module Exercise01 where

import Test.QuickCheck ((==>), Property)

{-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 n = mySndHelper (n + 1) 0

mySndHelper :: Integer -> Integer -> Integer
mySndHelper n xCarry
-- count the divisions by two
  | even n = mySndHelper (div n 2) (xCarry + 1)
-- as soon as only the term (2y + 1) is left, the answer is the number of divisions
  | odd n  = xCarry

prop_mySnd :: Integer -> Integer -> Property
prop_mySnd x y = x >= 0 && y >= 0 ==> mySnd (myPair x y) == y

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

myFstHelper :: Integer -> Integer
myFstHelper n
-- when x is greater than 0, the term (2^y)(2x+1) is even
  | even n = myFstHelper (div n 2)
-- as soon as y is 0, the term simplifies to (2x+1) and is odd
  | odd n  = div (n - 1) 2

prop_myFst :: Integer -> Integer -> Property
prop_myFst x y = x >= 0 && y >= 0 ==> myFst (myPair x y) == x

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

--this is the implementation for n < 10^6, it is kept only for verification
numberToEoNaive :: Integer -> String
numberToEoNaive n
  | n < 10    = digitToEo n
  | n == 10   = "dek"
  | n == 100  = "cent"
  | n == 1000 = "mil"
  | n `mod` 1000 == 0 && n < 1000000  = numberToEoNaive (n `div` 1000) ++ " " ++ numberToEoNaive 1000
  | n `mod` 100 == 0 && n < 1000      = numberToEoNaive (n `div` 100) ++ numberToEoNaive 100
  | n `mod` 10 == 0 && n < 100        = numberToEoNaive (n `div` 10) ++ numberToEoNaive 10
  | n < 100     = numberToEoNaive (n - (n `mod` 10)) ++ " " ++ numberToEoNaive (n `mod` 10)
  | n < 1000    = numberToEoNaive (n - (n `mod` 100)) ++ " " ++ numberToEoNaive (n `mod` 100)
  | n < 1000000 = numberToEoNaive (n - (n `mod` 1000)) ++ " " ++ numberToEoNaive (n `mod` 1000)

-- 169 tokens
{-WETT-}
unitBase :: Integer -> String
unitBase 1 = "dek"
unitBase 2 = "cent"
unitBase 3 = "mil"
unitBase unit = (if unit <= 9 then "m" else numberToEo $ div unit 6) ++ if mod unit 6 == 0 then "iliono" else "iliardo"

addUnits :: Integer -> Integer -> String
addUnits 0 _ = ""
addUnits value 0 = digitToEo value
addUnits 1 unit | unit <= 3 = unitBase unit
addUnits value unit = numberToEo value ++ (if unit <= 2 then "" else " ") ++ unitBase unit ++ if value > 1 && unit > 3 then "j" else ""

numberToEoHelper :: Integer -> Integer -> String
numberToEoHelper 0 _ = ""
numberToEoHelper n carriedUnits = unwords $ filter (/= "") [numberToEoHelper (div n divisor) nextCarriedUnits, addUnits (mod n divisor) carriedUnits]
  where nextCarriedUnits = if carriedUnits <= 2 then carriedUnits + 1 else carriedUnits - mod carriedUnits 3 + 3
        divisor = 10 ^ (nextCarriedUnits - carriedUnits)

numberToEo :: Integer -> String
numberToEo n = if n < 10 then digitToEo n else numberToEoHelper n 0
{-TTEW-}