ΠΛΗ31 ΜΑΘΗΜΑ 1.3
74
ΠΛΗ31 ΕΝΟΤΗΤΑ 1: ΑΝΑΖΗΤΗΣΗ Μάθηµα 1.3: Ευρετική Αναζήτηση ∆ηµήτρης Ψούνης
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ΠΛΗ31 ΜΑΘΗΜΑ 1.3
Transcript of ΠΛΗ31 ΜΑΘΗΜΑ 1.3
-
31 1:
1.3:
-
2 , 31, 1.3:
.
.
1.
1. h*(v)
2. H h(v)
3. g(v)
2. UCS1.
2.
3.
4.
5.
6.
7.
3. A*g(v)
2.
1. Greedy1.
2.
3.
4.
5.
6.
7.
3. A*1.
2.
3.
4.
5.
6.
7.
.
-
.
UCS A*
3 , 31, 1.3:
(-)
-
. 1. :
-
-
4 , 31, 1.3:
.
-
. 1.
:
5 , 31, 1.3:
3
4 4A B C
S G.
3
4
5
2
5
4
3
S
D E F
G
-
6 , 31, 1.3:
S
A
DB
D
A E
3 4
5 54
425 54 4
2
E
F
C
G
D
E
B F
C G
B
C E
F
G
B F
A C G
42 5 5
4
4 44 4
43
3
3
3
: S,A,B,E,F,G
: S,A,D,E,F,G
: S,D,A,B,E,F,G
: S,D,E,F,G
-
. 1. 1. h*(v)
v -, h*(v)
7 , 31, 1.3:
h*(v) v ( ) v -.
-, h*(v) .
:
: h*()=0 v : h*(v)=+
.
-
8 , 31, 1.3:
S
A
DB
D
A E
3 4
5 54
425 54 4
2
12 9
14
16 7
9
13 h*
E
F
C
G
D
E
B F
C G
B
C E
F
G
B F
A C G
42 5 5
4
4 44 4
43
3
3
3
: S,A,B,E,F,G
: S,A,D,E,F,G :
S,D,A,B,E,F,G
: S,D,E,F,G
0
3+
+ 7
0+
+ 3
7
0
3
+ 7
12
+ +
+
0
3
-
. 1. 1. h*(v) ,
.
:
9 , 31, 1.3:
.
-
. 1. 2. h(v)
.
.
10 , 31, 1.3:
h(v) v
h(v) , v -.
.
h(v) v -.
, : h(v)h*(v) v .
-
. 1. 2. h(v) **
.
11 , 31, 1.3:
s
,
.
.
v
th(v) h(v)h*(v)
-
. 1. 2. h(v): ,
.
12 , 31, 1.3:
,
.
-
. 1. 2. h(v): Manhattan - :
13 , 31, 1.3:
1 2 3 4
manhattan ((x1,y1),(x2,y2)) = |x1-x2|+|y1-y2|
1 2 3 4
Manhattan , .
1 2 3 4
1 4 3 2 3
2 3 2
3 2 1
4 3 2 1 2
1 2 3 4
1
2
3
4
(3,3)
-
. 1. 3. g(v)
H v.
* UCS
14 , 31, 1.3:
H g(v) v v.
* UCS .
v
t
s
h(v) h(v)h*(v)
g(v) v
-
15 , 31, 1.3:
S
A
DB
D
A E
3 4
5 54
425 54 4
2
12 9
14
16 7
9
13 h*
h 12/0
11/3 7/4
7/7 7/8 4/9 5/6
g
E
F
C
G
D
E
B F
C G
B
C E
F
G
B F
A C G
42 5 5
4
4 44 4
43
3
3
3
: S,A,B,E,F,G
: S,A,D,E,F,G :
S,D,A,B,E,F,G
: S,D,E,F,G
0
3+
+ 7
0+
+ 3
7
0
3
+ 7
12
+ +
+
0
3+/11
4/12
+/14 +/15
2/16
5/10
2/14
4/13
+/17 6/18
+/11
+/15 +/15
0/17 3/220/19
0/25
0/13
3/10
+/19
-
. 3. 1.
