Problem:
Score : 300 points

Problem Statement

You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black.
HW characters from A_{11} to A_{HW} represent the colors of the squares.
A_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.

We will repeatedly perform the following operation until all the squares are black:

Every white square that shares a side with a black square, becomes black.

Find the number of operations that will be performed.
The initial grid has at least one black square.

Constraints

1 \leq H,W \leq 1000

A_{ij} is # or ..

The given grid has at least one black square.

Input

Input is given from Standard Input in the following format:

H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}

Output

Print the number of operations that will be performed.

Sample Input 1

3 3
...
.#.
...

Sample Output 1

2

After one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.

Sample Input 2

6 6
..#..#
......
#..#..
......
.#....
....#.

Sample Output 2

3

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

{-# LANGUAGE BangPatterns #-} 

import Control.Monad
import Data.Maybe
import Data.List
import qualified Data.Set as Set
import qualified Data.Array.Unboxed as UA
import qualified Data.Vector as V

import qualified Data.ByteString.Char8 as BS

tuplify2 :: [b] -> (b, b)
tuplify2 (x:y:_) = (x,y)
tuplify2 _ = undefined
readInt :: BS.ByteString -> Integer
readInt = fst . fromJust . BS.readInteger
readIntTuple :: BS.ByteString -> (Integer, Integer)
readIntTuple = tuplify2 . map readInt . BS.words

getIntTuple :: IO (Integer, Integer)
getIntTuple = readIntTuple <$> BS.getLine

getByteStringNList :: (Integral a) => a -> IO [BS.ByteString]
getByteStringNList n = replicateM (fromIntegral n) BS.getLine

type Point = (Integer, Integer)
type Block = UA.UArray Point Bool
toBlock :: Integer -> Integer -> [Bool] -> Block
toBlock h w = UA.array ((1,1), (w,h)) . zip [(m, n) | n <- [1..h], m <- [1..w]]

main = do
    (h, w) <- getIntTuple
    wall <- concatMap ((map (=='#')) . BS.unpack) <$> getByteStringNList h
    let block = toBlock h w wall
    print . solve block $ findWall block 

solve :: Block -> [Point] -> Integer
solve block ps
  | isAllWall block = 0
  | otherwise = 1 + solve nextB nextP
      where (!nextB, !nextP) = nextBlock block ps

nextBlock :: Block -> [Point] -> (Block, [Point])
nextBlock block ps = ((UA.//) block [(p, True) | p <- nextPs], nextPs)
  where nextPs = filter ((not.id).((UA.!) block)) . filter (UA.inRange (UA.bounds block)) . Set.toList . Set.fromList . concatMap walk $ ps

walk :: Point -> [Point]
walk (px, py) = [(px+dx, py+dy) | (dx,dy) <- [(1,0),(0,1),(-1,0),(0,-1)]]

findWall :: Block -> [Point]
findWall = map fst . filter snd . UA.assocs

isAllWall :: Block -> Bool
isAllWall = all id . UA.elems