-- Ex1

mymin :: Int -> Int -> Int
mymin a b = if a < b then a
                     else b

-- Ex2

isInside :: Int -> Int -> Int -> Bool
isInside x a b = a <= x && x <= b

-- Ex3

myfunc :: Double -> Double -> Double
myfunc a b = ((sqrt a) + (sqrt b)) / 2

-- Ex4

myfib :: Int -> Int
myfib n = if n == 1 then 0
                    else if n == 2 then 1
                                   else myfib (n - 1) + myfib (n - 2)

-- Ex5

mygcd :: Int -> Int -> Int
mygcd a b = if b == 0 then a
                      else mygcd b (mod a b)

-- Ex6

mymindivisor :: Int -> Int -> Int
mymindivisor x start = if (rem x start) == 0 then start
                                             else mymindivisor x (start + 1)

mymaxdivisor :: Int -> Double
mymaxdivisor x = (fromIntegral x) / (fromIntegral (mymindivisor x 2))

-- Ex7

sumOdd :: Int -> Int -> Int
sumOdd a b = if a > b then 0
                      else if (mod a 2) == 0 then a + 1 + (sumOdd (a + 3) b)
                                             else a + (sumOdd (a + 2) b)

-- Ex8

isPrime :: Int -> Bool
isPrime x
    | x <= 3                           = True
    | (mod x 2) == 0 || (mod x 3) == 0 = False
    | otherwise = calc 6 x (sqrt (fromIntegral x))
    where
        calc :: Int -> Int -> Double -> Bool
        calc i x max
            | (fromIntegral (i - 1)) > max                 = True
            | (mod x (i - 1)) == 0 || (mod x (i + 1)) == 0 = False
            | otherwise = calc (i + 6) x max

-- Ex9

numLenT10 :: Int -> Int
numLenT10 x = calc x 1
    where
        calc :: Int -> Int -> Int
        calc x res
            | x == 0 = res
            | otherwise = calc (div x 10) (res * 10)

isPalindrome :: Int -> Bool
isPalindrome x = calc x (div (numLenT10 x) 10)
    where
        calc :: Int -> Int -> Bool
        calc x xT10
            | (div x 10) == 0 = True
            | (rem x 10) /= (div x xT10) = False
            | otherwise = calc (rem (div x 10) xT10) (div xT10 10)

countPalindromes :: Int -> Int -> Int
countPalindromes a b = calc a b 0
    where
        calc :: Int -> Int -> Int -> Int
        calc a b sum
            | a > b = sum
            | isPalindrome a = calc (a + 1) b (sum + 1)
            | otherwise = calc (a + 1) b sum

-- Ex10

sumDivisors :: Int -> Int
sumDivisors x = calc x 0 1 (div x 2)
    where
        calc :: Int -> Int -> Int -> Int -> Int
        calc x sum i max
            | i > max = sum
            | (rem x i) == 0 = calc x (sum + i) (i + 1) max
            | otherwise = calc x sum (i + 1) max


main :: IO ()
main = do
    print (mymin 5 6)              -- 5
    print (isInside 7 (-48) 299)   -- True
    print (myfunc 25 49)           -- 6
    print (myfib 8)                -- 13
    print (mygcd 48 18)            -- 6
    print (mymaxdivisor 2145)      -- 715
    print (sumOdd 2 6)             -- 8
    print (isPrime 6367)           -- True
    print (countPalindromes 1 100) -- 18
    print (sumDivisors 1800)       -- 4245