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TRtTONG DAI HQC AN GIANG KHOA KY THUAT - CONG NGHE - MOI TRlTONG NGUYEN THITHUY KIEU KHOA LILiN TOT NGHIEP DAI HQC NGANH Clf NHAN TIN HQC THIET KE PHAN MEM HO TRO GIANG DAY MON LY THUYET DO THI TRU6NG DAI HOC: AN GIANG THLfVIEN Giang vien huong dan: Ths Nguyen Thi Lan Quyen An Giang, 05/2011 KHOA.LU^N t6t NGHIEPNGUYEN THITHUY KIEU LCtt CAM ON Trong qua trinh thuc hi^n di tai thuc tap cuoi khoa ciing nhu khoa ludn tot nghiep, nhd su giilp nhiit tlnh cua qui Thdy Co, gia dlnh vd ban be da tqo moi diiu ' Men giiip em hodn thdnh tot de tai Em xin chdn thdnh g&i Idi cam on den: Ddu tien em goi Idi cam on chan thdnh den qui Thdy, Co khoa Ky thudt - Cong nghe - Moi tnedng da tan tinh gidng day, truyin dqt nhung Mnh nghiem qui ban, Men thuc hieu ich cho chung em bang cd tarn long yeu thudng, de chung em co su hieu biet lam hdnh trang vung chdc bu&c vdo ddi Em chan thdnh cam on co Nguyen Thi Lan Quyen, ngicdi ludn sdn sang hudng dan, giup dong vien de em hodn thdnh tot khoa ludn tot nghiep Cam on tdt cd cdc ban da hit long giup do, dong vien minh hodn thdnh tot de tai Cuoi cling xin gdi Idi cam on sdu sac den todn the gia dinh Cam on cha m? da sinh thdnh vd gido dudng khon Ion de co dupe kit qua hoc tap nhu ngdy horn Em xin chan thdnh cam on! An Giang, ngdy 09 thdng 05 ndm 2011 Sinh viin thuc Men: Nguyin Thi ThuyKieu MSSV: DTH072351 Thidt ke phan mem ho trg giang day mon Ly ThuySt D6 Thj KHOA LUAN TOT NGHIgPNGUYEN THITHUY KIEU TOM TAT BE TAI THIET KE PHAN MEM HO TRO GIANG DAY MON LY THUYET DO THI Sinh vien thuc hien: Nguyln Thi Thuy KiSu - MSSV: DTH072351 Giang vien huang din: Ths Nguyln Thi Lan Quyen Noi dung: Phan mem ho tr^ giang day mon ly thuyet thi nham mo phong true quan cac giai thuat chinh cua mon hoc mot each chinh xac, hieu qua Cac thuat toan chay true tiep tren may chi tiet, ro rang, de hieu giiip cho qua trinh giang day d^t k^t qua t6t han D6 tai ducrc thuc hien tai khoa Ky thuat - Cong nghe - Moi trucmg thuoc Trucmg Dai hoc An Giang Yeu cau: -Hieu ro thi -Hieu va van dung cac giai thuat tim kiem tren thi (DFS, BFS, tim duong di, tim cay khung) mot each chinh xac -Nam vung cac giai thuat xac dinh chu trinh tren thi (Euler, Hamilton)., ' -Cai dat chucmg trinh demo Moi trirong phat trien ung dung -Ngon ngu cai dat: C# -Moi truong Framework 4.0 Thiet ke ph^n mem h tro giang day mon Ly ThuySt D6 Thi KHOA LUAN TOT NGfflgPNGUYEN THITHUY KIEU MUC LUC lcsicAmon tomtatbetAi MIJC LUC, DANHMUCHINH DANHMUC BANG Phln I: Md BAU1 I.Ly chon dg tai1 II.Be tai nghien cuu2 1.Ten dg tai2 2.Muc dich nghien cuu2 3.Pham vi nghien cuu2 4.Rang biipc dg tai•.:2 III.Qua trinh thuc hign:2 PHAN H: NQl DUNG3 Chuong 1: TONG QUAN VE LY THUYET BO THI3 I.Binh nghta d6 thi3 Binh nghia d6 thi.'