module Exercise01 where

import Test.QuickCheck
import Data.List

{-H1.1a)-}
myPair :: Integer -> Integer -> Integer
myPair x y = (2^y) * (2*x + 1) -1

{-H1.1b)-}
mySnd :: Integer -> Integer
mySnd pair = mySnd' (pair+1) 0 where 
    mySnd' pair y
        | even pair = mySnd' (div pair 2) (y+1)
        | otherwise = y 

{-H1.1c)-}
myFst :: Integer -> Integer
myFst pair = myFst' (pair+1) where 
    myFst' pair
        | even pair = myFst' (div pair 2)
        | otherwise = div (pair - 1) 2 

{-H1.1d)-}
prop_myPair :: Integer -> Integer -> Integer -> Property
prop_myPair p x y = x>=0 && y >= 0 ==> p == myPair x y 

{-H2-}
digitToEo :: Integer -> String
digitToEo 0 = "nul"
digitToEo 1 = "unu"
digitToEo 2 = "du"
digitToEo 3 = "tri"
digitToEo 4 = "kvar"
digitToEo 5 = "kvin"
digitToEo 6 = "ses"
digitToEo 7 = "sep"
digitToEo 8 = "ok"
digitToEo 9 = "nau"

{-WETT-}
--split the number into digits and feed the reverse to listToString, the concatenate the words
numberToEo :: Integer  -> [Char]
numberToEo 0 = "nul" --handle special case
numberToEo num = unwords . listToString 0 . reverse $ read . return <$> show num

--handle a list of digits three at a time
listToString :: Integer -> [Integer] -> [[Char]]
listToString _ [] = mempty -- no digits -> no words
listToString 1 (1:0:0:xs) = listToString 2 xs ++ pure "mil" -- special case: only write mil instead of unu mil
listToString ending (a:b:c:xs) =  succ ending `listToString` xs ++ withEndingToString c "cent" ++  withEndingToString b "dek" ++ withEndingToString a "" ++ endingToString ending (a+2* ( b+c))
listToString ending xs = listToString ending $ xs ++ pure 0 -- fill with 0 if no triple left

endingToString :: Integer -> Integer -> [[Char]]
endingToString 0 _ = mempty -- keine endung bei 1
endingToString _ 0 = mempty -- keine Endung wenn alle 0
endingToString num 1 =  pure $ words "ignore mil miliono miliardo duiliono duiliardo triiliono triiliardo kvariliono kvariliardo kviniliono kviniliardo sesiliono sesiliardo sepiliono sepiliardo okiliono okiliardo nauiliono nauiliardo dekiliono dekiliardo" `genericIndex` num
endingToString num _ =  pure $ words "ignore mil milionoj miliardoj duilionoj duiliardoj triilionoj triiliardoj kvarilionoj kvariliardoj kvinilionoj kviniliardoj sesilionoj sesiliardoj sepilionoj sepiliardoj okilionoj okiliardoj nauilionoj nauiliardoj dekilionoj dekiliardoj"`genericIndex` num

withEndingToString :: Integer -> [Char] -> [[Char]]
withEndingToString 0  _ = mempty -- digit zero -> no word
withEndingToString 1 "" = pure "unu" -- special case 1 in einerstelle
withEndingToString 1 ending = pure ending -- specialcase 1 keine zahl, nur endung
withEndingToString number ending =  pure $ digitToEo number <> ending 

{-TTEW-}

generateEnding num = (if num <= 3 then "m" else numberToEo $ div num 2) ++ if even num then "iliono" else  "iliardo"
allEndings :: String
allEndings = unwords $ map generateEnding [2..21]
generateEndingPlural num = generateEnding num ++ "j"
allEndingsPlural :: String
allEndingsPlural = unwords $ map generateEndingPlural [2..21]