Tackled problem 1625

[cses-programming-tasks.git] / app / cses1625.hs

diff --git a/app/cses1625.hs b/app/cses1625.hs
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+{-# LANGUAGE RecordWildCards, NamedFieldPuns #-}
+
+import Data.Ix
+import qualified Data.Set as S
+import Control.Monad
+
+
+data Point = Point Int Int -- row, column
+  deriving (Show, Eq, Ord, Ix)
+
+type Grid = S.Set Point
+
+gridBounds = (Point 1 1, Point 7 7)
+pathStart = Point 1 1
+pathEnd = Point 7 1
+fullPathLength = 48
+
+-- gridBounds = (Point 1 1, Point 2 2)
+-- pathStart = Point 1 1
+-- pathEnd = Point 2 1
+-- fullPathLength = 3
+
+-- gridBounds = (Point 1 1, Point 4 4)
+-- pathStart = Point 1 1
+-- pathEnd = Point 4 1
+-- fullPathLength = 15
+
+data Direction = U | R | D | L
+  deriving (Show, Eq, Ord, Enum, Bounded)
+
+data DirectionConstraint =  CU | CR | CD | CL | Unknown
+  deriving (Show, Eq, Ord, Enum, Bounded)
+
+data State = State { visited :: Grid
+                   , pos :: Point
+                   , trail :: [Direction]
+                   , constraints :: [DirectionConstraint]
+                   }
+  deriving (Show, Eq, Ord)
+
+initialState :: [DirectionConstraint] -> State
+initialState cs = 
+  State { visited = S.singleton pathStart
+        , pos = pathStart
+        , constraints = cs
+        , trail = []
+        }
+
+
+main :: IO ()
+main = do
+  -- let cs = replicate fullPathLength Unknown
+  let cs = readConstraints "??????R??????U??????????????????????????LD????D?"
+  -- let cs = readConstraints "DRURRRRRDDDLUULDDDLDRRURDDLLLLLURULURRUULDLLDDDD"
+  let paths = allPaths cs
+  print $ length paths
+  -- print paths
+  -- line <- getLine
+  -- let n = read line
+  -- let nums = unfoldr collatzStep n
+  -- let outStr = intercalate " " $ map show nums
+  -- putStrLn outStr
+
+readConstraints :: String -> [DirectionConstraint]
+readConstraints = map readConstraint
+
+readConstraint :: Char -> DirectionConstraint
+readConstraint 'U' = CU
+readConstraint 'R' = CR
+readConstraint 'D' = CD
+readConstraint 'L' = CL
+readConstraint _ = Unknown
+
+delta :: Direction -> Point
+delta U = Point (-1) 0
+delta R = Point 0 1
+delta D = Point 1 0
+delta L = Point 0 (-1)
+
+(^+^) :: Point -> Point -> Point
+(Point x1 y1) ^+^ (Point x2 y2) = Point (x1 + x2) (y1 + y2)
+
+opposite :: Direction -> Direction -> Bool
+opposite U D = True
+opposite D U = True
+opposite L R = True
+opposite R L = True
+opposite _ _ = False
+
+
+compatible :: Direction -> DirectionConstraint -> Bool
+compatible U CU = True
+compatible R CR = True
+compatible D CD = True
+compatible L CL = True
+compatible _ Unknown = True
+compatible _ _ = False
+
+
+isComplete :: State -> Bool
+isComplete (State {..}) =
+  pos == pathEnd && length trail == fullPathLength
+
+successors :: State -> [State]
+successors state@(State {..}) 
+  | pos == pathEnd = []
+  | isComplete state = []
+  | otherwise =
+      do dir <- [minBound..maxBound] 
+         let givenDirection = head constraints
+         guard $ compatible dir givenDirection
+         let nextPos = pos ^+^ (delta dir)
+         guard $ inRange gridBounds nextPos
+         {-# SCC "setNonMember" #-} guard $ S.notMember nextPos visited
+         let nextVisited = S.insert nextPos visited
+         return $ State { visited = nextVisited
+                        , pos = nextPos
+                        , constraints = tail constraints
+                        , trail = dir : trail
+                        }
+
+allPaths :: [DirectionConstraint] -> [State]
+allPaths constraints = dfs [initialState constraints] []
+
+-- bfs :: [State] -> [State] -> [State]
+-- bfs [] visited = visited
+-- bfs (current:agenda) visited
+--   | isComplete current = bfs agenda (current : visited)
+--   | otherwise =
+--       let succs = successors current
+--           newAgenda = agenda ++ succs
+--       in bfs newAgenda visited
+
+dfs :: [State] -> [State] -> [State]
+dfs [] visited = visited
+dfs (current:agenda) visited
+  | isComplete current = dfs agenda (current : visited)
+  | otherwise =
+      let succs = successors current
+          newAgenda = succs ++ agenda
+      in dfs newAgenda visited