feat: sheet_3

Sheet_3/exercise-1.hs

+universalQ :: (a -> Bool) -> [a] -> Bool
+universalQ function list = foldr (&&) True (map function list)
+
+map' :: (a -> b) -> [a] -> [b]
+map' function list = foldr (\x acc -> function x : acc) [] list
+
+removeDuplicates :: Eq a => [a] -> [a]
+removeDuplicates list = foldr (\x acc -> if (filter (==x) acc) /= [] then acc else x : acc) [] list
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Sheet_3/exercise-2.hs

+data Rose a = Node a [Rose a] deriving Show
+
+zipWithRose :: (a -> b -> c) -> Rose a -> Rose b -> Rose c
+zipWithRose function (Node a1 children1) (Node a2 children2) = Node (function a1 a2) (zipWith (zipWithRose function) children1 children2)
+
+mapAndFold :: (a -> b) -> (b -> b -> b) -> Rose a -> b
+mapAndFold f g (Node r children) = g (f r) (foldr (g)  (map (mapAndFold f g) children))
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Sheet_3/exercise-3.hs

+dropMult :: Int -> [Int] -> [Int]
+dropMult x xs = [y | y <- xs, y `mod` x /= 0]
+
+dropAll :: [Int] -> [Int]
+dropAll (x:xs) = x : dropAll (dropMult x xs)
+
+primes :: [Int]
+primes = dropAll [2 ..]
+
+goldbach :: Int -> [(Int, Int)]
+goldbach n = [(x, y) | x <- takeWhile (<= n) primes, y <- takeWhile (<= n) primes, x + y == n, x `mod` 2 == 1, y `mod` 2 == 1, x <= y]
+
+range :: [a] -> Int -> Int -> [a]
+range (pre:xs) m n = if m > 0 && n > 0 then range xs (m - 1) (n - 1) else if m > 0 then range (xs:post) (m - 1) n else if n > 0 then range (pre:xs) m (n-1) else if m <= 0 && n <=0 then (pre:xs)++ [post] else []
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