??????? (Problem-Solving and Searching Methods)

1
Chapter 2

• ??????? (Problem-Solving and Searching Methods)

2
????

• ?????????????????,????????????????????????????
• ?????????????,?????????????????????? ?

3
2.1 ???? (Problem formulation)

• ???????????????,?????????????????
• ??????????????????????,????????????????????????

4
2.1.1 ??????????(Well-defined problems and
solutions)

• ??????????????????
• ??(states)
• ??(actions)

5
2.1.1 ??????????(Well-defined problems and
solutions)

• ?????????
• ????(initial state)?
• ??????(operator)????
• ??????(state space)
• ????(path)
• ??????(goal test)
• ??????(path cost)

6
2.1.1 ??????????(Well-defined problems and
solutions)

• ????????????(Finite state machine)???,????????????
  ????
• ????????????????????????,??????????????

lt?2.1 gt???????????
7
2.1.2 ??????? (Measuring problem-solving
performance)

• ????????????,??????????????

lt?2.2gt ????WHILE?WRITE?BEGIN???????
8
2.1.2 ??????? (Measuring problem-solving
performance)

• ????????????????(Problem space),????????????????,?
  ????????????
• ????????????????????,????????????,??????????

9
2.1.2 ??????? (Measuring problem-solving
performance)

• ????
• ????
• ???????????
• ????
• ????

lt?2.3gt ??????????
10
2.1.2 ??????? (Measuring problem-solving
performance)

• ?????????????????????,? (a)????????(traveling
  Salesman)???

11
2.1.2 ??????? (Measuring problem-solving
performance)

• ? (b)????A?????,????????????,?ABDCA?ACDBA?

12
2.1.2 ??????? (Measuring problem-solving
performance)

• ???????????????????????
• ????????????????????,??????????????????

13
2.1.2 ??????? (Measuring problem-solving
performance)

• ?2.1???????????????????????

?? ?????
????? ?????????
?????????? ????????
????????? ???????,???????
????????? ????????
?????????? ???????????
???? ???????
lt?2.1gt ???????????
14
2.1.2 ??????? (Measuring problem-solving
performance)

• ?????????????????????????????,????????????????????
  
• ??????,??????????,????????????????

15
2.1.2 ??????? (Measuring problem-solving
performance)

• ???????????????,??????????,????????????,??????????
  ???
• ???,??????????????????,???????????

16
2.1.2 ??????? (Measuring problem-solving
performance)

• ?????????????????
• (1)?????????
• (2)?????????
• (3)?????????????????????
• ?????????????????????

17
2.1.3 ???????? (Choosing states and actions)

• ??????????????????????????????????????????????

18
2.1.3 ???????? (Choosing states and actions)

• ?????????,???????????????,?????????
• ??????????????????(abstraction)?

19
2.1.4 ????-???????? (the 8-puzzle problem)

• ?2.6??3 x 3????,???8????????,???????
• ?????????????????

lt?2.63 x 3???gt
20
2.1.4 ????-???????? (the 8-puzzle problem)

• ?????????????,????????????????????,???????????????
  ???????????????,???????
• ????????????????????????????????,???????????
• ???????????????
• ???????????2.6????????
• ??????????1,?????????????

21
2.1.4 ????-???????? (the 8-puzzle problem)

• ??????????????,???????NP-complete,??????????????,?
  ????????????????????
• ??15??????????????????????????????????

22
2.2 ???? (Searching Strategies)

• ???????????????,??????????????????????
• ????????????,??????1????d??????????,??????d1?

23
2.2.1 ??????? (General search algorithm)

• ?2.7???????????????????????????
• ????????????????????????????,?????????17???,??????
  ?????,?????????????????

24
2.2.1 ??????? (General search algorithm)
lt?2.7gt ??????????????
25
2.2.1 ??????? (General search algorithm)

• ???????
• GENERAL-SEARCH (????, ??) ?? ?? ? ????
• ???????????
• ???????
• IF ???????? THEN?? ????
• ??????????????
• IF ??????????then?? ??
• ELSE ?????????????

26
?????

• ???(Completeness)
• ?????(Time complexity)
• ?????(Space complexity)
• ???(Optimality)

27
2.2.2 ???????? (Breadth-first search)

• ??????,????????,????????????????,?????????????
• ??????????,??????d????????????d1????????

28
2.2.2 ???????? (Breadth-first search)

• ?????????????????????????,??????????(Queuing
  function)???????????????

function BreadthFirst-Search (????) ?? ?? ? ????
?? GENERAL-SEARCH (????, ??????????????)
29
2.2.2 ???????? (Breadth-first search)

• ??????????????????,????????????1???,????????2????
  ?
• ?????,??????????????
• ????????,????????????????????

lt?2.8gt ??????????
30
2.2.3???????? (Depth-first search)

• ???????????????????????????,??????????,????????,??
  ???????????

