Data.Set

Please see the documentation of containers for details.

Set type

data Set a :: * -> *

A set of values a.

Instances

Foldable Set

Methods

fold :: Monoid m => Set m -> m

foldMap :: Monoid m => (a -> m) -> Set a -> m

foldr :: (a -> b -> b) -> b -> Set a -> b

foldr' :: (a -> b -> b) -> b -> Set a -> b

foldl :: (b -> a -> b) -> b -> Set a -> b

foldl' :: (b -> a -> b) -> b -> Set a -> b

foldr1 :: (a -> a -> a) -> Set a -> a

foldl1 :: (a -> a -> a) -> Set a -> a

toList :: Set a -> [a]

null :: Set a -> Bool

length :: Set a -> Int

elem :: Eq a => a -> Set a -> Bool

maximum :: Ord a => Set a -> a

minimum :: Ord a => Set a -> a

sum :: Num a => Set a -> a

product :: Num a => Set a -> a

Eq1 Set

Since: 0.5.9

Methods

liftEq :: (a -> b -> Bool) -> Set a -> Set b -> Bool

Ord1 Set

Since: 0.5.9

Methods

liftCompare :: (a -> b -> Ordering) -> Set a -> Set b -> Ordering

Show1 Set

Since: 0.5.9

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Set a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Set a] -> ShowS

Ord a => IsList (Set a)

Since: 0.5.6.2

Associated Types

type Item (Set a) :: *

Methods

fromList :: [Item (Set a)] -> Set a

fromListN :: Int -> [Item (Set a)] -> Set a

toList :: Set a -> [Item (Set a)]

Eq a => Eq (Set a)

Methods

(==) :: Set a -> Set a -> Bool

(/=) :: Set a -> Set a -> Bool

(Data a, Ord a) => Data (Set a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Set a -> c (Set a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Set a)

toConstr :: Set a -> Constr

dataTypeOf :: Set a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Set a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Set a))

gmapT :: (forall b. Data b => b -> b) -> Set a -> Set a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Set a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Set a -> r

gmapQ :: (forall d. Data d => d -> u) -> Set a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Set a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Set a -> m (Set a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Set a -> m (Set a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Set a -> m (Set a)

Ord a => Ord (Set a)

Methods

compare :: Set a -> Set a -> Ordering

(<) :: Set a -> Set a -> Bool

(<=) :: Set a -> Set a -> Bool

(>) :: Set a -> Set a -> Bool

(>=) :: Set a -> Set a -> Bool

max :: Set a -> Set a -> Set a

min :: Set a -> Set a -> Set a

(Read a, Ord a) => Read (Set a)

Methods

readsPrec :: Int -> ReadS (Set a)

readList :: ReadS [Set a]

readPrec :: ReadPrec (Set a)

readListPrec :: ReadPrec [Set a]

Show a => Show (Set a)

Methods

showsPrec :: Int -> Set a -> ShowS

show :: Set a -> String

showList :: [Set a] -> ShowS

Ord a => Semigroup (Set a)

Since: 0.5.7

Methods

(<>) :: Set a -> Set a -> Set a

sconcat :: NonEmpty (Set a) -> Set a

stimes :: Integral b => b -> Set a -> Set a

Ord a => Monoid (Set a)

Methods

mempty :: Set a

mappend :: Set a -> Set a -> Set a

mconcat :: [Set a] -> Set a

NFData a => NFData (Set a)

Methods

rnf :: Set a -> ()

type Item (Set a)

type Item (Set a) = a

Operators

Query

null :: Set a -> Bool

O(1). Is this the empty set?

size :: Set a -> Int

O(1). The number of elements in the set.

member :: Ord a => a -> Set a -> Bool

O(log n). Is the element in the set?

notMember :: Ord a => a -> Set a -> Bool

O(log n). Is the element not in the set?

isSubsetOf :: Ord a => Set a -> Set a -> Bool

O(n+m). Is this a subset? (s1 `isSubsetOf` s2) tells whether s1 is a subset of s2.

disjoint :: Ord a => Set a -> Set a -> Bool

O(n+m). Check whether two sets are disjoint (i.e. their intersection is empty).

disjoint (fromList [2,4,6])   (fromList [1,3])     == True
disjoint (fromList [2,4,6,8]) (fromList [2,3,5,7]) == False
disjoint (fromList [1,2])     (fromList [1,2,3,4]) == False
disjoint (fromList [])        (fromList [])        == True

Since: 0.5.11

Construction

empty :: Set a

O(1). The empty set.

singleton :: a -> Set a

O(1). Create a singleton set.

insert :: Ord a => a -> Set a -> Set a

O(log n). Insert an element in a set. If the set already contains an element equal to the given value, it is replaced with the new value.

delete :: Ord a => a -> Set a -> Set a

O(log n). Delete an element from a set.

