162 lines
4.9 KiB
Agda
162 lines
4.9 KiB
Agda
module Day16
|
||
|
||
import Prelude
|
||
import Node
|
||
import Aoc
|
||
import SortedMap
|
||
|
||
gridPoints : String → List (Char × Int × Int)
|
||
gridPoints text = go 0 0 (unpack text) Nil
|
||
where
|
||
go : Int → Int → List Char → List (Char × Int × Int) → List (Char × Int × Int)
|
||
go row col Nil points = points
|
||
go row col ('\n' :: cs) points = go (row + 1) 0 cs points
|
||
go row col (c :: cs) points = go row (col + 1) cs ((c,row,col) :: points)
|
||
|
||
Grid : U → U
|
||
Grid a = SortedMap Point a
|
||
|
||
getGrid : ∀ a. String → (Char → a) → Grid a
|
||
getGrid {a} text f = foldl update EmptyMap $ gridPoints text
|
||
where
|
||
update : Grid a → Char × Point → Grid a
|
||
update grid (c, pt) = updateMap pt (f c) grid
|
||
|
||
find : ∀ a. (a → Bool) → List a → Maybe a
|
||
find f Nil = Nothing
|
||
find f (x :: xs) = if f x then Just x else find f xs
|
||
|
||
fromList : ∀ k v. {{Ord k}} {{Eq k}} → List (k × v) → SortedMap k v
|
||
fromList xs = foldMap (\ a b => b) EmptyMap xs
|
||
|
||
data Dir : U where
|
||
North South East West : Dir
|
||
|
||
-- all of our co
|
||
|
||
dist : Point → Point → Int
|
||
dist (a,b) (c,d) =
|
||
let dr = if a < b then b - a else a - b
|
||
dc = if c < d then d - c else c - d
|
||
in dr + dc
|
||
|
||
dirs : List Dir
|
||
dirs = (North :: South :: East :: West :: Nil)
|
||
|
||
turn : Dir → Dir → Int
|
||
turn North North = 0
|
||
turn South South = 0
|
||
turn East East = 0
|
||
turn West West = 0
|
||
turn North South = 2000
|
||
turn South North = 2000
|
||
turn East West = 2000
|
||
turn West East = 2000
|
||
turn _ _ = 1000
|
||
|
||
DPoint : U
|
||
DPoint = Point × Dir
|
||
|
||
move : DPoint → DPoint
|
||
move ((r,c), North) = ((r - 1, c), North)
|
||
move ((r,c), South) = ((r + 1, c), South)
|
||
move ((r,c), East) = ((r, c + 1), East)
|
||
move ((r,c), West) = ((r, c - 1), West)
|
||
|
||
unmove : DPoint → DPoint
|
||
unmove ((r,c), South) = ((r - 1, c), North)
|
||
unmove ((r,c), North) = ((r + 1, c), South)
|
||
unmove ((r,c), West) = ((r, c + 1), East)
|
||
unmove ((r,c), East) = ((r, c - 1), West)
|
||
|
||
dirVal : Dir → Int
|
||
dirVal North = 0
|
||
dirVal South = 1
|
||
dirVal East = 2
|
||
dirVal West = 3
|
||
|
||
instance Ord Dir where
|
||
a < b = dirVal a < dirVal b
|
||
|
||
instance Eq Dir where
|
||
a == b = dirVal a == dirVal b
|
||
|
||
instance Eq DPoint where
|
||
(a,b) == (c,d) = a == c && b == d
|
||
|
||
instance Ord DPoint where
|
||
(a,b) < (c,d) = a < c || a == c && b < d
|
||
|
||
|
||
Cand : U
|
||
Cand = Int × Point × Dir
|
||
|
||
instance Eq Cand where
|
||
(s,pt) == (s',pt') = s == s' && pt == pt'
|
||
|
||
instance Ord Cand where
|
||
(s,pt) < (s',pt') = s < s' || s == s' && pt < pt'
|
||
|
||
min : Int → Int → Int
|
||
min x y = if x < y then x else y
|
||
|
||
-- todo is (est,dpoint) -> cost
|
||
-- scores helps us cut (dpoint -> cost) -- cost or est should be the same
|
||
-- We return the score map for part2 (which reconstructs the optimal paths)
|
||
part1 : Point → SortedMap DPoint Int → SortedMap Cand Int → SortedMap DPoint Int
|
||
part1 end scores todo =
|
||
let (Just (((est, pt),cost), todo)) = (pop todo) | Nothing => scores in
|
||
let (Just (_,best)) = lookupMap pt scores | _ => part1 end scores todo in
|
||
if best < cost then part1 end scores todo else
|
||
let scores = updateMap pt cost scores in
|
||
-- keep going so we collect all optimal paths
|
||
if fst pt == end then part1 end scores todo else
|
||
let todo = foldMap min todo $ mapMaybe (next pt cost) dirs in
|
||
part1 end scores todo
|
||
where
|
||
next : Point × Dir → Int → Dir → Maybe (Cand × Int)
|
||
next dp@(pt,dir) cost newdir = do
|
||
let cost = cost + turn dir newdir + 1
|
||
let dp' = move (pt, newdir)
|
||
case lookupMap dp' scores of
|
||
Nothing => Nothing
|
||
Just (_, best) => if best < cost
|
||
then Nothing
|
||
else Just ((cost + dist (fst dp') end, dp'), cost)
|
||
|
||
-- work backwards to collect optimal path
|
||
goBack : SortedMap DPoint Int → List (DPoint × Int) → SortedMap Point Unit → List Point
|
||
goBack scores Nil tiles = map fst $ toList tiles
|
||
goBack scores ((dp@(pt,dir),cost) :: todo) tiles =
|
||
let tiles = updateMap (fst dp) MkUnit tiles in
|
||
let next = filter valid $ mapMaybe (flip lookupMap scores ∘ (_,_ (fst $ unmove dp))) dirs in
|
||
goBack scores (next ++ todo) tiles
|
||
where
|
||
-- if the costs add up, this link is part of the path
|
||
valid : DPoint × Int → Bool
|
||
valid cand@((pt', dir'), cost') = cost == cost' + 1 + turn dir dir'
|
||
|
||
run : String -> IO Unit
|
||
run fn = do
|
||
putStrLn fn
|
||
text <- readFile fn
|
||
let pts = filter (_/=_ '#' ∘ fst) $ gridPoints text
|
||
let (Just (_, start)) = find (_==_ 'S' ∘ fst) pts | _ => putStrLn "no start"
|
||
let (Just (_,end)) = find (_==_ 'E' ∘ fst) pts | _ => putStrLn "no end"
|
||
|
||
let scores = fromList $ join $ map (\ x => map ( \d => ((snd x, d), 999999)) dirs) pts
|
||
let todo = updateMap (0, start, East) 0 EmptyMap
|
||
let scores = part1 end scores todo
|
||
let (ends@((_, e) :: es)) = mapMaybe (flip lookupMap scores) $ map (_,_ end) dirs | _ => putStrLn "no end"
|
||
let p1 = foldl min e $ map snd es
|
||
putStrLn $ "part1 " ++ show p1
|
||
let todo = filter (_==_ p1 ∘ snd) ends
|
||
let tiles = goBack scores todo EmptyMap
|
||
putStrLn $ "part2 " ++ show (length tiles)
|
||
|
||
main : IO Unit
|
||
main = do
|
||
run "aoc2024/day16/eg.txt"
|
||
run "aoc2024/day16/eg2.txt"
|
||
run "aoc2024/day16/input.txt"
|