.3 1.1B^ thi la mot cap G = (V, E), do:3 1.2B6 thi la mot cap G = (V, E), do:3 B6thicohudng3 3.Bo thi vo huong4 4.Khuygn va canhsong song5 II.Cac dang d6 thi dac biet 1.B6 thi don.•.'5 2.Bgthidu5 3.Bdthiphandoi•.6 4.Bo thi phan doi du6 III.Baccuadinh7 Bac7 Thigt ke phan mgm ho trp giang day mon Ly Thuyet Bo Thi KHOA LUAN TOT NGHIEP'NGUYEN THITHUY KIEU 2.Bac cua dinh thi co huung7 3.Binh treo, dinh co lap7 4.Cong thiic lien h? giua bac va s6 canh7 IV.Bilu dien thi bing ma tr|n'.: 1.Ma tran kS7 2.Ma tran lien thupc (ma tran lien k6t)8 V.Day chuyen va duong di9 1.Daychuygn9 2.Duong di9 3.Tinh chit "don" va "so cip"9 4.Chu trinh va mach9 Chuong 2: TINH LIEN THONG CUA DO THI11 I.DinhnghTa11 II.Thuat toan tim cac phin lien thong11 1.Duyettheo chieusau (Depth first search)12 1.1.Thuat toan DFS12 1.2.So dfi mo phong thuat toan DFS12 2.Duyet theo chiiu rging (Breadth-First Search)13 2.1.Thuat toan BFS13 2.2.So d6 mo phong thuat toan BFS13 3.VI du ling dung duyet thi14 Chuong 3: DO THI D^NG CAY16 I.Dinhnghia16 1.Do thi dang cay (hay gpi vin tit la cay)16 2.D6 thi dang rung (hay goi tit la rung)16 II.Cac dinh nghia tuong duong16 III.Caykhung16 1.Dinhnghia16 2.Dinhly16 IV.Cay khung s6 nho hhit17 Thiet ki phan mem h trp giang day mon Ly Thuyet D6 Thj KHOALUANTOTNGHIEPNGUYEN THITHUY KIEU 1.Dinh nghia d6 thi co trpng s617 2.Thuat toan Prim17 2.1.Gidi thieu thuat toan Prim'17 2.2.So mo phong thuat toan Prim18 3.Thuat toan Kruskal19 3.1.Thuat toan Kruskal19 3.2.So mo phong thuat toan Kruskal20 4.Vidp:21 4.1.Ling dung hai thuat toan tren dS tim cay khung co trQng so nh6 nhat21 4.2.Ling dung cho bai toan ket noi he thong mang22 Chuong : BAI TO AN DU6NG SI NGAN NHAT23 I.Bai toan23 1.Phat biSu bai toan23 2.Nhanxet.,23 II.Cac thuat toan tim ducmg di ngin nhit23 1.Thuat toan Dijkstra23 1.1.Gidi thieu thuat toan23 1.2.So d6 mo phong thuat toan Dijkstra 24 1.3.Vidu:25 2.Thuat toan Floyd26 2.1.Gioi thieu thuat toan Floyd26 2.2.So d6 mo phong thuat toan Floyd:."27 3.Thuat toan Bellman28 3.1Gidi thieu thuat toan Bellman28 3.2So d6 mo phong thuat toan Bellman28 3.3.Vidu:.