng thuat ngfl ghi trong
dau bai, giflp SV hieu ro Cdi vdo, Cdi ra Con nhflng thao tac dfldc ap dung, mac nhien
dd la nhflng thao tac ma SV 6 trinh dd hicn tai da bill, khong cin nhac lai nfla
Giang day Budc 2, GV din dll SV lim kilm/lua chon giai Ihual D l thly rang qua
trinh tim kiem giai thuat chinh la qua trinh tim each giai quyel bai loan Din dat SV thflc hien budc nay, nlu cfl theo dflng logic cua ndi dung, vdi each neu vin de phfl hdp, tfl nhien
Trang 5Tilp theo, ddi vdi Budc 3, budc vill chfldng trinh, day la budc GV din dat SV ma
hda giai thuSt tren (vill code) Bfldc nay ddi hdi phai hieu may linh, hicu ngdn ngfl lap irinh se dung, hieu each cai dai cac clu trflc dfl lieu lien quan bing ngdn ngfl lap trinh
dinh sfl dung Vdn de dat ra d budc nay ehinh la: Lcim the ndo de cd the viel gidi ihudl vua lim duac a Intdc tren hdng ngdn ngif Idp trinh djnh vif dting Khi din d^t SV thuc
hien budc viel chUdng trinh, bing each neu vin dl kheo leo dUa Iren nhflng kiln thflc da
cd vl clu Iruc dfl lieu, v6 ngon ngfl lap trinh da cd ciia SV, GV dfla SV vao hoan canh cd van dc Giai quylt vin de d bfldc nay chinh la chuyen tflng cau, tflng doan lenh Irong giai thual vfla tim dfldc d budc IrUdc sang each dien dai biing ngon ngfl lap Irinh dinh dung Kcl qua bfldc nay la mdt ehUdng Irinh hoan chinh
Dudi da\ ta se xel mol \ i du cu the
2 3 A p d u n g phUOng p h a p D H G Q V D t r o n g g i a n g d a y giai b a i t o a n " T a m Quan Hau"
Khi giang day Clu trflc dfl lieu va Giai thuat, mdi mdn hoc rat cd ban trong moi chUdng trinh dao lao, la gap rlt nghilu trudng hdp lUdng tu nhu giai mpt bai loan tren may linh Sau day la mdt vi du:
Trong cudn Cdu trite dif lieu vd Gidi thudt ciia tac gia Dd Xuan Ldi [5], d Chuong 3: De qui, sau phan nhflng kien Ihflc ve de qui, tac gia cd dfla ra 4 vi du ap dung tfl de den khd' 1) Tinh nf; 2) Tinh so hang thifn cita ddy FIBONACl; 3) Bin loan "Tlmp Hd Ngi', 4) Bai loan "Tdm Qudn Hdu " Qua 4 vi du nay, SV se ciing cd dUde kiln thflc li thuylt,
ed kha nang ap dung giai thuat de qui ddng thdi kien thflc chung ve giai mdi bai toan tren may tinh mdt Ian nfla dUdc ciing cd
Ta hay phac thao kich ban giang day vi du thfl 4 theo muc dieh ciia sach da dan: Bai
loan "Tdm Qudn Hgu"
Bdi tudn: Hay dat 8 quan hau len ban ed sao cho khdng quan nao an dUdc
quan nao! [5]
Budc I Xdc dtnh bdi lodn:
GV (Dung phif</ng phdp thuyel trinh)
Cdi vdu: Ban cd Vua va 8 quan hau (GVgidi thich the ndo Id hdn cd(hdn cd Vua) the ndo la qudn hdu vd khd ndng di, khd ndng dn ciia qudn hdu (iheo luai cd Vua))
Cdi ra- Mdt each dat 8 quan hau vao cac d tren ban cd sao cho khong quan nao an
dUdc quan nao
Bifdc 2 Lua chon hodc thiet ke gidi thudt:
GV {Nen cdu hui dua SV vdo linh hudng cd van de):
Lam thi nao de dat 8 quan hau len ban cd sao cho khdng quan nao an dUdc quan nao''
{Yeu cdu trd ldi bang ngdn ngif lieng Viet, chtfa van dung kien thifc Tin kien thifc Tudn dgc biet ndo vdu ddy)
Co the cd nhilu cau tra ldi TrUdng hdp gap SV da hoc dau do mdt each giai va ho
