Water jug problem ai part 6
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The document discusses various classical AI problems, including the water jug problem, the 8-queen problem, the 8-puzzle problem, and the missionaries and cannibals problem. It provides formulations for each problem, outlining state representations, production rules, and possible solutions. Each problem is aimed at demonstrating techniques in problem representation and search strategies within artificial intelligence.
Water jug problem ai part 6
- 1. AI Problem Representation ARTIFICIAL INTELLIGENCE PART #6
- 2. Water Jug Problem A Water Jug Problem: You are given two jugs, a 4-gallon one and a 3-gallon one, a pump which has unlimited water which you can use to fill the jug, and the ground on which water may be poured. Neither jug has any measuring markings on it. How can you get exactly 2 gallons of water in the 4- gallon jug?
- 3. State Representation We will represent a state of the problem as a tuple (x, y) where x represents the amount of water in the 4- gallon jug and y represents the amount of water in the 3- gallon jug. Initial state as (0,0). Goal state as (2,y).
- 4. Production Rules 1. (x,y) If x<4 -> (4,y) 2. (x,y) If y<3 ->(x,3) 3. (x,y) If x>0 ->(x-d,y) 4. (x,y) If y>0 ->(x,y-d) 5. (x,y) If x>0 ->(0,y) 6. (x,y) If y>0 ->(x,0) 7. (x,y) If (x+y>=4 and y>0) ->(4,y-(4-x)) 8. (x,y) If (x+y>=3 and x>0) ->(x-(3-y),3) 9. (x,y) If(x+y<=4 and y>0) ->(x+y,0) 10.(x,y) If (x+y<=3 and x>0) ->(0,x+y) 11.(0,2) ->(2,0)
- 5. WATER JUG: one of the Solution 4 Gallon Jug 3 Gallon Jug Rule applied 0 0 4 0 1 1 3 8 1 0 6 0 1 10 4 1 1 2 3 8 4 Gallon jug 3 Gallon jug pump
- 6. Search Tree : Water Jug Problem (0,0) (4,0) (4,3) (0,0) (1,3) (0,3) (4,3) (0,0) (3,0)
- 7. 8 Queen Problem Problem: Place 8 queens on a chess board so that none of them attack each other. Formulation- I - A state is an arrangement of 0 to 8 queens on the board - Operators add a queen to any square. This formulation is not a systematic way to find the solution, it takes a long time to get the solution. -
- 8. Formulation – II -A state is an arrangement of 0-8 queen with no one attacked. -Operators place a queen in the left most empty column. - More systematic than formulation-I 8 Queen Problem
- 9. Formulation –III - A state is an arrangement of 8 queens on in each column. -Operators move an attacked queen to another square in the same column. -Keep on shuffling the queen until the goal is reached. - This formulation is more systematic hence , it is also called as Iterative Formulation. 8 Queen Problem
- 10. 8 Queen Problem: one solution
- 11. 8 Puzzle Problem Start State Goal State
- 12. • State space (S) • Location of each of the 8 tiles(and the blank tile) • Start State (s) • Starting configuration Operators(O) • Four Operators : Right, Left, Up, Down • Goals(G) one of the goal configuration 8 Puzzle Problem
- 13. 8 Puzzle Tree
- 14. Missionaries and Cannibals • Three missionaries and three cannibals find themselves on a side of river. They agreed to get to the other side of river. • But missionaries are afraid of being eaten by cannibals so, the missionaries want to manage the trip in such a way that no. of missionaries on either side of the river is never less than the no. of cannibals on the same side. • The boat is able to hold only 2 people at a time.
- 15. Missionaries and Cannibals: State representation • State(#m,#c,1/0) #m – number of missionaries on first bank #c – number of cannibals on first bank • The last bit indicate whether the boat is in the first bank. Operators • Boat carries (1,0) or (0,1) or (1,1) or (2,0) or (0,2)
- 16. FIND SOLUTION ?