.
1
16 , 31, 1.3:
,
** .
-
. 3. 1. (1.)
17 , 31, 1.3:
GREEDY(S,T)=[(S,f(S))]=[]:
1. v f(v)f(u) u
2. v 3. v. v 3. v. v .
4. v
u v:
4.1 f(u)4.2 ( u , )
(u,f(u)) ( u )
f(u) ) (>=) u v (u,)
(u,) .
f(x) h(x)
-
. 2. 1. (1.)
:
18 , 31, 1.3:
:
f(x)=h(x).::
.
( ) f(v)=h(v).
:
.
, .
,
.
:
-
-
12
19 , 31, 1.3:
S
. 2. 1. (2. )
0 {(S,12)} {}
-
20 , 31, 1.3:
A D
12S(1)
11 7
0 {(S,12)} {}1 {(,11),(D,7)} {(S,12)}
-
21 , 31, 1.3:
A E
A D
12S(1)
11 7
(2)
4 5
0 {(S,12)} {}1 {(,11),(D,7)} {(S,12)}2 {(,4),(E,5)} {(S,12),(D,7)}
-
22 , 31, 1.3:
A E
A D
12S(1)
11 7
(2)
4 5(3)
B 4
0 {(S,12)} {}1 {(,11),(D,7)} {(S,12)}2 {(,4),(E,5)} {(S,12),(D,7)}3 {(B,4),(E,5)} {(S,12),(D,7),(A,4)}
-
23 , 31, 1.3:
A E
A D
12S(1)
11 7
(2)
4 5(3)
(4)
C E
B 4
+ 6
(4)
0 {(S,12)} {}1 {(,11),(D,7)} {(S,12)}2 {(,4),(E,5)} {(S,12),(D,7)}3 {(B,4),(E,5)} {(S,12),(D,7),(A,4)}4 {(C,+),(E,5)} {(S,12),(D,7),(A,4),(B,4)}
-
24 , 31, 1.3:
A E
A D
12S(1)
11 7
(2)
4 5(3)
(4)
(5)
B F
C E
B 4
+ 6
(4)+ 3
0 {(S,12)} {}1 {(,11),(D,7)} {(S,12)}2 {(,4),(E,5)} {(S,12),(D,7)}3 {(B,4),(E,5)} {(S,12),(D,7),(A,4)}4 {(C,+),(E,5)} {(S,12),(D,7),(A,4),(B,4)}5 {(C,+),(F,3)} {(S,12),(D,7),(A,4),(B,4),
(E,5)}
-
25 , 31, 1.3:
A E
A D
12S(1)
11 7
(2)
4 5(3)
(4)
(5)
(6)
G00
B F
C E
B 4
+ 6
(4)+ 3
(6)
0 {(S,12)} {}1 {(,11),(D,7)} {(S,12)}2 {(,4),(E,5)} {(S,12),(D,7)}3 {(B,4),(E,5)} {(S,12),(D,7),(A,4)}4 {(C,+),(E,5)} {(S,12),(D,7),(A,4),(B,4)}5 {(C,+),(F,3)} {(S,12),(D,7),(A,4),(B,4),
(E,5)}6 {(C,+),(G,0)} {(S,12),(D,7),(A,4),(B,4),
(E,5),(F,3)}
-
26 , 31, 1.3:
A E
A D
12S(1)
11 7
(2)
4 5(3)
(4)
(5)
(6)
0 {(S,12)} {}1 {(,11),(D,7)} {(S,12)}2 {(,4),(E,5)} {(S,12),(D,7)}
G
B F
C E
B 4
+ 6
(4)+ 3
(6)
0
(7)
3 {(B,4),(E,5)} {(S,12),(D,7),(A,4)}4 {(C,+),(E,5)} {(S,12),(D,7),(A,4),(B,4)}5 {(C,+),(F,3)} {(S,12),(D,7),(A,4),(B,4),
(E,5)}6 {(C,+),(G,0)} {(S,12),(D,7),(A,4),(B,4),
(E,5),(F,3)}7 {(C,+)} {(S,12),(D,7),(A,4),(B,4),
(E,5),(F,3),(G,0)}
: S-D-E-F-G : 13
: S-D-A-E-B-F-G: 7
-
. 2. 1. (3.) 1: : ()
, .
