Haskell Quiz/Amazing Mazes/Solution Kuklewicz

{- for http://haskell.org/haskellwiki/?title=Haskell_Quiz/Amazing_Mazes

by Chris Kuklewicz <haskell@list.mightyreason.com> copyright 2006, 3BSD license

The algorithm is from http://www.astrolog.org/labyrnth/algrithm.htm
and is the "Wilson's algorithm" in wall adder mode.

This array indices are strange: (odd,odd) array entries are the
spaces, the (even,even) are the wall intersections (which I call
nodes), and the (odd,even) and the (even,odd) are the possible wall
locations.  The value is 0 if empty and 1 if filled.  Negative value
are used at nodes only when adding walls to indicate the last
direction taken from that node.

This can generate and print a 100x100 maze in about 21 seconds on
1.33GHz G4 powerbook (OS X 10.4.8) using ghc-6.6 and compiling with "-O2".

TODO : add a solver

-}
module Main where

import Control.Monad
import Control.Monad.ST
import Data.Array.IArray
import Data.Array.MArray
import Data.Array.ST
import Data.Array.Unboxed
import Data.STRef
import System.Environment(getArgs)
import System.Random

type Maze = UArray (Int,Int) Int

buildMaze :: Int -> Int -> StdGen -> Maze
buildMaze height width g = runSTUArray (buildMazeM height width g)

initMaze height width = do
  let hwBounds@((hr1,wr1),(hr2,wr2)) = ((0,0),(2*height,2*width))
      hr = range (hr1,hr2)
      wr = range (wr1,wr2)
      perimeter = concat [ [(hr1,w) | w <- init $ wr] -- top
                         , [(hr2,w) | w <- tail $ wr] -- bottom
                         , [(h,wr1) | h <- tail $ hr] -- left
                         , [(h,wr2) | h <- init $ hr] ] -- right
      interior = [ (h,w) | h <- [2,4..pred hr2], w <- [2,4..pred wr2] ]
      sizeInterior = (height-1)*(width-1)  -- number of unused nodes
  m <- newArray hwBounds 0
  sequence_ [ writeArray m i 1 | i <- perimeter ]
  return (m,interior,sizeInterior)

buildMazeM height width g = do
  gRef <- newSTRef g
  let rand lu = do (val,g') <- liftM (randomR lu) (readSTRef gRef)
                   writeSTRef gRef g'
                   return val
  (m,interior,sizeInterior) <- initMaze height width
  let addNodes toAdd | toAdd<0  = error (show toAdd ++ " < 0 toAdd error")
                     | toAdd==0 = return m
                     | otherwise = do
        i <- rand (1,toAdd)
        node <- findNode i interior
        added <- connect [] node
        addNodes (toAdd-added)
      findNode i [] = error (show i ++ " [] error")
      findNode i (x:xs) | i < 1  = error (show i ++ " < 1 error")
                        | otherwise = do
        used <- readArray m x
        case used of
          1 -> findNode i xs
          0 -> if i==1 then return x
                       else findNode (pred i) xs
          e -> error (show (i,x,e) ++ " was found error") 
      connect nodes node = do
        used <- readArray m node
        if used > 0
          then do
            mapM_ addWall nodes
            return (length nodes)
          else do
            dir <- rand (1,4)
            writeArray m node (negate dir)
            let node' = op dir (op dir node)
                nodes' = if used == 0 then (node:nodes) else nodes
            connect nodes' node'
      op dir (h,w) = case dir of 1 -> (h-1,w)
                                 2 -> (h+1,w)
                                 3 -> (h,w-1)
                                 4 -> (h,w+1)
                                 _ -> error (show dir ++ " not a dir error")
      addWall node = do
        dir <- liftM negate (readArray m node)
        writeArray m node 1
        writeArray m (op dir node) 1
  addNodes sizeInterior
  
showMaze :: Maze -> [String]
showMaze m = let ((hr1,wr1),(hr2,wr2)) = bounds m
                 wr = range (wr1,wr2)
                 row h = concat [ display (m!(h,w)) | w <- wr ]
                 display 0 = "::"
                 display 1 = "##"
                 display _ = "??"  -- this indicates an error
             in map row (range (hr1,hr2))

main = do
  [h,w] <- fmap (map read) getArgs
  putStr . unlines . showMaze . buildMaze h w =<< newStdGen