Uninformed Search AI

1. Uninformed Search Strategies
K. HariNath
Assistant Professor,
Department of IT,
MGIT

2. Uninformed Search
An uninformed (a.k.a. blind, brute-force) search algorithm
generates the search tree without using any domain specific
knowledge.
No additional information about states beyond that provided in
the problem definition.
All they can do is generate successors and distinguish a goal
state from a non-goal state.
All search strategies are distinguished by the order in which
nodes are expanded.

3. BREADTH -
FIRST
SEARCH

4. Breadth-First Search
Expand shallowest unexpanded node
Implementation:
A FIFO queue, i.e., new successors go at
end.

5. Example-Graph

11. Breadth-First
Search Goal -
Node J
A ---
Current Waiting

12. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A

13. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A
A

14. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
A

15. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B
A

16. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
A

17. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
A
B

18. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B
A
B

19. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
A
B

20. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C
A
B

21. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
A
B

22. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
A
B
C

23. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
C
A
B
C

24. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
C D, E, F
A
B
C

25. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
C D, E, F
D
A
B
C

26. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
C D, E, F
D E, F
A
B
C

27. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
C D, E, F
D E, F
A
B
C
D

28. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
C D, E, F
D E, F
D
A
B
C
D

29. Breadth-First
Search Goal -
Node J
A ---
Current Waiting
A B, C
B C
B C, D
C D
C D, E, F
D E, F
D E, F, G,
H
A
B
C
D

30. Breadth-First
Search Goal -
Node J
Current Waiting
D E, F, G, H

31. Breadth-First
Search Goal -
Node J
Current Waiting
E
D E, F, G, H

32. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
D E, F, G, H

33. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E
D E, F, G, H

34. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E
E
D E, F, G, H

35. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
E
D E, F, G, H

36. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F
E
D E, F, G, H

37. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
E
D E, F, G, H

38. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
E
D E, F, G, H
F

39. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F
E
D E, F, G, H
F

40. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
E
F
D E, F, G, H

41. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H

42. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L

43. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G

44. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H

45. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L

46. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L
H

47. Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L
H
I

48. Breadth-First Search
Goal - Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L
H
I J, K, L

49. Breadth-First Search
Goal - Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L
H
I J, K, L
I

50. J
Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L
H
I J, K, L
I

51. J
Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L
H
I J, K, L
I
K, L

52. J
Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L
H
I
I
J
J, K, L
K, L

53. J
Breadth-First
Search Goal -
Node J
Current Waiting
E F, G, H
E F, G, H, I, J
F G, H, I, J
F G, H, I, J, K, L
G
E
F
GOAL
D E, F, G, H
H, I, J, K, L
G
H I, J, K, L
H
I
I
J
J, K, L
K, L

54. BFS Algorithm

55. Analyzing BFS
Good news:
– Complete
– Guaranteed to find the shallowest path to the goal This is not necessarily
the best path! But we can “fix” the algorithm to get the best path.
– Different start-goal combinations can be explored at the same time
Bad news:
– Exponential time complexity: O(bd ) (why?) This is the same for all
uninformed search methods
– Exponential memory requirements! O(bd) (why?) This is not good...

56. DEPTH - FIRST
SEARCH

57. DFS
■ In depth-first search, we start with
the root node and completely
explore the descendants of a node
before exploring its siblings (and
siblings are explored in a left- to-
right fashion).
■ Depth-first search always expands
the deepest node in the current
frontier of the search tree.
■ LIFO queue
Depth-first traversal: 1 → 2 → 4 → 5 → 3 → 6 → 7

