Ch 2 State Space Search - slides part 1.pdf

1
Ch 2 – Prob Solving by searching
To build a goal-based agent we need to answer the
following questions:
– What is the goal to be achieved?
– What are the actions?
– What relevant information is necessary to encode in
order to describe the state of the world, describe the
available transitions, and solve the problem?
Initial
state
Goal
state
Actions

2
What is the goal to be achieved?
 Could describe a situation we want to achieve, a
set of properties that we want to hold, etc.
 Requires defining a “goal test” so that we know
what it means to have achieved/satisfied our
goal.

3
What are the actions?
 Characterize the primitive actions or events that are
available for making changes in the world in order to
achieve a goal.
 Deterministic world: no uncertainty in an action’s
effects. Given an action (a.k.a. operator or move) and
a description of the current world state, the action
completely specifies
– whether that action can be applied to the current world
(i.e., is it applicable and legal), and
– what the exact state of the world will be after the action
is performed in the current world (i.e., no need for
“history” information to compute the new world).

4
Representing actions
Note also that actions in this framework can all
be considered as discrete events that occur at
an instant of time.
–For example, if “Sita is in class” and then
performs the action “go home,” then in the
next situation she is “at home.” There is no
representation of a point in time where she is
neither in class nor at home (i.e., in the state
of “going home”).

5
Representing actions
The number of actions / operators depends on the
representation used in describing a state.
– In the 8-puzzle, we could specify 4 possible moves for
each of the 8 tiles, resulting in a total of 4*8=32
operators.
– On the other hand, we could specify four moves for the
“blank” square and we would only need 4 operators.
Representational shift can greatly simplify a problem!

6
Representing states
 What information is necessary to encode about the world
to sufficiently describe all relevant aspects in solving the
goal? That is, what knowledge needs to be represented in
a state description to adequately describe the current state
or situation of the world?
 The size of a problem is usually described in terms of
the number of states that are possible.
– Tic-Tac-Toe has about 39 states.
– Checkers has about 1040 states.
– Rubik’s Cube has about 1019 states.
– Chess has about 10120 states in a typical game.

7
Defining a Problem as a State Space
1. Define a state space that contains all the possible
configurations of the relevant objects.
2. Specify one (or more) state(s) as the initial state(s).
3. Specify one (or more) state(s) as the goal state(s).
4. Specify a set of rules that describe available
actions (operators), considering:
 What assumptions are present in the informal
problem description?
 How general should the rules be?
 How much of work required to solve the problem
should be precompiled and represented in the rules?

8
2.2.1 Production Systems
 A set of rules (Knowledge Base) :
– LHS  RHS (if-part  then-part)
– Pattern  Action
– Antecedent  Consequent
 Knowledge containing information (temporary
or permanent) required to solve the current
task. (Working Memory)
 A control strategy to specify the order of testing
patterns and resolving possible conflicts
(Inference Engine)
 A rule applier.

9
Production System Major
Components
knowledge base
– contains essential information about the
problem domain
– often represented as facts and rules
inference engine
– mechanism to derive new knowledge from
the knowledge base and the information
provided by the user
– often based on the use of rules

10
Production (Rule-Based) System
Knowledge Base
Inference Engine
Working Memory
User
Interface
Agenda

11
Rule-Based System
 knowledge is encoded as IF … THEN rules
– these rules can also be written as production rules
 the inference engine determines which rule
antecedents are satisfied
– the left-hand side must “match” a fact in the working
memory
 satisfied rules are placed on the agenda
 rules on the agenda can be activated (“fired”)
– an activated rule may generate new facts through its
right-hand side
– the activation of one rule may subsequently cause the
activation of other rules

12
Example Rules
IF … THEN Rules
Rule: Red_Light
IF the light is red
THEN stop
Rule: Green_Light
IF the light is green
THEN go
antecedent
(left-hand-side)
consequent
(right-hand-side)
Production Rules
the light is red ==> stop
the light is green ==> go

13
Inference Engine Cycle
 describes the execution of rules by the
inference engine
– match
• update the agenda
– add rules whose antecedents are satisfied to the agenda
– remove non-satisfied rules from agendas
– conflict resolution
• select the rule with the highest priority from the agenda
– execution
• perform the actions on the consequent of the selected rule
• remove the rule from the agenda
 the cycle ends when
– no more rules are on the agenda, or
– an explicit stop command is encountered

