Jug Puzzle

In this puzzle, you have two empty jugs and an unlimited amount of water. The first jug, A, can hold 3 liters of water. The second jug, B, can hold 5 liters of water. The goal of this puzzle is to get exactly 4 liters of water. In this exercise, you will solve this puzzle using DFS and BFS.

State: JugA's size = 3, JugB's size = 5, Target = 4, JugA = 0, JugB = 0. (Both Jugs are empty at the start.)

Goal: (JugA == Target) or (JugB == Target). (In this case, only JugB can hold 4 liters).

Action: Fill A (FA), Fill B (FB), Pour A to B (AtoB), Pour B to A (BtoA), Empty A (EA), Empty B (EB). Follow this order of action when you expand the search graph. For the Pour actions, you can either pour until the target is full or the source is empty because there is no indicator on the jugs. Also, you cannot pour if the target is full.

Only expand actions that change the current state (i.e., do not expand AtoB if JugA is empty), and states are expanded only once (graph search, no duplicate).

Please solve it with Depth First Search.

Path: