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-- 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)
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