Trang 6Irinh bay each giai dd, GV (cd the) hdi ihem: Tinh de qui Irong each giai cua anh/chi the hien d chd nao? (la dang hpc giai Ihual di; qui), va kha nang cai dai each lam dd len may tinh? Cd bao nhieu each liim (cd bao nhieu nghiem)? Neu SV Ira ldi dUOc, Ihi day la SV dii hoc trfldc vii da hieu ro van dc, la yeu clu SV nay ngdi nghe vii theo ddi each giai quyli
ciia cae ban, sau dd sc dfldc gpi de nhan xet Ta se sfl dung SV nay de cflng din dll qua
trinh nhan thflc cua cac SV khac Iheo muc dich biii giang Dai da sd cac sinh vien chfla hgc hoiic da hoc nhflng khong nim chac vin de do dd Ira ldi khdng ro rang, khong diy du Thfldng giip cau Ira ldi:
SV, Hm dd 8 quan hau len ban cd rdi md ra mpt each dat
CJV ("iie ban hay nhan xet each liim Ircn
SV {Thdo ludn)
GV {long kil lai) Ciich liim do ciing cd the lim ra dfldc it nhll mpt each dai Tuy
nhien theo caeii liim dd khdng dc biel se ed bao nhieu each dai bdi sau mdi each tim dfldc, khd biet ed edn each niio nfla hay khdng? Ddng Ihdi, luu y rang, each lam dd khdng Iheo mdt chien lUdc rd rang niio ca nen rlt khd cai dai tren may linh Ai cd each Iam khac?
SV {Trinh bdy cdch khdc): Hm dai quan hau thfl nhll Ien mpt d bat ki tren ban cd vii
bo di hiing ngang, hang dpc, eac dudng cheo di qua d dd (dung but hoac phin vach dfldng danh diiu bo) Biin cti cdn lai hep hdn va em lai dat quan thfl 2 Ien phin edn Iai cua ban c6 vii lai bo di hiing ngang, hang dgc, cac dudng cheo di qua d cd quan thfl 2 do Ban cd bay gid hep hdn nfla Vii qua trinh tilp tuc cho din khi hit 8 quan hau
GV {Sau khi nghe cdc SV khdc nhgn xet, neu can hdi): Lieu qua trinh cd the di den
hoi hel ca 8 quan hau khdng"' Vi du sau quan thfl ;, vdi;/ < 8, din quan thfl j + 1 thi
khdng the dat vao dau dUde vi 6 nao cung cd dudng danh dau bd di qua Cd 6 bi vai dfldng danh dau bo di qua, d il nhll cUng cd mdt dudng danh dlu bd Giai quylt thi nao day''
SV- {Thdo lugn)
GV {Chc'n Igi) Khi dd pi-iai quay lui Qua trinh quay lui nhU sau: Nhic quan hauj
ra dc dat vao vi tri khac neu quan hau ; cd nhilu hdn 1 chd dc dat Ncii quan hau ? chi co
mdi chd dd de dat thdi Ihi khdng the dat nd ra chd khac, la nhic lilp quan j - 1 ra cho
den khl gap quan cd nhilu hdn 1 kha niing de dat, la se dat nd viio chd khac va qua trinh lai lilp tuc Dieu dd co nghia la qua trinh quay lui dfldc thflc hien cho d i n khi gap trfldng hdp cd the tiln dUdc la tiln ngay
Thfl vii quay lui nhu Ihl cho den khi dat hit dUdc 8 quan hau hoac quay lui din quan dau tien va quan dau tien cung dii dUdc thfl hit cac kha nang bay gid khdng con kha nang niio nfla
Day chinh la gai thual quay lui, mot phfldng phap khong de qui de giai bai toan nay
GV {Gui y, ddn ddi SV tim nghiem iheo gidi thudt de qui): Nlu bieu diln nghiem la mot veeld A'[.r, i^ ./„), mdi toa dp r, cfla nd Iflu vi tri cua mot quan hau thi nghiem
cua bai loan chinh la mol bp lam "gia Iri" cfla vectd nay LUu y rang, trong trfldng hdp long quat, mdi "gia tri" (, cd the la mol bd sd mdi cd the lUu dfldc vi tri cua quan hau
Neu the, di tim nghiem ciia bai loan tflc la di tim tflng tpa dd cua vectd X Cd the tim
Trang 7vectd X bing giai thuat de qui dfldc khdng?
