# Haskell Quiz/Amazing Mazes/Solution Abhinav

### From HaskellWiki

{- A solution to rubyquiz 31 (http://rubyquiz.com/quiz31.html). 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 the ASCII output representing the maze. 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. abhinav@xj9:rubyquiz# bin/AmazingMazes 10 10 0 0 9 9 +---+---+---+---+---+---+---+---+---+---+ | s > v | | | +---+---+ +---+ + +---+ + +---+ | v < < | | | | | | + +---+---+---+---+---+ + + + + | v | | | | + +---+---+---+ + +---+---+---+ + | > > > v | | | > v | +---+---+---+ + + +---+---+ + + | | v < | | > > ^ | v | + + + +---+---+---+ +---+---+ + | | | > > > > ^ | | v | + +---+---+---+---+---+---+ +---+ + | | | | v < < | + + + + + + +---+ +---+---+ | | | | | | v < | | + + +---+---+ +---+ +---+ +---+ | | | | v < | | + +---+ + + + +---+---+---+ + | | | > > > > e | +---+---+---+---+---+---+---+---+---+---+ Copyright 2012 Abhinav Sarkar <abhinav@abhinavsarkar.net> -} {-# LANGUAGE BangPatterns, TupleSections #-} module Main where import qualified Data.Map as M import AStar import Data.List (nub) import Data.Maybe (fromMaybe) import Control.Monad (foldM) import Control.Monad.State (State, get, put, evalState) import System.Environment (getArgs) import System.Random (Random, StdGen, randomR, randomRs, newStdGen, split) sliding :: Int -> Int -> [a] -> [[a]] sliding _ _ [] = [] sliding size step xs = take size xs : sliding size step (drop step xs) -- randomness -- type RandomState = State StdGen getRandomR :: Random a => (a, a) -> RandomState a getRandomR limits = do gen <- get let (val, gen') = randomR limits gen put gen' return val getRandomRs :: Random a => (a, a) -> RandomState [a] getRandomRs limits = do gen <- get return $ randomRs limits gen randomShuffle :: [a] -> RandomState [a] randomShuffle list = do let len = length list rs <- getRandomRs (0, len - 1) g <- get let (_, g') = split g put g' return $ map (list !!) . head . dropWhile ((/= len) . length) . map nub . sliding len 1 $ rs -- maze -- -- a cell with x and y coordinates type Cell = (Int, Int) -- a maze with width, height and a map of cell paths data Maze = Maze Int Int (M.Map Cell [Cell]) deriving (Show) -- a solution to a maze with the start and end cells and the path map data MazeSolution = MazeSolution Cell Cell (M.Map Cell Cell) -- get the neighbour cells nextCells :: Int -> Int -> Cell -> [Cell] nextCells width height (x, y) = filter (\(x', y') -> and [x' >= 0, x' < width, y' >= 0, y' < height]) . map (\(xd, yd) -> (x + xd, y + yd)) $ [(0,-1), (1,0), (0,1), (-1,0)] -- 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` if not . M.member n $ m then generateMaze_ n (Maze width height (M.insertWith' (++) n [start] (M.insertWith' (++) start [n] m))) else return mz) maze next -- 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) y <- getRandomR (0, height - 1) generateMaze_ (x, y) (Maze width height M.empty) -- render a maze and its solution as a string renderMaze :: Maze -> MazeSolution -> String renderMaze maze@(Maze width height _) solution = concatMap (renderMazeRow maze solution) [0 .. (height - 1)] ++ concat (replicate width "+---") ++ "+" -- render a row of a maze and the maze's solution as a string renderMazeRow :: Maze -> MazeSolution -> Int -> String renderMazeRow maze@(Maze width height _) solution rowIx = let (up, side) = unzip . map (renderMazeCell maze solution rowIx) $ [0 .. (width - 1)] in concat up ++ "+" ++ "\n" ++ concat side ++ "|" ++ "\n" -- render a cell of a maze and the maze's solution as a pair of strings renderMazeCell :: Maze -> MazeSolution -> Int -> Int -> (String, String) renderMazeCell (Maze _ _ cellMap) (MazeSolution start end solution) rowIx colIx = let cell = (colIx, rowIx) up = (colIx, rowIx - 1) side = (colIx - 1, rowIx) in ("+" ++ if up `elem` next cell then " " else "---", (if side `elem` next cell then " " else "|") ++ " " ++ mark cell ++ " ") where next = fromMaybe [] . flip M.lookup cellMap mark cell@(x, y) | cell == start = "s" | cell == end = "e" | otherwise = case M.lookup cell solution of Nothing -> " " Just (x', y') -> fromMaybe " " $ M.lookup (x' - x, y' - y) marks -- symbols to mark the solution path marks = M.fromList [((0,-1), "^"), ((1,0), ">"), ((0,1), "v"), ((-1,0), "<")] -- 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 . M.fromList . map (\a -> (a !! 0, a !! 1)) . filter ((== 2) . length) . sliding 2 1 . fromMaybe [] . fmap snd . astar start end (map (,1) . fromMaybe [] . flip M.lookup cellMap) $ (\(x, y) (x', y') -> abs (x - x') + abs (y - y')) main = do (width : height : sx : sy : ex : ey : _) <- fmap (map read) getArgs g <- newStdGen let mz = evalState (generateMaze width height) g putStrLn $ renderMaze mz (solveMaze mz (sx, sy) (ex, ey))

**Description:** The program generates the maze using the recursive backtracking algorithm. The maze is represented as a graph of connected cells.
The maze is solved using the A* graph search algorithm with the Manhattan distance as the heuristic.

Source: https://github.com/abhin4v/rubyquiz/blob/master/AmazingMazes.hs