Problem: You have two containers for holding water, a $4-$lt jug and a $3-$lt jug, and you have access to a water faucet for filling either jug to the top and a drain for emptying either jug. Neither of the jugs has any

markings to indicate how many gallons of water it contains when it is not entirely full. Thus, for example, if you want exactly $2$ lt of water, it is not possible to simply place the empty $3-$liter jug under the faucet and fill

it to exactly $2$ liters. The goal is to get the $4-$liter jug to have exactly $2$ liters of water in it$.$

Operators: There are a total of $6$ actions$/$operators at any state.

Fill either jug

Empty out either jug into the drain

Empty the water in one jug into the other jug $($until nothing is left in the one being emptied or until the other is full$).$

Representation: Think of a nice and compact representation of the state. It should not be a description the current state in natural language, but a compact encoding. If this proves difficult, you can ask$/$check the hint

$($to be given later$).$

Note: A compact representation can be described as one that is easy to code and will make it easy for you to quickly represent your search tree without writing verbal notes, and for others to understand the search

tree just following the states. Compact representation was described in class in the context of the N$-$queen, TSP and river crossing problems.

Answer the following questions according to this description.

Question $1$:

Write your representation in a few lines

Question $2$:$$

Write your solution here $($sequence of states$)$ and a verbal but compact description of your actions to reach the goal state.

Also attach a scanned page of your partial search tree showing the goal state and solution path $($pdf expected$).$