ttnt-01-search

8/7/2019 TTNT-01-Search

1/71

TR TU NHN TO

Tm kim Ref: http://www.cs.cmu.edu/~awm/tutorials


2/71

2 Ni dung trnh by Bi ton tm kim

Tm kim Theo chiu Rng Tnh ti u, Tnh y , phc tp thi

Cy Tm kim

Tm kim Theo chiu Su


3/71

3 Mt bi ton Tm kimGOAL

b c

a

Lm sao i t S n G? V s bin i c th

t nht l g?

START

d

pq

h

f

r


4/71

4Hnh thc ho mt bi ton tm kim

Mt bi ton tm kim c nm thnh phn:

Q , S , G , succs , cost Q l mt tp hu hn cc trng thi. S Q mt tp khc rng cc trng thi ban u.

. succs : Q P(Q) l mt hm nhn mt trng thi lm

u vo v tr v kt qu l mt tp trng thi. succs(s)ngha l tp cc trng thi c th n t s trong mtbc.

cost : Q , Q S Dngl mt hm nhn hai trngthi, s v s, lm u vo. N tr v chi ph mt bcca vic di chuyn t s n s. Hm chi ph ch cnh ngha khi s l trng thi con ca s.


5/71

5 Bi ton Tm kim

START

GOAL

d

bc

e

h

a

f

Q = {START, a , b , c, d, e , f, h , p , q , r, GOAL}

S = { START }

G = { GOAL }succs(b) = { a }succs(e) = { h , r}succs(a) = NULL etc.

cost(s,s) = 1 cho tt c cc bin i

p q r


6/71

6 Bi ton Tm kim

START

GOAL

d

b ce

h

a

f

Q = {START, a , b , c, d, e , f, h , p , q , r, GOAL}

S = { START }

G = { GOAL }succs(b) = { a }succs(e) = { h , r}succs(a) = NULL etc.

cost(s,s) = 1 cho tt c cc bin i

p q r


7/71


8/71

8

Cc Bi ton Tm kim

Lp lch

8-Hu

G na?

Gii ton


9/71

9 Tm kim Theo Chiu Rng

START

GOAL

d

b ce

h

a

f

Gn nhn tt c trng thi c th i n c t S trong 1 bc nhngkhng th i n c trong t hn 1 bc.

Sau gn nhn tt c trng thi c th i n c t S trong 2 bcnhng khng th i n c trong t hn 2 bc.

Sau gn nhn tt c trng thi c th i n c t S trong 3 bcnhng khng th i n c trong t hn 3 bc.

V.v n khi trng thi Goal c i n.

p q r


10/71

10

GOAL

b c

a

Tm kim Theo Chiu Rng

START

d

pq

e

h

f

r

0 bc tstart


11/71

11

GOAL

b c

a

Tm kim Theo Chiu Rng1 bc tstart

START

d

pq

e

h

f

r

0 bc tstart


12/71

12

GOAL

b c

a


START

d

pq

e

h

f

r

0 bc tstart

2 bc tstart


13/71

13

GOAL

b c

a


START

d

pq

e

h

f

r

0 bc tstart

2 bc tstart

3 bc tstart


14/71

14

GOAL

b c

a

Tm kim Theo Chiu Rng1 bc t

start

4 bc tstart

START

d

pq

e

h

f

r

0 bc tstart

2 bc tstart

3 bc tstart


15/71

15 Ghi nh ng i!

START

GOAL

d

bc

e

h

a

f

Ngoi ra, khi gn nhn mt trng thi, ghi nhn trng thitrc . Ghi nhn ny c gi l con tr quay lui. Lchs trc c dng pht sinh con ng li gii, khi tm c ch:Ti n ch. Ti thy mnh f trc . V ti rtrc khi ti f. V. do con ng li gii l S e r f G

p q r


16/71

16

GOAL

b c

a

Con tr quay lui1 bc t

start

4 bc tstart

START

d

pq

e

h

f

r

0 bc tstart

2 bc tstart

3 bc tstart


17/71

17

GOAL

b c

a

Con tr quay lui1 bc tstart

4 bc tstart

START

d

pq

e

h

f

r

0 bc tstart

2 bc tstart

3 bc t

start


18/71

18 Bt u Tm kim Theo chiu RngVi bt k trng thi s no gn nhn, ghi nh:

previous(s) l trng thi trc trn ng i ngn nht t trng thiSTART n s.

Trong vng lp th kca thut ton ta bt u vi Vkc nh nghal t cc tr n thi m t tr n thi start i n c n k bc

Sau , trong sut vng lp, ta s tnh Vk+1, c nh ngha l tp cctrng thi m t trng thi start i n c ng k+1 bc

Chng ta bt u vi k= 0, V0= {START} v nh ngha,previous(START) = NULL

Sau ta s thm vo nhng trng thi mt bc t START vo V1.V tip tc.


