Search Problems. A search problem consists of: A solution is a sequence of actions (a plan) which transforms the start state to a goal state
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2 S Polms A s olm onsists o: A stt s A susso untion N, 1.0 A stt stt nd gol tst E, 1.0 A solution is sun o tions ( ln) wi tnsoms t stt stt to gol stt
3 Exml: Romni Stt s: Citis Susso untion: Go to dj ity wit ost = dist Stt stt: Ad Gol tst: Is stt == Bust? Solution?
4 Anot S T S: Exnd out ossil lns Mintin ing o unxndd lns Ty to xnd s w t nods s ossil
5 Gnl T S Imotnt ids: Fing Exnsion Exlotion sttgy Dtild sudood is in t ook!
6 Gnl T S Imotnt ids: Fing Exnsion Exlotion sttgy Dtild sudood is in t ook! Min ustion: wi ing nods to xlo?
7 Exml: T S G S d
8 Stt Gs vs. S Ts S d G E NODE in in t s t is n nti PATH in t olm g. S d W onstut ot on dmnd nd w onstut s littl s ossil. G G
9 Stts vs. Nods Nods in stt s gs olm stts Rsnt n sttd stt o t wold Hv sussos, n gol / non-gol, v multil dssos Nods in s ts lns Rsnt ln (sun o tions) wi sults in t nod s stt Hv olm stt nd on nt, t lngt, dt & ost T sm olm stt my ivd y multil s t nods Polm Stts S Nods Pnt Dt 5 Nod Ation Dt 6
10 Rviw: Dt Fist S S d G G S G d d Sttgy: xnd dst nod ist Imlmnttion: Fing is LIFO stk
11 Rviw: Bdt Fist S Sttgy: xnd sllowst nod ist Imlmnttion: Fing is FIFO uu S d G S S Tis d G G
12 S Algoitm Potis Comlt? Guntd to ind solution i on xists? Otiml? Guntd to ind t lst ost t? Tim omlxity? S 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 m Dt o t sllowst solution Mx dt o t s t
13 DFS Algoitm Comlt Otiml Tim S DFS Dt Fist S N N N N O(B Ininit LMAX ) O(LMAX) Ininit START GOAL Ininit ts mk DFS inomlt How n w ix tis?
14 DFS Wit yl king, DFS is omlt.* m tis 1 nod nods 2 nods m nods Algoitm Comlt Otiml Tim S DFS w/ Pt Cking Y N O( m+1 ) O(m) * O g s nxt ltu.
15 BFS Algoitm Comlt Otiml Tim S DFS BFS w/ Pt Cking Y N O( m+1 ) O(m) Y N* O( s+1 ) O( s ) s tis 1 nod nods 2 nods s nods m nods Wn is BFS otiml?
16 Comisons Wn will BFS outom DFS? Wn will DFS outom BFS?
17 Ittiv Dning Ittiv dning uss DFS s suoutin: 1. Do DFS wi only ss o ts o lngt 1 o lss. 2. I 1 ild, do DFS wi only ss ts o lngt 2 o lss. 3. I 2 ild, do DFS wi only ss ts o lngt 3 o lss..nd so on. Algoitm Comlt Otiml Tim S DFS BFS ID w/ Pt Cking Y N O( m+1 ) O(m) Y N* O( s+1 ) O( s ) Y N* O( s+1 ) O(s)
18 Costs on Ations d GOAL 2 START Noti tt BFS inds t sotst t in tms o num o tnsitions. It dos not ind t lst-ost t. W will uikly ov n lgoitm wi dos ind t lst-ost t.
19 Uniom Cost S Exnd st nod ist: Fing is ioity uu S 1 d G 2 1 S 0 d Cost ontous G G 10
20 Pioity Quu Rs A ioity uu is dt stutu in wi you n inst nd 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, nd movs it om t uu. You n ds ky s ioity y using it gin Unlik gul uu, instions n t onstnt tim, usully O(log n) W ll nd ioity uus o ost-snsitiv s mtods
21 Uniom Cost S Algoitm Comlt Otiml Tim S DFS BFS UCS w/ Pt Cking Y N O( m+1 ) O(m) Y N O( s+1 ) O( s ) Y* Y O( C*/ ) O( C*/ ) C*/ tis * UCS n il i tions n gt itily
22 Don wit S? UCS!
23 Uniom Cost Issus Rmm: xlos insing ost ontous T good: UCS is omlt nd otiml! T d: Exlos otions in vy dition No inomtion out gol lotion Stt Gol [dmo: s dmo mty]
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