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### Water Jug Problem in Artificial Intelligence – State Space Search

**Water Jug Problem Definition,**

*“You are given two jugs, a 4-liter one and a 3-liter one. Neither has any measuring markers on it. There is a pump that can be used to fill the jugs with water. How can you get exactly 2 liters of water into a 4-liter jug.”*

### Video Tutorial:

**Representation of water Jug Problem in terms of state-space search,**

State: (x, y)

where x represents the quantity of water in a 4-liter jug and y represents the quantity of water in a 3-liter jug.

That is, x = 0, 1, 2, 3, or 4 y = 0, 1, 2, 3

Start state: (0, 0).

Goal state: (2, n) for any n.

Here need to start from the current state and end up in a goal state.

**Production Rules for Water Jug Problem in Artificial Intelligence**

1 | (x, y) is X<4 ->(4, Y) | Fill the 4-liter jug |

2 | (x, y) if Y<3 -> (x, 3) | Fill the 3-liter jug |

3 | (x, y) if x>0 -> (x-d, d) | Pour some water out of the 4-liter jug. |

4 | (x, y) if Y>0 -> (d, y-d) | Pour some water out of the 3-liter jug. |

5 | (x, y) if x>0 -> (0, y) | Empty the 4-liter jug on the ground |

6 | (x, y) if y>0 -> (x,0) | Empty the 3-liter jug on the ground |

7 | (x, y) if X+Y >= 4 and y>0 -> (4, y-(4-x)) | Pour water from the 3-liter jug into the 4-liter jug until the 4-liter jug is full |

8 | (x, y) if X+Y>=3 and x>0 -> (x-(3-y), 3)) | Pour water from the 4-liter jug into the 3-liter jug until the 3-liter jug is full. |

9 | (x, y) if X+Y <=4 and y>0 -> (x+y, 0) | Pour all the water from the 3-liter jug into the 4-liter jug. |

10 | (x, y) if X+Y<=3 and x>0 -> (0, x+y) | Pour all the water from the 4-liter jug into the 3-liter jug. |

11 | (0, 2) -> (2, 0) | Pour the 2-liter water from the 3-liter jug into the 4-liter jug. |

12 | (2, Y) -> (0, y) | Empty the 2-liter in the 4-liter jug on the ground. |

**The solution to Water Jug Problem in Artificial Intelligence**

1. Current state = (0, 0)

2. Loop until the goal state (2, 0) reached

– Apply a rule whose left side matches the current state

– Set the new current state to be the resulting state

(0, 0) – Start State

(0, 3) – Rule 2, Fill the 3-liter jug

(3, 0) – Rule 9, Pour all the water from the 3-liter jug into the 4-liter jug.

(3, 3) – Rule 2, Fill the 3-liter jug

(4, 2) – Rule 7, Pour water from the 3-liter jug into the 4-liter jug until the 4-liter jug is full.

(0, 2) – Rule 5, Empty the 4-liter jug on the ground

(2, 0) – Rule 9, Pour all the water from the 3-liter jug into the 4-liter jug.

**Goal State reached**

**Another solution to Water Jug Problem in Artificial Intelligence**

(0, 0) – Start State

(4, 0) – Rule 1, Fill the 4-liter jug

(1, 3) – Rule 8, Pour water from the 4-liter jug into the 3-liter jug until the 3-liter jug is full.

(1, 0) – Rule 6, Empty the 3-liter jug on the ground

(0, 1) – Rule 10, Pour all the water from the 4-liter jug into the 3-liter jug.

(4, 1) – Rule 1, Fill the 4-liter jug

(2, 3) – Rule 8, Pour water from the 4-liter jug into the 3-liter jug until the 3-liter jug is full.

**Goal State reached**

### Summary

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