19/71

19

GOAL

b c

a

BFS

START

d

pq

e

h

f

rV0


20/71

20

GOAL

b c

a

BFS

START

d

pq

e

h

f

rV0

V1


21/71

21

GOAL

b c

a

BFS

START

d

p q

h

f

rV0

V1

V2


22/71

22

GOAL

b c

a

BFS

START

d

pq

h

f

rV0

V1

V2

V3


23/71

23

GOAL

b c

a

BFSV4

START

d

pq

h

f

rV0

V1

V2

V3


24/71

24 Tm kim Theo Chiu RngV0 := S (tp cc trng thi ban u)previous(START) := NIL

k:= 0while (khng c trng thi ch trong Vkv Vkkhc rng) do

Vk+1 := tp rng k

Vi mi trng thi strong succs(s)Nu scha gn nhn

t previous(s) := sThm svo Vk+1

k:= k+1IfVkrng th FAILUREElse xy dng li gii: t Si l trng thi th itrn ng i ngnnht. nh ngha Sk= GOAL, v vi mi i


25/71

25

GOAL

b c

a

BFSV4

START

d

p q

h

f

rV0

V1

V2

V3


26/71

26 Mt cch khc: i lui

START

GOAL

d

bc

e

h

a

f

Gn nhn tt c cc trng thi c th n G trong 1 nhng khng th in n trong t hn 1 bc.

Gn nhn tt c cc trng thi c th n G trong 2 nhng khng th in n trong t hn 2 bc.

V.v. cho n khi n start.

Nhn s bc ti ch xc nh ng i ngn nht. Khng cnthm thng tin lu tr.

p q r


27/71

27 Cc chi tit ca Theo Chiu Rng Vn tt nu c nhiu hn mt trng thi ch.

Vn tt nu c nhiu hn mt trng thi u. Thut ton ny hot ng theo kiu tin t u.

Thu t ton no ho t n theo ki u tin t u

c gi l suy din tin. Bn cng c th hot ng quay lui t ch.

Thut ton ny rt ging thut ton Dijkstra.

Bt k thut ton no hot ng theo kiu quay luit ch c gi l suy din li.

Li so vi tin. Ci no tt hn?


28/71


29/71

29

Theo Chiu Rng Chi ph Thp nht

Vk= tp cc trng thi c th n c trong ng kbc, v vi n ng i k-bcchi ph thp nht th t chi ph hn bt k ng i no c di nh hn k. Ni cchkhc, Vk= tp trng thi m gi tr ca n thay i so vi vng lp trc.

V0 := S (tp trng thi u)previous(START) := NILg(START) = 0k:= 0while V khc rn do

Vk+1 := rngVi mi s trong VkVi mi strong succs(s)

Nu scha c gn nhnHAY nu g(s) + Cost(s,s) < g(s)

t previous(s) := st g(s) := g(s) + Cost(s,s)Thm svo Vk+1

k:= k+1Nu GOAL cha gn nhn, thot FAILURE

Ngli xy dng li gii theo: t Sk l trng thi th ktrn ng i ngnnht. nh ngha Sk= GOAL, v vi mi i


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30 Tm kim Chi ph ng nht Mt cch tip cn BFS n gin v mt khi

nim khi c chi ph chuyn i Dng hng i u tin


31/71

31

Hng i u tin

Mt hng i u tin l mt cu

trc d liu trong ta c ththm v ly cc cp (thing, value)vi cc ton t sau:

n - r ueue .

Insert-PriQueue(PQ, thing, value) thm (thing, value) vo hng i.

Pop-least(PQ) tr v cp (thing, value) vi gi tr thp nht, vloi b n khi hng i.


32/71

32 Hng i u tinMt hng i u tin l mt cutrc d liu trong ta c th

thm v ly cc cp (thing, value)vi cc ton t sau:

Init-PriQueue PQ khi to PQ rng.

Insert-PriQueue(PQ, thing, value) thm (thing, value) vo hng i.Pop-least(PQ) tr v cp (thing, value) vi gi tr thp nht, v

loi b n khi hng i.

Hng i u tin c th cci t theo mt cch sao chochi ph ca cc ton t thm vly l

Rt r (d khng

tuyt i, nhng rkhng tin c!)

O(log(s mc trong hng i u tin))


33/71

33 Tm kim Chi ph ng nht (UCS) Mt cch tip cn BFS n gin v mt khi

nim khi c chi ph chuyn i Dng hng i u tin

ang i m u tin ca trng thi s = g(s) = chi ph

n s dng ng i cho bi con trquay lui.


