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 p = mySndRec (p + 1) 0

mySndRec p x
  | even p = mySndRec (p `div` 2) x + 1
  | odd p = x

{-H1.1c)-}
myFst :: Integer -> Integer
myFst p = myFstRec (p + 1)

myFstRec p
  | even p = myFstRec (p `div` 2)
  | odd p = (p - 1) `div` 2

{-H1.1d)-}
prop_myPair :: Integer -> Integer -> Integer -> Property
prop_myPair p x y =
  x >= 0 && y >= 0 && p >= 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-}
numberToEo :: Integer -> String
numberToEo 0 = "nul"
numberToEo n = unwords $ numberToEoList n

numberToEoList :: Integer -> [String]
numberToEoList 0 = []
numberToEoList n
  | n < 10 = [digitToEo n]
  | n < 100 = convertSmall n 10 "dek"
  | n < 1000 = convertSmall n 100 "cent"
  | otherwise = convertLarge n

convertSmall :: Integer -> Integer -> String -> [String]
convertSmall n cutoff s = ((if mult > 1 then digitToEo mult else "") ++ s) : numberToEoList rem
  where
    (mult, rem) = n `divMod` cutoff

convertLarge :: Integer -> [String]
convertLarge n =
  (if power > 1 || mult > 1 then numberToEoList mult else []) ++ [s] ++ numberToEoList rem
  where
    power = logThousand n 0
    (mult, rem) = n `divMod` (1000 ^ power)
    s = thousandString power mult

logThousand :: Integer -> Integer -> Integer
logThousand 0 c = pred c
logThousand n c = logThousand (n `div` 1000) $ succ c

expandedDigitTo :: Integer -> String
expandedDigitTo 1 = "m"
expandedDigitTo 10 = "dek"
expandedDigitTo power = digitToEo power

thousandString :: Integer -> Integer -> String
thousandString 1 _ = "mil"
thousandString power 1 = expandedDigitTo (power `div` 2) ++ if even power then "iliono" else "iliardo"
thousandString power _ = thousandString power 1 ++ "j"
{-TTEW-}