Jul 16, 2015
Trn thc t c nhiu bi ton lin quan ti mt tp cc i tng v nhng mi lin h gia chng, i hi ton hc phi t ra mt m hnh biu din mt cch cht ch v tng qut bng ngn ng k hiu, l th. Nhng tng c bn ca n c a ra t th k th XVIII bi nh ton hc Thu S Leonhard Euler, ng dng m hnh th gii bi ton v nhng cy cu Konigsberg ni ting. Mc d L thuyt th c khoa hc pht trin t rt lu nhng li c nhiu ng dng hin i. c bit trong khong vi mi nm tr li y, cng vi s ra i ca my tnh in t v s pht trin nhanh chng ca Tin hc, L thuyt th cng c quan tm n nhiu hn. c bit l cc thut ton trn th c nhiu ng dng trong nhiu lnh vc khc nhau nh: Mng my tnh, L thuyt m, Ti u ho, Kinh t hc v.v... Chng hn nh tr li cu hi: Hai my tnh trong mng c th lin h c vi nhau hay khng?; hay vn phn bit hai hp cht ho hc c cng cng thc phn t nhng li khc nhau v cng thc cu to cng c gii quyt nh m hnh th. Hin nay, mn hc ny l mt trong nhng kin thc c s ca b mn khoa hc my tnh. L thuyt th l mt phn quan trng trong ni dung chng trnh chuyn ca mn Tin hc ti cc trng chuyn. Hu nh trong cc thi hc sinh gii u c cc bi ton lin quan n l thuyt th, do hc sinh c c kt qu cao chng ta cn trang b cho cc em mt nn tng tt cng nh cc k thut ci t cc bi ton c bn ca l thuyt th. Tuy nhin, l thuyt th l mt mn hc cn tn nhiu thi gian truyn t, c mt s vn th cn thit cho hc sinh trong cc k thi, mt s khc khng cn thit, c bit l mt s vn cn chng mnh, cc nh l. Mt khc mt s vn li phi c trang b su nhm gip hc sinh gii quyt tt vn trong cc thi li khng c trong nhiu ti liu l thuyt th c in. Nhng vn thng lin quan n ng dng ca l thuyt th gii quyt cc bi ton thc t.Mt vn kh khn m gio vin gp phi l qu thi gian ca chng ta rt t m ni dung ging dy nhiu. Do vn chn la nhng chuyn no dy v dy n u, nhng vn no nh hng cho hc sinh t hc cn phi t ra cho Gio vin ging dy cc lp chuyn Tin hc v cc i tuyn chun b cho cc k thi Hc sinh gii. Trong phm vi mt chuyn , khng th ni k v ni ht nhng vn ca l thuyt th m ch gii thiu cc bi ton c bn ca L thuyt th trong Tin hc cng vi phng php truyn t cho hc sinh. Tp bi ging ny s xem xt l thuyt th di gc ngi lp trnh, tc l kho st nhng thut ton c bn nht c th d dng ci t trn my tnh mt s ng dng ca n. Cc khi nim tru tng v cc php chng minh s c din gii mt cch hnh thc cho n gin v d hiu ch khng phi l nhng chng minh cht ch dnh cho ngi lm ton. Ngoi ra cng cung cp mt s bi tp trn mng c phn loi thnh cc dng gip gio vin c ngun bi tp cung cp cho hc sinh sau khi ging dy cc chuyn . Li gii ca cc bi tp c cung cp di dng chng trnh.
Ni dung chuyn l thuyt th Mc ch Trang b cho hc sinh cc kin thc c bn cn thit v th gii quyt cc bi ton thi hc sinh gii. Cc khi nim c bn 1. Cc phng php tm kim trn th 2. Chu trnh le v Hammilton 3. Cy Khung 4. ng i Ngn nht 5. Lung trn mng 6. Bi tp theo ch 7. Cc bi ton th trong cc k thi Quc gia 8. Chng trnh gii Ni dung cc bi ging t phn 1 ti phn 6 c son trn slide trong file nh km
7. Bi tp theo ch Chuyn Tm kim theo chiu rng (BFS)
Lucky NumbersM bi: LUCKYNUM
Trong mt s nc chu , 8 v 6 c coi l nhng ch s may mn. Bt c s nguyn no ch cha ch s 8 v 6 c coi l s may mn, v d 6, 8, 66, 668, 88, 886 . Nguyn l mt hc sinh rt thch ton. Nguyn thch cc s may mn nhng ch thch cc s c dng S = 8866 trong S c t nht mt ch s v ch s 6 v 8 khng nht thit phi ng thi xut hin. V d, 8, 88, 6, 66, 86, 886, 8866 l cc s c dng S. Cho trc mt s nguyn dng X (1 < X < 10 000), Nguyn mun tm s may mn nh nht dng S, c khng qu 200 ch s v chia ht cho X. Nhim v ca bn l vit mt chng trnh tm s cho Nguyn.
D liu vo D liu vo gm nhiu b d liu tng ng vi nhiu test. Dng u tin cha mt s nguyn dng khng ln hn 20 l s lng cc b d liu. Cc dng tip theo cha cc b d liu. Trn mi dng tip theo cha mt s nguyn X tng ng vi mi b d liu. D liu ra Vi mi b d liu, ghi ra trn mt dng s may mn dng S nh nht chia ht cho X. Trng hp khng tn ti s S c khng qu 200 ch s nh vy, ghi -1. V dLUCKYNUM.INP LUCKYNUM.OUT
4 6 8 43 51. VOI06 Qun tng
6 8 86 -1
M bi: QBBISHOP
Xt bn c vung kch thc nn. Cc dng c nh s t 1 n n, t di ln trn. Cc ct c nh s t 1 n n t tri qua phi. nm trn giao ca dng i v ct j c gi l (i,j). Trn bn c c m (0 m n) qun c. Vi m > 0, qun c th i (ri, ci), i = 1,2,..., m. Khng c hai qun c no trn cng mt . Trong s cc cn li ca bn c, ti (p, q) c mt qun tng. Mi mt nc i, t v tr ang ng qun tng ch c th di chuyn n c nhng trn cng ng cho vi n m trn ng i khng phi qua cc c qun
Cn phi a qun tng t xut pht (p, q) v ch (s,t). Gi thit l ch khng c qun c. Nu ngoi qun tng khng c qun no khc trn bn c th ch c 2 trng hp: hoc l khng th ti c ch, hoc l ti c sau khng qu 2 nc i (hnh tri). Khi trn bn c cn c cc qun c khc, vn s khng cn n gin nh vy. Yu cu: Cho kch thc bn c n, s qun c hin c trn bn c m v v tr ca chng, xut pht v ch ca qun tng. Hy xc nh s nc i t nht cn thc hin a qun tng v ch hoc a ra s -1 nu iu ny khng th thc hin c. Input Dng u tin cha 6 s nguyn n, m, p, q, s, t. Nu m > 0 th mi dng th i trong m dng tip theo cha mt cp s nguyn ri , ci xc nh v tr qun th i. Hai s lin tip trn cng mt dng c ghi cch nhau t nht mt du cch. Output Gm 1 dng duy nht l s nc i tm c ExampleQBBISHOP.INP 837214 54 34 QBBISHOP.OUT 3
47 Hn ch: Trong tt c cc test: 1 n 200. C 60% s lng test vi n 20.Gm cM bi: VMUNCH
Bessie rt yu bi c ca mnh v thch th chy v chung b vo gi vt sa bui ti. Bessie chia ng c ca mnh l 1 vng hnh ch nht thnh cc vung nh vi R (1