58. Depth-First
Search Goal -
Node J
Current

59. Depth-First
Search Goal -
Node J
Current
A

60. Depth-First
Search Goal -
Node J
Current
A
A

61. Depth-First
Search Goal -
Node J
Current
A
B
A

62. Depth-First
Search Goal -
Node J
Current
A
B
A
B

63. Depth-First
Search Goal -
Node J
Current
A
B
D
A
B

64. Depth-First
Search Goal -
Node J
Current
A
B
D
A
B
D

65. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D

66. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G

67. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D

68. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H

69. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H

70. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D

71. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D
B

72. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D
B
A

73. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
D
B
A

74. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
C
D
B
A

75. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
C
D
B
A

76. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
C
E
D
B
A

77. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
E
D
B
A

78. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
E
I
D
B
A

79. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
E
I
D
B
A
E

80. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
E
D
B
A

81. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
J
E
D
B
A

82. Depth-First
Search Goal -
Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
J
E
D
B
A
GOAL

83. Analyzing DFS
Not Optimal
Not Complete
Time Complexity-O(bm)-(m is maximum depth of any
node)
Space Complexity-O(bm)

84. UNIFORM-
COST
SEARCH

85. Fixing BFS To Get An Optimal Path
Use a priority queue instead of a simple
queue
Insert nodes in the increasing order of the
cost of the path so far
Guaranteed to find an optimal solution!
This algorithm is called uniform-cost search

86. Continued
Instead of Expanding shallowest node the node n with
the Lowest Path Cost g(n) is expanded
Differences
--Goal Test is applied to a node when it is selected
for expansion
--Test is added in case a better path is found to a
node currently on frontier

87. Example 1

89. Example 2

91. Uniform Cost
Search Goal -
Node G
𝑺𝟎 ---
Current
Waiting
Ordered

92. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎

93. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎
𝑺𝟎

94. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑺𝟎

95. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨𝟏
𝑺𝟎

96. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨𝟏 𝑮𝟏𝟐
𝑺𝟎

97. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑺𝟎
𝑨𝟏

98. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏
𝑺𝟎
𝑨𝟏

99. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑺𝟎
𝑨𝟏

100. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐
𝑺𝟎
𝑨𝟏

101. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑺𝟎
𝑨𝟏

102. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑺𝟎
𝑨𝟏
𝑪𝟐

103. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐
𝑺𝟎
𝑨𝟏
𝑪𝟐

104. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑫𝟑, 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑺𝟎
𝑨𝟏
𝑪𝟐

105. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑫𝟑, 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑫𝟑
𝑺𝟎
𝑨𝟏
𝑪𝟐

106. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑫𝟑, 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑫𝟑 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑺𝟎
𝑨𝟏
𝑪𝟐

107. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑫𝟑, 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑫𝟑 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑺𝟎
𝑨𝟏
𝑪𝟐
𝑫𝟑

108. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑫𝟑, 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑫𝟑 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑫𝟑
𝑺𝟎
𝑨𝟏
𝑪𝟐
𝑫𝟑

109. Uniform Cost
Search Goal -
Node G
𝑺
𝟎
---
Current
Waiting
Ordered
𝑺𝟎 𝑨𝟏, 𝑮𝟏𝟐
𝑨
𝟏
𝑮𝟏𝟐
𝑨𝟏 𝑪𝟐, 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑩𝟒, 𝑮𝟏𝟐
𝑪𝟐 𝑫𝟑, 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑫𝟑 𝑩𝟒, 𝑮𝟒, 𝑮𝟏𝟐
𝑫𝟑 𝑩𝟒, 𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐
𝑺𝟎
𝑨𝟏
𝑪𝟐
𝑫𝟑

110. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐

111. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐

112. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑩𝟒
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐

113. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐

114. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑮𝟒
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐

115. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑮𝟒 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐

116. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑮𝟒 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑩𝟒
𝑮𝟒
𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐

117. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑮𝟒 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑩𝟒
𝑮𝟒
𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐
GOAL

118. Uniform Cost
Search Goal -
Node G
𝑩𝟒
Current
Waiting
Ordered
𝑩𝟒 𝑮𝟒, 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑮𝟒 𝑮𝟔, 𝑫𝟕, 𝑮𝟏𝟐
𝑩𝟒
𝑮𝟒
𝑮𝟒, 𝑮𝟔, 𝑮𝟏𝟐
GOAL
Solve using BFS &
DFS Compare
Costs

120. Analyzing Uniform Cost Search
Optimal
Complete(If Cost of every step exceeds some
positive constant Ꜫ)
Time Complexity-O(b1+(c*/Ꜫ))
Space Complexity-O(b1+(c*/Ꜫ))
UCS examines all the nodes at Goal Depth to
see if one has a lower cost.