SV (Dd cd kien thifc ve de qui): Cd the! Ta tim lln Ifldl tflng loa dd cua vectd A Dlu tien tim x'l, sau dd tim ,7;2, Gia sfl ta da tim dfldc Xj, the thi viec lim ,r,, i gidng het
each tim i,j nhflng kich thfldc ban cd bay gid nhd hon do Irfl di nhflng 6 da bi danh dlu
bd trfldc dd vii bay gid phai Irfl lilp di nhflng 6 do dat quan hau / Trfldng hdp suy bien la trfldng hdp lim cg
GV: Rat tdt Tuy nhien khi thfl dai quiin bau ,7, lam ihe nao de biel kit qua cua viec thfl nhfl thi la DliOC hay KHONG DLfOC de cdn thfl diil Ucp quan hau 7 -f 1 hay quay lui?
SV {Nhd lgi ndi dung dd thdo ludn 0 iren) Vice dai quan hau / lii DliOC khi vii chi
khi tit ca cac quan hau tiep iheo deu cd ehd (chfl khong phai DUOC cd nghia lii hicn lai
d ma ta dat quan hau / la 6 tfl do, khdng quan tam den cac quan liep sau)
The Ihi vice kiem tra xem dat quan hau thfl •; vao mdt d tu do niio dd cd Dl/OC hay khdng chinh la viec thfl dai quan hau Ihfl / 4 1 Neu viC'c dai quan hau ,7 + 1 mil DUOC tflc la viec dat quan hau thfl / la DUOC Nlu \ iec dat quiin hau thfl / + 1 la khdng the cd nghia la \ iiie dat quan hau / vao d tu do vfla rdi la KHONG DUOC, la phai cit quan hau ,7 di de thfl lai vao d tu do khac Chfl y rang nlu quan hau / da lii quan hau cuoi eiing thi chi cin dat nd vao d tfl do nao dd la DUOC, khdng cdn phai thfl quan hau tiep theo nfla
Tinh de qui the hien d chd: Viec thfl quan hau thfl 7 \- 1 gidng het each Iam vdi viec thfl
dat quan hau / nhflng kich thfldc ban cd bay gid nho hdn do da trfl di eac hang, cac cdt, cae dfldng cheo qua d da cd quan hau trfldc va gid lai them quan hau 7 TrUdng hdp suy biln la trfldng hdp dat quan hau thfl 8
GV Rlt tot Bay gid
ta khdng chpn, dat quan hau
theo thfl IU mpt each nglu
nhien nfla ma ta hay danh
sd thfl tfl cac quan hau bang
each dat 8 quan hau len dau
8 cdt (Hinh I) Sd thfl tfl
ciia cdt chinh la chi sd ciia
quan hau Hdn nfla ta qui
dinh mdi quan hau chi dUdc
dat vao mpt hang nao dd
thuoc cdt cua minh, ta cd
egt ma quan hau dflng dlu
(cot cd chi sd la chi sd quan
hau) hoan loan tfl do vdi nd
Mudn xem d nao trong edt
ciia nd cd tfl do ddi vdi nd hay khdng ta chi cin kiem Ira himg va cae dudng cheo qua d do
cd tfl do hay khdng
Tren Hinh 1, chi sd hang la /, chi sd cdt la 7 Chi sd cot cung la sd hieu (chi sd) cua quan hau
