ФП (И+КН.1+избираема) 2022/23

-- -- -- -- -- -- взима първите n елемента на списък take' :: Int -> [a] -> [a] take' 0 _ = [] take' n [] = [] take' n (x:xs) = x : take' (n-1) xs -- премахва първите n елемента от списък drop' :: Int -> [a] -> [a] drop' 0 xs = xs drop' _ [] = [] drop' n (_:xs) = drop' (n-1) xs -- декартово произведение cartesian :: [a] -> [b] -> [(a,b)] cartesian [] ys = [] -- ? cartesian (x:xs) ys = map (\y -> (x, y)) ys ++ cartesian xs ys concatMap f = concat . map f --list comprehension cartesian' xs ys = [ (x,y) | x <- xs, y <- ys ] example xs ys = [ combine x y | x <- xs, y <- ys, x+y == 2 ] where combine x y = x + 10 * y enum :: [b] -> [(Int, b)] enum = enum' 0 where enum' :: Int -> [c] -> [(Int, c)] enum' _ [] = [] enum' i (x:xs) = (i,x) : enum' (i+1) xs zip' :: [a] -> [b] -> [(a,b)] zip' xs ys = [ (x,y) | (ix, x) <- enum xs , (iy, y) <- enum ys , ix == iy ] zipWith' :: (a -> b -> c) -> [a] -> [b] -> [c] zipWith' f xs ys = [ f x y | (ix, x) <- enum xs , (iy, y) <- enum ys , ix == iy ] zipWith'' :: (a -> b -> c) -> [a] -> [b] -> [c] zipWith'' f xs = map (uncurry f) . zip' xs --zipWith'' f xs ys = map (uncurry f) (zip' xs ys) -- обещанията (stream-овете) от Scheme се изрично се оценяват лениво, -- в Хаскел това е по подразбиране за всички промениливи -- безкрайните списъци са просто списъци, за които може да игнорираме края им - пишем рекурсии без дъно f = f concat' :: [[a]] -> [a] concat' = foldr (++) [] ones = 1 : ones zeroes = zipWith (-) ones ones from :: Int -> [Int] from n = n : from (n+1) repeat' :: Int -> [Int] repeat' x = x : repeat' x --nats' = from 1 nats = 1 : zipWith (+) ones nats fibs = 1 : 1 : zipWith (+) fibs (tail fibs) sieve :: [Int] -> [Int] sieve (x:xs) = x : filter ((0 /=) . (`mod` x)) (sieve xs) --filter (\y -> (y `mod` x) /= 0) (sieve xs) primes = sieve (from 2) cycle' :: [a] -> [a] cycle' xs = go xs where go [] = xs go (y:ys) = ys iterate' :: (a -> a) -> a -> [a] iterate' f x = x : map f (iterate' f x) -- поток от Питагоровите тройки. Питагорова тройка е наредена тройка (a, b, c), за която a^2 + b^2 = c^2. -- pythagoreanTriples_notWorks = -- [ (a,b,c) -- | a <- nats -- , b <- nats -- , c <- nats -- , a^2 + b^2 == c^2 -- ] -- pythagoreanTriples_strangeOrder = [ (a, b, a^2+b^2) | a <- nats , b <- nats ] pythagoreanTriples = [ (a, b, floor c) | (a, b) <- orderedPairs , a < b , gcd a b == 1 , let c :: Double c = sqrt (fromIntegral (a^2+b^2)) , c == fromIntegral (floor c) ] orderedPairs :: [(Int, Int)] orderedPairs = [ (i, d-i) | d <- nats , i <- [1 .. d-1] ] sumLast k n = k : go [k] where go memory = x : go (take n (x:memory)) where x = sum memory