14
The Water Jugs Problem
 2 jugs
– 5 gallon
– 3 gallon
 How can you get exactly 4 gallons into the 5
gallon jug?
 Possible operators:
– Empty jug
– Fill jug from tap
– Pour contents from one jug into another
• Empty contents of one jug into the other
• Transfer some of contents of one jug to fill-up the other
5
3

Water Jugs Problem – Solution 1
16
Table 2.2 Solution Path 1
Rule
Applied
5-g jug 3-g jug Step No
Initial state 0 0
1 5 0 1
8 2 3 2
4 2 0 3
6 0 2 4
1 5 2 5
8 4 3 6
Goal state 4 -

Water Jugs Problem – Solution 2
17
Table 2.2 Solution Path 2
Rule Applied 5-g jug 3-g jug Step No
Initial state 0 0
3 0 3 1
5 3 0 2
3 3 3 3
7 5 1 4
2 0 1 5
5 1 0 6
3 1 3 7
5 4 0 8
Goal state 4 -

Missionaries and Cannibals
18
RN Left side of rule  Right side of rule
Rules for boat going from left bank to right bank of the river
L1 ([n1M, m1C, 1B], [n2M, m2C, 0B])  ([(n1-2)M, m1C, 0B], [(n2+2)M, m2C, 1B])
L2 ([n1M, m1C, 1B], [n2M, m2C, 0B])  ([(n1-1)M,(m1-1)C,0B],[(n2+1)M,(m2+1)C, 1B])
L3 ([n1M, m1C, 1B], [n2M, m2C, 0B])  ([n1M, (m1-2)C, 0B], [n2M, (m2+2)C, 1B])
L4 ([n1M, m1C, 1B], [n2M, m2C, 0B])  ([(n1-1)M, m1C,0B],[(n2+1)M, m2C, 1B])
L5 ([n1M, m1C, 1B], [n2M, m2C, 0B])  ([n1M, (m1-1)C, 0B], [n2M, (m2+1)C, 1B])
Rules for boat coming from right bank to left bank of the river
R1 ([n1M, m1C, 0B], [n2M, m2C, 1B])  ([(n1+2)M, m1C, 1B], [(n2-2)M, m2C, 0B])
R2 ([n1M, m1C, 0B], [n2M, m2C, 1B])  ([(n1+1)M,(m1+1)C,1B],[(n2-1)M,(m2-1)C, 0B])
R3 ([n1M, m1C, 0B], [n2M, m2C, 1B])  ([n1M, (m1+2)C, 1B], [n2M, (m2-2)C, 0B])
R4 ([n1M, m1C, 0B], [n2M, m2C, 1B])  ([(n1+1)M, m1C,1B],[(n2-1)M, m2C, 0B])
R5 ([n1M, m1C, 0B], [n2M, m2C, 1B])  ([n1M, (m1+1)C, 1B], [n2M, (m2-1)C, 0B])

Missionaries and Cannibals - solution
19
Start  ([3M, 3C, 1B], [0M, 0C, 0B]]
L2: ([2M, 2C, 0B], [1M, 1C, 1B])
R4: ([3M, 2C, 1B], [0M, 1C, 0B])
L3: ([3M, 0C, 0B], [0M, 3C, 1B])
R4: ([3M, 1C, 1B], [0M, 2C, 0B])
L1: ([1M, 1C, 0B], [2M, 2C, 1B])
R2: ([2M, 2C, 1B], [1M, 1C, 0B])
L1: ([0M, 2C, 0B], [3M, 1C, 1B])
R5: ([0M, 3C, 1B], [3M, 0C, 0B])
L3: ([0M, 1C, 0B], [3M, 2C, 1B])
R5: ([0M, 2C, 1B], [3M, 1C, 0B])
1M,1C 
1M 
2C 
1C 
2M 
1M,1C 
2M 
1C 
2C 
1C 
L3: ([0M, 0C, 0B], [3M, 3C, 1B]) 2C  Goal state

20
2.2.2 State Space Search
 State Space consists of 4 components
1. A set S of start (or initial) states
2. A set G of goal (or final) states
3. A set of nodes representing all possible
states
4. A set of arcs connecting nodes
representing possible actions in different
states.