34/71

34

Bt u UCS

GOAL

b c

a2

81

2

25

PQ = { (S,0) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1

2


35/71

35

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (S,0) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1

Lp:1. Ly trng thi chi ph

thp nht t PQ2. Thm cc con


36/71

36

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (p,1), (d,3) , (e,9) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




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38

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (b,4) , (e,5) , (c,11) , (q,16) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




39/71

39

GOAL

b c

a2

81

2

25

Lp UCS


thp nht t PQ2. Thm cc conPQ = { (b,4) , (e,5) , (c,11) , (q,16) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1


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40

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (e,5) , (a,6) , (c,11) , (q,16) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




41/71

41

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (a,6),(h,6),(c,11),(r,14),(q,16) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




42/71

42

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (h,6),(c,11),(r,14),(q,16) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




43/71

43

GOAL

b c

a2

81

2

25

Lp UCS

PQ = {(q,10), (c,11),(r,14) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




44/71

44

GOAL

b c

a2

81

2

25

Lp UCS

PQ = {(q,10), (c,11),(r,14) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




45/71

45

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (c,11),(r,13) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




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47

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (f,18) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1



L UCS


48/71

48

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (G,23) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1



L UCS


49/71

49

GOAL

b c

a2

81

2

25

Lp UCS

PQ = { (G,23) }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1



Kt th UCS


50/71

50

GOAL

b c

a2

81

2

25

Kt thc UCS

PQ = { }

START

d

pq

e

h

f

r

9 913

5

34

4

15

1




51/71

51

Biu din cy tm kim

START

GOAL

d

b

p

c

e

h

a

f

r

nh gi mt thut ton tm kim


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52

nh gi mt thut ton tm kim

Tnh y : thut ton c bo m tm thy li gii nu chay khng?

C bo m tm thy ti u? (n s tm thy ng i c chiph t nht?) phc tp v thi gian hc t v khn ian s d n b nh

Cc bin:N s trng thi ca bi ton

B nhn t phn nhnh trung bnh (s con trung

bnh) (B>1)L di ng i t start n goal vi s bc

ngn nht

Chng ta nh gi thut ton nh th no?

nh gi mt thut ton


53/71

53

nh gi mt thut ton

N s trng thi trong bi ton

B tha s phn nhnh trung bnh (s con trung bnh) (B>1)

L di ng i t start n goal vi s bc (chi ph) t nhtQ kch c hng i u tin trung bnh

Thut ton Ti u Thi gian Khng gian

BFSBreadth First

Search CNu tt c

chuyn icng chiph

O(min(N,BL

)) O(min(N,BL

))

LCBFS Least CostBFS

C C O(min(N,BL)) O(min(N,BL))

UCS UniformCost Search

C C O(log(Q) * min(N,BL)) O(min(N,BL))


54/71

54 Tm kim Theo Chiu SuGOAL

b c

e

a2

81

2

55

2

Mt thay th cho BFS. Lun m t node va mi mnht, nu n c bt k node con cha th no. Ngc liquay li node trc trn ng i.

START

d

pq

h

f

r

9 91

3

5

34

4

15

1


55/71

55 DFS trn thc t

STARTSTART dSTART d b

GOAL

d

b c

e

a

f

START d b a

START d cSTART d c aSTART d eSTART d e rSTART d e r f

START d e r f cSTART d e r f c aSTART d e r f GOAL

p q r


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Th t t DFS


57/71

57

Thut ton DFS

Ta dng mt cu trc d liu gi l Path biu din ng i t START ntrng thi hin ti.

VD. Path P = Cng vi mi node trn ng i, chng ta phi nh nhng con no ta vnc th m. VD. ti im sau, ta c

P =

Thut ton DFS


58/71

58

Thut ton DFS

t P = While (P khc rng v top(P) khng l ch)

if m rng ca top(P) rngthen

loi b top(P) (pop ngn xp)e se

gi s mt thnh vin ca m rng ca top(P)loi s khi m rng ca top(P)to mt mc mi trn nh ng i P:

s (expand = succs(s))

If P rngtr v FAILURE

Elsetr v ng i cha trng thi ca P

Thut ton ny c thc vit gn di

dng qui, dng ngnxp ca chng trnh ci t P.

nh gi mt thut ton


59/71

59

g

Thu t ton Ti u Thi ian Khn ian



L di ng i t start n goal vi s bc (chi ph) t nhtQ kch c hng i u tin trung bnh

BFSBreadth First

Search CNu chi

ph chuyni nhnhau

O(min(N,BL

)) O(min(N,BL

))