27 , 31, 1.3:
.
2: :
-
3: :
, .
-
. 2. 1. (4.)
:
, .
.
28 , 31, 1.3:
.
: (bd)
: (bd)
-
. 2. 2. UCS
2 UCS (Uniform Cost Search) ,
.
UCS
29 , 31, 1.3:
UCS
( Dijkstra)
-
. 2. 2. UCS (1.)
30 , 31, 1.3:
UCS(S,T)=[(S,f(S))]=[]:
1. v f(v)f(u) u
2. v 3. v. v 3. v. v .
4. v
u v:
4.1 f(u)4.2 ( u , )
(u,f(u)) ( u )
f(u) ) (>=) u v (u,)
(u,) .
f(x) g(x)
-
. 2. 2. UCS (1.)
:
31 , 31, 1.3:
UCS:
f(x)=g(x).::
.
( ) f(v)=g(v).
:
.
, .
,
.
:
-
-
32
S 0
, 31, 1.3:
. 2. 2. UCS (2. )
0 {(S,0)} {}
-
33 , 31, 1.3:
A D
3 4S 0
(1)
3 4
0 {(S,0)} {}1 {(A,3),(D,4)} {(S,0)}
-
34 , 31, 1.3:
DB
54
A D
3 4S 0
(1)
3 4
(2)
7 8
0 {(S,0)} {}1 {(A,3),(D,4)} {(S,0)}2 {(D,4),(B,7)} {(S,0),(A,3)}
-
35 , 31, 1.3:
A E
5 2
DB
54
A D
3 4S 0
(1)
3 4
(2)
7 8
(3)
9 6
0 {(S,0)} {}1 {(A,3),(D,4)} {(S,0)}2 {(D,4),(B,7)} {(S,0),(A,3)}3 {(B,7),(E,6)} {(S,0),(A,3),(D,4)}
-
36 , 31, 1.3:
5 4
A E
5 2
DB
54
A D
3 4S 0
(1)
3 4
(2)
7 8
(3)
9 6
(4)
B F11 10
0 {(S,0)} {}1 {(A,3),(D,4)} {(S,0)}2 {(D,4),(B,7)} {(S,0),(A,3)}3 {(B,7),(E,6)} {(S,0),(A,3),(D,4)}4 {(B,7),(F,10)} {(S,0),(A,3),(D,4),(E,4)}
-
37 , 31, 1.3:
54 5 4
A E
5 2
DB
54
A D
3 4S 0
(1)
3 4
(2)
7 8
(3)
9 6
(4)(5)
EC B F11 1011 12
0 {(S,0)} {}1 {(A,3),(D,4)} {(S,0)}2 {(D,4),(B,7)} {(S,0),(A,3)}3 {(B,7),(E,6)} {(S,0),(A,3),(D,4)}4 {(B,7),(F,10)} {(S,0),(A,3),(D,4),(E,4)}5 {(F,10),(C,11)} {(S,0),(A,3),(D,4),(E,4),(B,7)}
-
38 , 31, 1.3:
54 5 4
A E
5 2
DB
54
A D
3 4S 0
(1)
3 4
(2)
7 8
(3)
9 6
(4)(5)
(6)
G
3
EC B F1111 12 10
13
(6)