Problem solving by search
 Represent the problem as STATES and
OPERATORS that transform one state into
another state.
 A solution to the problem is an OPERATOR
SEQUENCE that transforms the INITIAL
STATE into a GOAL STATE.
 Finding the sequence requires SEARCHING
the STATE SPACE by GENERATING the
paths connecting the two.
21

22
Missionaries and Cannibals: Initial
State and Actions
 initial state:
– all missionaries, all
cannibals, and the
boat are on the left
bank
 5 possible actions:
– one missionary
crossing
– one cannibal crossing
– two missionaries
crossing
– two cannibals crossing
– one missionary and
one cannibal crossing

23
Missionaries and Cannibals: State
Space
1c
1m
1c
2c
1c
2c
1c
2m
1m
1c
1m
1c
1c
2c
1m
2m
1c
2c
1c
1m

24
Missionaries and Cannibals: Goal
State and Path Cost
 goal state:
– all missionaries, all
cannibals, and the
boat are on the
right bank.
 path cost
– step cost: 1 for each
crossing
– path cost: number of
crossings = length of
path
 solution path:
– 4 optimal solutions
– cost: 11

25
Example: Measuring problem!
 Problem: Using these three buckets, measure
7 liters of water.
3 l 5 l
9 l

26
 (1 possible) Solution:
a b c
0 0 0
3 0 0
0 0 3
3 0 3
0 0 6
3 0 6
0 3 6
3 3 6
1 5 6
0 5 7
3 l 5 l
9 l
a b c
Initial state
Goal state

27
 Another Solution:
a b c
0 0 0
0 5 0
3 2 0
3 0 2
3 5 2
3 0 7
3 l 5 l
9 l
a b c

28
Which solution do we prefer?
• Solution 1:
a b c
0 0 0
3 0 0
0 0 3
3 0 3
0 0 6
3 0 6
0 3 6
3 3 6
1 5 6
0 5 7
• Solution 2:
a b c
0 0 0
0 5 0
3 2 0
3 0 2
3 5 2
3 0 7

29
8-queens
• State: any arrangement of up to 8 queens on the board
• Initial state: no queens on the board
• Operation: add a queen to any empty square
• Goal state: no queen is attacked (like the above board).

30
8-queens… Improved states
• State: an arrangement of n (up to 8) queens, 1 each in the n
leftmost columns
• Operation: add a queen in leftmost empty column such that it is
not attacked by the other queens.
Improvement: Just 2057 possible states instead of P(64,8)  648

31
Control Strategies
 Control strategy is one of the most
important component of intelligent
systems and specify the order in which
rules are applied in a given current state.
 A good control strategy should have the
following properties:
– Cause motion
– Be systematic

32
Data/Goal-driven Strategies
 Data-driven search = forward chaining.
– Start from an initial state and work towards a
goal state.
– Examples seen so far
 Goal-driven search = backward chaining.
– Start from a goal state and work towards an
initial state.
– Prolog programming, theorem proving …

33
Seven problem characteristics
1. Decomposability of a problem
 Towers of Hanoi
2. Can solution steps be ignored or undone?
 Ignorable : theorem proving
 Some of the lemmas proved can be ignored
 Recoverable : 8 tile puzzle
 solution steps can be undone (backtracking)
 Irrecoverable : chess
 solution steps can not be undone

34
3. Is the universe predictable?
• 8-puzzel (yes)
• Bridge/chess (no)  but we can use
probabilities of each possible outcomes
4. Is a good solution absolute or relative?
• More than one solution?
• traveling salesman problem

35
5. Is the solution a state or a path ?
- Given a sequence of formulae, does a statement
follow from them?
- water jug problem  path / plan
6. What is the role of knowledge?
knowledge for perfect program of chess
(need knowledge to constrain the search)
newspaper story understanding
(need knowledge to recognize a solution)
7. Does the task require interaction with a
person? solitary/ conversational

36
Toy Problems vs.
Real-World Problems
Toy Problems
– concise and exact
description
– used for illustration
purposes (e.g. here)
– used for performance
comparisons
– all the above
examples
Real-World Problems
– no single, agreed-
upon description
– people care about the
solutions (useful)

37
Real-World Problem:
Touring in Romania
Oradea
Bucharest
Fagaras
Pitesti
Neamt
Iasi
Vaslui
Urziceni
Hirsova
Eforie
Giurgiu
Craiova
Rimnicu Vilcea
Sibiu
Dobreta
Mehadia
Lugoj
Timisoara
Arad
Zerind
120
140
151
75
70
111
118
75
71
85
90
211
101
97
138
146
80
99
87
92
142
98
86

