9/9/7 CE 7: Atiiil Intllign ing 07 Polms Outlin Polm s & Dit Fox Uninom Mtos Dt-Fist Bt-Fist Uniom-Cost Wit slis om Dn Wl, Pit Al, Dn Klin, tut Russll, Anw Moo, Luk Zttlmoy Agnt vs. Envionmnt Tys o Agnts Rlx An gnt is n ntity tt ivs n ts. A tionl gnt slts tions tt mximiz its utility untion. Ctistis o t ts, nvionmnt, n tion s itt tnius o slting tionl tions. Agnt nsos? Atutos Pts Ations Envionmnt ol oint Utility-s Pln Ask wt i ol Bs Agnts Disions s on (yotsiz) onsuns o tions Must v mol o ow t wol volvs in sons to tions At on ow t wol WOULD BE tu Polm (k tt ) Inut: t o stts Otos [n osts] tt stt ol stt [tst] Outut: Pt: stt [My ui sotst t] stt stisying gol tst [omtims just n stt tt sss tst]
9/9/7 Exml: Tvling in Romni Exml: imlii P-Mn tt s: Citis usso untion: Ros: o to jnt ity wit ost = istn tt stt: A ol tst: Is stt == Bust? olution? Inut: A stt s A susso untion A stt stt A gol tst Outut: N,.0 E,.0 tt izs? tt s Polm: Et ll o t oo Pmn ositions: 0 0 x x = = 0 0 Pmn ing: u, own, lt, igt Foo onigutions: 0 ost ositions: ost ositions: 0 tt s g: E no is stt T susso untion is snt y s Egs my ll wit osts In s g, stt ous only on! W n ly uil tis g in mmoy (so w on t) Riiulously tiny s g o tiny s olm 0 x x 0 x x = 6.8 x 0 Ts tt s vs. Ts N,.0 A s t: tt stt t t oot no E,.0 Ciln oson to sussos Nos ontin stts, oson to PLAN to tos stts Egs ll wit tions n osts Tis is now / stt Possil utus Fo most olms, w n nv tully uil t wol t tt E NODE in in t s t is n nti PATH in t stt s g. W onstut ot on mn n w onstut s littl s ossil. T
9/9/7 tt s vs. Ts T Consi tis -stt g: How ig is its s t (om )? Imotnt: Lots o t stutu in t s t! Exml: Romni ing wit T : Exn out otntil lns (t nos) Mintin ing o til lns un onsition Ty to xn s w t nos s ossil nl T Dt-Fist Imotnt is: Fing Exnsion Exlotion sttgy Min ustion: wi ing nos to xlo?
9/9/7 Dt-Fist Dt-Fist ttgy: xn st no ist Imlmnttion: Fing is LIFO stk ttgy: xn st no ist Imlmnttion: Fing is LIFO stk Algoitm Potis Algoitm Potis Comlt: unt to in solution i on xists? Otiml: unt to in t lst ost t? Tim omlxity? omlxity? Ctoon o s t: is t ning to m is t mximum t solutions t vious ts Num o nos in nti t? + + +. m = O( m ) m tis no nos nos m nos Dt-Fist (DF) Potis Bt-Fist Wt nos os DF xn? om lt ix o t t. Coul oss t wol t! I m is init, tks tim O( m ) m tis How mu s os t ing tk? Only s silings on t to oot, so O(m) Is it omlt? m oul ininit, so only i w vnt yls Is it otiml? No, it ins t ltmost solution, glss o t o ost no nos nos m nos
9/9/7 Bt-Fist Bt-Fist (BF) Potis ttgy: xn sllowst no ist Imlmnttion: Fing is FIFO uu Wt nos os BF xn? Posss ll nos ov sllowst solution Lt t o sllowst solution tks tim O( ) tis How mu s os t ing tk? Hs ougly t lst ti, so O( ) no nos nos nos Tis Is it omlt? must init i solution xists, so ys! Is it otiml? Only i osts ll (mo on osts lt) m nos DF vs BF Algoitm Comlt Otiml Tim DF BF w/ Pt Cking N unlss init N O( m ) O(m) Y Y O( ) O( ) Mmoy Limittion? uos: Hz CPU B min mmoy 00 instutions / xnsion 5 yts / no 0 M xnsions / s Mmoy ill in 60 s min Ittiv Dning Ittiv ning uss DF s suoutin:. Do DF wi only ss o ts o lngt o lss.. I il, o DF wi only ss ts o lngt o lss.. I il, o DF wi only ss ts o lngt o lss..n so on. Algoitm Comlt Otiml Tim DF BF ID w/ Pt Cking Y N O( m ) O(m) Y Y O( ) O( ) Y Y O( ) O() BF vs. Ittiv Dning Fo = 0, = 5: BF = + 0 + 00 +,000 + 0,000 + 00,000 =, ID = 6 + 50 + 00 +,000 + 0,000 + 00,000 =,56 Ov = (,56 -,) /, = % Mmoy BF: 00,000; ID: 50 0 5
9/9/7 Costs on Ations Uniom Cost TART 5 8 Noti tt BF ins t sotst t in tms o num o tnsitions. It os not in t lst-ost t. 9 8 OAL Exn st no ist: Fing is ioity uu TART 8 9 8 5 OAL ttgy: xn st no ist: Fing is ioity uu (ioity: umultiv ost) Cost ontous Uniom Cost 0 9 5 6 7 8 9 8 5 8 0 7 6 Uniom Cost (UC) Potis Wt nos os UC xn? Posss ll nos wit ost lss tn st solution! I tt solution osts C* n s ost t lst ε, tn t tiv C t is ougly C*/ε C*/ε C Tks tim O( C*/ε ) (xonntil in tiv t) tis C How mu s os t ing tk? Hs ougly t lst ti, so O( C*/ε ) Is it omlt? Assuming st solution s init ost n minimum ost is ositiv, ys! Is it otiml? Ys! Uniom Cost ttgy: xn lowst t ost T goo: UC is omlt n otiml! T : Exlos otions in vy ition No inomtion out gol lotion tt ol Uniom Cost Algoitm Comlt Otiml Tim DF BF UC w/ Pt Cking C*/ε tis Y N O( m ) O(m) Y Y O( ) O( ) Y* Y O( C*/ε ) O( C*/ε ) 6
9/9/7 Uniom Cost: P-Mn Cost o o tion Exlos ll o t stts, ut on All ts s lgoitms t sm xt o ing sttgis T On Quu Contully, ll ings ioity uus (i.. olltions o nos wit tt ioitis) Ptilly, o DF n BF, you n voi t log(n) ov om n tul ioity uu, y using stks n uus Cn vn o on imlmnttion tt tks vil uuing ojt To Do: Look t t ous wsit: tt://www.s.wsington.u/s7/7s Do t ings (C ) Do P0 i nw to Pyton tt P, wn it is ost 7