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 256x256 maze in about 38 seconds on
1.33GHz G4 powerbook (OS X 10.4.8) using ghc-6.6 and compiling with "-O2".

-- Usage:
-- ./mazer height width
-- which defaults to starting at 1 1 and stopping at height width
-- ./mazer height width rowStart colStart rowStop,colStop
-- where row and col are in [1..height] and [1..width] respectively
-}
module Main (main) where

import Control.Monad(when)
import Data.Array.ST(runSTUArray,readArray,writeArray,newArray)
import Data.Array.Unboxed(UArray,(!),bounds,range)
import Data.List -- (foldl')
import qualified Data.Set as S(fromDistinctAscList,null,size,toList,delete)
import Data.STRef(newSTRef,readSTRef,writeSTRef)
import System.Environment
import System.Random(StdGen,newStdGen,randomR)

type Maze = UArray (Int,Int) Int

main = do
  [hw,iFrom,iTo] <- handleArgs
  putStr . unlines . showMaze . buildMaze hw iFrom iTo =<< newStdGen

handleArgs = do
  args <- getArgs
  case length args of
    2 -> let [h,w] = map read args
         in return [(h,w),(1,1),(h*2-1,w*2-1)]
    6 -> let [h,w,r1,c1,r2,c2] = map read args
         in return [(h,w),(r1*2-1,c1*2-1),(r2*2-1,c2*2-1)]
    _ -> fail "Incorrect command line args, need 2 or 6 numbers"

blank,solid,startFrom,endAt,onPath :: Int
blank = 0; solid = 5; startFrom = 6; endAt = 7; onPath = 8
-- up down left right = 1 2 3 4

showMaze :: Maze -> [String]
showMaze m = let ((hr1,wr1),(hr2,wr2)) = bounds m
                 row h = foldr ($) "" [ display (m!(h,w)) | w <- range (wr1,wr2) ]
                 display 0 = (':':).(':':)
                 display 5 = ('#':).('#':)
                 display 6 = ('[':).(']':)
                 display 7 = ('{':).('}':)
                 display 8 = ('<':).('>':)
                 display _ = (':':).(':':) -- default is blank
             in map row (range (hr1,hr2))

buildMaze :: (Int,Int) -> (Int,Int) -> (Int,Int) -> StdGen -> Maze
buildMaze hw iFrom iTo g = runSTUArray (buildMazeM hw iFrom iTo 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 = S.fromDistinctAscList [ (h,w) | h <- [2,4..pred hr2], w <- [2,4..pred wr2] ]
  m <- newArray hwBounds blank
  sequence_ [ writeArray m i solid | i <- perimeter ]
  return (m,interior)

buildMazeM hw@(height,width) iFrom iTo g = do
  gRef <- newSTRef g
  (m,interior) <- initMaze hw
  let rand lu = do (val,g') <- fmap (randomR lu) (readSTRef gRef)
                   writeSTRef gRef g'
                   return val
      addNodes toAdd | S.null toAdd = return ()
                     | otherwise = do
        i <- rand (0, pred (S.size toAdd))
        let node = (S.toList toAdd) !! i
        added <- connect [] node
        addNodes (foldl' (flip S.delete) toAdd added)
      connect nodes node = do
        used <- readArray m node
        if used == solid
          then do mapM_ addWall nodes
                  return nodes
          else do dir <- rand (1,4)
                  writeArray m node dir
                  let node' = op dir (op dir node)
                      nodes' = if used == blank then (node:nodes) else nodes
                  connect nodes' node'
      addWall node = do dir <- readArray m node
                        writeArray m node solid
                        writeArray m (op dir node) solid
  addNodes interior
  found <- solveFromTo m iFrom iTo
  when (not found) (fail "Solution not found")
  return m

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")

rev 1 = 2; rev 2 = 1; rev 3 = 4; rev 4 = 3

solveFromTo m iFrom iTo | iFrom == iTo = writeArray m iTo endAt >> return True
                        | otherwise = do
  writeArray m iFrom startFrom
  writeArray m iTo endAt
  let search point [] = return False
      search point (dir:dirs) = do
        let wall = op dir point
            point' = op dir wall
            dir' = rev dir
        wallValue <- readArray m wall
        if wallValue/=blank
          then search point dirs
          else do writeArray m wall dir'
                  point'Value <- readArray m point'
                  writeArray m point' dir'
                  if point'Value == endAt
                    then return True
                    else do found <- search point' (delete dir' [1..4])
                            if found then return True
                                     else search point dirs
  found <- search iFrom [1..4]
  when found (markSolution m iTo)
  return found

markSolution m iTo = do
  let path point = do
        dir <- readArray m point
        when (dir /= startFrom) $
               do writeArray m point onPath
                  path (op dir point)
  path iTo
  writeArray m iTo endAt