38
Touring in Romania:
Search Problem Definition
 initial state:
– In(Arad)
 possible Actions:
– DriveTo(Zerind), DriveTo(Sibiu),
DriveTo(Timisoara), etc.
 goal state:
– In(Bucharest)
 step cost:
– distances between cities

39
Searching for solutions
 An agent with several immediate options of
unknown value can decide what to do by first
examining different possible sequences of
actions that lead to states of known value, and
then choosing the best sequence.
 search (through the state space) for
• a goal state
• a sequence of actions that leads to a goal state
• a sequence of actions with minimal path cost
that leads to a goal state

40
Search Trees
 search tree: tree structure defined by initial
state and successor function
 Touring Romania (partial search tree):
In(Arad)
In(Zerind) In(Sibiu) In(Timisoara)
In(Arad) In(Oradea) In(Fagaras) In(Rimnicu Vilcea)
In(Sibiu) In(Bucharest)

41
Search Nodes
 search nodes: the nodes in the search tree
 data structure:
– state: a state in the state space
– parent node: the immediate predecessor in the
search tree
– action: the action that, performed in the parent
node’s state, leads to this node’s state
– path cost: the total cost of the path leading to this
node
– depth: the depth of this node in the search tree

42
Expanded Search Nodes
in Touring Romania Example
In(Arad)

43
Fringe Nodes
in Touring Romania Example
fringe nodes: nodes that have not been
expanded
In(Arad)

44
A General State-Space Search Algorithm
open := {S}; closed :={};
repeat
n := select(open); /* select one node from open for
expansion */
if n is a goal
then exit with success; /* delayed goal testing */
expand(n)
/* generate all children of n
put these newly generated nodes in open
(check duplicates)
put n in closed (to check duplicates) */
until open = {};
exit with failure

45
Key Features of the General
Search Algorithm
 systematic
– guaranteed to not generate the same state
infinitely often
– guaranteed to come across every state
eventually
 incremental
– attempts to reach a goal state step by step
(rather than guessing it all at once)

46
In(Arad) In(Oradea) In(Rimnicu Vilcea)
In(Zerind) In(Timisoara)
In(Fagaras)
In(Sibiu)
General Search Algorithm:
Touring Romania Example
In(Arad)
fringe
selected

47
Evaluating Search Strategies
• Completeness: Is it guaranteed that a solution will be
found?
• Optimality: Is the best solution found when several
solutions exist?
• Time complexity: How long does it take to find a solution?
• Space complexity: How much memory is needed to
perform a search?
• Branching factor (b)
1 + b + b2 + b3 + ... + bd
b nodes
b nodes
b nodes

48
Search Cost vs. Total Cost
 search cost:
– time (and memory) used to find a solution
 total cost:
– search cost + path cost of solution
 optimal trade-off point:
– further computation to find a shorter path
becomes counterproductive

49
Uninformed vs. Informed Search
 uninformed search (blind search)
– no additional information about states beyond
problem definition
– only goal states and non-goal states can be
distinguished
– E.g., BFS, DFS, DFID, UCS,…
 informed search (heuristic search)
– additional information about how “promising” a state
is available
– Greedy HDFS, BeFs, A*, …

50
Breadth-First Search
 strategy:
– expand root node
– expand successors of root node
– expand successors of successors of root
node
– etc.
 implementation:
– use FIFO queue to store fringe nodes in
general tree search algorithm

51
Breadth First Search Algorithm
open := [Start]; // Initialize
closed := [ ];
while open != [ ] // While states remain
{ remove the leftmost state from open, call it X;
if X is a goal return success; // Success
else
{ generate children of X;
put X on closed;
eliminate children of X
on open or closed; // loops
put remaining children at the
END of open; } // QUEUE
}
return failure;

52
depth
=
3
Breadth-First Search: Missionaries
and Cannibals
depth
=
0
depth
=
1
depth
=
2

53
Breadth-First Search: Evaluation
completeness yes
optimality shallowest
time complexity O(bd+1)
space complexity O(bd+1)

54
Time complexity of BFS
• If a goal node is found on depth d of the tree, all nodes
up till that depth are created.
G
b
d
 Thus: O(bd+1)

55
 In General: bd+1
Space complexity of BFS
• Largest number of nodes in QUEUE is reached on
the level d of the goal node.
G
b
d