0 {(S,0)} {}1 {(A,3),(D,4)} {(S,0)}2 {(D,4),(B,7)} {(S,0),(A,3)}3 {(B,7),(E,6)} {(S,0),(A,3),(D,4)}4 {(B,7),(F,10)} {(S,0),(A,3),(D,4),(E,4)}5 {(F,10),(C,11)} {(S,0),(A,3),(D,4),(E,4),(B,7)}6 {(G,13),(C,11)} {(S,0),(A,3),(D,4),(E,4),(B,7),
(F,10)}
F
-
39 , 31, 1.3:
54 5 4
A E
5 2
DB
54
A D
3 4S 0
(1)
3 4
(2)
7 8
(3)
9 6
(4)(5)
(6)(7)
G
3
EC B F1111 12 10
13
(6)
0 {(S,0)} {}1 {(A,3),(D,4)} {(S,0)}2 {(D,4),(B,7)} {(S,0),(A,3)}3 {(B,7),(E,6)} {(S,0),(A,3),(D,4)}4 {(B,7),(F,10)} {(S,0),(A,3),(D,4),(E,4)}5 {(F,10),(C,11)} {(S,0),(A,3),(D,4),(E,4),(B,7)}6 {(G,13),(C,11)} {(S,0),(A,3),(D,4),(E,4),(B,7),(F,10)}7 {(G,13)} {(S,0),(A,3),(D,4),(E,4),(B,7),(F,10),(C,11)}
-
40 , 31, 1.3:
54 5 4
A E
5 2
DB
54
A D
3 4S 0
(1)
3 4
(2)
7 8
(3)
9 6
(4)(5)
(6)(7)
G
3
EC B F1111 12 10
13
(6)
(8)
0 {(S,0)} {}1 {(A,3),(D,4)} {(S,0)}2 {(D,4),(B,7)} {(S,0),(A,3)}3 {(B,7),(E,6)} {(S,0),(A,3),(D,4)}4 {(B,7),(F,10)} {(S,0),(A,3),(D,4),(E,4)}5 {(F,10),(C,11)} {(S,0),(A,3),(D,4),(E,4),(B,7)}6 {(G,13),(C,11)} {(S,0),(A,3),(D,4),(E,4),(B,7),(F,10)}7 {(G,13)} {(S,0),(A,3),(D,4),(E,4),(B,7),(F,10),(C,11)}8 {} {(S,0),(A,3),(D,4),(E,4),(B,7),(F,10),(C,11),(G,13)}
: S-D-E-F-G : 13
:S-A-D-E-B-F-C-G: 8
-
. 2. 2. UCS (3.) 1: : ()
, .
41 , 31, 1.3:
.
2:
-
3: :
, .
-
. 2. 2. UCS (4.)
:
, .
.
42 , 31, 1.3:
.
: (bd)
: (bd)
-
. 2. 3. A*
3 A*,
h g, .
O A* ,
43 , 31, 1.3:
O A* , .
-
. 2. 3. * (1.)
44 , 31, 1.3:
*(S,T)=[(S,f(S))]=[]:
1. v f(v)f(u) u
2. v 3. v. v 3. v. v .
4. v
u v:
4.1 f(u)4.2 ( u , )
(u,f(u)) ( u )
f(u) ) (>=) u v (u,)
(u,) .
f(x) g(x)+h(x)
-
. 2. 2. A* (1.)
:
45 , 31, 1.3:
A*:
f(x)=g(x)+h(x).::
.
( ) f(v)=g(v)+h(v).
:
.
, .
,
.
