$($@htdf find$-$path$)$

$($@signature String String Map $->($listof String$)$ or false$)$

;; try to find path between from and to$,$ while enforcing door lock rules

;$($define $($find$-$path start to castle$)$ false$)$ ;stub

$($define $($find$-$path start to castle$)$

;; path is $($listof String$),$ the path from start to the current room

;; key$-$gained is $($listof Natural$),$ the keys that gain so far

$($local $[($define $($fn$-$for$-$room r path key$-$gained$)$

$($cond $[($string$=?$ to $($room$-$name r$)$ to$)($append path $($list to$))]$

$[($member$?($room$-$name r$)$ path$)$ false$]$

$[$else

$($fn$-$for$-$los $($room$-$exits r$)$

$($append path $($list $($room$-$name r$)))$

$($append $($room$-$keys r$)$ key$-$gained$))]))$

$($define $($fn$-$for$-$los los path key$-$gained$)$

$($cond $[($empty$?$ los$)$ false$]$

$[$else

$($local $[($define approved$-$los $($real$-$exits los key$-$gained$))$

$($define try $($fn$-$for$-$room

$($generate$-$room

$($first approved$-$los$)$ castle$)$

path

key$-$gained$))]$

$($if $($not $($false$?$ try$))$

try

$($fn$-$for$-$los $($rest approved$-$los$)$

path key$-$gained$)))]))$

$($define $($real$-$exits rooms keys$)$

$($local $[($define $($fn$?$ r$)$

$($all$-$in$?($room$-$locks $($generate$-$room r castle$))$ keys$))]$

$($filter fn$?$ rooms$)))$

$($define $($all$-$in$?$ locs keys$)$

$($andmap $(\backslash$lambda $($n$)($member$?$ n keys$))$ locs$))]$

$($if $($not $($empty$?($room$-$locks $($generate$-$room start castle$))))$ false

$($fn$-$for$-$room $($generate$-$room start castle$)$ empty

empty$))))$

$($@problem $2)$

;;

;; Convert the function above to use tail recursion. Call this new function

;; find$-$path$/$tr$,$ so that the grader can test both versions.

;;

;; HINT: You will need $3$ worklists working together $($in tandem$).$

;;

$($@htdf find$-$path$/$tr$)$

$($@signature String String Map $->($listof String$)$ or false$)$

;; try to find path between from and to$,$ while enforcing door lock rules

$($check$-$expect $($find$-$path$/$tr $"$A$""$B$"$ MAP$)$ false$)$

$($check$-$expect $($find$-$path$/$tr $"$A$""$D$"$ MAP$)$ false$)$

$($check$-$expect $($find$-$path$/$tr $"$C$""$E$"$ MAP$)$ false$)$

;$($define $($find$-$path$/$tr start to castle$)$ false$)$ ;stub