56
Exponential Complexity:
Important Lessons
 memory requirements are a bigger problem for
breadth-first search than is the execution time
 time requirements are still a major factor
 exponential-complexity search problems
cannot be solved by uninformed methods for
any but the smallest instances

57
Depth-First Search
 strategy:
– always expand the deepest node in the
current fringe first
– when a sub-tree has been completely
explored, delete it from memory and “back
up”
 implementation:
– use LIFO queue (stack) to store fringe nodes
in general tree search algorithm

58
Depth First Search Algorithm
open := [Start]; // Initialize
closed := [ ];
while open != [ ] // While states remain
{ remove the leftmost state from open, call it X;
if X is a goal return success; // Success
else
{ generate children of X;
put X on closed;
eliminate children of X
on open or closed; // loops
put remaining children at the
START of open; } // STACK
}
return failure;

59
depth
=
3
Depth-First Search:
depth
=
0
depth
=
1
depth
=
2

60
Depth-First Search: Evaluation
completeness no
optimality no
time complexity O(bd+1)
space complexity O(bd)

61
Time complexity of DFS
• In the worst case:
• the goal node may be on the right-most branch,
G
d
b
 Time complexity O(bd+1)

62
Space complexity of DFS
• Largest number of nodes in QUEUE is reached in
bottom left-most node.
...
 Order: O(b*d)

63
Evaluation of Depth-first & Breadth-first
• Completeness: Is it guaranteed that a solution will be found?
• Yes for BFS
• No for DFS
• Optimality: Is the best solution found when several solutions exist?
• No for both BFS and DFS if edges are of different length
• Yes for BFS and No for DFS if edges are of same length
• Time complexity: How long does it take to find a solution?
• Worst case: both exponential
• Average case: DFS is better than BFS
• Space complexity: How much memory is needed to perform a
search?
• Exponential for BFS
• Linear for DFS

64
Depth-first vs Breadth-first
 Use depth-first when
– Space is restricted
– High branching factor
– There are no solutions with short paths
– No infinite paths
 Use breadth-first when
– Possible infinite paths
– Some solutions have short paths
– Low branching factor

65
Depth-First Iterative Deepening (DFID)
 BF and DF both have exponential time complexity O(bd)
BF is complete but has exponential space complexity
DF has linear space complexity but is incomplete
 Space is often a harder resource constraint than time
 Can we have an algorithm that
– is complete and
– has linear space complexity ?
 DFID by Korf in 1987
First do DFS to depth 0 (i.e., treat start node as having
no successors), then, if no solution found, do DFS to
depth 1, etc.
until solution found do
DFS with depth bound c
c = c+1

66
depth
=
3
Iterative Deepening Search:
depth
=
0
depth
=
1
depth
=
2

67
Depth-First Iterative Deepening (DFID)
 Complete (iteratively generate all nodes up to
depth d)
 Optimal if all operators have the same cost.
Otherwise, not optimal but does guarantee
finding solution of fewest edges (like BF).
 Linear space complexity: O(bd), (like DF)
 Time complexity is exponential O(bd), but a
little worse than BFS or DFS because nodes
near the top of the search tree are generated
multiple times.
 Worst case time complexity is exponential
for all blind search algorithms !

68
Iterative Deepening Search:
Evaluation
completeness yes
time complexity O(bd)
space complexity O(bd)

69
Uniform/Lowest-Cost (UCS/LCFS)
 BFS, DFS, DFID do not take path cost into account.
 Let g(n) = cost of the path from the start node to an
open node n
 Algorithm outline:
– Always select from the OPEN the node with the
least g(.) value for expansion, and put all newly
generated nodes into OPEN
– Nodes in OPEN are sorted by their g(.) values (in
ascending order)
– Terminate if a node selected for expansion is a goal
 Called “Dijkstra's Algorithm” in the algorithms
literature and similar to “Branch and Bound
Algorithm” in operations research literature

70
A Uniform-cost Search Algorithm
open := {S}; closed :={};
repeat
n := select(open); /* select the 1st node from open
for expansion */
if n is a goal
then exit with success; /* delayed goal testing */
expand(n)
/* generate all children of n
put these newly generated nodes in open
(check duplicates)
sort open (by path cost g(n))
put n in closed (check duplicates) */
until open = {};
exit with failure

