My Haskell TronBot for the Google AI Challenge

My bot turned out to be the top scoring Haskell bot, so here's the code
Published on March 1, 2010 under the tag haskell

This is the code for my entry in the Google AI Challenge 2010. It turned out to be the best Belgian and the best Haskell bot (screenshot), so I thought some people might be interested in the code. Luckily, I have been writing this bot in Literate Haskell since the beginning, for a few reasons:

module Main where

This is the actual code of my bot, as submitted in the contest. The only changes made after the deadline are:

Anyway, some disclaimers.

Disclaimer 1: This is quite a large source file/blogpost. If you’re not interested at all, this could be a boring read.

Disclaimer 2: This code is unfinished. There are some situations in which this bot will make very bad decisions. Possibly, there are situations that can crash him, which leads us to disclaimer 3.

Disclaimer 3: I cannot be held responsible if my bot initiates a nuclear attack in an attempt to wipe out the human race.

Before we begin, our Bot uses three important strategies:

We start, as always, by importing the needed modules.

import System.Time
import System.IO
import Control.Monad
import Control.Applicative ((<$>))
import Data.Ord (comparing)
import Data.List (transpose, nub, sortBy)
import qualified Data.Set as S
import Data.Set (Set, (\\))
import qualified Data.Array.Unboxed as UA
import Data.Array.Unboxed ((!))
import Control.Concurrent
import Data.Maybe (fromJust, isNothing, isJust, listToMaybe)

To represent Tiles – positions on the 2D grid – we use a simple tuple.

type Tile = (Int, Int)

Because of this, we can write a very concise function to find the adjacent tiles. As you can see, I inline this function here to avoid some overheads. I use this on several places throughout the code.

adjacentTiles :: Tile -> [Tile]
adjacentTiles (x, y) = [ (x, y - 1)
                       , (x + 1, y)
                       , (x, y + 1)
                       , (x - 1, y)
                       ]
{-# INLINE adjacentTiles #-}

There’s a simple formula for calculating the Pythagorean distance between tiles. We use this in combination with the “real” distance (the distance when taking walls etc. into account). We can leave this distance squared, not taking the sqrt is a little faster, and we only have to compare distances, and x^2 < y^2 implies x < y, because distances are always non-negative.

distanceSquared :: Tile -> Tile -> Int
distanceSquared (x1, y1) (x2, y2) = (x1 - x2) ^ 2 + (y1 - y2) ^ 2

Now, we need a data structure for the board.

data BoardBase = BoardBase { baseWidth         :: Int
                           , baseHeight        :: Int
                           , baseWalls         :: UA.UArray Tile Bool
                           , baseBotPosition   :: Tile
                           , baseEnemyPosition :: Tile
                           } deriving (Show)

However, we also want a board structure that can be adjusted very quickly. We will therefore wrap the BoardBase in another structure, capable of making a few quick adjustments.

This Board will be used to consider “possible” moves. When we make a move on this Board type, we just have to add a wall to the Set, and an element to the list of positions.

data Board = Board { boardBase              :: BoardBase
                   , boardAdditionalWalls   :: Set Tile
                   , boardBotPositionList   :: [Tile]
                   , boardEnemyPositionList :: [Tile]
                   } deriving (Show)

We can create a Board from a BoardBase very quickly.

boardFromBase :: BoardBase -> Board
boardFromBase base = Board { boardBase = base
                           , boardAdditionalWalls = S.empty
                           , boardBotPositionList = [baseBotPosition base]
                           , boardEnemyPositionList = [baseEnemyPosition base]
                           }

Now, let’s define some easy functions we can apply on a Board. The positions of the bot and the enemy are determined by the last move added to their list of moves.

boardBotPosition :: Board -> Tile
boardBotPosition = head . boardBotPositionList
{-# INLINE boardBotPosition #-}
boardEnemyPosition :: Board -> Tile
boardEnemyPosition = head . boardEnemyPositionList
{-# INLINE boardEnemyPosition #-}

Later on, we will construct “possible” next Boards. Given such a Board, we want to determine the first move our Bot made, since that would be the move our AI will choose. This might give no result, so we wrap it in a Maybe type.

boardBotMove :: Board -> Maybe Tile
boardBotMove = listToMaybe . tail . reverse . boardBotPositionList

Checking if a certain tile is a wall is quite simple – but we need to remember we also have to check the additional walls in the Board. We first check for boundaries to prevent errors, then we check in the walls first, because Array access is faster than Set access here. Also, we really want to inline this function, because it is called over 9000 times.

isWall :: Board -> Tile -> Bool
isWall board tile@(x, y) =  x < 0 || x >= baseWidth base
                         || y < 0 || y >= baseHeight base
                         || (baseWalls base) ! tile
                         || tile `S.member` boardAdditionalWalls board
  where
    base = boardBase board
{-# INLINE isWall #-}

