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

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".

-}
module Main where

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
| otherwise = do
node <- findNode i interior
findNode i [] = error (show i ++ " [] error")
findNode i (x:xs) | i < 1  = error (show i ++ " < 1 error")
| otherwise = do
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
if used > 0
then do
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")
dir <- liftM negate (readArray m node)
writeArray m node 1
writeArray m (op dir node) 1

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
```