• K >V -b - l i
Hinh 1 Moi qudn hdu chi ditOc ddt trong cgt cua minh Diidng cheo di len vd duifng cheo di xuong qua 6 (3,6)
Trang 8GV (tlocm chlnh gidi Ihuat): Ai cd Ihfi' difin dat Ciich lam trfin mdt ciich chat che ti
CO aiiii thual: Thti ddt qudn lidu j ten ldn luot cdc hdng hdt ddu til hdng 1 trong col cia
nd "(cpt j) cho den khi DUOC hodc het cdc hdng (din hdng 8) md vdn KHONG DLfOC thi cimg (hoil
SV Cliinh hdy)
GV {Choi hli)- Giiii thuat thti dat quan hau j nhu sau:
ThiV (•;, q); II Thil dat qudn hau -j, q Id hien Boolean de'lifu ket qud
1 1 = 0 ; I/Ban ddu gdn chi st> himg hdng 0
2 IJp:
3 i := 1+1,1 tidng chi si) hdng len 1
4 q:= l-alse, // Tnfdc khi thtr gfin q := False
5 Neu 6 (l.l) 'J'lJ DO thi
6 begin
7 DAT quan hau J viio 6 (j,'/);
8 Neu quan hau ;; chua phai lit quan cudi thi Thiir (/ !- 1, (/),
Neu KHONG DUOC thi c A l ' QUAN H A U j di, ngUOc lai q =
7Vite;
0 end;
Cho den khi: DUOC hoac da thii den hang cufii ma van chUa DUOC Ihi eung thoi;
Return,
9,
11
GV iCiaig cd):
' Trong giai thuiit tren, thao tiic d ddng 8 chinh lii thao tiic kifi'm tra xem thao tiic 6 dong 7 cd DUOC hay KHONG DUOC Qui Udc DUOC se giin cho q ;= Tiue, trudng hdp KHONG DUOC, do Ifinh giin d dong 4, q vSn bang Fii/.st
- Theo gldl thuat trfin, ta chi cdn goi 'lYy(l,q) dc' thir dat quan hau 1 Ifin ifa lupt cac hiing ciia nd, khi gap trudng hdp DUOC, vdng liip dtfng va niiing -V luu lai mist phUOng an dat, do lit nghifim ddu tien Neu phai thli dfin hiing 8 vii vdn KHONG DUOC thi giai thuat cung dtfng Day lii trudng hop vo nghtem Tuy nhien bill toan kinh dien nay cd nghifim, ta
se thdy dieu ndy khi ehay thii chuong trinh NhUng bai loiin cd bao nhifiu nghiem? Viec cdi tien gidi thuat trfin de' tim tiep eae each dat khac lit nhifim vu ve nha ctia SV ta sfi noi
d phin sau
- LUu y rang eung ed thfi' dat 8 quan hau vao cudi 8 cpt/dau 8 hang/cudi 8 hang
Tun difilc gidi thudt SV tam thodt khoi linh huong cd vdn de
Budc 3 Viit chifong Irinh (difdi day la qua trinh dan dat SV trinh bay giai thual trfin
dudi dang mdt thti tuc bdng ngon ngii PASCAL);
GV {Difa SV vdo hoiin cdnh cu vdn de): Viet giiii thuat nhu trfin chi ngUdi hifi'u con may khong hifi'u dude Dieu kifin "Neu 6 [i j) TU DO "; Cac thao tac dat DAT quan hau,
CAT qudn hau cdn phdi ma nhu thfi ndo de' may hieu dUdc?
