The document discusses the water jug problem and its solution using state space search within the context of artificial intelligence. It outlines the rules for manipulating two jugs of 4 liters and 3 liters to achieve exactly 2 liters in the 3-liter jug. The solution involves a series of steps and rules that can be represented graphically or in a tabular format.

1. Topic To Be Covered:
Water Jug Problem Solution Using State
Space Search
Jagdamba Education Society's
SND College of Engineering & Research Centre
Department of Computer Engineering
SUBJECT: Artificial Intelligence & Robotics
Lecture No-08(UNIT-02)
Prof.Dhakane Vikas N

2. Water Jug Problem With State Space Search
What is Water Jug Problem?????
 The state space for this problem
can be described as of ordered
pair of integers(x, y)
 Such that x->0,1,2,3,4
(Representing the number of
gallon or liter of water into the
4-litre jug.)
 x->0,1,2,3(Representing the
number of gallon or liter of
water into the 3-litre jug.)
 Goal state is (n,2) for any value
of n, since the problem does not
specify how many liters need to
be in the 4-litre Jug

3. Water Jug Problem With State Space Search
General Solution to Water Jug Problem
 We want exact 2-litre water into 3-litre jug(X->4-litre Jug & Y->3-liter
Jug)
Step-1:x=0,y=0
Step-2:x=0,y=3
Step-3:x=3,y=0
Step-4:x=3,y=3
Step-5:x=4,y=2
 Now, we have to solve this problem using artificial intelligence(Means
,how computer will know that this problem has to solved in particular
way.)
 For this we use state Space.

4. Water Jug Problem With State Space Search
Rule Set TO Solve Water Jug Problem Using State Space
We want exact 2-litre water into 3-litre jug(X->4-litre Jug & Y->3-liter Jug)
Rule:1 (For filling X-Jug Completely)
(x, y)->(4,y)
Rule:2 (For filling Y-Jug Completely)
(x, y)->(x,3)
Rule:3 (To take some water out of X)
(x, y)->(x-d, y) when X>0

5. Water Jug Problem With State Space Search
Rule Set TO Solve Water Jug Problem Using State Space
We want exact 2-litre water into 3-litre jug(X->4-litre Jug & Y->3-liter Jug)
Rule:4 (To take some water out of Y)
(x, y)->(x, y-d) when Y>0
Rule:5 (TO Empty X-Completely)
(x, y)->(0,y) when X>0
Rule:6 (TO Empty Y-Completely)
(x, y)->(x,0) when Y>0

6. Water Jug Problem With State Space Search
Rule Set TO Solve Water Jug Problem Using State Space
We want exact 2-litre water into 3-litre jug(X->4-litre Jug & Y->3-liter Jug)
Rule:7 (To Fill X using Y)
(x, y)->(4, y-(4-X)) when Y>0,x+y>=4
Rule:8 (To Fill Y using X)
(x, y)->(x-(3-Y),3) when X>0,x+y>=3
Rule:9 (TO add everything from X& Y into->X )
(x, y)->(x+y,0) when x+y<=4,y>0
Rule:10 (TO add everything from Y&X into->Y )
(x, y)->(0,x+y) when x+y<=3,x>0

7. Water Jug Problem With State Space Search
Solution to Water Jug Problem Using State Space
We want exact 2-litre water into 3-litre jug(X->4-litre Jug & Y->3-liter Jug)
 We can apply above rules and solve water jug problem using Graphical or
Tree representation & Another way to solve this is Tabular
Representation.
 We will solve WJP using Tabular Representation As Below.
X Y Rules
0 0 -
0 3 (2)
3 0 (9)
3 3 (2)
4 2(DesiredAnswer) (7)
0 2 (5)
2(DesiredAnswer) 0 (9)