71
UCS example
A
D
B
E
C
F
G
S
3
4
4
4
5 5
4
3
2
AFTER open closed
ITERATION
0 [S(0)] [ ]
1 [A(3), D(4)] [S(0)]
2 [D(4), B(7)] [S(0), A(3)]
3 [E(6), B(7)] [S(0), A(3), D(4)]
4 [B(7), F(10)] [S(0), A(3), D(4), E(6)]
5 [F(10), C(11)]
6 [C(11), G(13)]
7 [G(13)]

72
Uniform-Cost -- analysis
Complete (if cost of each edge is not infinitesimal)
– The total # of nodes n with g(n) ≤ g(goal) in the state
space is finite
– Goal node will eventually be generated (put in OPEN)
and selected for expansion (and passes the goal test)
Optimal
– When the first goal node is selected for expansion (and
passes the goal test), its path cost is less than or equal to
g(n) of every OPEN node n (and solutions entailed by n)
Exponential time and space complexity, O(bd)
where d is the depth of the solution path of the least
cost solution

73
Bidirectional Search
 idea: run two simultaneous searches:
– one forward from the initial state,
– one backward from the goal state,
until the two fringes meet.
The solution path must cross the meeting
point.
Start Goal

74
Bidirectional Search: Caveats
 What search strategy for forward/backward
search?
– breadth-first search
 How to check whether a node is in the other
fringe?
– hash table
 must know goal state for backward search
 must be able to compute predecessors and
successors for a given state

75
Bidirectional Search: Evaluation
completeness yes
time complexity O(bd/2)
space complexity O(bd/2)

76
Comparing Uninformed Search
Strategies
Breadth
-First
Uniform-
Cost
Depth-
First
Depth-
Limite
d
Iterative
Deepening
Bidirectiona
l Breadth-F.
complete? Yes Yes No No Yes Yes
optimal? Yes Yes No No Yes Yes
time
complexity
O(bd+1) O(b1+⌊C*/ε⌋) O(bd+1) O(bl) O(bd) O(bd/2)
space
complexity
O(bd+1) O(b1+⌊C*/ε⌋) O(bd) O(bl) O(bd) O(bd/2)

77
When to use what
Depth-First Search:
– Space is limited
– High branching factor
– No infinite branches
Breadth-First Search:
– Some solutions are known to be shallow
Iterative-Deepening Search:
– Space is limited and the shortest solution path is required
Uniform-Cost Search:
– Actions have varying costs
– Least cost solution is the required
The only uninformed search that worries about costs.

78
Repeated states
 Repeated states can be a source of great inefficiency:
identical subtrees will be explored many times!
– Failure to detect repeated states can turn a linear problem
into an exponential one !
How much effort to invest in detecting repetitions?

79
Strategies for repeated states
 Do not expand the state that was just generated
– constant time, prevents cycles of length one, ie.,
A,B,A,B….
 Do not expand states that appear in the path
– time linear in the depth of node, prevents some cycles
of the type A,B,C,D,A
 Do not expand states that were expanded before
– can be expensive! Use hash table to avoid looking at
all nodes every time.

80
Summary: uninformed search
 Problem formulation and representation is key!
– State formulation with care (8-queens)
– Action formulation with care (8-puzzle)
 Implementation as expanding directed graph of
states and transitions
 Appropriate for problems where no solution is
known and many combinations must be tried
 Problem space is of exponential size in the number
of world states -- NP-hard problems
 Fails due to lack of space and/or time.

Homework
1. Explain the seven characteristics of AI problems.
2. Define state space search.
3. Compare the search strategies BFS, DFS, DFID, UCS,
based time complexity, space complexity, optimality and
completeness.
4. A farmer is stranded on an island with 3 of his belongings:
cabbage, goat and tiger. He has a small boat capable of
carrying him and one of his belongings. He cannot leave
cabbage and goat unattended (the cabbage will be eaten
by the goat) and cannot leave tiger and goat unattended
(the tiger will eat the goat). Design a state-space
representation for this search problem and draw the state-
space showing the first 3 levels.
81

Homework
5. In the rabbit leap problem, three east-bound rabbits
stand in a line blocked by three west-bound rabbits as
shown below. They are crossing a stream with stones
placed in a line. A rabbit can only move forward or
jump over one rabbit to get to an unoccupied stone.
Design a state-space representation for this search
problem and draw the state-space showing the first 3
levels. Find a solution path in the state space.
82

Ch 2 State Space Search - slides part 1.pdf

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