Data.HashSet

unordered-containers-0.2.20: Efficient hashing-based container types

Copyright | 2011 Bryan O'Sullivan
License | BSD-style
Maintainer | johan.tibell@gmail.com
Stability | provisional
Portability | portable
Safe Haskell | Safe
Language | Haskell2010

Data.HashSet

Contents

- Construction
- Combine
- Basic interface
- Transformations
- Difference and intersection
- Folds
- Filter
- Conversions
  - Lists
- HashMaps

Description

# Introduction

`HashSet` allows you to store unique elements, providing efficient insertion, lookups, and deletion. A `HashSet` makes no guarantees as to the order of its elements.

If you are storing sets of Data.Ints consider using Data.IntSet from the containers package.

## Examples

All the examples below assume `HashSet` is imported qualified, and uses the following `dataStructures` set.

    >>> import qualified Data.HashSet as HashSet
    >>> let dataStructures = HashSet.fromList ["Set", "Map", "Graph", "Sequence"]

### Basic Operations

Check membership in a set:

    >>> -- Check if "Map" and "Trie" are in the set of data structures.
    >>> HashSet.member "Map" dataStructures
    True
    >>> HashSet.member "Trie" dataStructures
    False

Add a new entry to the set:

    >>> let moreDataStructures = HashSet.insert "Trie" dataStructures
    >>> HashSet.member "Trie" moreDataStructures
    > True

Remove the `"Graph"` entry from the set of data structures.

    >>> let fewerDataStructures = HashSet.delete "Graph" dataStructures
    >>> HashSet.toList fewerDataStructures
    ["Map","Set","Sequence"]

Create a new set and combine it with our original set.

    >>> let unorderedDataStructures = HashSet.fromList ["HashSet", "HashMap"]
    >>> HashSet.union dataStructures unorderedDataStructures
    fromList ["Map","HashSet","Graph","HashMap","Set","Sequence"]

### Using custom data with HashSet

To create a `HashSet` of your custom type, the type must have instances for `Eq` and `Hashable`. The `Hashable` typeclass is defined in the hashable package, see the documentation for information on how to make your type an instance of `Hashable`.

We'll start by setting up our custom data type:

    >>> :set -XDeriveGeneric
    >>> import GHC.Generics (Generic)
    >>> import Data.Hashable
    >>> data Person = Person { name :: String, likesDogs :: Bool } deriving (Show, Eq, Generic)
    >>> instance Hashable Person

And now we'll use it!

    >>> let people = HashSet.fromList [Person "Lana" True, Person "Joe" False, Person "Simon" True]
    >>> HashSet.filter likesDogs people
    fromList [Person {name = "Simon", likesDogs = True},Person {name = "Lana", likesDogs = True}]

## Performance

The implementation is based on hash array mapped tries. A `HashSet` is often faster than other `Ord`-based set types, especially when value comparisons are expensive, as in the case of strings.

Many operations have a average-case complexity of \(O(\log n)\). The implementation uses a large base (i.e. 16) so in practice these operations are constant time.

Synopsis

- data HashSet a
- empty :: HashSet a
- singleton :: Hashable a => a -> HashSet a
- union :: Eq a => HashSet a -> HashSet a -> HashSet a
- unions :: Eq a => [HashSet a] -> HashSet a
- null :: HashSet a -> Bool
- size :: HashSet a -> Int
- member :: (Eq a, Hashable a) => a -> HashSet a -> Bool
- insert :: (Eq a, Hashable a) => a -> HashSet a -> HashSet a
- delete :: (Eq a, Hashable a) => a -> HashSet a -> HashSet a
- isSubsetOf :: (Eq a, Hashable a) => HashSet a -> HashSet a -> Bool
- map :: (Hashable b, Eq b) => (a -> b) -> HashSet a -> HashSet b
- difference :: (Eq a, Hashable a) => HashSet a -> HashSet a -> HashSet a
- intersection :: Eq a => HashSet a -> HashSet a -> HashSet a
- foldl' :: (a -> b -> a) -> a -> HashSet b -> a
- foldr :: (b -> a -> a) -> a -> HashSet b -> a
- filter :: (a -> Bool) -> HashSet a -> HashSet a
- toList :: HashSet a -> [a]
- fromList :: (Eq a, Hashable a) => [a] -> HashSet a
- toMap :: HashSet a -> HashMap a ()
- fromMap :: HashMap a () -> HashSet a

# Documentation

data HashSet a #

A set of values. A set cannot contain duplicate values.

