Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l Wnsy om 3m-5m 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! l-dignosti on w tions: n go to ny, ut v ioity in you own C 88: Atiiil Intllign Fll 0 Ltu : Quu-Bs 8/30/0 Dn Klin UC Bkly Multil slis om tut Russll, Anw Moo Toy Rlx Agnts Agnts tt Pln A Polms 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 Consi ow t wol I Cn lx gnt tionl? [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 Consi ow t wol WOULD BE [mo: ln st / slow ] Polms A s olm onsists o: A stt s A susso untion (wit tions, osts) 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: Ros: 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 Wt s in tt? T wol stt siis vy lst til o t nvionmnt A s stt ks only t tils n (sttion) Polm: Pting tts: (x,y) lotion Ations: NEW usso: ut lotion only ol tst: is (x,y)=end Polm: Et-All-Dots tts: {(x,y), ot oolns} Ations: NEW usso: ut lotion n ossily ot ooln ol tst: ots ll ls Wol stt: Agnt ositions: 0 Foo ount: 30 ost ositions: Agnt ing: NEW tt izs? How mny Wol stts? 0x( 30 )x( )x4 tts o ting? 0 tts o t-ll-ots? 0x( 30 ) Ts Anot T 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 : Exn out ossil lns Mintin ing o unxn lns Ty to xn s w t nos s ossil
nl T Exml: T Imotnt is: Fing Exnsion Exlotion sttgy Dtil suoo is in t ook! Min ustion: wi ing nos to xlo? tt s vs. Ts Rviw: Dt Fist W onstut ot on mn n w onstut s littl s ossil. E NODE in in t s t is n nti PATH in t olm g. ttgy: xn st no ist Imlmnttion: Fing is LIFO stk 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 (ug) T vg ning to B (t vg num o sussos) C* Cost o lst ost solution s m Dt o t sllowst solution 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: BF using 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 (ioity: umultiv ost) Cost ontous 4 6 3 9 5 3 7 0 8 8 3 9 8 7 0 5 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