import Data.List (sort)

--------------------
-- Exercise 1
--------------------
data Car = Car
 { model :: Model
 , make :: Make
 , year :: Integer
 , color :: Color
 , power :: Horsepower
 } deriving (Show, Eq, Ord)

----------
-- a)
----------

newtype Model = Model String
    deriving (Show, Eq, Ord)

newtype Make = Make String
    deriving (Show, Eq, Ord)

data Color = RGB
    { r :: Integer
    , g :: Integer
    , b :: Integer
    } deriving (Show, Eq, Ord)

type Horsepower = Integer

----------
-- b)
----------
ford = Car {
    make = Make "Ford",
    model = Model "Fiesta",
    color = RGB {
        r = 0xFF,
        g = 0x00,
        b = 0x00
    },
    power = 70,
    year = 2017
}

ferrari = Car {
    make = Make "Ferrari",
    model = Model "Testarossa",
    color = RGB 0x00 0xFF 0x00,
    power = 27,
    year = 1991
}

zoe = Car {
    make = Make "Renault",
    model = Model "Zoe",
    color = RGB 0xFF 0xFF 0xFF,
    power = 70,
    year = 2023
}

sorted = sort [zoe, ferrari, ford]
-- >>> sorted
-- [Car {model = Model "Fiesta", make = Make "Ford", year = 2017, color = RGB {r = 255, g = 0, b = 0}, power = 70},Car {model = Model "Testarossa", make = Make "Ferrari", year = 1991, color = RGB {r = 0, g = 255, b = 0}, power = 27},Car {model = Model "Zoe", make = Make "Renault", year = 2023, color = RGB {r = 255, g = 255, b = 255}, power = 70}]

--------------------
-- Exercise 2
--------------------
data Tree a
    = Node (Tree a) a (Tree a)
    | Leaf a

----------
-- a)
----------
collect :: Tree a -> [a]
collect x =
    case x of
        Node a b c -> [b] ++ concat (map collect [a, c])
        Leaf a -> [a]

----------
-- b)
----------
data PolyTree a =
    PolyTree a [PolyTree a]
    deriving (Show)

----------
-- c)
----------
tree =
    PolyTree 1 [
        PolyTree 2 [
            PolyTree 5 [],
            PolyTree 6 [],
            PolyTree 7 []
        ],
        PolyTree 3 [
            PolyTree 8 []
        ]
    ]

-- >>> show tree
-- "PolyTree 1 [PolyTree 2 [PolyTree 5 [],PolyTree 6 [],PolyTree 7 []],PolyTree 3 [PolyTree 8 []]]"

--------------------
-- Exercise 3
--------------------
data NatNumber =
    Z
    | S NatNumber
    deriving (Show)

eval :: NatNumber -> Integer
eval x =
    case x of
        Z -> 0
        S a -> 1 + eval a

-- >>> Z
-- Z
-- >>> eval (S (S (S Z)))
-- 3

uneval :: Integer -> NatNumber
uneval x
    | x < 0 = error "negative numbers are not natural numbers"
    | x == 0 = Z
    | otherwise = S (uneval (x - 1))

-- >>> uneval (-1)
-- negative numbers are not natural numbers
-- >>> uneval 0
-- Z
-- >>> uneval 1
-- S Z
-- >>> uneval 3
-- S (S (S Z))

addNat :: NatNumber -> NatNumber -> NatNumber
addNat a b =
    case (a, b) of
        (Z, b) -> b
        (S a, b) -> S (addNat a b)

-- >>> eval (addNat (uneval 7) (uneval 2))
-- 9

mulNat :: NatNumber -> NatNumber -> NatNumber
mulNat a b =
    case (a, b) of
        (Z, b) -> Z
        (S a, b) -> addNat (mulNat a b) b

-- >>> eval (mulNat (uneval 3) (uneval 2))
-- 6

fact :: NatNumber -> NatNumber
fact x =
    case x of
        Z -> S Z
        S a -> mulNat (S a) (fact a)

-- >>> eval (fact Z)
-- 1
-- >>> eval (fact (S (S Z)))
-- 2

--------------------
-- Exercise 3
--------------------
type Program = [(Integer, Integer)]
type Input = Integer
type Output = [Integer]

execute :: Program -> Input -> Output
execute program input =
    reverse (internal program input [])
    where
        internal :: Program -> Input -> Output -> Output
        internal [] input output = input:output

        internal ((a,b):coefficients) input output
            | mod (input * a) b == 0 =
                internal program (div (input * a) b) (input:output)
            | otherwise = internal coefficients input output

fibProgram :: Program
fibProgram =
    [ (91,33)
    , (11,13)
    , (1,11)
    , (399,34)
    , (17,19)
    , (1,17)
    , (2,7)
    , (187,5)
    , (1,3)
    ]

-- Should evaluate to True
-- >>> sum (execute fibProgram 31250) == 26183978971946924
-- True