What now follows is the function with which we read the Board from a number of lines. This is quite boring code, so you can safely skip it.

readBoard :: Int -> Int -> [String] -> Board
readBoard width height lines' = boardFromBase
    BoardBase { baseWidth         = width
              , baseHeight        = height
              , baseWalls         = walls
              , baseBotPosition   = find '1'
              , baseEnemyPosition = find '2'
              }
  where
    string = concat $ transpose $ map (take width) lines'
    matrix = UA.listArray ((0, 0), (width - 1, height - 1)) string
    walls = UA.amap (== '#') matrix
    find c = head [ i | i <- UA.indices matrix, matrix ! i == c ]

Although we do not use the next function in the AI, it is quite handy for testing reasons, when playing around with ghci.

readBoardFromFile :: FilePath -> IO Board
readBoardFromFile file = do
    h <- openFile file ReadMode
    line <- hGetLine h
    let [width, height] = map read $ words line
    contents <- hGetContents h
    return $ readBoard width height (lines contents)

Next is a function to inspect the entire Board, to determine it’s value later on. It uses a flood fill based approach.

It starts one flood fill starting from the enemy, and one starting from our bot. This determines the space left for each combatant. Also, when the two flood meet, we have found a path between them. This double flood fill is illustrated here in this animation:

Flood fill illustration

The function returns:

inspectBoard :: Board -> (Int, Int, Maybe Int)
inspectBoard board =
    floodFill (S.singleton botPosition, S.singleton enemyPosition)
              S.empty (0, 0) 0 Nothing
  where
    botPosition = boardBotPosition board
    enemyPosition = boardEnemyPosition board

Because we have to make all decisions in under one second, we have a depth limit for our flood fill. When this limit is reached, the result will be the same as if we encountered walls in all directions.

    maxDepth = 25

This is a small auxiliary function that extends isWall with the enemy and bot positions - we do not want to fill any of those two positions.

    isBlocked tile = isWall board tile
                   || tile == botPosition
                   || tile == enemyPosition

This is the main queue-based flood fill function. It’s arguments are:

It works in a fairly straightforward recursive way.

    floodFill :: (Set Tile, Set Tile) -> Set Tile
              -> (Int, Int) -> Int -> Maybe Int -> (Int, Int, Maybe Int)
    floodFill (neighbours1, neighbours2) set
              (fill1, fill2) currentDepth currentDistance

If we reached our search limit, or we have no more tiles to inspect, we just return what we currently have.

        | (S.null neighbours1 && S.null neighbours2)
            || maxDepth <= currentDepth = (fill1, fill2, currentDistance)

Otherwise, we expand our search.

        | otherwise =
            floodFill (validNext1, validNext2) newSet
                      (fill1 + S.size validNext1, fill2 + S.size validNext2)
                      (currentDepth + 1) distance
      where

The next tiles to add are those adjacent to the current neighbours of the flood.

        getNext = S.filter (not . isBlocked) . S.fromList
                . concatMap adjacentTiles . S.toList

        next1 = getNext neighbours1
        next2 = getNext neighbours2

If the enemy is in the next set of neighbours, we have found our distance. If there is no intersection at all, we haven’t reached the enemy yet. We have to do a little trickery here, because the distance could be even or odd.

        odd' = if S.null (next1 `S.intersection` next2)
                   then Nothing
                   else Just (2 * currentDepth + 1)
        even' = if S.null (next1 `S.intersection` neighbours2) &&
                   S.null (next2 `S.intersection` neighbours1)
                    then Nothing
                    else Just (2 * currentDepth)
        distance = currentDistance `mplus` odd' `mplus` even'

Now, we enlarge our Set of already added tiles and remove them from the next tiles to add (since they are already added). We also filter out the non-accessible Tiles, and we make sure no Tiles appear in both validNext1 and validNext2.

        newSet = set `S.union` neighbours1 `S.union` neighbours2
        validNext1 = next1 \\ newSet
        validNext2 = next2 \\ newSet

The algorithm needs to be able to determine the “best” choice in some way or another. So we need to be able compare two games. To make this easier, we can assign a Score to a game - and we then make these Scores comparable.

data Score = Win
           | Loss
           | Draw

In theory, these are the only possible outcomes. In reality, these values are often situated at the bottom of our game tree – and we can’t look down all the way. Therefore, we also have a Game score – describing a game in progress.

