```Haskell – Exercicio 1

isSorted :: (Ord a) => [a] -> Bool isSorted (a:b:t) = a <= b && isSorted (b:t) isSorted _ = True

inits :: [a] -> [[a]] inits [] = [[]] inits l = inits (init l) ++ [l]

– Exercicio 2

maximumMB :: (Ord a) => [Maybe a] -> Maybe a maximumMB = foldl (\acc x -> if x maiorQue acc then x else acc) Nothing where maiorQue (Just a) (Just b) = a > b maiorQue _ Nothing = True maiorQue Nothing _ = False

– Exercicio 3

data LTree a = Tip a

Fork (LTree a) (LTree a)

listaLT :: LTree a -> [a] listaLT (Tip a) = [a] listaLT (Fork a b) = listaLT a ++ listaLT b

instance (Show a) => Show (LTree a) where show (Tip a) = show a ++ “\n” show (Fork a b) = mostra 1 a ++ mostra 1 b

mostra :: (Show a) => Int -> LTree a -> String mostra n (Tip a) = replicate n ‘.’ ++ show a ++ “\n” mostra n (Fork a b) = mostra (n + 1) a ++ mostra (n + 1) b

– Exercicio 4

maxSumInit :: (Num a, Ord a) => [a] -> a maxSumInit l = foldl (\acc x -> max (sum x) acc) (sum l) (inits l)

– Exercicio 5

type RelP a = [(a,a)] type RelL a = [(a,[a])] type RelF a = ([a], a -> [a])

convLP :: RelL a -> RelP a convLP l = concat (map junta l) where junta (x,xs) = map (\y -> (x,y)) xs

convPL :: (Eq a) => RelP a -> RelL a convPL [(x,y)] = [(x,[y])] convPL (h:t) = junta h (convPL t) where junta (a,b) l = if a elem map (fst) l then map ((c,d) -> if c == a then (c,b:d) else (c,d)) l else (a,[b]):l

criaRelPint :: Int -> IO (RelP Int) criaRelPint 0 = return [] criaRelPint n = do putStr “Introduz dois numeros (separados por um espaco): “ (num1,num2) <- fmap (span (/= ‘ ‘)) getLine fmap ((read num1,read num2) :) $ criaRelPint (n - 1)

convFP :: (Eq a) => RelF a -> RelP a convFP (l,f) = convLP $ map (\x -> (x,f x)) l

convPF :: (Eq a) => RelP a -> RelF a convPF x = ((map fst y),f) where y = convPL x f a = foldl (\acc (b,c) -> if a == b then c else acc) [] y