Trang 9SV: ???
GV: Nlu diing mang (.'):[lj,,7:[2], ,.,x[j] .,.r|8]), vdi cac phin ifl cd kieu nguyen
de Iflu tru nghiem thi gia tri cac phin tfl cua mang phai Iflu Ihdng tin gi?
SV {Nhd Igi cdch dung vecto X delifu nghiem dd ndi d tren): Gia In cua :r,\j\ lUu vi
tri cua quan hau ,7 Neu qui dinh quan hSu ,7 chi dfldc dai trong cpl 7, lflc lii mdi quan hau chi dfldc dat trong cdt cua minh ma khong dfldc dat sang cot khac thi ,^[7] chi cin Iflu chi
sd cua hang ma quan hau 7 dfldc dat vao la du Cu the: x[j\ -^- 1 lflc la quan hau 7 dfldc dat vao hang t (cfla cot 7) Ndi each khac nlu ly] 1 tflc la quiin hau 7 dUde dai vao 6 ii :i)
Nhu vay, moi bg 8 gid Iri cua mang nay do chuifng trinh lim dUOc sc la mgl nghiem (mol phudng an dat 8 quan hau ma khdng quan nao an dfldc quiin nao)
GV: Khi niio 0 (/ /) tU do ddi vdi quan hau;/?
SV: O (/.;/) lii T U DO ddi vdi quan hau 7 khi vii chi khi hang / TU DO, dudng cheo
di len qua d (z.;/) TlJ DO, dUdng cheo di xudng qua d (/, /) TU DO (Cdl / dfldng nhien
la IU do ddi vdi quan hau / nen khdng cin kiem ira nfla)
GV: Dc ki hieu (de ma) su kien hang 1 tu do hay khdng la lam thi niio?
SV: {Thdo luan)
GV: Ta dung mang a[i] cd cac phin tfl kieu Boolean de lUu trfl kel qua tU do hay khdng cua cac himg Y nghia cac gia Iri cfla mang nay nhfl sau: Nlu a[i] = True thi hang
I tu do, ngUdc Iai thi khdng Vi du a[3] = True cd nghia la hang 3 tU do Ban cd cd 8
hang nen /, cd 8 gia tri cd nghia Nen cbo / ehay tfl 1 ldi 8
GV: Lam ihl nao de ki hieu (de ma) sfl kien dfldng cheo di len qua d (/ 7) ed tU do hay khdng? Ai cd nhan xet vc cac 6 ma dUdng cheo di Icn qua d (/, 7) di qua"*
SV: Dudng cheo di len qua d (/ y) la dudng cheo di qua cac 6 cd ehi sd himg cdng ehi sd cot bang nhau va bang chinh 1/ + /) Mdi gia iri eua long (/ )- 7} lUdng flng vdi mdt dudng cheo di Ien
GV: Ai cd the ma hda sU kien dUdng cheo di len qua d (v, /) tu do/khdng tu do? SV- De lhay rang:
(/ +.7) nhd nhll khi / nhd nhll (bang 1) vii ,7 nhd nhat (bang 1), tflc la bang 2
(i + i) Idn nhll khi / ldn nhll (bang 8) va,? ldn nhll (bang 8), tflc la bang 16
(/ +.7) chay tfl 2 tdl 16 ed 15 gia tri tflc la ban cd cd 15 dudng cheo di len (dem tren hinh vc ta ciing thly ban cd cd 15 dudng cheo di Icn)
Ta dung mang h'\i f 7], (7 -h 7) chay tU 2 tdi 16, dc ma sfl ifl do hay khdng cua eac dfldng cheo di len qua 6 {i,j)] Y nghia cac gia In cua mang nay nhu sau: Neu b[i + 7] = Trwe thi dudng cheo di Ien qua d {i.j} tU do, ngUdc lai thi khdng
Hudn todn tifcfng lif ninf tren GV se hui va SV se difa ra cdch md hda difdng cheu di xudng cjiia d {1.;/) cd lif do bay khdng nhu sau:
GV: Lam the nao de ki hieu (ma) dudng cheo di xudng qua d (/ y) cd tu do hay khdng? Ai cd nhan xet ve cac d ma dfldng cheo di xudng qua 0 (/, /) di qua?
