import Data.List -- Exercise 1 fun1 :: [Integer] -> Integer fun1 = product . map (\n -> n-2) . filter even -- not tested fun2 :: Integer -> Integer fun2 = until (== 1) fun2 . last . takeWhile odd . iterate (\n -> 3*n + 1) . sum . takeWhile even . iterate (`div` 2) -- Exercise 2 data Tree a = Leaf | Node Integer (Tree a) a (Tree a) deriving (Show, Eq) -- Note: I hope I was allowed to make new functions and wasn't supposed to put -- all the code in `foldTree`, although the exercise didn't say anything in this -- regard. treeHeight :: Tree a -> Int treeHeight Leaf = 0 treeHeight (Node _ Leaf _ Leaf) = 0 treeHeight (Node _ tl _ tr) = 1 + max (treeHeight tl) (treeHeight tr) treeInsertBalanced :: Tree a -> a -> Tree a treeInsertBalanced Leaf a = Node 0 Leaf a Leaf treeInsertBalanced t@(Node _ Leaf e Leaf) a = Node 1 (Node 0 Leaf a Leaf) e Leaf treeInsertBalanced t@(Node _ tl e Leaf) a = Node 1 tl e (Node 0 Leaf a Leaf) treeInsertBalanced t@(Node h tl@(Node hl _ _ _) e tr@(Node hr _ _ _)) a | hl <= hr = Node (toInteger newh1) newtl e tr | otherwise = Node (toInteger newh1) tl e newtr where newtl = treeInsertBalanced tl a newtr = treeInsertBalanced tr a newh1 = max (treeHeight newtl) (treeHeight tr) + 1 newh2 = max (treeHeight tl) (treeHeight newtr) + 1 foldTree :: [a] -> Tree a foldTree = foldr (flip treeInsertBalanced) Leaf -- Exercise 3 xor :: [Bool] -> Bool xor = odd . foldl (\s x -> if x then s+1 else s) 0 map' :: (a -> b) -> [a] -> [b] map' f = foldr (\x s -> f x : s) [] myFoldl :: (a -> b -> a) -> a -> [b] -> a myFoldl f base xs = foldr (flip f) base (reverse xs) -- Exercise 4 cartProd :: [a] -> [b] -> [(a, b)] cartProd xs ys = [(x,y) | x <- xs, y <- ys] sieveSundaram :: Integer -> [Integer] sieveSundaram n = take (fromInteger n) . map (\x -> (2*x) + 1) . (\\) [1..n] . filter (<=n) . map (\(i,j) -> i + j + (2*i*j)) . filter (\(i,j) -> i <= j) $ cartProd [1..n] [1..n]