Difference between revisions of "Bowling"
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| − | __TOC__ |
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| − | |||
| − | == The problem == |
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| − | |||
| − | Convert a list of number of pins knocked over by each ball into a final score for a game of ten pin bowling. |
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| − | |||
| − | == Solution by Eric Kidd == |
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| − | |||
| − | [http://www.randomhacks.net/articles/2007/04/28/bowling-in-haskell On his blog]. This is a recursive solution. |
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| − | |||
| − | == Short Solution by Chris Kuklewicz == |
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| − | |||
| − | <haskell> |
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| − | import Control.Monad.State |
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| − | |||
| − | score = sum . evalState (replicateM 10 (State scoreFrame)) |
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| − | where scoreFrame (10:rest@(a:b:_)) = (10+a+b,rest) |
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| − | scoreFrame (x:y:rest) | x+y < 10 = (x+y,rest) |
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| − | | otherwise = (10+head rest,rest) |
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| − | |||
| − | score2 = fst . (!!10) . iterate addFrame . (,) 0 |
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| − | where addFrame (total,10:rest@(a:b:_)) = (total+10+a+b ,rest) |
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| − | addFrame (total,x:y:rest) | x+y < 10 = (total+x+y ,rest) |
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| − | | otherwise = (total+x+y+head rest,rest) |
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| − | </haskell> |
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| − | |||
| − | == Solution by Chris Kuklewicz == |
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| − | |||
| − | Listed here. This has a monad-using parser with inferred type: |
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| − | <haskell>StateT [Int] (Error String) Frame</haskell> |
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| − | The constraint that there are 10 frames is declared by using (replicateM 10). All invalid input lists should be recognized. |
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| − | |||
| − | <haskell> |
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| − | module Bowling(Frame(..),Game(..),toGame,toBalls,score) where |
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| − | |||
| − | import Control.Monad(replicateM,when) |
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| − | import Control.Monad.State(get,put,evalStateT,StateT(..)) |
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| − | import Control.Monad.Error(throwError) |
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| − | import Data.Array.IArray(Array,(!),elems,listArray,inRange) |
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| − | |||
| − | -- | Representation of a finished Game of bowling |
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| − | data Game = Game { gameScore :: Int |
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| − | , tenFrames :: Array Int Frame } |
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| − | deriving (Show,Eq) |
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| − | |||
| − | -- | Compact representation of a Frame from a finished Game |
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| − | data Frame = Normal { frameScore, first, second :: Int} |
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| − | | Spare { frameScore, first :: Int} |
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| − | | Strike { frameScore, next :: Int} |
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| − | deriving (Show,Eq) |
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| − | |||
| − | -- | Convert a list of pins to a final score |
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| − | score :: [Int] -> Int |
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| − | score balls = case toGame balls of |
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| − | Left msg -> error msg |
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| − | Right g -> gameScore g |
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| − | |||
| − | -- | Convert a Game to a list of (list of pins) for each frame |
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| − | toBalls :: Game -> [[Int]] |
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| − | toBalls (Game {tenFrames = frames}) = map decode (elems frames) ++ final |
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| − | where decode (Normal {first=x,second=y}) = [x,y] |
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| − | decode (Spare {first=x}) = [x,10-x] |
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| − | decode (Strike {}) = [10] |
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| − | final = case (frames ! 10) of |
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| − | Normal {} -> [] |
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| − | Spare {frameScore=s} -> [[s-10]] |
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| − | Strike {frameScore=s,next=10} -> [[10],[s-20]] |
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| − | Strike {frameScore=s,next=a} -> [[a,s-a-10]] |
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| − | |||
| − | -- | Try to convert a list of pins to a Game |
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| − | toGame :: [Int] -> Either String Game |
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| − | toGame balls = do |
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| − | frames <- parseFrames balls |
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| − | return $ Game { gameScore = sum (map frameScore frames) |
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| − | , tenFrames = listArray (1,10) frames |
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| − | } |
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| − | |||
| − | -- This will only return an error or a list of precisely 10 frames |
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| − | parseFrames balls = flip evalStateT balls $ do |
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| − | frames <- replicateM 10 (StateT parseFrame) |
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| − | remaining <- get |
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| − | case (last frames,remaining) of |
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| − | (Normal {} , []) -> return frames |
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| − | (Spare {} , _:[]) -> return frames |
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| − | (Strike {} , _:_:[]) -> return frames |
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| − | _ -> err balls "Too many balls" |
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| − | |||
| − | parseFrame balls@(10:rest) = do |
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| − | case rest of |
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| − | (a:b:_) -> do |
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| − | checkBalls [a,b] |
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| − | when ((a /= 10) && (a+b > 10)) $ |
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| − | err balls "More than 10 pins in frame after a strike" |
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| − | return (Strike (10+a+b) a,rest) |
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| − | _ -> err balls "Too few balls after a strike" |
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| − | |||
| − | parseFrame balls@(x:y:rest) = do |
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| − | checkBalls [x,y] |
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| − | case compare (x+y) 10 of |
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| − | GT -> err balls "More than 10 pins in a frame" |
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| − | LT -> return (Normal (x+y) x y,rest) |
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| − | EQ -> case rest of |
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| − | [] -> err balls "No ball after a spare" |
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| − | (a:_) -> do checkBall a |
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| − | return (Spare (10+a) x,rest) |
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| − | |||
| − | parseFrame balls = err balls "Not enough balls" |
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| − | |||
| − | err balls s = throwError (s ++ " : " ++ show (take 23 balls)) |
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| − | checkBalls = mapM_ checkBall |
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| − | checkBall x = when (not (inRange (0,10) x)) |
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| − | (throwError $ "Number of pins is of out range (0,10) : " ++ show x) |
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| − | </haskell> |
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| − | |||
| − | [[Category:Code]] |
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