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-- module Main where
silnia :: (Eq p, Num p) => p -> p
silnia n = if n == 0 then 1 else n * silnia (n -1)
fibs :: [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
-- Zadanie 1
f :: [Integer] -> [Integer]
f (p : xs) = filter (\x -> x `mod` p /= 0) xs
primes :: [Integer]
primes = map head (iterate f [2 ..])
-- Zadanie 2
primes' :: [Integer]
primes' = 2 : [p | p <- [3 ..], all (\q -> p `mod` q /= 0) (takeWhile (\q -> q * q <= p) primes')]
-- Zadanie 3
permi :: [a] -> [[a]]
permi [] = [[]]
permi (x : []) = [[x]]
permi (p : xs) = concat [(iter [] perm) | perm <- permi xs]
where
iter pref [] = [pref ++ [p]]
iter pref suf = (pref ++ (p : suf)) : (iter (pref ++ [head suf]) (tail suf))
perms :: [a] -> [[a]]
perms [] = [[]]
perms (x : []) = [[x]]
perms xs = iter [] [] xs
where
iter res pref [] = res
iter res pref (x : xs) = iter (res ++ (map (\ys -> x : ys) (perms (pref ++ xs)))) (pref ++ [x]) xs
-- Zadanie 4
sublist :: [a] -> [[a]]
sublist [] = [[]]
sublist (x : xs) = sxs ++ (map (\xs -> x : xs) sxs)
where
sxs = sublist xs
-- Zadanie 5
qsortBy :: (a -> a -> Bool) -> [a] -> [a]
qsortBy _ [] = []
qsortBy _ [x] = [x]
qsortBy cmp (x : xs) = le ++ [x] ++ ge
where
le = qsortBy cmp [y | y <- xs, cmp x y]
ge = qsortBy cmp [y | y <- xs, cmp y x]
-- Zadanie 6
-- subtable :: [a] -> Int -> [b] -> ([a] -> [a]) -> [a]
-- subtable [] _ _ _ = []
-- subtable _ _ [] _ = []
-- subtable xs maxLen ys f = getSubtableBounded (f (take maxLen xs)) ys
-- where
-- getSubtableBounded [] _ = []
-- getSubtableBounded _ [] = []
-- getSubtableBounded (x : xs) (_ : ys) = x : (getSubtableBounded xs ys)
-- natsBounded xs = iter [] 1 xs
-- where
-- iter res _ [] = res
-- iter res num (x : xs) = iter (res ++ [num]) (num + 1) xs
-- generateCantorTable :: [a] -> [b] -> ([a] -> [a]) -> [a]
-- generateCantorTable _ [] f = []
-- generateCantorTable [] _ f = []
-- generateCantorTable xs ys f = concat [subtable xs maxLen ys f | maxLen <- natsBounded xs]
-- (><) :: [a] -> [b] -> [(a, b)]
-- (><) xs ys = zip (generateCantorTable xs ys reverse) (generateCantorTable ys xs id)
-- (><) :: [a] -> [b] -> [(a, b)]
-- (><) [] _ = []
-- (><) _ [] = []
-- (><) xs ys = iterXS xs ys
-- where iterXS xs ys
-- Zadanie 7
data Tree a = Node (Tree a) a (Tree a) | Leaf
data Set a = Fin (Tree a) | Cofin (Tree a)
treeFromList :: Ord a => [a] -> Tree a
treeFromList [] = Leaf
treeFromList [x] = Node Leaf x Leaf
treeFromList xs =
let center xs =
let iter pref crawl [] = (pref, crawl)
iter pref crawl [x] = (pref, crawl)
iter pref crawl (x : y : xs) = iter (head crawl : pref) (tail crawl) xs
in iter [] xs xs
in let (st, nd) = center xs in Node (treeFromList (reverse st)) (head nd) (treeFromList (tail nd))
setFromList :: Ord a => [a] -> Set a
setFromList xs = Fin (treeFromList xs)
setEmpty :: Ord a => Set a
setEmpty = Fin Leaf
setFull :: Ord a => Set a
setFull = Cofin Leaf
setToList :: Ord a => Set a -> [a]
setToList (Fin t) = treeToList t
setToList (Cofin t) = treeToList t
treeToList :: Ord a => Tree a -> [a]
treeToList Leaf = []
treeToList (Node t1 a t2) = treeToList t1 ++ [a] ++ treeToList t2
merge :: Ord a => [a] -> [a] -> [a]
merge [] ys = ys
merge xs [] = xs
merge (x : xs) (y : ys) = if x < y then x : (merge xs (y : ys)) else y : (merge (x : xs) ys)
setUnion :: Ord a => Set a -> Set a -> Set a
setUnion (Fin t1) (Fin t2) =
setFromList (treeToList t1 `merge` treeToList t2)
setUnion (Fin t1) (Cofin t2) =
Cofin (treeFromList [x | x <- treeToList t2, x `notElem` treeToList t1])
setUnion (Cofin t1) (Fin t2) = setUnion (Fin t2) (Cofin t1)
setUnion (Cofin t1) (Cofin t2) =
Cofin (treeFromList [x | x <- treeToList t1, x `elem` treeToList t2])
setIntersection :: Ord a => Set a -> Set a -> Set a
setIntersection (Fin t1) (Fin t2) =
setFromList [x | x <- treeToList t1, x `elem` treeToList t2]
setIntersection (Fin t1) (Cofin t2) =
setFromList [x | x <- treeToList t1, x `notElem` treeToList t2]
setIntersection (Cofin t1) (Fin t2) =
setIntersection (Fin t1) (Cofin t2)
-- setIntersection (Cofin t1) (Cofin t2) =
-- Cofin (treeFromList [x | x <- treeToList t1, ])
treeMember :: Ord a => a -> Tree a -> Bool
treeMember _ Leaf = False
treeMember x (Node t1 y t2) =
(x == y) || if x < y then treeMember x t1 else treeMember x t2
setMember :: Ord a => a -> Set a -> Bool
setMember x (Cofin t) = not (x `treeMember` t)
setMember x (Fin t) = x `treeMember` t
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