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63 lines
2.6 KiB
Haskell
63 lines
2.6 KiB
Haskell
#!/usr/bin/runhaskell
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import Data.Maybe
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-- given two points, returns the average of them
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average :: (Int, Int) -> (Int, Int) -> (Int, Int)
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average (x, y) (x', y') = ((x + x') `div` 2, (y + y') `div` 2)
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-- given a maze and a tuple of position and wall position, returns
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-- true if the wall position is not blocked (first position is unused)
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notBlocked :: [String] -> ((Int, Int), (Int, Int)) -> Bool
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notBlocked maze (_, (x, y)) = ' ' == (maze !! y) !! x
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-- given a list, a position, and an element, returns a new list
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-- with the new element substituted at the position
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-- (it seems such a function should exist in the standard library;
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-- I must be missing it)
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substitute :: [a] -> Int -> a -> [a]
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substitute orig pos el =
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let (before, after) = splitAt pos orig
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in before ++ [el] ++ tail after
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-- given a maze and a position, draw a '*' at that position in the maze
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draw :: [String] -> (Int, Int) -> [String]
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draw maze (x,y) = substitute maze y $ substitute row x '*'
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where row = maze !! y
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-- given a maze, a previous position, and a list of tuples of potential
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-- new positions and their wall positions, returns the solved maze, or
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-- None if it cannot be solved
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tryMoves :: [String] -> (Int, Int) -> [((Int, Int), (Int, Int))] -> Maybe [String]
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tryMoves _ _ [] = Nothing
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tryMoves maze prevPos ((newPos,wallPos):more) =
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case solve' maze newPos prevPos
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of Nothing -> tryMoves maze prevPos more
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Just maze' -> Just $ foldl draw maze' [newPos, wallPos]
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-- given a maze, a new position, and a previous position, returns
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-- the solved maze, or None if it cannot be solved
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-- (assumes goal is upper-left corner of maze)
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solve' :: [String] -> (Int, Int) -> (Int, Int) -> Maybe [String]
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solve' maze (2, 1) _ = Just maze
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solve' maze pos@(x, y) prevPos =
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let newPositions = [(x, y - 2), (x + 4, y), (x, y + 2), (x - 4, y)]
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notPrev pos' = pos' /= prevPos
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newPositions' = filter notPrev newPositions
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wallPositions = map (average pos) newPositions'
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zipped = zip newPositions' wallPositions
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legalMoves = filter (notBlocked maze) zipped
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in tryMoves maze pos legalMoves
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-- given a maze, returns a solved maze, or None if it cannot be solved
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-- (starts at lower right corner and goes to upper left corner)
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solve :: [String] -> Maybe [String]
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solve maze = solve' (draw maze start) start (-1, -1)
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where startx = length (head maze) - 3
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starty = length maze - 2
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start = (startx, starty)
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-- takes unsolved maze on standard input, prints solved maze on standard output
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main = interact main'
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where main' x = unlines $ fromMaybe ["can't solve"] $ solve $ lines x
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