SV: Dfldng cheo di xudng qua 6 [i.j) la dfldng cheo di qua cac 6 cd chi sd hang trfl
Trang 10chi sd cpl bing nhau va bang chinh (/ - 7) Mdi gia tri cua hieu (i - j) Ifldng flng vdi m6t
dfldng cheo di xudng,
GV, Ai CO the mii hda sfl kien dudng cheo di xudng q u a d {i.j) tfl do/khdng Ifl do?
SV: Dl thly ring:
Hieu ( / - , ; ) nhd nhit khi / (.SY; mV) nhd nhll (bang I) v a j (.vd Z?//nf) ldn nhit (bang 8), tflc lii bing - 7
Hieu (/ - 7 ) Idn nhat khi •/ (,vf?/nV) It^nnhal (bing 8) va.7 (.vrW;/rriV") nho nhat (bing I), tflc lii bing +7
(i - /] chay ifl - 7 tdi I 7 cd 15 gia tri lflc la ban cd cd 15 dfldng cheo di xudng (dim tren hinh vc ta cung lhay ban cd cd 15 dfldng cheo di xudng)
Ta diing mang c\i - 7J, {1 — 7) chay ifl —7 [di ' 7, d l Iflu sfl Ifl do hay khdng
eua dudng cheo di xudng qua d (; 7) Y nghia cac gia tri cua mang nay nhfl sau: Neu
f [( /' = Tl ur thi dudng cheo di xudng qua 6 (i,j) tfl do, ngfldc Iai thi khdng GV: Vdi each ma nhu iren cau: Neu d (;, j) IU do dUdc \iel the nao?
SV: Ciiu: Nlu {(bang t lif du) vii (dudng cheo di len qua d (/ 7) tif do) va (dudng
cheo di xudng qua d (i.)} tif do))., bay gid cd the viel lii:
if {{a\i] = True] and {b\i + ,7] - True) and {e\i - ,7] = Ti uc))
Hay viet gpn la 1 fia\i.] and b[i + j] and c[i - }\)
GV: Thao tac diit quan hau ,7 vao d (7,, j) dfldc viit Ihl nao''
SV: x\j\ := i;
GV {Goiy): Tinh trang hang /, dfldng cheo di len, dfldng cheo di xudng qua d (i, 7)
bay gid thi nao''
SV: Khong tu do nfla
GV {Cbdi lai) Ngoiii viec gan ,j [yj = / cdn phai ghi lai tinh trang 6 ( r / ) khdng IU
do nfla Al cd the hoiin chinh thao tae dat quan hau j vao hang 1 trong cpt cua nd?
SV: Thao tac dat quan hau y vao hang / trong cdt / diiPc vill nhfl sau:
:r[j] -^ 1;
o\i] : - Fahe,
h[i + i\ - TuTc,
i\t — j \ = Fahe;
GV: Thao tac cdt quan hau khdi d (/ ;) dugc viel thfi ndo?
SV: la chi cdn doi trang thiii TU DO cua 0 ( 1 7 ) thanh Irang thiii KHONG TU DO:
u\t] = T, ,„
I>\i + 7] : = •/', , „ ,
c\i - i] := i'rue:
Khong can quan tam den gia tri ciia r[7] nita Coi T[7] la bifin tU do (bien chua dUdc gdn tri)
GV Cac ban SV hay vifit lai giai thuat trfin bdng eiich thay cac cau triiu tUdng bang