:
-
-
46
12+012
, 31, 1.3:
S
. 2. 3. A* (2. )
0 {(S,12)} {}
-
47 , 31, 1.3:
A D
3 4
12+012S
(1)
11+3=14
7+4=11
0 {(S,12)} {}1 {(A,14),(D,11)} {(S,12)}
-
48 , 31, 1.3:
A E
5 2
A D
3 4
12+012S
(1)
11+3=14
7+4=11
(2)
4+9=13
5+6=11
0 {(S,12)} {}1 {(A,14),(D,11)} {(S,12)}2 {(A,13),(E,11)} {(S,12),(D,11)}
-
49 , 31, 1.3:
5 4
A E
5 2
A D
3 4
12+012S
(1)
11+3=14
7+4=11
(2)
4+9=13
5+6=11
(3)
+
B F+11=+
3+10=13
0 {(S,12)} {}1 {(A,14),(D,11)} {(S,12)}2 {(A,13),(E,11)} {(S,12),(D,11)}3 {(A,13),(B,+)(F,13)} {(S,12),(D,11),(E,11)}
-
50 , 31, 1.3:
4 5 4
A E
5 2
A D
3 4
12+012S
(1)
11+3=14
7+4=11
(2)
4+9=13
5+6=11
(3)
+
(4)
4+B B F
+11=+
4+13=17
3+10=13
0 {(S,12)} {}1 {(A,14),(D,11)} {(S,12)}2 {(A,13),(E,11)} {(S,12),(D,11)}3 {(A,13),(B,+)(F,13)} {(S,12),(D,11),(E,11)}4 {(B,17),(F,13)} {(S,12),(D,11),(E,11),(A,13)}
-
51 , 31, 1.3:
4 5 4
A E
5 2
A D
3 4
12+012S
(1)
11+3=14
7+4=11
(2)
4+9=13
5+6=11
(3)
+
(4)
4+ (5)
G
3
B B F+11=+
4+13=17
3+10=13
0+13=13
(5)
0 {(S,12)} {}1 {(A,14),(D,11)} {(S,12)}2 {(A,13),(E,11)} {(S,12),(D,11)}3 {(A,13),(B,+)(F,13)} {(S,12),(D,11),(E,11)}4 {(B,17),(F,13)} {(S,12),(D,11),(E,11),(A,13)}5 {(B,17),(G,13)} {(S,12),(D,11),(E,11),(A,13),(F,13)}
-
52 , 31, 1.3:
4 5 4
A E
5 2
A D
3 4
12+012S
(1)
11+3=14
7+4=11
(2)
4+9=13
5+6=11
(3)
+
(4)
4+ (5)
G
3
B B F+11=+
4+13=17
3+10=13
0+13=13
(5)
(6)
0 {(S,12)} {}1 {(A,14),(D,11)} {(S,12)}2 {(A,13),(E,11)} {(S,12),(D,11)}3 {(A,13),(B,+)(F,13)} {(S,12),(D,11),(E,11)}4 {(B,17),(F,13)} {(S,12),(D,11),(E,11),(A,13)}5 {(B,17),(G,13)} {(S,12),(D,11),(E,11),(A,13),(F,13)}6 {(B,17)} {(S,12),(D,11),(E,11),(A,13),(F,13),(G,13)}
: S-D-E-F-G : 13
:S-D-A-E-F-G: 6
-
. 2. 3. A*(3.)
1: :
() ,
53 , 31, 1.3:
,
.
2: :
-! 3: :
, .
-
. 2. 3. * (4.)
:
, .
.
54 , 31, 1.3:
.
: (bd)
: (bd)
-
. 1 S - T:
55 , 31, 1.3:
4 A
: h(S)=3, h(A)=2, h(B)=1, h(E)=2
1
2
1
3
2
S
E
-
. .
56 , 31, 1.3:
-
.
57 , 31, 1.3:
-
. S
58 , 31, 1.3:
-
. S
59 , 31, 1.3:
-
. S
60 , 31, 1.3:
-
. UCS S
61 , 31, 1.3:
-
. * S
62 , 31, 1.3:
-
. 1 Robbie
. 1 Robbie. .
63 , 31, 1.3:
Robbie.
1.1 3, 2 Robbie - G.
-
64 , 31, 1.3:
2 Robbie.
3: Robbie:
-
65 , 31, 1.3:
() S G
-
66 , 31, 1.3:
(B) UCS S G
-
67 , 31, 1.3:
() * S G
-
. 2
68 , 31, 1.3:
Robbie, -, ,
S, , G, . Robbie .
.
.
G. .
O Robbie . Robbie ,
.
( ): ()
.
() ( ).
-
69 , 31, 1.3:
S,9
A,8 B,6
C,5
E,3 I,2
G,0
F,1
2
2
2
3
2
1
3
2
2
2
4
H,8 D,43
-
70 , 31, 1.3:
. .
. ( ) (depth-first search), Robbie .
.
.
. , Robbie .
-
71 , 31, 1.3:
. .
( ) (breadth-first search). .
.
-
72 , 31, 1.3:
. .
( ) (greedy search), .
.
.
-
73 , 31, 1.3:
. .
( ) (branch and bound search),
. .
.
-
74 , 31, 1.3:
. *.
( ) *. .
.