•'.29 III.Ling dung cac thuat toan tim dudng di ngan nhat vao thirc te30 • Chuong 5: DO THI EULER VA HAMILTON31 I D6 thi Euler,.31 Bai toan chigc ciu31 • Cac dinh nghia31 Thi^t kg phan mlm h trg giang day m6n Ly Thuygt Do Thi KHOALUANTOTNGfflgP .NGUYEN THITHUY KIEU 3.Binh ly Euler32 4.Thuat toan tim chu trinh Euler (Thuat toan Fleury)32 4.1.Gioi thieu thuat toan32 4.2.So mo phong thuat toan Euler:33 II B6 thi Hamilton34 1.Binhnghia35 2.Qui t^e d tim chu trinh Hamilton35 3.Thuat toan tim chu trinh Hamilton:35 3.1.Thuat toan quay lui de tim chu trinh Hamilton35 3.2.So mo phong thuat toan Hamilton36 Chuong 6: CAI SAT CHl/GNG TRINH37 ' I NSn tang thuc hien chuong trinh•.37 II Thilt k giao dien37 1.Giao dien chinh cua phan mem37 2.Giao dien ve thi•38 3.Giao dien xac djnh tinh lien thong cua thi39 4.Giao dien tim cgy khung nho nhlt40 5.Giao dien tim duong di ngln nhdt41 6.Giao dien duong di Euler va Hamilton42 7.Giao dien cua tny giup43 Phln m: KET LUAN, :44 I.MQt s6 k^t qua dat duoc44 II.Chuadatduoc 44 HI Huong phat trien:45 ThietkephSnmemho trqgiing day monLy ThuyetBo Thi KHOA LUAN TOT NGHIEP, NGUYEN THITHUY KIEU DANH MUC HINH Hinh 1.1: Dd thi co hudmg3 Hinh 1.2: Do thi vd huang4 Hinh 1.3: Do thi du.'5 Hinh 1.4: Do thi du vaphdn ddi du6 Hinh 1.5: Chu trinh vd mach cua dd thi10 Hinh 2.1: Thanh phan lien thong cua thi11 Hinh 2.2: Saddmd phong thudt todn DFS12 Hinh 2.3: Sadd mo phong thudt todn BFS:13 Hinh 2.2: Duyet thi (DFS) & (BFS)14 Hinh 3.1: Do thi dang cay16 Hinh 3.2: Sa mo phong thudt todn Prim18 Hinh 3.3: Sa mo phong thudt todn Kruskal20 Hinh 3:4: Tim cay khung (Prim) & (Kruskal)21 Hinh 3.5: Cay khung nhd nhdt22 Hinh 3.6: Sa mang22 Hinh 4.1: Do thi tim duang di ngdn nhdt bang Dijkstra24 Hinh 4.2: Dd thi tim duang di ngdn nhdt bdng Dijkstra25 Hinh 4.3: Sa dd mo phong thudt todn Floyd27 Hinh 4.4: Sa mdphong thudt todn Bellman28 Hinh 5.1: Chide cdu dKonigsberg29 Hinh 4.5: Do thi tim dudrigdingdn nhdt bdng Bellman:31 Hinh 5.2: Dd thi Euler32 Hinh 5.3: Sa md phong thudt todn Euler33 Hinh 5.4: Dd thi tim chu trinh Euler34 Hinh 5.5: Khdi thdp nhi di$n diu'.34 Hinh 5.6: Dd thi Hamilton35 Hinh 5:7: Sa md phong thudt todn Hamilton36 Hinh 6.1: Giao dien chinh cua phan mem37 Hinh 6.2: Minh hoa vedd thi vd huang vd khdng cd trongsd38 Hinh 6.3: Minh hoa duyet thi bdng thudt todn BFS39 Thiet ke phan mem ho tr^ gi^ng day mon Ly Thuyet Do Thi KHOA LUAN TOT NGHIEPNGUYEN THITHXJY KIEU Hinh 6.4: Minh hoa tim cay khung nho nhdt bang thudt toan Prim40 Hinh 6.5: Minh hoa tim duang di ngan nhdt bang thudt toan Dijkstra41 Hinh 6.6 :Minh ve tim chu trinh Hamilton bang thuat toan Hamilton42 Hinh 6.7: Minh hoa hu&ngdative canh ciia thi43 DANH MUC BANG r •-* Bang duyet theo chieu sdu (DFS).'14 Bang duy?t theo chiiu sdu (BFS)15 Bang tim cay khung co trpngso nho nhdt bang thuat toan Kruskal21 Bang tim