# Bowling

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## 1 The problem

Convert a list of number of pins knocked over by each ball into a final score for a game of ten pin bowling.

## 2 Solution by Eric Kidd

On his blog. This is a recursive solution.

## 3 Short Solution by Chris Kuklewicz

```import Control.Monad.State

score = sum . evalState (replicateM 10 (State scoreFrame))
where scoreFrame (10:rest@(a:b:_)) = (10+a+b,rest)
scoreFrame (x:y:rest) | x+y < 10 = (x+y,rest)
| otherwise = (10+head rest,rest)

score2 = fst . (!!10) . iterate addFrame . (,) 0
where addFrame (total,10:rest@(a:b:_))      = (total+10+a+b       ,rest)
addFrame (total,x:y:rest) | x+y < 10  = (total+x+y          ,rest)
| otherwise = (total+x+y+head rest,rest)```

## 4 Solution by Chris Kuklewicz

Listed here. This has a monad-using parser with inferred type:

`StateT [Int] (Error String) Frame`

The constraint that there are 10 frames is declared by using (replicateM 10). All invalid input lists should be recognized.

```module Bowling(Frame(..),Game(..),toGame,toBalls,score) where

import Control.Monad(replicateM,when)
import Control.Monad.State(get,put,evalStateT,StateT(..))
import Control.Monad.Error(throwError)
import Data.Array.IArray(Array,(!),elems,listArray,inRange)

-- | Representation of a finished Game of bowling
data Game = Game { gameScore :: Int
, tenFrames :: Array Int Frame }
deriving (Show,Eq)

-- | Compact representation of a Frame from a finished Game
data Frame = Normal { frameScore, first, second :: Int}
| Spare  { frameScore, first :: Int}
| Strike { frameScore, next :: Int}
deriving (Show,Eq)

-- | Convert a list of pins to a final score
score :: [Int] -> Int
score balls = case toGame balls of
Left msg -> error msg
Right g -> gameScore g

-- | Convert a Game to a list of (list of pins) for each frame
toBalls :: Game -> [[Int]]
toBalls (Game {tenFrames = frames}) = foldr (:) final (map decode (elems frames))
where decode (Normal {first=x,second=y}) = [x,y]
decode (Spare {first=x}) = [x,10-x]
decode (Strike {}) = [10]
final = case (frames ! 10) of
Normal {} -> []
Spare {frameScore=s} -> [[s-10]]
Strike {frameScore=s,next=10} -> [[10],[s-20]]
Strike {frameScore=s,next=a} -> [[a,s-a-10]]

-- | Try to convert a list of pins to a Game
toGame :: [Int] -> Either String Game
toGame balls = do
frames <- parseFrames balls
return \$ Game { gameScore = sum (map frameScore frames)
, tenFrames = listArray (1,10) frames
}

-- This will only return an error or a list of precisely 10 frames
parseFrames balls = flip evalStateT balls \$ do
frames <- replicateM 10 (StateT parseFrame)
remaining <- get
case (last frames,remaining) of
(Normal {} , []) -> return frames
(Spare {}  , _:[]) -> return frames
(Strike {} , _:_:[]) -> return frames
_ -> err balls "Too many balls"

parseFrame balls@(10:rest) = do
case rest of
(a:b:_) -> do
checkBalls [a,b]
when ((a /= 10) && (a+b > 10)) \$
err balls "More than 10 pins in frame after a strike"
return (Strike (10+a+b) a,rest)
_ -> err balls "Too few balls after a strike"

parseFrame balls@(x:y:rest) = do
checkBalls [x,y]
case compare (x+y) 10 of
GT -> err balls "More than 10 pins in a frame"
LT -> return (Normal (x+y) x y,rest)
EQ -> case rest of
[] -> err balls "No ball after a spare"
(a:_) -> do checkBall a
return (Spare (10+a) x,rest)

parseFrame balls = err balls "Not enough balls"

err balls s = throwError (s ++ " : " ++ show (take 23 balls))
checkBalls = mapM_ checkBall
checkBall x = when (not (inRange (0,10) x))
(throwError \$ "Number of pins is of out range (0,10) : " ++ show x)```