15699 exhaustive search
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Blind search
• Types of Blind search :
– Breadth first search– Depth first search– Depth first iterative deepening(DFID)– Bidirectional search
Breadth first search
• Expands all the states one step away from the first state, expands two steps away from the start state and so on. Until a goal state is reached.
• Implemented using two steps– OPEN list- those states that are to be expanded– CLOSED lists- those states that are already
expanded.
Breadth First Search
3
Application1: Given the following state space (tree search), give the sequence of visited nodes when using BFS (assume that the nodeO is the goal state):
A
B C ED
F G H I J
K L
O
M N
Breadth First Search
4
A,
A
B C ED
Breadth First Search
5
A, B,
A
B C ED
F G
Breadth First Search
6
A, B,C
A
B C ED
F G H
Breadth First Search
7
A, B,C,D
A
B C ED
F G H I J
Breadth First Search
8
A, B,C,D,E
A
B C ED
F G H I J
Breadth First Search
9
A, B,C,D,E, F,
A
B C ED
F G H I J
Breadth First Search
10
A, B,C,D,E, F,G
A
B C ED
F G H I J
K L
Breadth First Search
11
A, B,C,D,E, F,G,H
A
B C ED
F G H I J
K L
Breadth First Search
12
A, B,C,D,E, F,G,H,I
A
B C ED
F G H I J
K L M
Breadth First Search
13
A, B,C,D,E, F,G,H,I,J,
A
B C ED
F G H I J
K L M N
Breadth First Search
14
A, B,C,D,E, F,G,H,I,J, K, A
B C ED
F G H I J
K L M N
Breadth First Search
15
A, B,C,D,E, F,G,H,I,J, K,L A
B C ED
F G H I J
K L
O
M N
Breadth First Search
16
A, B,C,D,E, F,G,H,I,J, K,L, M, A
B C ED
F G H I J
K L
O
M N
Breadth First Search
17
A, B,C,D,E, F,G,H,I,J, K,L, M,N, A
B C ED
F G H I J
K L
O
M N
Breadth First Search
18
A, B,C,D,E, F,G,H,I,J, K,L, M,N, Goal state: O
A
B C ED
F G H I J
K L
O
M N
Breadth First Search
19
The returned solution is the sequence of operators in the path:A, B, G, L, O
A
B C ED
F G H I J
K L
O
M N
Water Jug problem using BFS
What Criteria are used to Compare different search techniques ?
21
• Completeness: Is the technique guaranteed to find an answer (if there is one).
• Optimality :Highest quality solution when there are several solution are there for the problem
• Time Complexity: How long does it take to find a solution.
• Space Complexity: How much memory does it take to find a solution.
Time and space complexity are measured in terms of:
• The (maximum) branching factor b is defined as the maximum nodes created when a new node is expanded.
• The length of a path to a goal is the depth d.
• The maximum length of any path in the state space m.
Breadth First Search (BFS)
22
• Complete? Yes.• Optimal? Yes(unit cost)• Time Complexity: O(bd) • Space Complexity: O(bd)
Algorithm• Input: START and GOAL states• Local variables: OPEN, CLOSED, STATE-X, SUCCs, FOUND;• OUTPUT: Yes Or No• Method:Initalize OPEN list with START and CLOSED=ᵩ;FOUND= false;While(OPEN≠ᵩ and FOUND= false) do{Remove the first state from OPEN and call it STATE-X;Put STATE-X in the front of closed list{maintained as stack};If STATE-X=GOAL then FOUND= true else{Perform EXPAND operation on STATE-X, producing a list of SUCCs;Remove the successors from those states, if any that are in the CLOSED list;Append SUCCs at the end of OPEN list; /*queue*/}} /* end of while*/If FOUND= true then return Yes else return NoStop
Depth First Search (DFS)
24
Depth First Search (DFS)
25
Application2: Given the following state space (tree search), give the sequence of visited nodes when using DFS (assume that the nodeO is the goal state):
A
B C ED
F G H I J
K L
O
M N
Depth First Search
26
A,
A
B C ED
Depth First Search
27
A,B,
A
B C ED
F G
Depth First Search
28
A,B,F,
A
B C ED
F G
Depth First Search
29
A,B,F, G,
A
B C ED
F G
K L
Depth First Search
30
A,B,F, G,K,
A
B C ED
F G
K L
Depth First Search
31
A,B,F, G,K, L,
A
B C ED
F G
K L
O
Depth First Search
32
A,B,F, G,K, L, O: Goal State
A
B C ED
F G
K L
O
Depth First Search
33
The returned solution is the sequence of operators in the path: A, B, G, L, O
A
B C ED
F G
K L
O
Depth First Search (DFS)
34
• Complete? No (Yes on finite trees, with no loops).