#### Instances

Instances details

Foldable HashSet # |
Instance details Defined in Data.HashSet.Internal Methods fold :: Monoid m => HashSet m -> m # foldMap :: Monoid m => (a -> m) -> HashSet a -> m # foldMap' :: Monoid m => (a -> m) -> HashSet a -> m # foldr :: (a -> b -> b) -> b -> HashSet a -> b # foldr' :: (a -> b -> b) -> b -> HashSet a -> b # foldl :: (b -> a -> b) -> b -> HashSet a -> b # foldl' :: (b -> a -> b) -> b -> HashSet a -> b # foldr1 :: (a -> a -> a) -> HashSet a -> a # foldl1 :: (a -> a -> a) -> HashSet a -> a # toList :: HashSet a -> [a] # null :: HashSet a -> Bool # length :: HashSet a -> Int # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # sum :: Num a => HashSet a -> a # product :: Num a => HashSet a -> a #
Eq1 HashSet # |
Instance details Defined in Data.HashSet.Internal Methods liftEq :: (a -> b -> Bool) -> HashSet a -> HashSet b -> Bool #
Ord1 HashSet # |
Instance details Defined in Data.HashSet.Internal Methods liftCompare :: (a -> b -> Ordering) -> HashSet a -> HashSet b -> Ordering #
Show1 HashSet # |
Instance details Defined in Data.HashSet.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> HashSet a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [HashSet a] -> ShowS #
NFData1 HashSet # | Since: 0.2.14.0
Instance details Defined in Data.HashSet.Internal Methods liftRnf :: (a -> ()) -> HashSet a -> () #
Hashable1 HashSet # |
Instance details Defined in Data.HashSet.Internal Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> HashSet a -> Int #
Lift a => Lift (HashSet a :: Type) # | Since: 0.2.17.0
Instance details Defined in Data.HashSet.Internal Methods lift :: Quote m => HashSet a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => HashSet a -> Code m (HashSet a) #
(Data a, Eq a, Hashable a) => Data (HashSet a) # |
Instance details Defined in Data.HashSet.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HashSet a -> c (HashSet a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (HashSet a) # toConstr :: HashSet a -> Constr # dataTypeOf :: HashSet a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (HashSet a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (HashSet a)) # gmapT :: (forall b. Data b => b -> b) -> HashSet a -> HashSet a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r # gmapQ :: (forall d. Data d => d -> u) -> HashSet a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> HashSet a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) #
(Hashable a, Eq a) => Monoid (HashSet a) # | `mempty` = `empty` `mappend` = `union` \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. #### Examples Expand
    >>> mappend (fromList [1,2]) (fromList [2,3])
    fromList [1,2,3]
Instance details Defined in Data.HashSet.Internal Methods mempty :: HashSet a # mappend :: HashSet a -> HashSet a -> HashSet a # mconcat :: [HashSet a] -> HashSet a #
(Hashable a, Eq a) => Semigroup (HashSet a) # | `<>` = `union` \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. #### Examples Expand
    >>> fromList [1,2] <> fromList [2,3]
    fromList [1,2,3]
Instance details Defined in Data.HashSet.Internal Methods (<>) :: HashSet a -> HashSet a -> HashSet a # sconcat :: NonEmpty (HashSet a) -> HashSet a # stimes :: Integral b => b -> HashSet a -> HashSet a #
(Eq a, Hashable a) => IsList (HashSet a) # |
Instance details Defined in Data.HashSet.Internal Associated Types
type Item (HashSet a) |
Instance details Defined in Data.HashSet.Internal type Item (HashSet a) = a
Methods fromList :: [Item (HashSet a)] -> HashSet a # fromListN :: Int -> [Item (HashSet a)] -> HashSet a # toList :: HashSet a -> [Item (HashSet a)] #
(Eq a, Hashable a, Read a) => Read (HashSet a) # |
Instance details Defined in Data.HashSet.Internal Methods readsPrec :: Int -> ReadS (HashSet a) # readList :: ReadS [HashSet a] # readPrec :: ReadPrec (HashSet a) # readListPrec :: ReadPrec [HashSet a] #
Show a => Show (HashSet a) # |
Instance details Defined in Data.HashSet.Internal Methods showsPrec :: Int -> HashSet a -> ShowS # show :: HashSet a -> String # showList :: [HashSet a] -> ShowS #
NFData a => NFData (HashSet a) # |
Instance details Defined in Data.HashSet.Internal Methods rnf :: HashSet a -> () #
Eq a => Eq (HashSet a) # | Note that, in the presence of hash collisions, equal `HashSet`s may behave differently, i.e. extensionality may be violated:
    >>> data D = A | B deriving (Eq, Show)
    >>> instance Hashable D where hashWithSalt salt _d = salt
    >>> x = fromList [A, B]
    >>> y = fromList [B, A]
    >>> x == y
    True
    >>> toList x
    [A,B]
    >>> toList y
    [B,A]
In general, the lack of extensionality can be observed with any function that depends on the key ordering, such as folds and traversals.
Instance details Defined in Data.HashSet.Internal Methods (==) :: HashSet a -> HashSet a -> Bool # (/=) :: HashSet a -> HashSet a -> Bool #
Ord a => Ord (HashSet a) # |
Instance details Defined in Data.HashSet.Internal Methods compare :: HashSet a -> HashSet a -> Ordering # (<) :: HashSet a -> HashSet a -> Bool # (<=) :: HashSet a -> HashSet a -> Bool # (>) :: HashSet a -> HashSet a -> Bool # (>=) :: HashSet a -> HashSet a -> Bool # max :: HashSet a -> HashSet a -> HashSet a # min :: HashSet a -> HashSet a -> HashSet a #
Hashable a => Hashable (HashSet a) # |
Instance details Defined in Data.HashSet.Internal Methods hashWithSalt :: Int -> HashSet a -> Int # hash :: HashSet a -> Int #
type Item (HashSet a) # |
Instance details Defined in Data.HashSet.Internal type Item (HashSet a) = a

# Construction

empty :: HashSet a #

\(O(1)\) Construct an empty set.

