How to draw the three jugs water problem?

hi there
we have 3 water jugs that the capacity of first jug is 12 and capacity of second jug is 8 and capacity of third jug is 3.
the initial state is: (0,0,0)
the successor function is:
1) add e i
2)pour to another one: [12,x,y],[x,8,z],[x,y,3]
3)empty is: [0,y,z],[x,0,z],[x,y,0]
and the goal state is: (1,1,1)
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now i want to draw its state tree. i did it by myself but i'm not really sure that it is right or not?

          (0,0,0)
     /       |      \
(12,0,0)  (0,8,0)   (0,0,3)

now the child node for(12,0,0) is: (12,0,0),(12,8,0),(12,8,3),(0,8,3),(0,0,3),(0,0,0),(9,8,3),(12,8,0),(4,8,3),(12,0,3),(12,5,3),(12,5,3),(12,8,0)

which (12,0,0),(0,0,0)==>because it is in root,(12,8,0)==>cause same
are fail node and we don't expand them.


i think if i expand (0,0,3), i will reach to my goal state:
the child for the node (0,0,3): (3,0,0),(0,3,0),(0,0,3),(1,1,1) (1,1,1) is the goal state am i right?

[edit]Spurious bold removed, Code block added - OriginalGriff[/edit]

Tags: Algorithms