cay khung co trpngso nho nhdt bang thuat toan Prim21 Bang hiin thi chi tiit cita thudt toan26 Bang Men thi dudng di chi tiet cua thuat toan29 Thi^t k^ phfin m^n ho trg giang day mon Ly Thuy^t 06 Thi KHOALUANTOTNGHIEPNGUYEN THI THUY KIEU Phan I: Md BAU GIOOE THIEU BE TAI I Ly chon de tai -Ngay nay, hau het cac tac nghiep nhieu linh vuc nhu: kinh te, chinli tri, quan su, van hoa,, cang dupe tu dpng hoa, la kdt qua ciia su van dung khoa hoc may tinh hien dai hay noi khac hem la nhd su phat trien vupt bac ciia nganh "Cong nghe thong tin" da tao nhieu phan mem ling dung thong minh, co the lam viec thay ngudi vdi toe nhanh chdng chinh xac, mang lai hieu qua kinh te va nang cao chat lupng cupc song -Trudng dai hpc An Giang la mot nhung tnrong dai hpc Ion d khu vpc dong bang song Cuu Long co ca sd vat chat hien dai va da dang, dac biet la so lupng sinh vien rat dong Be dam bao ca ve so lupng va chat hrong sinh vien hpc tai trudng, ddi hoi nha trudng phai thay ddi phucmg phap giang day sau cho pbu hop vdi su phat triep cua xa hoi, vi the viec ting dung cdng nghe thong tin vao qua trinh d^y hoc la rat cin thidt Bdi vdi sinh vien chuyen nganh cdng nghe thong tin d6 bit kip vdi su thay ddi nhanh chong cua cdng nghe, thay ddi hinh thiic giang day de kich thich tu duy, sang tao ciia sinh vien la mpt dieu het sue quan trpng -Ly thuyet thi la mpt nhiing mdn hpc ciia nganh cdng nghe thong tin La mot linh vuc lau ddi ciia toan hpc va cd vai trd rat quan trpng su phat trien ciia cdng nghe thong tin LTng dung ciia ly thuyet thi d khap noi, tu ly thuyet trd choi cho den cac linh vuc tri tue nhan tao, mang may tinh, co sd du lieu Cac kien thiic ve ly thuyet thi het siic bd ich cho sinh vien chuyen ng^nh cdng nghe thong tin, sinh vien dupe trang bi kien thiic hd trp giai quyet cac bai toan cd y nghia thuc td cao nhu tim dudng di ngin nhat, tim cay khung, ma dupe tiep can vdi nhieu kien thiic hay, bd ich ciia toan hpc, nhung bai toan lien quan den lich sii ciia toan hpc nhu thi Euler, thi Hamilton, Ly thuyet thi that su la mdn hpc rat bo ich va cd rat nhieu ling dung_ thuc te Tuy nhien, phuong phap giang day mang tinh thu cdng mpt phan la mat nhieu thdi gian, mac khac la lam cho mdn hoc trd nen nham chan lam cho sinh vien khdng thu vdi mdn hpc -Tir do, van dung nhung kien thiic da hpc tren ldp ve mdn ly thuyet thi tdi tien hanh nghien ciiu va quyet dinh chpn de tai " Thiet ke phan mem ho trp giang day mdn Ly Thuyet Bo Thi" nham ciing cd kien thiic, nang cao trinh dp chuyen mdn ciia ban than, nang cao chat lupng day hpc mdn ly thuyet