    >>> HashSet.empty
    fromList []

singleton :: Hashable a => a -> HashSet a #

\(O(1)\) Construct a set with a single element.

    >>> HashSet.singleton 1
    fromList [1]

# Combine

union :: Eq a => HashSet a -> HashSet a -> HashSet a #

\(O(n+m)\) Construct a set containing all elements from both sets.

To obtain good performance, the smaller set must be presented as the first argument.

    >>> union (fromList [1,2]) (fromList [2,3])
    fromList [1,2,3]

unions :: Eq a => [HashSet a] -> HashSet a #

Construct a set containing all elements from a list of sets.

# Basic interface

null :: HashSet a -> Bool #

\(O(1)\) Return `True` if this set is empty, `False` otherwise.

    >>> HashSet.null HashSet.empty
    True
    >>> HashSet.null (HashSet.singleton 1)
    False

size :: HashSet a -> Int #

\(O(n)\) Return the number of elements in this set.

    >>> HashSet.size HashSet.empty
    0
    >>> HashSet.size (HashSet.fromList [1,2,3])
    3

member :: (Eq a, Hashable a) => a -> HashSet a -> Bool #

\(O(\log n)\) Return `True` if the given value is present in this set, `False` otherwise.

    >>> HashSet.member 1 (Hashset.fromList [1,2,3])
    True
    >>> HashSet.member 1 (Hashset.fromList [4,5,6])
    False

insert :: (Eq a, Hashable a) => a -> HashSet a -> HashSet a #

\(O(\log n)\) Add the specified value to this set.

    >>> HashSet.insert 1 HashSet.empty
    fromList [1]

delete :: (Eq a, Hashable a) => a -> HashSet a -> HashSet a #

\(O(\log n)\) Remove the specified value from this set if present.

    >>> HashSet.delete 1 (HashSet.fromList [1,2,3])
    fromList [2,3]
    >>> HashSet.delete 1 (HashSet.fromList [4,5,6])
    fromList [4,5,6]

isSubsetOf :: (Eq a, Hashable a) => HashSet a -> HashSet a -> Bool #

\(O(n \log m)\) Inclusion of sets.

#### Examples

Expand

    >>> fromList [1,3] `isSubsetOf` fromList [1,2,3]
    True

    >>> fromList [1,2] `isSubsetOf` fromList [1,3]
    False

Since: 0.2.12

# Transformations

map :: (Hashable b, Eq b) => (a -> b) -> HashSet a -> HashSet b #

\(O(n)\) Transform this set by applying a function to every value. The resulting set may be smaller than the source.

    >>> HashSet.map show (HashSet.fromList [1,2,3])
    HashSet.fromList ["1","2","3"]

# Difference and intersection

difference :: (Eq a, Hashable a) => HashSet a -> HashSet a -> HashSet a #

\(O(n)\) Difference of two sets. Return elements of the first set not existing in the second.

    >>> HashSet.difference (HashSet.fromList [1,2,3]) (HashSet.fromList [2,3,4])
    fromList [1]

intersection :: Eq a => HashSet a -> HashSet a -> HashSet a #

\(O(n)\) Intersection of two sets. Return elements present in both the first set and the second.

    >>> HashSet.intersection (HashSet.fromList [1,2,3]) (HashSet.fromList [2,3,4])
    fromList [2,3]

# Folds

foldl' :: (a -> b -> a) -> a -> HashSet b -> a #

\(O(n)\) Reduce this set by applying a binary operator to all elements, using the given starting value (typically the left-identity of the operator). Each application of the operator is evaluated before before using the result in the next application. This function is strict in the starting value.

foldr :: (b -> a -> a) -> a -> HashSet b -> a #

\(O(n)\) Reduce this set by applying a binary operator to all elements, using the given starting value (typically the right-identity of the operator).

# Filter

filter :: (a -> Bool) -> HashSet a -> HashSet a #

\(O(n)\) Filter this set by retaining only elements satisfying a predicate.

# Conversions

## Lists

toList :: HashSet a -> [a] #

\(O(n)\) Return a list of this set's elements. The list is produced lazily.

fromList :: (Eq a, Hashable a) => [a] -> HashSet a #

\(O(n \min(W, n))\) Construct a set from a list of elements.

# HashMaps

toMap :: HashSet a -> HashMap a () #

\(O(1)\) Convert to set to the equivalent `HashMap` with `()` values.

    >>> HashSet.toMap (HashSet.singleton 1)
    fromList [(1,())]

fromMap :: HashMap a () -> HashSet a #

\(O(1)\) Convert from the equivalent `HashMap` with `()` values.

    >>> HashSet.fromMap (HashMap.singleton 1 ())
    fromList [1]