I tried to do a prolog code to answer these questions please fix it for me fully as I know it include some errors specially last question. $\%$ Question $1$

$\%$ Define connections between rooms in the house

connected$($outside$,$ porch$1).$

connected$($porch$1,$ kitchen$).$

connected$($kitchen$,$ living$\_$room$).$

connected$($living$\_$room, corridor$).$

connected$($corridor$,$ wc$).$

connected$($corridor$,$ bedroom$).$

connected$($bedroom$,$ outside$).$

connected$($corridor$,$ master$\_$bedroom$).$

connected$($master$\_$bedroom, porch$2).$

connected$($porch$2,$ outside$).$

$\%$ Define bidirectional connections

$\%$ If X is connected to Y$,$ then Y is also connected to X

adjacent$($X$,$ Y$)$ :$-$ connected$($X$,$ Y$).$

adjacent$($X$,$ Y$)$ :$-$ connected$($Y$,$ X$).$

$\%$ Define the path predicate using depth$-$first search algorithm

$\%$ B case for depth$-$first search: reached the destination

path$($A$,$ B$,$ Path$)$ :$-$

depth$\_$first$([],$ A$,$ B$,$ RevPath$),$

reverse$($RevPath$,$ Path$).$

$\%$ The resulting path is then reversed to give the correct order and is returned as the third argument of the path$/3$ predicate.

depth$\_$first$($Path$,$ B$,$ B$,[$B$|$Path$]).$

depth$\_$first$($Visited$,$ A$,$ B$,$ Path$)$ :$-$

adjacent$($A$,$ C$),$

C $\backslash ==$ B$,$

$\backslash +$ member$($C$,$ Visited$),\%$ Avoid loops

depth$\_$first$([$A$|$Visited$],$ C$,$ B$,$ Path$).$

$\%$ Provide all possible paths

all$\_$paths$($A$,$ B$,$ Paths$)$ :$-$

findall$($Path$,$ path$($A$,$ B$,$ Path$),$ Paths$).$

$\%$ The findall$/3$ predicate collects all solutions of the path$/3$ predicate into a list $($Paths$).$

$\%$ It gathers all possible paths between A and B and stores them in the variable Paths.

$\%$ Provide error message for incorrect input

path$($A$,$ B$,\_)$ :$-$

$\backslash +$ connected$($A$,\_),$

$\backslash +$ connected$(\_,$ A$),$

$\backslash +$ connected$($B$,\_),$

$\backslash +$ connected$(\_,$ B$),$

format$(\text{'}$Error: ~w or ~w does not exist in the plan of the house.$\text{'},[$A$,$ B$]),$ fail.

$\%$ Define the predicate to find a path from A to B

path$($A$,$ B$,$ Path$)$ :$-$

travel$($A$,$ B$,[$A$],$ Q$),$

reverse$($Q$,$ Path$).$

travel$($X$,$ X$,$ P$,[$X$|$P$]).$

travel$($X$,$ Y$,$ V$,$ P$)$ :$-$

connected$($X$,$ Z$),$

Z $\backslash ==$ Y$,$

$\backslash +$member$($Z$,$ V$),$

travel$($Z$,$ Y$,[$Z$|$V$],$ P$).$

$\%$ Define the predicate to find a common destination from two origins

common$\_$destination$($Origin$1,$ Origin$2,$ Destination, Path$)$ :$-$

path$($Origin$1,$ Destination, Path$1),$

path$($Origin$2,$ Destination, Path$2),$

append$($Path$1,$ Path$2,$ Path$).$

$\%$ Q$3$

connected$($outside$,$ porch$1,1).$

connected$($porch$1,$ kitchen, $1).$

connected$($kitchen$,$ living$\_$room, $3).$

connected$($living$\_$room, porch$2,5).$

connected$($porch$2,$ outside, $1).$

connected$($livingroom$,$ corridor, $2).$

connected$($corridor$,$ bedroom, $1).$

connected$($corridor$,$ wc$,2).$

connected$($corridor$,$ master$\_$bedroom, $2).$

$\%$ Define the predicate to find a path from Location$1$ to Location$2$ with cost

path$\_$with$\_$cost$($Location$1,$ Location$2,$ Path, Cost$)$ :$-$

travel$\_$with$\_$cost$($Location$1,$ Location$2,[$Location$1],$ Q$,$ Cost$),$

reverse$($Q$,$ Path$).$

travel$\_$with$\_$cost$($X$,$ X$,$ P$,[$X$|$P$],0).$

travel$\_$with$\_$cost$($X$,$ Y$,$ V$,$ P$,$ Cost$)$ :$-$

connected$($X$,$ Z$,$ C$),$

Z $\backslash ==$ Y$,$

$\backslash +$member$($Z$,$ V$),$

travel$\_$with$\_$cost$($Z$,$ Y$,[$Z$|$V$],$ P$,$ RemainingCost$),$

$\%$ Define the predicate to find a common destination from two origins with the same cost

common$\_$destination$\_$same$\_$cost$($Origin$1,$ Origin$2,$ Destination, Path, Cost$)$ :$-$

path$\_$with$\_$cost$($Origin$1,$ Destination, Path$1,$ Cost$),$

path$\_$with$\_$cost$($Origin$2,$ Destination, Path$2,$ Cost$),$

append$($Path$1,$ Path$2,$ Path$).$