31
2.2.3???????? (Depth-first search)

• ???????????????????,??????????????

function DEPTH-FIRST-SEARCH (????) ?? ?? ? ????
??GENERAL-SEARCH (????, ??????????????)
32
2.2.3???????? (Depth-first search)

• ????????????,????????????,??2.9???

lt?2.9gt ?????????
33
2.2.3???????? (Depth-first search)

• ???????????,?????????????
• ????????????????????????????????????

34
2.2.3???????? (Depth-first search)

• ????????????,?????????????????
• ???????,??????????????,???????????,??????????????
  

35
2.2.4. ?????????(best-first search)

• ?????????????????????????????
• ???????????,???????????
• ??,?????????,????????????

36
2.2.4. ?????????(best-first search)

• ????????????????,????????????????
• ???????,?????????????????????????????

37
2.2.4. ?????????(best-first search)

• ????????????????????????????

function BEST-FIRST-SEARCH (????, ????) ?? ?? ?
???? ???? ? ??????????????
??GENERAL-SEARCH (????, ????)
38
2.2.4. ?????????(best-first search)

• ???????,????o,???x,????????
• F(x)???????????????1
• ????????o???2 Y(X)
• Y(X) 0 ?????????x???0
• 1 ?????????x???1
• 2 ?????????x???2

39
2.2.4. ?????????(best-first search)

• ???????????
• ?????????

A1 A2 A3
A4 A5 A6
A7 A8 A9
40
2.2.4. ?????????(best-first search)

• ??????,?
• F(A1)(222) ?1 (000) ? 2 (000) 6
• F(A2)(22) ?1 (00) ? 2 (00) 4
• F(A3)(222) ?1 (000) ? 2 (000) 6
• F(A4)(22) ?1 (00) ? 2 (00) ? 2 4
• F(A5)(2222) ?1 (000) ? 2 (000) 8
• F(A6)(22) ?1 (00) ? 2 (00) 4
• F(A7)(222) ?1 (000) ? 2 (000) 6
• F(A8)(22) ?1 (00) ? 2 (00) ? 2 4
• F(A9)(222) ?1 (000) ? 2 (000) ? 2 6

41
2.2.4. ?????????(best-first search)

• ??????A5?????A1,???????

X A2 A3
A4 O A6
A7 A8 A9
42
2.2.4. ?????????(best-first search)

• ????????,???
• F(A2)(11) ?1 (10) ? 2 (-10) 3
• F(A3)(112) ?1 (010) ? 2 (-100) 5
• F(A4)(11) ?1 (10) ? 2 (0-1) 3
• F(A6)(12) ?1 (10) ? 2 (00) 5
• F(A7)(112) ?1 (010) ? 2 (-100) 5
• F(A8)(12) ?1 (10) ? 2 (00) 5
• F(A9)(022) ?1 (010) ? 2 (0-10) 5

43
2.2.4. ?????????(best-first search)

• ????,A3?A6?A7?A8 ?A9???????,??????A3?????A7,?????
  ??

X A2 O
A4 O A6
X A8 A9
44
2.2.4. ?????????(best-first search)

• ????????,???
• F(A2)(01) ?1 (11) ? 2 (-10) 4
• F(A4)(01) ?1 (01) ? 2 (40) 7
• F(A6)(11) ?1 (11) ? 2 (00) 6
• F(A8)(11) ?1 (01) ? 2 (-10) 3
• F(A9)(101) ?1 (011) ? 2 (-100) 5

45
2.2.4. ?????????(best-first search)

• ??????A4?????A6,???????

X A2 O
O O X
X A8 A9
46
2.2.4. ?????????(best-first search)

• ????????,???
• F(A2)(01) ?1 (11) ? 2 (-10) 4
• F(A8)(11) ?1 (01) ? 2 (-10) 3
• F(A9)(100) ?1 (011) ? 2 (-10-1) 3

47
2.2.4. ?????????(best-first search)

• ??????A2?????A8,???????

X O O
O O X
X X A9

• ??????A9,????????

48
???????(Depth-limited Search)

• ????Depth-First Search????????????????
• ?????????????
• ???????????

49
???????(Iterative Deepening Search)

• ??for???????????,?????depth-limited search
• ?????depth-first search?breadth-first search???
• ??????????

50
???????(b??branch?d??depth)
?? Breadth-first Depth-first Best-first Depth-limited ?????
Time bd bm bd bl bd
Space bd bm bd bl bd
??? Yes No Yes No Yes
??? Yes No Yes Yes, if lgtd Yes