thi ciia nganh cdng nghe thong tin trudng dai hpc An Giang Thidt kd phdn mdm ho trp giang day mdn Ly Thuydt Bd ThiTrang KHOA LUAN TOT NGHIEP • NGUYEN THI THUYKIEU ? Vi du: Tim chu trinh Euler cho thi Hinh 5.4: B8 thi tint chu trinh Euler Caidat: „ Bl: Nap dinh v y ciia thi vao stack (thudng la dinh 1) „ B2: Thuc hien vong lap den stack rong - .Xet dinh v tren dinh stack: •„ Neu la dinh co lap thi lay khoi stack -> ket qua •„ Neu dinh u ke voi v thi nap u vao stack va xoa canh vu > Ketluan: Do thi dang xet khong phai la thi Euler Vi thi C6 mot dinh bac va m6t dinh bac nen theo dmh ly Euler ta khong the nao di duyet qua tat ca cac canh noi tiep nhau, moi canh qua dung mot Ian n Bb thi Hamilton Khai niem dufrng di Hamilton co ngudn goc tir bai toan: "Xuit phat tir mot dinh ciia khoi thap nhi dien du (hinh 5.4), di doc theo cac canh cua khoi cho di qua tat ca cac dinh khac, moi dinh qua diing mot Ian, sau trd ve dinh xuat phat" Bai toan dirge nha toan hoc Hamilton phat bieu vao nam 1859 Hinh 5.5: Khdi thap nhi dien deu Thiet ke phan mem ho trg giang day mon Ly Thuyet Do Thj Trang 34 NGUYEN THITHUY KIEU KHOA LU^N TOT NGHIEP Dinh nghia -Day chuyen Hamilton la day chuyen di qua tat ca cac dinh ciia thi va di qua mi dinh mpt Ian -Chu trinh Hamilton la day chuyen Hamilton xuat phat tir mot dinh, di qua tat ca cac dinh khac cua thi, moi dinh diing mpt Ian va quay trd ve nod xuit phat -B6 thi Hamilton la dd thi co chua it nhlt mot chu trinh Hamilton -Vi dp: Xet don thi (GO, (G2), (G3) sau: Hinh S 6: Do thi Hamilton •Bd thi (GO cd chu trinh Hamilton (1, 2, 3, 4, 5,1) •Dd thi (G2) khdng cd chu trinh Hamilton vi deg(l) = nhung cd dudng di Hamilton (1, 2, 3, 4) •Bd thi (G3) khdng cd ca chu trinh Hamilton lln dudng di Hamilton 2.Qui the di tim chu trinh Hamilton Xet mpt thi G = (V, E) gdm n dinh, qua trinh tim chu trinh ' Hamilton chung ta cd thf van dung cac qui tSc sau day: •Qui tacl: Lay het cac canh ke vdi dinh bac •Qui tac 2: Khdng cho phat sinh chu trinh it hon n canh •Qui tac 3: Neu da lay hai canh ke vdi dinh v thi cd the bd tat ca cac canh lai ke vdi v •Qui tac 4: Duy tri tinh lien thong va bao dam bac mdi dinh ludn ldn hom hay bang 3.Thuat toan tim chu trinh Hamilton 3.1 Thuat toan quay lui de tim chu trinh Hamilton -Luu tru thi da cho dudi dang danh sach Ke(v) -Lift ke cac chu trinh Hamilton thu dupe bang vif c phat trifn day cac dinh Bl: BStdiu tir dinh 1, v[l]=l B2: Tim va luu dinh cd canh ndi vdi v[i] va dinh j chua tham trudc B3: Neu dinh j la v[n] va v[l] cd canh ndi vdi no thi xuat thi Hamilton Nf u dinh j