main = do
    print $ "hello world"
    print $ "Enter some text right in console!"

plus :: Int -> Int -> Int
plus x y = x + y

minus :: Int -> Int -> Int
minus x y = x - y

mult :: Int -> Int -> Int
mult x y = x * y

divs :: Int -> Int -> Int
divs x y = x / y

divs' :: Int -> Int -> Int
divs' x y = div x y

mods :: Int -> Int -> Int
mods x y = mod x y

addThree :: Int -> Int -> Int -> Int
addThree x y z = x + y + z

factorial :: Int -> Int
factorial n = product [1..n]

bigger :: Int -> Int -> Bool
bigger x y = if x > y then x else y

lucky :: Int -> String
lucky 7 = "You got the right number!"
lucky x = "Sorry, you're out of luck!"

sayMe :: Int -> String
sayMe 1 = "One"
sayMe 2 = "Two"
sayMe 3 = "Three"
sayMe 4 = "Four"
sayMe 5 = "Five"
sayMe x = "Not between 1 and 5"

guessTheNumber :: Int -> String
guessTheNumber 10 = "How did you do that? You got it, mate!"
guessTheNumber x = "You are out of luck, sorry!"

factorial' :: Int -> Int
factorial' 0 = 1
factorial' 1 = 1
factorial' n = n * factorial (n-1)

charName :: Char -> String
charName 'a' = "Albert"
charName 'b' = "Broseph"
charName 'c' = "Cercil"

addVectors1 :: (Ord a, Num a) => (a,a) -> (a,a) -> (a,a)
addVectors1 x y = (fst x + fst y, snd x + snd y)

addVectors2 :: (Ord a, Num a) => (a,a) -> (a,a) -> (a,a)
addVectors2 (x1,y1) (x2,y2) = (x1+x2,y1+y2)

first :: (a,b,c) -> a
first (x, _, _) = x

second :: (a,b,c) -> b
second (_, y, _) = y

third :: (a,b,c) -> c
third (_, _, z) = z

head :: [Int] -> Int
head [] = error "Can't call head on empty list, dummy"
head (x:_) = x

-- here we don't care about our first argument

length :: [Int] -> Int
length [] = 0
length (_:xs) = 1 + length xs

-- but here we are interested in our first argument

sum :: [Int] -> Int
sum [] = 0
sum (x:xs) = x + sum xs

bmiTell :: (RealFloat a) => a -> String
bmiTell bmi
    | bmi <= 18.5 = "You are underweight"
    | bmi <= 25.0 = "You are normal weight"
    | bmi <= 30.0 = "You are overweight"
    | otherwise = "If you contunue to eat, you are gonna die"

bmiTell1 :: (RealFloat a) => a -> a -> String
bmiTell1 weight height
    | weight / height ^ 2 <= 18.5 = "You are underweight"
    | weight / height ^ 2 <= 25.0 = "You are normal weight"
    | weight / height ^ 2 <= 30.0 = "You are overweight"
    | otherwise = "You are a whale, congratulations"

bmiTell2 :: (RealFloat a) => a -> a -> String
bmiTell2 weight height
    | bmi <= 18.5 = "You are underweight"
    | bmi <= 25.0 = "You are normal weight"
    | bmi <= 30.0 = "You are overweight"
    | otherwise = "You are a whale, congratulations"
        where
            bmi = weight / height ^ 2

bmiTell3 :: (RealFloat a) => a -> a -> String
bmiTell3 weight height
    | bmi <= skinny = "You are underweight"
    | bmi <= normal = "You are normal weight"
    | bmi <= overweight = "You are overweight"
    | otherwise = "You are a whale, congratulations"

max1 :: Int -> Int -> Int
max1 a b
    | a > b = a
    | otherwise = b

min1 :: Int -> Int -> Int
min1 a b
    | a > b = b
    | otherwise = a

maxThree :: Int -> Int -> Int -> Int
maxThree a b c = if (a > b) && (a > c) then a else if (b > a) && (b > c) then b else c

maxThree1 :: Int -> Int -> Int -> Int
maxThree1 a b c
    | (a > b) && (a > c) = a
    | (b > a) && (b > c) = b
    | otherwise = c

myCompare :: Int -> Int -> String
myCompare a b
    | a > b = "GT"
    | a < b = "LT"
    | otherwise = "EQ"

lastDigit :: Int -> Int
lastDigit n = mod n 10

removeLastDigit :: Int -> Int
removeLastDigit n = div n 10

areNotEqualOneLine :: Int -> Int -> Bool
areNotEqualOneLine a b = a == b

areNotEqualGuards :: Int -> Int -> Bool
areNotEqualGuards a b
    | a == b = True
    | otherwise = False

