module Exercise01 where

import Test.QuickCheck

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

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

{-H1.1c)-}
myFst :: Integer -> Integer
myFst z = div (div (z + 1) (2 ^ mySnd z) - 1) 2

{-H1.1d)-}
prop_myPair :: Integer -> Integer -> Integer -> Property
prop_myPair x y p = 
        p >= 0 && x >= 0 && y >= 0 ==> myPair (myFst p) (mySnd p) == p && (myFst(myPair x y), mySnd(myPair x y)) == (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-}
decToEo :: Integer -> String
decToEo 1 = "dek"
decToEo 2 = "cent"

milPrefix :: Integer ->String
milPrefix k     | k < 4         = " m"
                | k > 19       = " " ++ decToEo 1
                | otherwise     = " " ++ digitToEo (div k 2)

milToEo :: Integer -> Integer -> String
milToEo k pref  | pref == 0             =""
                | k == 1                = milPrefix k ++ "il"
                | even k                = milPrefix k ++ "iliono" ++ (if pref /= 1 then "j" else "")
                | odd k                 = milPrefix k ++ "iliardo" ++ (if pref /= 1 then "j" else "")



digitToEo2 :: Integer -> Integer -> String                                     
digitToEo2 n k  | mod (div n (10^k)) 10 == 0            = ""
                | k == 0                                = " " ++ digitToEo (mod n 10) 
                | mod (div n (10^k)) 10 == 1            = " " ++ decToEo k
                | otherwise                             = " " ++ digitToEo (mod (div n (10^k)) 10) ++ decToEo k
numberToEoRek :: Integer -> Integer-> String
numberToEoRek n set     | div n 1000 < 1                = [c | str <- [digitToEo2 n k | k <- [2,1,0]] , c <- str]
                        | div n 1000 == 1 && set == 1   = milToEo set (mod (div n 1000) 1000) ++ numberToEoRek (mod n 1000) 0
                        | otherwise                     = numberToEoRek (div n 1000) (set+1) ++ milToEo set (mod (div n 1000) 1000) ++ numberToEoRek (mod n 1000) 0

numberToEo :: Integer -> String
numberToEo 0 = "nul"
numberToEo n = drop 1 (numberToEoRek n 1)
{-TTEW-}