The Game constructor simply holds some fields so we can determine it’s value:

           | Game Int Int (Maybe Int) Int Int
           deriving (Eq, Show)

To choose the best game, we need a way to compare games. That’s why we implement the Ord class. A win is always the best, and a loss is always the worse.

instance Ord Score where
    Win  <= _    = False
    Loss <= _    = True

We only see a draw as worse if our bot would have less space otherwise. This is a quite pessimistic view, but well, we can’t risk too much.

    Draw <= (Game botSpace enemySpace _ _ _) =
         botSpace >= enemySpace

Comparing two games is harder, since we have to make “guesses” here.

    (Game bs1 es1 ds1 aw1 pd1) <= (Game bs2 es2 ds2 aw2 pd2)

When there is a space difference: choose direction with most free space.

        | sp1 /= sp2 = sp1 <= sp2

When the enemy is not reachable: choose direction with most adjacent walls, as this fills our space quite efficiently.

        | isNothing ds1 && isNothing ds2 = aw1 <= aw2

When the enemy is reachable from both situations, we choose smallest distance. First we try the “real” distance, then the Pythagorean distance.

        | isJust ds1 && isJust ds2 =
            if ds1 /= ds2 then fromJust ds1 >= fromJust ds2
                          else pd1 >= pd2

Now, there are some edge cases left. We prefer to create situations were we “lock up” the other bot, but only if it means we have more space than the other bot.

        | isJust ds1 && isNothing ds2 = bs2 >= es2
        | isNothing ds1 && isJust ds2 = bs1 >= es1
      where

The free space mentioned is determined as the bot space minus the enemy space.

        sp1 = bs1 - es1
        sp2 = bs2 - es2

We’re not going to write everything twice, so if pattern matching failed, try the other way around:

    a <= b = b >= a

Okay, when building our game tree, we need to find out if a certain node in the Alpha-Beta tree is a leaf. A leaf means the game ends - so there’s either a collision, or a draw.

gameIsLeaf :: Board -> Bool
gameIsLeaf board =  botPosition == enemyPosition
                 || isWall board botPosition
                 || isWall board enemyPosition
  where
    botPosition = boardBotPosition board
    enemyPosition = boardEnemyPosition board

If the game is a leaf, the value is trivial to determine:

gameLeafValue :: Board -> Score
gameLeafValue board
    | botPosition == enemyPosition = Draw
    | botCrashed && enemyCrashed   = Draw
    | botCrashed                   = Loss
    | enemyCrashed                 = Win
    | otherwise                    = error "Not a leaf node."
  where
    botPosition = boardBotPosition board
    enemyPosition = boardEnemyPosition board
    botCrashed = isWall board botPosition
    enemyCrashed = isWall board enemyPosition

If the game is not a leaf, we have to make an estimate of the value. This is basically just calling some functions to fill in the fields of the Game constructor of Score.

gameNodeValue :: Board -> Score
gameNodeValue board =
    Game botSpace enemySpace distance numberOfAdjacentWalls distanceSquared'
  where
    botPosition = boardBotPosition board
    enemyPosition = boardEnemyPosition board

    distanceSquared' = distanceSquared botPosition enemyPosition

    allAdjacent = nub $ adjacentTiles =<< boardBotPositionList board
    numberOfAdjacentWalls = length (filter (isWall board) allAdjacent)

    (botSpace, enemySpace, distance) = inspectBoard board

Now, we have a function to create the child values of a node in the game tree. This function creates 4 new boards, with all the directions the bot (or the enemy, if isBot is False) can move to.

gameNodeChildren :: Board -> Bool -> [Board]
gameNodeChildren board isBot = do
    adjacent <- adjacentTiles position
    if isBot
        then return board
            { boardAdditionalWalls   = walls
            , boardBotPositionList   = adjacent : botPositionList
            , boardEnemyPositionList = enemyPositionList
            }
        else return board
            { boardAdditionalWalls   = walls
            , boardBotPositionList   = botPositionList
            , boardEnemyPositionList = adjacent : enemyPositionList
            }
  where
    position = (if isBot then boardBotPosition else boardEnemyPosition) board
    walls = position `S.insert` boardAdditionalWalls board

    botPositionList = boardBotPositionList board
    enemyPositionList = boardEnemyPositionList board

We now have our main minimax search function. The maxDepth argument gives us a depth limit for our search, and also indicates if it’s our turn or the enemy’s turn (it’s our turn when it’s even, enemy’s turn when it’s odd).

The contact argument tells us if there is a way for our bot to reach the enemy. If the enemy cannot be reached, we do not have to consider it’s turns, sparing us some valuable resources.

This function uses a simple form of (deep) Alpha-beta pruning. I’m pretty sure botSearch and enemySearch could be written as one more abstract function, but I think it’s pretty clear now, too.