inside :: Int -> Int -> Int -> Bool
inside a b x
    | (x >= a) && (x <= b) = True
    | otherwise = False

factoriel :: Int -> Int
factoriel 0 = 1
factoriel 1 = 1
factoriel n = n * factoriel (n-1)

factIter :: Int -> Int
factIter n = helper n 1
    where
        helper :: Int -> Int -> Int
        helper 0 result = result
        helper leftOver result = helper (leftOver - 1) (result*leftOver)

fibonacci :: Int -> Int
fibonacci 0 = 0
fibonacci 1 = 1
fibonacci n = fibonacci (n-1) + fibonacci (n-2)

fibIter :: Int -> Int -> Int
fibIter n = helper n 1 0
    where
        helper :: Int -> Int -> Int -> Int
        helper 0 n1 _ = n1
        helper 1 _ n2 = n2
        helper n n1 n2 = helper (n-1) n2 (n2+n1)

-- Recursion 1

reverseInteger :: Int -> Int
reverseInteger n = (mod n 10)*10 + reverseInteger (div n 10)

isPalindrome :: Int -> Bool
isPalindrome n = n == reverseInteger n

sumDigitsRec :: Int -> Int
sumDigitsRec n = mod n 10 + sumDigitsRec (div n 10)

powRec :: Int -> Int -> Int
powRec _ n = 1
powRec x n = x * powRec (n-1)

isPrime :: Int -> Bool
isPrime 1 = False
isPrime 2 = True
isPrime n = n >= 1 && helper 2
    where
        helper :: Int -> Bool
        helper i
            | (fromIntegral i) >= (sqrt $ fromIntegral n) = True
            | mod n i == 0 = False
            | otherwise = helper (i+1)

sumDivs :: Int -> Int
sumDivs n = helper 1
    where
        helper :: Int -> Int
        helper currentDiv
            | currentDiv >= n = n
            | mod n currentDiv == 0 = currentDiv + helper (currentDiv+1)
            | otherwise = helper (currentDiv+1)

isPerfect :: Int -> Bool
isPerfect n = n == sumDivs n

hasIncDigits :: Int -> Bool
hasIncDigits 0 = False
hasIncDigits n = (n < 10) || mod n 10 >= mod (div n 10) 10 && hasIncDigits (div n 10)

-- Recursion 2

numDig :: Int -> Int
numDig n
    | n < 0 = error "n was negative"
    | n < 10 = 1
    | otherwise = 1 + numDig (div n 10)

isNarcisticc :: Int -> Bool
isNarcisticc n = n == helper n (numDig n)
    where
        helper :: Int -> Int -> Int
        helper 0 nd = 0
        helper leftover nd = (mod leftover 10)^nd + helper (div leftover 10) nd

calculateSum :: Int -> Int -> Int
calculateSum x n = helper 0 0
    where
        helper :: Int -> Int -> Int
        helper sumOfDegree degree
            | n <= degree = sumOfDegree + x ^ degree
            | otherwise = helper (sumOfDegree + x ^ degree) (degree+1)

findMax :: Int -> Int
findMax n = helper n 0
    where
        helper :: Int -> Int -> Int
        helper 0 currMax = currMax
        helper num currMax
            | (mod num 10) > currMax = helper (div num 10) (mod num 10)
            | otherwise = helper (div num 10) currMax

sumNumbers :: Int -> Int -> Int
sumNumbers start finish = helper $ min start finish
    where
         helper :: Int -> Int
         helper i
          | i > max start finish = 0
          | hasDecDigits i = i + helper (i+1)
          | otherwise = helper (i+1)

-- actually it is equivalent with hasIncDigits, the only difference is the sign (<=)

hasDecDigits :: Int -> Bool
hasDecDigits n = n < 10 || mod n 10 <= mod (div n 10) 10 && hasDecDigits (div n 10)

subNum :: Int -> Int -> Bool
subNum x y = helper y (10^countDigits x)
    where
        helper :: Int -> Int -> Bool
        helper y dNum
            | x > y = False
            | mod y dNum == x = True
            |otherwise = helper (div y 10) dNum

digitalRoot :: Int -> Int
digitalRoot n
 | n <= 9 = n
 | otherwise = digitalRoot (sumDigits n)

sumDigits :: Int -> Int
sumDigits n
   | div n 10 == 0 = n
   | otherwise = mod n 10 + sumDigits (div n 10)

mySin :: Integer -> Double -> Double
mySin 0 x = x
mySin n x = ((-1)^n * x^(2*n + 1)) / (fromIntegral $ factoriel (2*n + 1)) + mySin (n - 1) x