module Exercise01 where

import Test.QuickCheck



{-H1.1a)-}
myPair :: Integer -> Integer -> Integer
myPair x y | x >= 0 && y >= 0 = (2 ^ y) * (2 * x + 1) - 1

{-H1.1b)-}
mySnd :: Integer -> Integer
mySnd x | x >= 0 = mySndHelper (div (x + 1) (2 * myFst x + 1)) 0

-- 2^x, 0 -> x
mySndHelper :: Integer -> Integer -> Integer
mySndHelper x y | x == 1 = y
mySndHelper x y = mySndHelper (div x 2) (y + 1)

{-H1.1c)-}
myFst :: Integer -> Integer
myFst x | x >= 0 = myFstHelper (x + 1)

-- (2^y)(2x+1) -> x
myFstHelper :: Integer -> Integer
myFstHelper x | even x = myFstHelper (div x 2)
myFstHelper x | x > 0 = div (x - 1) 2

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

{-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-}
digitToEoExp :: Integer -> String
digitToEoExp 1 = "m"
digitToEoExp 10 = "dek"
digitToEoExp x = digitToEo x

numberToEo :: Integer -> String
numberToEo 0 = "nul"
numberToEo n =  unwords (filter (/="") [threeDigitToEoExp x (mod (div n (10^(3*x))) 1000) |  x <- reverse [0..21]])

threeDigitToEoExp :: Integer -> Integer -> String
threeDigitToEoExp e 0 = ""
threeDigitToEoExp 0 x = threeDigitToEo x
threeDigitToEoExp 1 x = if x == 1 then "mil" else threeDigitToEo x ++ " mil"
threeDigitToEoExp e x = threeDigitToEo x ++ " " ++ digitToEoExp (div e 2) ++ (if even (mod e 2) then "iliono" else "iliardo") ++ (if x > 1 then "j" else "")

threeDigitToEo :: Integer -> String
threeDigitToEo n | n < 10 = digitToEo n
threeDigitToEo n | n < 100 = (if n >= 20 then digitToEo (div n 10) else "") ++ "dek" ++ (if mod n 10 > 0 then " " ++ threeDigitToEo (mod n 10) else "")
threeDigitToEo n = (if n >= 200 then digitToEo (div n 100) else "") ++ "cent" ++ (if mod n 100 > 0 then " " ++ threeDigitToEo (mod n 100) else "")
{-TTEW-}