For one unfamiliar with minimax trees or Alpha-beta pruning, this function simply returns the possible Board with the best Score.

searchGameTree :: Board -> Int -> Bool -> (Score, Score) -> (Board, Score)
searchGameTree parent maxDepth contact (lower, upper)
    | gameIsLeaf parent && isBot = (parent, gameLeafValue parent)
    | maxDepth <= 0 = (parent, gameNodeValue parent)
    | otherwise =
         if isBot then botSearch children (lower, upper) parent
                  else enemySearch children (lower, upper) parent
  where
    isBot = maxDepth `mod` 2 == 0
    children = gameNodeChildren parent isBot

    botSearch [] (l, _) current = (current, l)
    botSearch (x : xs) (l, u) current =
        let newDepth = if contact then maxDepth - 1 else maxDepth - 2
            (board, value) = searchGameTree x newDepth contact (l, u)
        in if value >= u
               then (board, value)
               else if value > l then botSearch xs (value, u) board
                                 else botSearch xs (l, u) current

    enemySearch [] (_, u) current = (current, u)
    enemySearch (x : xs) (l, u) current =
        let (board, value) = searchGameTree x (maxDepth - 1) contact (l, u)
        in if value <= l
                then (board, value)
                else if value < u then enemySearch xs (l, value) board
                                  else enemySearch xs (l, u) current

First, we want to make a quick (but stupid) decision, in case we’re on a very slow processor or if we don’t get a lot of CPU ticks. The following function does that, providing a simple “Chaser” approach.

simpleDecision :: Board -> Tile
simpleDecision board

In case we really have no valid options, we just go north.

    | null valid = head directions

If there are some non-wall options, we pick the first one in the list, which will conveniently be the Tile closest to the enemy.

    | otherwise = head valid
  where

We take the adjacentTiles of the botPosition, and sort them according to distance to the enemy. That way, we get our “Chaser” behaviour.

    botPosition = boardBotPosition board
    directions = sortBy (comparing distance) $ adjacentTiles botPosition
    valid = filter (not . isWall board) directions
    distance = distanceSquared (boardEnemyPosition board)

The next function performs one turn, meaning:

takeTurn :: IO ()
takeTurn = do

The first line tells us the board dimensions. We then take the next height lines and read the board from it.

    [width, height] <- (map read . words) <$> getLine
    board <- readBoard width height <$> replicateM height getLine

We have an MVar to hold our decision. We begin by filling it by something simple and then improve that simple result in another thread.

    mvar <- newMVar $ simpleDecision board
    calculationThread <- forkIO $ makeMinMaxDecision board mvar

We wait 900 ms. After that time has passed, our MVar should contain a reasonably smart decision. We take it and finish off our calculation thread.

    threadDelay $ 900 * 1000
    result <- takeMVar mvar
    killThread calculationThread

Now, all that is left is printing the direction our AI made.

    putStrLn $ tileToDirection board result
  where

This is the function that is executed in another thread. It simply tries to calculate a smart decision using minMaxDecision and then puts it in the MVar. We also do a simple inspectBoard to determine if there is a path between us and the enemy.

It also uses a form of iterative deepening; first, the best decision for depth 2 is calculated. Then, we try to find the best decision for depth 4, then 6, and so on. Tests seemed to show that it usually gets to depth 8 or 10 before it is killed.

    makeMinMaxDecision board mvar = makeMinMaxDecision' 2
      where
        (_, _, distance) = inspectBoard board
        contact = isJust distance

        makeMinMaxDecision' depth = do
            let (best, _) = searchGameTree board depth contact (Loss, Win)
                move = boardBotMove best
            when (isJust move) $ swapMVar mvar (fromJust move) >> return ()
            makeMinMaxDecision' $ depth + 2

We need to determine the direction of a tile from it’s coordinates, because the game engine is expecting a direction - and we only have a Tile.

    tileToDirection board position
        | position == (x, y - 1) = "1"
        | position == (x + 1, y) = "2"
        | position == (x, y + 1) = "3"
        | position == (x - 1, y) = "4"
        | otherwise              = "Error: unknown move."
      where
        (x, y) = boardBotPosition board

Our main function must set the correct buffering options and then loop forever. At this point, it’s very cool we have a stateless bot, since we can now just forever takeTurn.

main :: IO ()
main = do
    hSetBuffering stdin LineBuffering
    hSetBuffering stdout LineBuffering
    forever takeTurn

An auxiliary function to help timing. We only take the seconds and the picoseconds into account, because when we’re taking more than minutes, well, we’re fucked anyway.

toMs :: ClockTime -> ClockTime -> Int
toMs t1 t2 = let d = diffClockTimes t2 t1
             in tdSec d * 1000 + fromIntegral (tdPicosec d `div` 1000000000)

That’s it. As always, all criticism and questions are welcome. By the way, you can find the .lhs file here.

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