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 p
    | even p = 0
    | otherwise = mySnd (p `div` 2) + 1

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

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

numberToEo :: Integer -> String
numberToEo 0 = "nul"
numberToEo n = init $ getString n 0

getString :: Integer -> Integer -> String 
getString 0 _ = ""
getString 1 3 = "mil "
getString x p = getString (x `div` 10) (p + 1) ++ 
    if pm == 0 
        then if xmmm > 0 
            then getDigit 0 " " ++ posToEo (p `div` 3) xmmm 
        else "" 
    else if xm > 0 
        then getDigit 1 "" ++ if pm == 1 then "dek " else "cent "
    else ""
    where
        pm = p `mod` 3
        xm = x `mod` 10
        xmmm = x `mod` 1000
        getDigit n s = if xm > n then digitToEo xm ++ s else ""

posToEo :: Integer -> Integer -> String
posToEo 0 _ = ""
posToEo 1 _ = "mil "
posToEo p x = (if p < 4 then "m" else if p < 20 then digitToEo $ p `div` 2 else "dek") ++ 
    (if even p then "iliono" else "iliardo") ++ 
    if x > 1 then "j " else " "

{-TTEW-}