vln chua phai la v[n] thi tifp tuc B2 Thiet kephan mem ho trp giang day mdn Ly Thuyet Do Thi Trang 35 KHOALUAN TOT NGHIEP NGUYEN THITHUY KIEU 3.2 Sff mo phdng thuat toan Hamilton i Bit Chon v[i] =1 vdi i=1 Chgn]k4vti] va v[i]^j Hinh 5.7: Sff dd md phdng thuat todn Hamilton Thiet ke phan mem ho trg giang day mon Ly Thuyet Do Thi Trang 36 KHOALUAN TOTNGHlgP NGUYEN THJTHUY KIEU Chmmg 6: CAI DAT CHtfOfNG TRINH Nen tang thuc hicn chirong trinh Chuang trinh viet bing ngon ngu C# bp Visual Studio 2010 Cai dat de mo phong, minh hpa true tiep cac giai thuat chinh cua mon hpc mpt each chinh xac, hipu qua cua mon Ly Thuyet Do Thi Giao dien thiet ke tren bp Visual Studio 2010 kdt hpp vdi Dotnetbar V 8.8 Voi chuong trinh co th^ chay tren cac he dieu hanh da cM dat h6 trp Framework 4.0 (windows 7, windows xp, windows vista ) n Thilt ke giao dien Giao dien chinh cua phan mem MATRANBOTH! ' ' " *.Vav, :'•• ,*-.!.*:^ '^ -,V '.-.-h.).' rV -*t ^ • ^C.^-.2 Ai^i^ • " • - • • •.'*"•^ L fizi "" ikt!1^!'—1 ^ ' GIAO VIEN HU'O'NG DAN:- ••- ' ; NGUYEN THJ LAN QUYEN • V"' * ; ;SINH VIEN THU'C HIEI^: " NGUYEN TH| THUYKIEU Hinh 6.1: Giao dien chinh cuaphan mem ' Thi^t ke phan mem li trp giang day mon Ly Thuy^ D6 Thi Trang 37 KHOA LUAN TOT NGHIEP NGUYEN THI THUY.KIEU Giao dien ve thi Muln ^e dd thi trade tien chpn Tab ve thi Sau chpn loai thi can ve (co hudng hoac vo hudng), tiep theo chpn loai thi (co so hoac khong co so) de ve: •' Click chupt giua la ve nut •Click chupt trai la ve canh •Click chupt phai chpn cac thupc tinh (xda, siia, di chuyen, bd qua doi vdi dinh) hay (xoa, siia, bo qua d6i vdi canh) •Khi ve xong d6 thi co thS chpn chiic nang luu de luu thi dudi dang filetxt •Khi mu6n sii dung thi da liru trudc chpn chiic nang load thi •Khi dang ve d6 thi mu6n xoa va ve lai ban diu chpn chiic nang xoa d6 thi tdt ca cac thong s6 ciia d6 thi se dupe dua ve gia tri mat dinh ban • - dlu •Khi ve d6 thi thi thong tin vl dinh va trpng so se dupe hin thi d DataGridView cua giao dien Mac khac ta cd thi chinh sua true tilp trpng s6 tren ma tran hoac xoa canh trpng so ciia canh dupe siia 0, sau chpn luu thay doi de hoan cac thao tac tren ^^Mf — _ "^ ~^ ^4 ^!^, ^ ^*-—4^ J!P^ ^^i,— ^-^^J ^r\ ,u^ liian ^a s? • ^o ' , " j 4w* 'Vddothi , t^3[ Tirtilienthdng ' S^^Caykhungnhdnh^l s/ StfongtSngBurihSt^ *^ ^J'B^QngdiEtiler-HBnimton CBdlHcdtHiong 5/B5 thi vfi hddng t nj Bo thi cd bong so ^ Bo Us khcg co b^ngso C^njathLCdhJfftHllWMang ChcndS.W-Cdb^rgsdllKhdnscobc gE6 Load anii LUuciS thi ^j^^Iclapband^j^ MATRANDOTHj l \ ;4 |5 ' ? 