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Haskell Quiz/Amazing Mazes/Solution Kuklewicz

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m (Use Data.Set and pick from Set.toList)
(Add solver, now a complete solution)
Line 15: Line 15:
 
direction taken from that node.
 
direction taken from that node.
   
This can generate and print a 100x100 maze in about 21 seconds on
+
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".
 
1.33GHz G4 powerbook (OS X 10.4.8) using ghc-6.6 and compiling with "-O2".
   
TODO : add a solver
+
-- 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 where
+
module Main (main) where
   
import Control.Monad
+
import Control.Monad(when)
import Control.Monad.ST
+
import Data.Array.ST(runSTUArray,readArray,writeArray,newArray)
import Data.Array.IArray
+
import Data.Array.Unboxed(UArray,(!),bounds,range)
import Data.Array.MArray
+
import Data.List -- (foldl')
import Data.Array.ST
+
import qualified Data.Set as S(fromDistinctAscList,null,size,toList,delete)
import Data.Array.Unboxed
+
import Data.STRef(newSTRef,readSTRef,writeSTRef)
import Data.List(foldl')
+
import System.Environment
import Data.STRef
+
import System.Random(StdGen,newStdGen,randomR)
import Data.Set(Set)
 
import qualified Data.Set as S
 
import System.Environment(getArgs)
 
import System.Random
 
   
 
type Maze = UArray (Int,Int) Int
 
type Maze = UArray (Int,Int) Int
   
buildMaze :: Int -> Int -> StdGen -> Maze
+
main = do
buildMaze height width g = runSTUArray (buildMazeM height width g)
+
[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
+
initMaze (height,width) = do
 
let hwBounds@((hr1,wr1),(hr2,wr2)) = ((0,0),(2*height,2*width))
 
let hwBounds@((hr1,wr1),(hr2,wr2)) = ((0,0),(2*height,2*width))
 
hr = range (hr1,hr2)
 
hr = range (hr1,hr2)
Line 46: Line 46:
 
, [(h,wr2) | h <- init $ hr] ] -- right
 
, [(h,wr2) | h <- init $ hr] ] -- right
 
interior = S.fromDistinctAscList [ (h,w) | h <- [2,4..pred hr2], w <- [2,4..pred wr2] ]
 
interior = S.fromDistinctAscList [ (h,w) | h <- [2,4..pred hr2], w <- [2,4..pred wr2] ]
m <- newArray hwBounds 0
+
m <- newArray hwBounds blank
sequence_ [ writeArray m i 1 | i <- perimeter ]
+
sequence_ [ writeArray m i solid | i <- perimeter ]
 
return (m,interior)
 
return (m,interior)
   
buildMazeM height width g = do
+
buildMazeM hw@(height,width) iFrom iTo g = do
 
gRef <- newSTRef g
 
gRef <- newSTRef g
let rand lu = do (val,g') <- liftM (randomR lu) (readSTRef gRef)
+
(m,interior) <- initMaze hw
  +
let rand lu = do (val,g') <- fmap (randomR lu) (readSTRef gRef)
 
writeSTRef gRef g'
 
writeSTRef gRef g'
 
return val
 
return val
(m,interior) <- initMaze height width
+
addNodes toAdd | S.null toAdd = return ()
let addNodes toAdd | S.null toAdd = return m
 
 
| otherwise = do
 
| otherwise = do
 
i <- rand (0, pred (S.size toAdd))
 
i <- rand (0, pred (S.size toAdd))
Line 63: Line 63:
 
connect nodes node = do
 
connect nodes node = do
 
used <- readArray m node
 
used <- readArray m node
if used > 0
+
if used == solid
then do
+
then do mapM_ addWall nodes
mapM_ addWall nodes
+
return nodes
return nodes
+
else do dir <- rand (1,4)
else do
+
writeArray m node dir
dir <- rand (1,4)
+
let node' = op dir (op dir node)
writeArray m node (negate dir)
+
nodes' = if used == blank then (node:nodes) else nodes
let node' = op dir (op dir node)
+
connect nodes' node'
nodes' = if used == 0 then (node:nodes) else nodes
+
addWall node = do dir <- readArray m node
connect nodes' node'
+
writeArray m node solid
op dir (h,w) = case dir of 1 -> (h-1,w)
+
writeArray m (op dir node) solid
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 interior
 
addNodes interior
+
found <- solveFromTo m iFrom iTo
showMaze :: Maze -> [String]
+
when (not found) (fail "Solution not found")
showMaze m = let ((hr1,wr1),(hr2,wr2)) = bounds m
+
return 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
+
op dir (h,w) = case dir of
[h,w] <- fmap (map read) getArgs
+
1 -> (h-1,w)
putStr . unlines . showMaze . buildMaze h w =<< newStdGen
+
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
  +
if dir == startFrom
  +
then return ()
  +
else do writeArray m point onPath
  +
path (op dir point)
  +
path iTo
  +
writeArray m iTo endAt
 
</haskell>
 
</haskell>

Revision as of 16:06, 9 November 2006

{- 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
        if dir == startFrom
          then return ()
          else do writeArray m point onPath
                  path (op dir point)
  path iTo
  writeArray m iTo endAt