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+-- Using the idea of canonical representation of buildings from
+-- https://andars.github.io/aoc_day11.html by Andrew Foote,
+-- plus my extension of represening the pairs as an integer.
+
+-- This version is A* search, using a list for the agenda.
+
+module Main(main) where
+
+import Data.List (subsequences, (\\), sort, sortOn, nub, findIndices)
+import Data.Ord (comparing)
+import Data.Char (isDigit)
+
+data Item = Generator String | Microchip String deriving (Show, Eq)
+type Floor = [Item]
+data Building = Building Int [Floor] deriving (Show, Eq)
+data CBuilding = CBuilding Int Integer deriving (Show, Eq)
+data Agendum = Agendum {current :: Building, trail :: [CBuilding], cost :: Int}
+
+instance Ord Item where
+    compare (Generator a) (Generator b) = compare a b
+    compare (Microchip a) (Microchip b) = compare a b
+    compare (Generator _) (Microchip _) = LT
+    compare (Microchip _) (Generator _) = GT
+
+instance Ord Building where
+    compare b1 b2 = comparing estimateCost b1 b2
+
+building1 = Building 0 [
+    (sort [Generator "polonium", Generator "thulium", 
+     Microchip "thulium", Generator "promethium", Generator "ruthenium",
+     Microchip "ruthenium", Generator "cobalt", Microchip "cobalt"]),
+    (sort [Microchip "polonium", Microchip "promethium"]),
+    [],
+    []
+    ]
+
+building0 = Building 0 [
+    (sort [Generator "polonium", Generator "thulium", 
+     Microchip "thulium", Generator "promethium"]),
+    (sort [Microchip "polonium", Microchip "promethium"]),
+    [],
+    []
+    ]
+
+building2 = Building 0 [
+    (sort [Generator "polonium", Generator "thulium", 
+     Microchip "thulium", Generator "promethium", Generator "ruthenium",
+     Microchip "ruthenium", Generator "cobalt", Microchip "cobalt",
+     Generator "elerium", Microchip "elerium",
+     Generator "dilithium", Microchip "dilithium"]),
+    (sort [Microchip "polonium", Microchip "promethium"]),
+    [],
+    []
+    ]
+
+
+buildingTest = Building 0 [
+    sort([Microchip "hydrogen", Microchip "lithium"]),
+    [Generator "hydrogen"],
+    [Generator "lithium"],
+    []]
+
+canonical :: Building -> CBuilding
+canonical (Building f floors) = CBuilding f (read $ filter (isDigit) $ show $ sort pairs)
+    where names = nub $ map (\(Generator n) -> n) $ filter (isGenerator) $ concat floors
+          floorOf (Generator g) = head (findIndices 
+                                                (\fl -> (Generator g) `elem` fl) 
+                                                floors)
+          floorOf (Microchip g) = head (findIndices 
+                                                (\fl -> (Microchip g) `elem` fl) 
+                                                floors)
+          pairs = foldl (\ps n -> (floorOf (Generator n), floorOf (Microchip n)):ps) [] names
+
+
+
+main :: IO ()
+main = do 
+    part1 
+    part2 
+
+
+part1 :: IO ()
+part1 = print $ length $ trail $ aStar (initAgenda building1) []
+
+part2 :: IO ()
+part2 = print $ length $ trail $aStar (initAgenda building2) []
+
+initAgenda :: Building -> [Agendum]
+initAgenda b = [Agendum {current = b, trail=[], cost = estimateCost b}]
+
+
+aStar :: [Agendum] -> [CBuilding] -> Agendum
+aStar [] _ = Agendum {current=buildingTest, trail=[], cost=0}
+aStar (currentAgendum:agenda) closed = 
+    if isGoal reached then currentAgendum
+    else if creached `elem` closed 
+        then aStar agenda closed
+        else aStar newAgenda (creached:closed) 
+    where 
+        reached = current currentAgendum
+        creached = canonical reached
+        newAgenda = 
+            sortOn (cost) $ 
+            agenda ++ (candidates currentAgendum closed)
+
+
+candidates :: Agendum -> [CBuilding] -> [Agendum]
+candidates agendum closed = newCandidates
+    where
+        candidate = current agendum
+        previous = trail agendum
+        succs = legalSuccessors $ successors candidate
+        excludable = previous ++ closed
+        nonloops = filter (\s -> not $ (canonical s) `elem` excludable) succs
+        newCandidates = map (\n -> makeAgendum n) nonloops
+        makeAgendum new = Agendum {current = new, 
+                                    trail = (canonical candidate):previous, 
+                                    cost = estimateCost new + length previous + 1}
+
+isGoal :: Building -> Bool
+isGoal (Building f floors) =
+    f+1 == height && (all (null) $ take f floors)
+    where height = length floors
+
+isLegal :: Building -> Bool
+isLegal (Building f floors) = 
+    null floor 
+    ||
+    not (any (isGenerator) floor)
+    ||
+    any (safePair) pairs
+    where floor = floors!!f
+          pairs = [(i, j) | i <- floor, j <- floor, isGenerator i]
+          safePair (Generator e, Microchip f) = e == f
+          safePair (Generator _, Generator _) = False
+
+isGenerator :: Item -> Bool
+isGenerator (Generator _) = True
+isGenerator (Microchip _) = False
+
+successors :: Building -> [Building]
+successors (Building f floors) = [updateBuilding f floors nf is | nf <- nextFloors, is <- items]
+    where 
+        floor = floors!!f
+        items = filter (\is -> length is == 1 || length is == 2) $ subsequences floor
+        nextFloors = if f == 0 then [1]
+                     else if f+1 == length floors then [f-1]
+                     else [f+1, f-1]
+
+legalSuccessors :: [Building] -> [Building]
+legalSuccessors = filter (isLegal)
+
+updateBuilding :: Int -> [Floor] -> Int -> [Item] -> Building
+updateBuilding oldF oldFloors newF items = Building newF newFloors
+    where newFloors = map (updateFloor) $ zip [0..] oldFloors
+          updateFloor (f, fl) 
+            | f == oldF = sort $ fl \\ items
+            | f == newF = sort $ items ++ fl
+            | otherwise = fl
+
+estimateCost :: Building -> Int
+estimateCost (Building _ floors) = 
+    sum $ map (\(c, f) -> c * length f) $ zip [0..] $ reverse floors
+