Combine

union :: Ord a => Set a -> Set a -> Set a

O(m*log(n/m + 1)), m <= n. The union of two sets, preferring the first set when equal elements are encountered.

unions :: (Foldable f, Ord a) => f (Set a) -> Set a

The union of a list of sets: (unions == foldl union empty).

difference :: Ord a => Set a -> Set a -> Set a

O(m*log(n/m + 1)), m <= n. Difference of two sets.

intersection :: Ord a => Set a -> Set a -> Set a

O(m*log(n/m + 1)), m <= n. The intersection of two sets. Elements of the result come from the first set, so for example

import qualified Data.Set as S
data AB = A | B deriving Show
instance Ord AB where compare _ _ = EQ
instance Eq AB where _ == _ = True
main = print (S.singleton A `S.intersection` S.singleton B,
              S.singleton B `S.intersection` S.singleton A)

prints (fromList [A],fromList [B]).

Filter

filter :: (a -> Bool) -> Set a -> Set a

O(n). Filter all elements that satisfy the predicate.

partition :: (a -> Bool) -> Set a -> (Set a, Set a)

O(n). Partition the set into two sets, one with all elements that satisfy the predicate and one with all elements that don't satisfy the predicate. See also split.

split :: Ord a => a -> Set a -> (Set a, Set a)

O(log n). The expression (split x set) is a pair (set1,set2) where set1 comprises the elements of set less than x and set2 comprises the elements of set greater than x.

splitMember :: Ord a => a -> Set a -> (Set a, Bool, Set a)

O(log n). Performs a split but also returns whether the pivot element was found in the original set.

take :: Int -> Set a -> Set a

Take a given number of elements in order, beginning with the smallest ones.

take n = fromDistinctAscList . take n . toAscList

Since: 0.5.8

drop :: Int -> Set a -> Set a

Drop a given number of elements in order, beginning with the smallest ones.

drop n = fromDistinctAscList . drop n . toAscList

Since: 0.5.8

splitAt :: Int -> Set a -> (Set a, Set a)

O(log n). Split a set at a particular index.

splitAt !n !xs = (take n xs, drop n xs)

map :: Ord b => (a -> b) -> Set a -> Set b

O(n*log n). map f s is the set obtained by applying f to each element of s.

It's worth noting that the size of the result may be smaller if, for some (x,y), x /= y && f x == f y

mapMonotonic :: (a -> b) -> Set a -> Set b

O(n). The

mapMonotonic f s == map f s, but works only when f is strictly increasing. The precondition is not checked. Semi-formally, we have:

and [x < y ==> f x < f y | x <- ls, y <- ls]
                    ==> mapMonotonic f s == map f s
    where ls = toList s

Folds

foldr :: (a -> b -> b) -> b -> Set a -> b

O(n). Fold the elements in the set using the given right-associative binary operator, such that foldr f z == foldr f z . toAscList.

For example,

toAscList set = foldr (:) [] set

foldl :: (a -> b -> a) -> a -> Set b -> a

O(n). Fold the elements in the set using the given left-associative binary operator, such that foldl f z == foldl f z . toAscList.

For example,

toDescList set = foldl (flip (:)) [] set

lookupMin :: Set a -> Maybe a

O(log n). The minimal element of a set.

Since: 0.5.9

lookupMax :: Set a -> Maybe a

O(log n). The maximal element of a set.

Since: 0.5.9

maxView :: Set a -> Maybe (a, Set a)

O(log n). Retrieves the maximal key of the set, and the set stripped of that element, or Nothing if passed an empty set.

minView :: Set a -> Maybe (a, Set a)

O(log n). Retrieves the minimal key of the set, and the set stripped of that element, or Nothing if passed an empty set.

elems :: Set a -> [a]

O(n). An alias of toAscList. The elements of a set in ascending order. Subject to list fusion.

toList :: Set a -> [a]

O(n). Convert the set to a list of elements. Subject to list fusion.

fromList :: Ord a => [a] -> Set a

O(n*log n). Create a set from a list of elements.

If the elements are ordered, a linear-time implementation is used, with the performance equal to fromDistinctAscList.

toAscList :: Set a -> [a]

O(n). Convert the set to an ascending list of elements. Subject to list fusion.

toDescList :: Set a -> [a]

O(n). Convert the set to a descending list of elements. Subject to list fusion.

fromAscList :: Eq a => [a] -> Set a

O(n). Build a set from an ascending list in linear time. The precondition (input list is ascending) is not checked.

fromDescList :: Eq a => [a] -> Set a

O(n). Build a set from a descending list in linear time. The precondition (input list is descending) is not checked.

Since: 0.5.8

fromDistinctAscList :: [a] -> Set a

O(n). Build a set from an ascending list of distinct elements in linear time. The precondition (input list is strictly ascending) is not checked.

fromDistinctDescList :: [a] -> Set a

O(n). Build a set from a descending list of distinct elements in linear time. The precondition (input list is strictly descending) is not checked.