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Abhinav Sarkar 2012-09-19 23:59:37 +05:30
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AmazingMazes.hs
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@ -1,13 +1,16 @@
{-
A solution to rubyquiz 31 (http://rubyquiz.com/quiz31.html).
Generate a rectangular maze given the width and height. The maze should be
solvable for any start and end position and there should be one possible
solution a given pair of start and end positions.
Generate a rectangular maze given its width and height. The maze should be
solvable for any start and end positions and there should be only one possible
solution for any pair of start and end positions.
Generate an ASCII output representing the maze.
Generate the ASCII output representing the maze.
Given the maze produced, find the solution. Produce ASCII output to visualize the solution.
Find the solution of the maze. Produce ASCII output to visualize the solution.
The maze generation algorithm used is recursive backtracking and the maze
solution algorithm used is A*.
Usage: ./AmazingMazes <width> <height> <start_x> <start_y> <end_x> <end_y>
Coordinates are zero based.
@ -75,14 +78,14 @@ nextCells width height (x, y) =
. map (\(xd, yd) -> (x + xd, y + yd))
$ [(0,-1), (1,0), (0,1), (-1,0)]
-- generate a random maze given the start cell and empty maze
-- generate a random maze given the start cell and an empty maze
generateMaze_ :: Cell -> Maze -> RandomState Maze
generateMaze_ start maze@(Maze width height cellMap) = do
!next <- randomShuffle . filter (not . flip M.member cellMap) $ nextCells width height start
if null next
then return $ Maze width height (M.insertWith' (++) start [] cellMap)
else
foldM (\mz@(Maze _ _ m) n -> (M.keys m) `seq`
foldM (\mz@(Maze _ _ m) n -> M.keys m `seq`
if not . M.member n $ m
then generateMaze_ n
(Maze width height
@ -90,7 +93,7 @@ generateMaze_ start maze@(Maze width height cellMap) = do
else return mz)
maze next
-- generate a random maze given the maze width and height
-- generate a random maze given the maze width and height using recursive backtracking
generateMaze :: Int -> Int -> RandomState Maze
generateMaze width height = do
x <- getRandomR (0, width - 1)
@ -130,7 +133,8 @@ renderMazeCell (Maze _ _ cellMap) (MazeSolution start end solution) rowIx colIx
-- symbols to mark the solution path
marks = M.fromList [((0,-1), "↑"), ((1,0), "→"), ((0,1), "↓"), ((-1,0), "←")]
-- solve the maze using astar give the maze and the start and end cells
-- solve the maze using A* given the maze and the start and end cells using
-- Manhattan distance as the heuristic
solveMaze :: Maze -> Cell -> Cell -> MazeSolution
solveMaze maze@(Maze _ _ cellMap) start end =
MazeSolution start end
@ -139,7 +143,7 @@ solveMaze maze@(Maze _ _ cellMap) start end =
. filter ((== 2) . length)
. sliding 2 1
. fromMaybe [] . fmap snd
. astar start end (map ((,1)) . fromMaybe [] . flip M.lookup cellMap)
. astar start end (map (,1) . fromMaybe [] . flip M.lookup cellMap)
$ (\(x, y) (x', y') -> abs (x - x') + abs (y - y'))
main = do