C 88: Atiiil Intllign Fll 009 Ltu : Quu-Bs 9//009 Dn Klin UC Bkly Multil slis om tut Russll, Anw Moo Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l tomoow om m-3m in o 75 T l tim is otionl, ut P0 itsl is not On sumit, you soul gt mil om t utog Pojt : On t w toy tt ly n sk ustions. It s long tn most! Ot tion 07 ws on u, Fiys -m My OHs Mony w in t l, Tusy k in 7 o I OHs on w sit Agnts tt Pln A Polms Toy Uninom Mtos (t viw o som) Dt-Fist Bt-Fist Uniom-Cost Huisti Mtos (nw o ll) y Rlx gnts: Coos tion s on unt t (n my mmoy) My v mmoy o mol o t wol s unt stt Do not onsi t utu onsuns o ti tions At on ow t wol I Cn lx gnt tionl? Rlx Agnts [mo: lx otiml / loo ] ol Bs Agnts ol-s gnts: Pln Ask wt i 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 [mo: ln st / slow ] Polms A s olm onsists o: A stt s A susso untion A stt stt n gol tst N,.0 E,.0 A solution is sun o tions ( ln) wi tnsoms t stt stt to gol stt
Exml: Romni tt s tt s: Citis usso untion: o to j ity wit ost = ist tt stt: A ol tst: Is stt == Bust? olution? tt s g: A mtmtil snttion o s olm Fo vy s olm, t s osoning stt s g T susso untion is snt y s W n ly uil tis g in mmoy (so w on t) Riiulously tiny s g o tiny s olm tt izs? Ts Polm: Et ll o t oo Pmn ositions: 0 x = 0 Foo ount: 30 ost ositions: Pmn ing: u, own, lt, igt N,.0 E,.0 A s t: Tis is wt i t o lns n outoms tt stt t t oot no Ciln oson to sussos Nos ontin stts, oson to PLAN to tos stts Fo most olms, w n nv tully uil t wol t Anot T nl T : Exn out ossil lns Mintin ing o unxn lns Ty to xn s w t nos s ossil Imotnt is: Fing Exnsion Exlotion sttgy Dtil suoo is in t ook! Min ustion: wi ing nos to xlo?
Exml: T tt s vs. Ts E NODE in in t s t is n nti PATH in t olm g. W onstut ot on mn n w onstut s littl s ossil. tts vs. Nos Rviw: Dt Fist Nos in stt s gs olm stts Rsnt n stt stt o t wol Hv sussos, n gol / non-gol, v multil ssos Nos in s ts lns Rsnt ln (sun o tions) wi sults in t no s stt Hv olm stt n on nt, t lngt, t & ost T sm olm stt my iv y multil s t nos Polm tts Nos Pnt Dt 5 ttgy: xn st no ist Imlmnttion: Fing is LIFO stk No Ation Dt 6 Rviw: Bt Fist Algoitm Potis ttgy: xn sllowst no ist Imlmnttion: Fing is FIFO uu Tis Comlt? unt to in solution i on xists? Otiml? unt to in t lst ost t? Tim omlxity? omlxity? Vils: n Num o stts in t olm T vg ning to B (t vg num o sussos) C* Cost o lst ost solution s Dt o t sllowst solution m Mx t o t s t 3
DF Algoitm Comlt Otiml Tim DF Dt Fist N N N N O(B Ininit LMAX ) O(LMAX) Ininit DF Wit yl king, DF is omlt.* m tis no nos nos TART OAL m nos Ininit ts mk DF inomlt How n w ix tis? Algoitm Comlt Otiml Tim DF w/ Pt Cking Y N O( m+ ) O(m) Wn is DF otiml? * O g s nxt ltu. BF Algoitm Comlt Otiml Tim DF BF w/ Pt Cking Y N O( m+ ) O(m) Y N* O( s+ ) O( s ) Comisons Wn will BF outom DF? s tis no nos nos Wn will DF outom BF? s nos m nos Wn is BF otiml? 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. 3. I il, o DF wi only ss ts o lngt 3 o lss..n so on. Algoitm Comlt Otiml Tim DF BF ID w/ Pt Cking Y N O( m+ ) O(m) Y N* O( s+ ) O( s ) Y N* O( s+ ) O(s) TART 3 Costs on Ations 5 8 OAL Noti tt BF ins t sotst t in tms o num o tnsitions. It os not in t lst-ost t. W will uikly ov n lgoitm wi os in t lst-ost t. 9 8 4 4 3 4
Uniom Cost Pioity Quu Rs Exn st no ist: Fing is ioity uu Cost ontous 4 6 3 9 5 3 7 0 8 8 3 9 8 5 7 0 6 A ioity uu is t stutu in wi you n inst n tiv (ky, vlu) is wit t ollowing otions:.us(ky, vlu).o() insts (ky, vlu) into t uu. tuns t ky wit t lowst vlu, n movs it om t uu. You n s ky s ioity y using it gin Unlik gul uu, instions n t onstnt tim, usully O(log n) W ll n ioity uus o ost-snsitiv s mtos Uniom Cost Uniom Cost Issus Algoitm Comlt Otiml Tim DF BF UC w/ Pt Cking Y N O( m+ ) O(m) Y N O( s+ ) O( s ) Y* Y O( C*/ε ) O( C*/ε ) Rmm: xlos insing ost ontous T goo: UC is omlt n otiml! 3 C*/ε tis * UC n il i tions n gt itily T : Exlos otions in vy ition No inomtion out gol lotion tt ol [mo: s mo mty] Huistis Huistis Any stimt o ow los stt is to gol Dsign o tiul s olm Exmls: Mnttn istn, Eulin istn 0 5. 5
Bst Fist / y Bst Fist / y Exn t no tt sms losst A ommon s: Bst-ist tks you stigt to t (wong) gol Wost-s: lik lygui DF in t wost s Cn xlo vyting Cn gt stuk in loos i no yl king Wt n go wong? [mo: gy] Lik DF in omltnss (init stts w/ yl king) on Wong? 6