Below is PS$4$

"import java.util.$*$;

public class WaterJug $\{$

$$ static class State $\{$

$$ int$[]$ jugs;

$$ List path;

$$ State$($int$[]$ jugs, List path$)\{$

$$ this.jugs $=$ jugs;

$$ this.path $=$ path;

$\}$

$\}$

$$ public static void main$($String$[]$ args$)\{$

$$ Scanner scanner $=$ new Scanner$($System$.$in$)$;

$$ int c$1=$ scanner.nextInt$()$;

$$ int c$2=$ scanner.nextInt$()$;

$$ int c$3=$ scanner.nextInt$()$;

$$ int d $=$ scanner.nextInt$()$;

$$ int$[]$ capacities $=\{$c$1,$ c$2,$ c$3\}$;

$$ int$[]$ initialState $=\{$c$1,0,0\}$;

$$ List result $=$ bfs$($initialState$,$ capacities, d$)$;

$$ if $($result $!=$ null$)\{$

$$ for $($int$[]$ state : result$)\{$

$$ System.out.println$($state$[0]+""+$ state$[1]+""+$ state$[2])$;

$\}$

$\}$else$\{$

$$ System.out.println$("$Not Possible"$)$;

$\}$

$\}$

$$ private static List bfs$($int$[]$ initialState, int$[]$ capacities, int target$)\{$

$$ Queue queue $=$ new LinkedList$<>()$;

$$ Set visited $=$ new HashSet$<>()$;

$$ List initialPath $=$ new ArrayList$<>()$;

$$ initialPath.add$($initialState$)$;

$$ queue.add$($new State$($initialState$,$ initialPath$))$;

$$ visited.add$($Arrays$.$toString$($initialState$))$;

$$ while $(!$queue.isEmpty$())\{$

$$ State currentState $=$ queue.poll$()$;

$$ int$[]$ jugs $=$ currentState.jugs;

$$ List path $=$ currentState.path;

$//$ Check if any jug has the target amount

$$ for $($int amount : jugs$)\{$

$$ if $($amount $==$ target$)\{$

$$ return path;

$\}$

$\}$

$//$ Try all possible pours between the jugs

$$ for $($int i $=0$; i $<3$; i$++)\{$

$$ for $($int j $=0$; j $<3$; j$++)\{$

$$ if $($i $!=$ j$)\{$

$$ int$[]$ newState $=$ pour$($jugs$,$ i$,$ j$,$ capacities$)$;

$$ String newStateString $=$ Arrays.toString$($newState$)$;

$$ if $(!$visited.contains$($newStateString$))\{$

$$ visited.add$($newStateString$)$;

$$ List newPath $=$ new ArrayList$<>($path$)$;

$$ newPath.add$($newState$)$;

$$ queue.add$($new State$($newState$,$ newPath$))$;

$\}$

$\}$

$\}$

$\}$

$\}$

$$ return null;

$\}$

$$ private static int$[]$ pour$($int$[]$ state, int from, int to$,$ int$[]$ capacities$)\{$

$$ int$[]$ newState $=$ Arrays.copyOf$($state$,3)$;

$$ int amountToPour $=$ Math.min$($newState$[$from$],$ capacities$[$to$]-$ newState$[$to$])$;

$$ newState$[$from$]-=$ amountToPour;

$$ newState$[$to$]+=$ amountToPour;

$$ return newState;

$\}$

$\}$

$"$

Answer please

$"$It would be possible to model the water transfer problem $($PS$4)$ using a graph and solve it using depth$-$first search.

true

false"