nhom 07
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TIU LUN MN HC PHN TCH THIT K THUT TON. ti: LP BI TON NPC (Nondeterministic Polynomial Completeness)
Ging vin hng dn: TS. Hong Quang Thnh vin thc hin: Nhm 7 1. Trn L Ngc ([email protected]) 2. Hunh Quc Lc ([email protected]) 3. Trn Th Hnh ([email protected]) 4. V Th Tnh ([email protected]) 5. Nguyn Th Bch Lin ([email protected]) NI DUNG Phn loi bi ton Lp bi ton P Lp bi ton NP Lp bi ton NPC Mt s bi ton thuc lp NPC 2 Phn loi bi ton Bi ton Gii c Khng gii c Lp khng a thc Lp a thc 2 lp 2 lp ? 3 NPC Lp NP Lp bi ton c phc tp a thc (Polynomial time P) Lp P Ltphpttcnhngbitoncth gii c bng thut ton n nh trong thi gian a thc (tc l tn ti thut ton gii quyt n vi thi gian chy a thc). phc tp tnh ton ca nhng bi ton ny l O(nk), k hng s. Nhng bi ton c phc tp dng O(k), O(log(n)), O(n), O(nlog(n)), nk
u l nhng bi ton thuc lp P. 4 Lp bi ton c phc tp khng a thc Tp cc bi ton c phc tp ly tha O(an) hoc giai tha O(n!) l khng thuc lp a thc Cc bi ton khng thuc lp a thc ch gii c vi mt ln d liu u vo nht nh. 5 V d: Cho mt tp hp c n phn t, hy lit k tt c cc tp con khc trng ca tp hp ny.S tp con ca mt tp hp c n phn t l 2n-1.Ligiituyc nhngkhithhinli giinybngbtk thuttonnothphi tn t nht 2n-1 bc. N S ln thc hin Ghi ch 16Khong vi chc ngn My tnh c th gii 32Khong 4 tCn nhng my tnh tc cao v tn rt nhiu thi gian 33Khong 8 t Lp bi ton NP (Nondeterministic Polynomial time) Chng ta u bit rng tnh xc nh l mt trong ba c tnh quan trng ca thut ton. Mi bc ca thut ton phi c xc nh duy nht v c th thc thi c. Nu c s phn chia trng hp ti mt bc th thng tin ti bc phi y thut ton c th t quyt nh chn la trng hp no. Vy th iu g s xy ra nu ta a ra mt "thut ton" c tnh khng n nh? Ti mt bc ca "thut ton", ta a ra mt s trng hp chn la nhng khng cung cp y thng tin "thut ton" t quyt nh? 6 Lp bi ton NP 7 Vd: Tac mtlichdnkhiidulch:"Khiihtkhuvnny,bn hy chn mt con ng m bn cm thy thch. Tt c u dn n bo tng lch s".Khu vn Vin bo tng 1 23 Khch du lchMy tnh Tisaolicpnnhngthutton khngnnhdmytnhkhngththc hin mt thut ton nh vy? .. Go(Khu vn); ??? Choose(1,2,3); Go(Vin bo tng); Khi nghin cu v thut ton khng n nh, dkhngdnggiibitonnoina, chngtascnhnghiubitvhnch ca nhng thut ton n nh thng thng. 2 V d 2: Bi ton ngi bn hng (TSP) - C mt ngi giao hng cn i giao hng ti n thnh ph.-Xutphttmtthnhphno,iquaccthnhphkhc giao hng v tr v thnh ph ban u.- Mi thnh ph ch n mt ln - Khong cch t mt thnh ph n cc thnh ph khc l xc nh.Hy tm mt chu trnh sao cho tng di cc cnh nh hn M? Lp bi ton NP -Lit k tng con ng c th i -Sosnhchiudimiconng tm c vi M+ Tm c mt con ng ph hp+ Xt ht tt c cc con ng -Chnmtconngcthv tnh chiu di ca n.- So snh chiu di ny vi M + Nu