• Optimal? No
• Time Complexity: O(bd), where m is the maximum depth.
• Space Complexity: O(d), where m is the maximum depth.
Main idea: Expand node at the deepest level (breaking ties left to right).
Depth First Iterative Deepening Search (DFID)
DFID combines the benefits of BFS and DFS: Like DFS the memory requirements are very modest (O(d)). Like BFS, it is complete when the branching factor is finite.
In general, iterative deepening is the preferred uninformed search method when there is a large search space and the depth of the solution is not known.
Depth First Iterative Deepening Search
36
Given the following state space (tree search), give the sequence of visited nodes when using IDS:
A
B C ED
F G H I J
K L
O
M N
Limit = 0
Limit = 1
Limit = 2
Limit = 3
Limit = 4
DLS with bound = 0
Depth First Iterative Deepening Search
Depth First Iterative Deepening Search
38
A,
ALimit = 0
Depth First Iterative Deepening Search
39
A, Failure
ALimit = 0
DLS with bound = 1
Depth First Iterative Deepening Search
Depth First Iterative Deepening Search
41
A,
A
B C EDLimit = 1
Depth First Iterative Deepening Search
42
A,B,
A
B C EDLimit = 1
Depth First Iterative Deepening Search
43
A,B, C,
A
B C EDLimit = 1
Depth First Iterative Deepening Search
44
A,B, C, D,
A
B C EDLimit = 1
Depth First Iterative Deepening Search
45
A,B C, D, E, A
B C EDLimit = 1
Depth First Iterative Deepening Search
46
A,B, C, D, E, Failure A
B C EDLimit = 1
Depth First Iterative Deepening Search
47
A,
A
B C ED
Limit = 2
Depth First Iterative Deepening Search
48
A,B,
A
B C ED
F GLimit = 2
Depth First Iterative Deepening Search
49
A,B,F,
A
B C ED
F GLimit = 2
Depth First Iterative Deepening Search
50
A,B,F, G,
A
B C ED
F GLimit = 2
Depth First Iterative Deepening Search
51
A,B,F, G, C,
A
B C ED
F G HLimit = 2
Depth First Iterative Deepening Search
52
A,B,F, G, C,H,
A
B C ED
F G HLimit = 2
Depth First Iterative Deepening Search
53
A,B,F, G, C,H, D, A
B C ED
F G H I JLimit = 2
Depth First Iterative Deepening Search
54
A,B,F, G, C,H, D,I A
B C ED
F G H I JLimit = 2
Depth First Iterative Deepening Search
55
A,B,F, G, C,H, D,I J,
A
B C ED
F G H I JLimit = 2
Depth First Iterative Deepening Search
56
A,B,F, G, C,H, D,I J, E
A
B C ED
F G H I JLimit = 2
Depth First Iterative Deepening Search
57
A,B,F, G, C,H, D,I J, E, Failure
A
B C ED
F G H I J
K L
O
M N
Limit = 2
DLS with bound = 3
Depth First Iterative Deepening Search
Depth First Iterative Deepening Search
59
A,
A
B C ED
Limit = 3
Depth First Iterative Deepening Search
60
A,B,
A
B C ED
F G
Limit = 3
Depth First Iterative Deepening Search
61
A,B,F,
A
B C ED
F G
Limit = 3
Depth First Iterative Deepening Search
62
A,B,F, G,
A
B C ED
F G
K LLimit = 3
Depth First Iterative Deepening Search
63
A,B,F, G,K,
A
B C ED
F G
K LLimit = 3
Depth First Iterative Deepening Search
64
A,B,F, G,K, L,
A
B C ED
F G
K LLimit = 3