LCBFS Least CostBFS

C C O(BL) O(min(N,BL))

UCS UniformCost Search C C O(log(Q) * min(N,BL)) O(min(N,BL))DFS Depth First

Search


60/71

nh gi mt thut ton


61/71

61

g



L di ng i t start n goal vi s bc (chi ph) t nhtLMAX di ng i di nht t start n bt c u

Q kch c hng i u tin trung bnh

Thut ton Ti u Thi gian Khng gianBFS Breadth First

SearchC Nu chi

ph chuyni nhnhau

O(min(N,BL)) O(min(N,BL))

LCBFSLeast CostBFS C C O(min(N,BL)) O(min(N,BL))



DFS** Depth FirstSearch

Gi s Khng gian Tmkim khng chu trnh

nh gi mt thut ton


62/71

62

g



L di ng i t start n goal vi s bc (chi ph) t nhtLMAX di ng i di nht t start n bt c u


Thut ton Ti u Thi gian Khng gianBFS Breadth First

SearchC Nu chi

ph chuyni nhnhau

O(min(N,BL)) O(min(N,BL))

LCBFSLeast CostBFS C C O(min(N,BL)) O(min(N,BL))



DFS** Depth FirstSearch

C K O(BLMAX) O(LMAX)

Gi s Khng gian Tmkim khng chu trnh

Cu hi suy ngh


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63

Cu hi suy ngh

Lm sao ngn

nga lp v tntrong DFS ?

A

B

Lm sao bt bucn a ra mt ligii ti u?

A

B

C

Cu hi suy ngh


64/71

A

B

64

Cu hi suy ngh

Lm sao ngn


Tr li 1:PC-DFS (Path Checking DFS):

Dont recurse on a stateif that state is already inthe current path

A

B

C


Tr li 2:

MEMDFS (Memorizing DFS):

Remember all statesexpanded so far. Neverexpand anything twice.

Cu hi suy ngh


65/71

A

B

65

Cu hi suy ngh

Lm sao ngn



Khng gi li mt trng

thi nu n c trnng i

A

B

C


Tr li 2:

MEMDFS (Memorizing DFS):

Nh tt c trng thi m. Khng bao gi mhai ln.

Cu hi suy ngh


66/71

A

B

66

Cu hi suy ngh

Lm sao ngn



Khng gi li mt trngthi nu n c trnng i

A

B

C


Tr li 2:

MEMDFS (Memoizing DFS):

Nh tt c trng thi m. Khng bao gi mhai ln.



67/71


BFS Breadth FirstSearch

C Nu chiph chuyn O(min(N,B

L)) O(min(N,BL))


B tha s phn nhnh trung bnh (s con trung bnh) (B>1)L di ng i t start n goal vi s bc (chi ph) t nht

LMAX di ng i khng chu trnh di nht t start n bt c u


nhau (1)

LCBFS Least CostBFS




PCDFS Path CheckDFS

C K

O(B

LMAX

) O(LMAX)MEMDFS MemoizingDFS

C K O(min(N,BLMAX)) O( min(N,BLMAX))

Lp Su dn


68/71

Lp su dn l mt thut ton n gindng DFS lm mt th tc con:

1. Thc hin DFS ch tm cc ng i c di 1 hay t hn. (DFS b cc

68

2. Nu 1 tht bi, thc hin DFS ch tmcc ng i c di 2 hay t hn.3. Nu 2 tht bi, thc hin DFS ch tm

cc ng i c di 3 hay t hn.

.v tip tc cho n khi thnhcng.

Chi ph l

O(b1

+ b2

+ b3

+ b4

+ bL

) = O(bL

)

nh gi mt thut ton


69/71


BFS Breadth First C Nu chi O min N BL O min N BL

N s trng thi trong bi tonB tha s phn nhnh trung bnh (s con trung bnh) (B>1)

L di ng i t start n goal vi s bc (chi ph) t nht

LMAX di ng i khng chu trnh di nht t start n bt c u


earc p c uy ni nh

nhau (1)

LCBFS Least CostBFS




PCDFS Path CheckDFS C K O(BLMAX) O(LMAX)MEMDFS Memoizing

DFSC K O(min(N,BLMAX)) O( min(N,BLMAX))

ID IterativeDeepening C(1) O(BL) O(L)

iu cn nm


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iu cn nm

Hiu thu o v BFS, LCBFS, UCS, DFS.

Hiu cc khi nim v vic liu mt tm kim ly , ti u hay khng, phc tp v thi

70

Hiu tng ng sau lp su dn.

Thc mc


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Thc mc71

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