diff --git a/src/Data/RomanNum.hs b/src/Data/RomanNum.hs index e782317..731da2e 100644 --- a/src/Data/RomanNum.hs +++ b/src/Data/RomanNum.hs @@ -1,14 +1,18 @@ +{-# LANGUAGE GeneralizedNewtypeDeriving #-} module Data.RomanNum ( RomanNum(..) , nullus + , parse , plus , r + , validate ) where import Data.Map (Map, (!)) import qualified Data.Map as Map (fromList) +import Text.Read (readMaybe) -newtype RomanNum = RomanNum Int +newtype RomanNum = RomanNum Int deriving (Eq, Ord, Enum) data RomanChar = I | V | X | L | C | D | M deriving (Bounded, Eq, Ord, Enum, Show, Read) @@ -45,14 +49,53 @@ instance Show RomanNum where times count letter = take count $ repeat letter r :: String -> RomanNum -r "" = nullus -r "nullus" = nullus -r n@[_] = RomanNum (values ! (read n)) -r (digit:nextDigit:otherDigits) = - let (rChar, nextRChar) = (read [digit], read [nextDigit]) in - if rChar < nextRChar - then RomanNum (values ! nextRChar - values ! rChar) `plus` r otherDigits - else RomanNum (values ! rChar) `plus` r(nextDigit:otherDigits) +r = either error id . parse + +validate :: String -> Bool +validate = either (\_ -> False) (\_ -> True) . parse + +readDigit :: Char -> Either String Int +readDigit c = maybe errMsg (Right . (values !)) $ readMaybe [c] + where + errMsg = Left $ "Not a roman digit: «" ++ c:"»" + +log10 :: Int -> Int +log10 n = length (show n) - 1 + +parse :: String -> Either String RomanNum +parse "" = Right nullus +parse "nullus" = Right nullus +parse s = RomanNum <$> + (mapM readDigit s >>= mapM analyzeBlock . romanGroups >>= romanSum) + where + romanGroups [] = [] + romanGroups (x:xs) = + let groups = romanGroups xs in + case groups of + (group@(y:_):otherGroups) + | x <= y -> (x:group):otherGroups + _ -> [x]:groups + + analyzeBlock [n] = Right (log10 n, n) + analyzeBlock l@(n1:n2:ns) + | n1 == 10 ^ p = + if n1 < n2 && 10*n1 >= n2 && null ns + then Right (p, n2 - n1) + else if n1 == n2 && all (== n1) ns && length ns < 2 + then Right (p, (length ns +2)*n1) + else invalidSequence l + where + p = log10 n1 + analyzeBlock l = invalidSequence l + + romanSum [] = Right 0 + romanSum [(_, n)] = Right n + romanSum ((p1, n1):blocks@((p2, n2):otherBlocks)) + | p1 > p2 = (n1+) <$> romanSum blocks + | p1 == p2 && n1 == 5*10^p1 && n2 < n1 = (n1+n2+) <$> romanSum otherBlocks + | otherwise = invalidSequence [n1, n2] + invalidSequence l = + Left $ "Invalid sequence : " ++ concat (show . RomanNum <$> l) nullus :: RomanNum nullus = RomanNum 0