1 J li ">1 1 i (1 ,0 ^i ji 1 * ' f ^ [ • *- i L_j LUuthayddi Hlnh 6.2: Minh hga ve dd thi vo hie&ng vd khong co sd Thiet ke phan mem h trp giang day mon Ly Thuylt D6 Thi Trang38 KHOA LUAN.TOT NGHIgP .NGUYEN THJ THUY KIEU Giao dien xac dinh tinh lien thong cua thi •, Ta dung hai thuat toan duyet theo chieu sau (pFS), duypt theo chieu rng (BFS) dl xac dinh tinh lien thong cua d6 thi •Truac duyet ta chpn dmh bit diu roi chpn DFS hay BFS thuat toan chay va chp hifn ket qua a bn dudi goc trai man hinh Hinh 6.3: Minh hoa duyet db thi bang thuat toan BFS Thiet ke phan mem ho tro giang day mon Ly Thuyet 06 Thi Trang 39 KHOA LUAN TOT NGHIEP NGUYEN THITHUY KIEU Giao dien tim cay khung nho nhat • Be tim cay khung co trpng so nho nhat ta ap dung hai thuat toan Rruskal, Prim Doi vdd thuat toan Prim ta chpn dinh bit dau de xet Hinh 6.4: Minh hoa dm cay khung nho nhat bang thuat toan Prim Thiet ke phan mem ho tro giang day mon Ly Thuyet Do Thi Trang 40 NGUYEN THITHUY KIEU KHOA LUAN TOT NGHIEP ' Giao dicn tim duong di ngan nhat •Gom thuat toan Dijkstra, Floyd, Bellman de tim ducmg di ngan nhat cua d6 thi •Khi ve hoac load thi xong ta chpn dinh bat dau va dinh ket thuc roi chpn thuat toan d6 tim duong di ng^n nMt Khi thi co trpng so am chi co th thuc hien thao tac tim dtrdng di ngin nhat ddi vdi thuat ••toan Bellman •Bang kSt qua hien thi duong di chi tiet nam ben trai goc duai giao dien / Ddong di rgln nhal ' ^J^ Oddng ^^^ EUer Han^nton Oiikslra |i^ ^^| Floyd ^Y^ Bellman Start jl _„ ^g di rgan nhli,_ '! _, - End ~"! Chpn djnh , MATRANDOTH! J2 ,3 ' I ' ^1 > i T "' " ' " ' ,,.;• "• • i • L- '" ^"• S l ' - ' 1 ' HBBB BBI^BRH • * i > 0' ^ "^,s1 (-)(-)(•)(-!( (11) !•) (41) (-> '(43 (33 (-.) i 19 II ' " ^?.! ^^ :i : || r 19 •' I II d.5: Minh hoa tint dwcmg di ngan nhat bang thuat toan Dijkstra Thiet ke phan mem ho trp giang day mon Ly Thuyet Bo Thi Trang 41 KHOA LUAN TOT NGHIEP NGUYEN THJ THUY KIEU Giao dien dirong di Euler va Hamilton Be tim duoc chu trinh cua d6 thi Euler ta chon yao thuat toan Euler, ngu^c lai chon Hamilton (J.d ;MinA Apa tim chu trinh Hamilton b&ng thuat todn Hamilton Thi^t k8 pMn mSm h trg giang day mon Ly Thuy^t B6 Thi Trang 42 KHOA LUAN TOT NGHIgP NGUYEN THITHUY KIEU Giao dien cua tro giup • < Trp giup la de giiip cho nguoi dung su d\mg phan mem dupe de dang hon Huong dan chon loai thi can ve, cac thao tac chinh sua dinh, each load, luu, xoa thj nhu the nao, each ve canh, thay doi so dupe minh hpa hinh anh ro rang chi tiet ^^C -1 ia ^Di^ lri^ '"l>n ^*'J^^ 1/^^^1 ^^ Si-"/ f ^^^^ " ' ^^i
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