Depth First Iterative Deepening Search
65
A,B,F, G,K, L, C, A
B C ED
F G H
K LLimit = 3
Depth First Iterative Deepening Search
66
A,B,F, G,K, L, C,H, A
B C ED
F G H
K LLimit = 3
Depth First Iterative Deepening Search
67
A,B,F, G,K, L, C,H, D,
A
B C ED
F G H I J
K LLimit = 3
Depth First Iterative Deepening Search
68
A,B,F, G,K, L, C,H, D,I,
A
B C ED
F G H I J
K L MLimit = 3
Depth First Iterative Deepening Search
69
A,B,F, G,K, L, C,H, D,I,M,
A
B C ED
F G H I J
K L MLimit = 3
Depth First Iterative Deepening Search
70
A,B,F, G,K, L, C,H, D,I,M, J,
A
B C ED
F G H I J
K L M NLimit = 3
Depth First Iterative Deepening Search
71
A,B,F, G,K, L, C,H, D,I,M, J,N,
A
B C ED
F G H I J
K L M NLimit = 3
Depth First Iterative Deepening Search
72
A,B,F, G,K, L, C,H, D,I,M, J,N, E,
A
B C ED
F G H I J
K L M NLimit = 3
Depth First Iterative Deepening Search
73
A,B,F, G,K, L, C,H, D,I,M, J,N, E,Failure
A
B C ED
F G H I J
K L
O
M NLimit = 3
DLS with bound = 4
Depth First Iterative Deepening Search
Depth First Iterative Deepening Search
75
A,
A
B C ED
Limit = 4
Depth First Iterative Deepening Search
76
A,B,
A
B C ED
F G
Limit = 4
Depth First Iterative Deepening Search
77
A,B,F,
A
B C ED
F G
Limit = 4
Depth First Iterative Deepening Search
78
A,B,F, G,
A
B C ED
F G
K L
Limit = 4
Depth First Iterative Deepening Search
79
A,B,F, G,K,
A
B C ED
F G
K L
Limit = 4
Depth First Iterative Deepening Search
80
A,B,F, G,K, L,
A
B C ED
F G
K L
OLimit = 4
Depth First Iterative Deepening Search
81
A,B,F, G,K, L, O: Goal State
A
B C ED
F G
K L
OLimit = 4
Depth First Iterative Deepening Search
82
The returned solution is the sequence of operators in the path: A, B, G, L, O
A
B C ED
F G
K L
O
Depth First Iterative Deepening Search
• Advantage:
It gives the best solution by combining BFS and DFS.
• Disadvantage:
It performs wasted computation before reaching the goal depth
Bi-directional Search (BDS)
84
• Main idea: Start searching from both the initial state and the goal state, meet in the middle.
• Complete? Yes• Optimal? Yes• Time Complexity: O(bd/2), where d is
the depth of the solution.• Space Complexity: O(bd/2), where d is
the depth of the solution.
Bi-directional Search (BDS)ADVANTAGES• The merit of bidirectional search is its speed. Sum of the
time taken by two searches (forward and backward) is much less than the O(bd) complexity.
• It requires less memory.DISADVANTAGES• Implementation of bidirectional search algorithm is difficult
because additional logic must be included to decide which search tree to extend at each step.
• One should have known the goal state in advance.• The algorithm must be too efficient to find the intersection
of the two search trees.
Comparison of search algorithms
Basic Search Algorithms
Comparison of search algorithms
87
b: Branching factord: Depth of solutionm: Maximum depth
l : Depth Limit
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