121. COMPARISION

122. DEPTH - LIMITED
SEARCH

123.  The embarrassing failure of depth-first search in infinite state spaces can
be alleviated by supplying depth-first search with a predetermined
depth limit .
 That is, nodes at depth are treated as if they have no successors. This
approach is called depth-limited search. The depth limit solves the
infinite-path problem.
 Depth-limited search can be implemented as a simple modification to
the general tree or graph-search algorithm.
 Notice that depth-limited search can terminate with two kinds of failure:
The standard failure value indicates no solution.
The cutoff value indicates no solution within the depth limit.
DEPTH-LIMITED-SEARCH

124. DEPTH-LIMITED SEARCH (EXAMPLE-1)

125.  A,
A
B C E
D
Limit = 2
Depth-Limited Search (DLS)

126.  A,B,
A
B C E
D
F G
Limit = 2
Depth-Limited Search (DLS)

127.  A,B,F
,
A
B C E
D
F G
Limit = 2
Depth-Limited Search (DLS)

128.  A,B,F
,
 G,
A
B C E
D
F G
Limit = 2
Depth-Limited Search (DLS)

129. E
 A,B,F,
 G,
 C,
A
B C D
F G H
Limit = 2
Depth-Limited Search (DLS)

130. E
 A,B,F,
 G,
 C,H,
A
B C D
F G H
Limit = 2
Depth-Limited Search (DLS)

131.  A,B,F
,
 G,
 C,H,
 D,
A
B C E
D
F G H I J
Limit = 2
Depth-Limited Search (DLS)

132.  A,B,F
,
 G,
 C,H,
 D,I
A
B C E
D
F G H I J
Limit = 2
Depth-Limited Search (DLS)

133.  A,B,F
,
 G,
 C,H,
 D,I
 J,
A
B C E
D
F G H I J
Limit = 2
Depth-Limited Search (DLS)

134.  A,B,F
,
 G,
 C,H,
 D,I
 J,
 E
A
B C E
D
F G H I J
Limit = 2
Depth-Limited Search (DLS)

135.  A,B,F
,
 G,
 C,H,
 D,I
 J,
 E,Failure
A
B C E
D
F G H I J
Limit = 2
Depth-Limited Search (DLS)

136.  DLS algorithm returns Failure (no solution)
 The reason is that the goal is beyond the limit (Limit =2): the goal depth is
(d=4)
A
B C D E
F G H I J
K L
O
M N
Limit = 2
Depth-Limited Search (DLS)

137. Depth-Limited Search
Depth – 3, Goal – Node J
Current
0
1
2
3

138. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
0
1
2
3

139. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
A
0
1
2
3

140. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
A
0
1
2
3

141. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
A
0
1
2
B
3

142. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
A
B
0
1
2
3

143. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
A
B
0
1
2
D
3

144. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
0
1
2
3

145. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
0
1
2
3

146. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
0
1
2
3

147. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
0
1
2
3

148. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
0
1
2
3

149. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D
0
1
2
3

150. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D
0
1
2
3 B

151. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D
0
1
2
3 B
A

152. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
D
0
1
2
3 B
A

153. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
C
D
B
0
1
2
3
A

154. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
C
D
B
0
1
2
3
A

155. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
C
D
B
A
0
1
2
3
E

156. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
E
D
B
A
0
1
2
3

157. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
E
I
D
B
A
0
1
2
3

158. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
E
I
D
B
A
E
0
1
2
3

159. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
0
1
2
E
D
B
A
3

160. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
J
0
1
2
E
D
B
A
3

161. Depth-Limited Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
J
E
GOAL
0
1
2
D
B
A
3

162. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3

163. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A

164. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
A

165. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
B
A

166. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
B
A
B

167. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
B
D
A
B

168. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
B
D
A
B
D

169. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
B
D
G
A
B
D

170. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
B
D
G
A
B
D
G

171. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
B
D
G
A
B
D
G
D

172. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
3
A
B
D
G
A
B
D
G
D
H

173. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
A
B
D
G
A
B
D
G
D
H
H
3

174. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
A
B
D
G
A
B
D
G
D
H
H
3
D

175. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
Current
A
B
D
G
A
B
D
G
D
H
H
D
3 B

176. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
3
Current
A
B
D
G
A
B
D
G
D
H
H
D
B
A

177. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
3
Current
A
B
D
G
A
B
D
G
D
H
H
C
D
B
A

178. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
3
Current
A
B
D
G
A
B
D
G
D
H
H
C
C
D
B
A

179. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
3
Current
A
B
D
G
A
B
D
G
D
H
H
C
C
D
B
A
GOAL

180. Depth-Limited Search
Depth – 3, Goal – Node C
0
1
2
3
Depth is Large
Current
A
B
D
G
A
B
D
G
D
H
H
C
C
D
B
A
GOAL

181. Depth-Limited Search
Depth – 2, Goal – Node J
Current
0
1
2
3

182. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
0
1
2
3

183. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
A
0
1
2
3

184. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
A
0
1
2
3

185. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
0
1
2
B
3

186. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
0
1
2
3

187. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
0
1
2
3

188. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
B
0
1
2
3

189. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
B
A
0
1
2
3

190. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
B
0
1
2
A
3

191. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
C
B
A
0
1
2
3

192. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
B
A
0
1
2
3

193. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
E
B
A
0
1
2
3

194. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
E
B
A
0
1
2
C
3

195. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
F
C
E
B
A
0
1
2
C
3

196. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
F
C
E
F
B
A
0
1
2
C
3

197. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
F
C
E
F
B
A
Search
Finished
0
1
2
C
3
NO
GOAL

198. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
F
C
E
F
B
A
Search
Finished
0
1
2
C
3
NO
GOAL
Depth is Small

199. Depth-Limited Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
F
C
E
F
B
A
Search
Finished
NO GOAL
0
1
2
3
Depth is Small
Increase
Depth
Iteratively
C

201. Analysing Depth-Limit Search
Not Optimal
Not Complete
Time Complexity- O(bl)
Space Complexity-O(bl)

202. ITERATIVE
DEEPENING
SEARCH

203. Iterative Deepening Search
 It’s a Depth First Search, but it does it one level at a time, gradually
increasing the limit, until a goal is found.
 Combine the benefits of depth-first and breadth-first search
 Like DFS, modest memory requirements
 Like BFS, it is complete when branching factor is finite, and optimal
when the path cost is a non decreasing function of the dept of the
node.

204.  May seem wasteful because states are generated multiple times
 But actually not very costly, because nodes at the bottom level are
generated only once.
 In practice, however, the overhead of these multiple expansions is
small, because most of the nodes are towards leaves (bottom) of the
search tree:
• Thus, the nodes that are evaluated several times (towards top of
tree) are in relatively small number.
 Iterative depending is the preferred uninformed search method when
the search space is large and the depth of the solution is unknown
Iterative Deepening Search

205. Iterative Deepening Search with l=0

206. Iterative Deepening Search with l=1

207. Iterative Deepening Search with l=2

208. Iterative Deepening Search with l=3

209. Iterative Deepening Search
Depth – 0, Goal – Node J
Current
0
1
2
3

210. Iterative Deepening Search
Depth – 0, Goal – Node J
Current
A
0
1
2
3

211. Iterative Deepening Search
Depth – 0, Goal – Node J
Current
A
A
0
1
2
3

212. Iterative Deepening Search
Depth – 0, Goal – Node J
Current
A
A
0
1
2
3
Search Finished NO
GOAL
Increase Depth by 1

213. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
0
1
2
3

214. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
A
0
1
2
3

215. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
A
A
0
1
2
3

216. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
A
B
A
0
1
2
3

217. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
A
B
A
B
0
1
2
3

218. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
A
B
A
B
0
1
2
A
3

219. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
A
B
A
B
C
0
1
2
A
3

220. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
A
B
A
B
C
C
0
1
2
A
3

221. Iterative Deepening Search
Depth – 1, Goal – Node J
Current
A
B
A
B
C
C
0
1
2
3
A
Search Finished
NO GOAL
Increase Depth by 1

222. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
0
1
2
3

223. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
0
1
2
3

224. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
A
0
1
2
3

225. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
A
0
1
2
3

226. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
A
0
1
2
B
3

227. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
0
1
2
3

228. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
0
1
2
3

229. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
B
0
1
2
A
3

230. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
B
0
1
2
A
3

231. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
C
B
A
0
1
2
3

232. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
B
A
0
1
2
3

233. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
E
B
A
0
1
2
3

234. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
E
B
A
0
1
2
C
3

235. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
E
F
B
A
0
1
2
C
3

236. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
E
F
B
A
0
1
2
C
3

237. Iterative Deepening Search
Depth – 2, Goal – Node J
Current
A
B
D
A
B
D
C
E
C
E
F
B
A
0
1
2
3
Search Finished
NO GOAL
Increase Depth by
C

238. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
0
1
2
3

239. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
0
1
2
3

240. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
A
0
1
2
3

241. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
A
0
1
2
3

242. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
A
0
1
2
B
3

243. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
A
B
0
1
2
3

244. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
A
B
0
1
2
D
3

245. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
0
1
2
3

246. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
0
1
2
3

247. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
0
1
2
3

248. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
0
1
2
3

249. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
0
1
2
3

250. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D
0
1
2
3

251. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D
0
1
2
3 B

252. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
D
0
1
2
3 B
A

253. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
D
0
1
2
3 B
A

254. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
C
D
B
0
1
2
3
A

255. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
C
D
B
0
1
2
3
A

256. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
C
D
B
A
0
1
2
3
E

257. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
D
B
A
0
1
2
3
E

258. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
E
I
D
B
A
0
1
2
3

259. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
C
E
I
D
B
A
0
1
2
3
E

260. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
0
1
2
E
D
B
A
3

261. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
J
0
1
2
E
D
B
A
3

262. Iterative Deepening Search
Depth – 3, Goal – Node J
Current
A
B
D
G
A
B
D
G
D
H
H
C
E
I
J
C
E
I
J
E
GOAL
0
1
2
D
B
A
3

264. Combines the best of breadth-first and
depth-first search strategies.
• Completeness:
• Time complexity:
• Space complexity:
• Optimality:
Yes,
O(b d)
O(bd)
Yes, if step cost = 1
Iterative Deepening Search

265. ■ Complete? Yes (b finite)
■ Time? d b1 + (d-1)b2 + … + bd = O(bd)
■ Space? O(bd)
■ Optimal? Yes, if step costs identical
Properties of Iterative Deepening Search

266. Both search forward from
initial state, and
backwards from goal.
Stop when the two
searches meet in
the middle.
Motivation: bd/2 + bd/2 is
much less than bd Implementation
Replace the goal test
with a check to see
whether the frontiers of
the two searches
intersect, if yes
 solution is found
Bidirectional
Search
Start Goal

268. Bidirectional
Search
■ Not always optimal, even if both
searches are BFS
■ Check when each node is expanded
or selected for expansion
■ Can be implemented using BFS or
iterative deepening (but at least one
frontier needs to be kept in memory)
■ Significant weakness
Space requirement
■ Time Complexity is good

269. Bidirectional
Search
■ Problem: how do we search backwards from
goal??
– predecessor of node n = all nodes that have n
as successor
– this may not always be easy to compute!
– if several goal states, apply predecessor
function to them just as we applied successor
(only works well if goals are explicitly known;
may be difficult if goals only characterized
implicitly).
– for bidirectional search to work well, there
must be an efficient way to check whether a
given node belongs to the other search tree.
– select a given search algorithm for each half.

270. • Completeness:
• Time complexity:
• Space complexity:
• Optimality:
Yes,
2*O(b d/2) = O(b d/2)
O(b m/2)
Yes
• To avoid one by one comparison, we need a hash
table of size O(b m/2)
• If hash table is used, the cost of comparison is O(1)
Bidirectional Search

271. Comparison Uninformed Search Strategies