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 = if even p then 0 else 1 + mySnd (div p  2)

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

{-H1.1d)-}
prop_myPair :: Integer -> Integer -> Integer -> Property
prop_myPair p x y = p >=0 && 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-}
eoInfix :: Integer -> String
eoInfix 1 = " mil"
eoInfix 2 = " miliono"
eoInfix 3 = " miliardo"
eoInfix 20 = " dekiliono"
eoInfix 21 = " dekiliardo"
eoInfix n = " " ++ digitToEo (div n 2) ++ if even n then "iliono" else "iliardo"

numberToEo :: Integer -> String
numberToEo n = numberToEoHelper n 1

numberToEoHelper :: Integer -> Integer -> String
numberToEoHelper 0 1 = "nul"
numberToEoHelper n k 
 | beginning == 0 = numberToEoLessThan1000 rest
 | beginning == 1 && k == 1 = "mil" ++ lastThreeDigits
 | mod beginning 1000 == 0 = numberToEoHelper beginning (k + 1) ++ lastThreeDigits
 | otherwise = numberToEoHelper beginning (k + 1) ++ eoInfix k ++ j ++ lastThreeDigits
      where beginning = div n 1000
            rest = mod n 1000
            lastThreeDigits = if rest == 0 then "" else " " ++ numberToEoLessThan1000 rest
            j = if k > 1 && mod beginning 1000 > 1 then "j" else ""

numberToEoLessThan1000 :: Integer -> String
numberToEoLessThan1000 n 
 | n == 0 = ""
 | n < 10 = digitToEo n
 | otherwise = if d == 1 then suffix else digitToEo d ++ suffix
 where l = if n < 100 then 10 else 100
       d = div n l
       rest = mod n l
       space = if rest == 0 then "" else " "
       suffix = (if l == 10 then "dek" else "cent") ++ space ++ numberToEoLessThan1000 rest


{-TTEW-}