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Set

A set of unique values. The values can be any comparable type. This includes Int, Float, Time, Char, String, and tuples or lists of comparable types.

Insert, remove, and query operations all take O(log n) time.

Sets

type Set t = Set_elm_builtin (Dict.Dict t ())

Represents a set of unique values. So (Set Int) is a set of integers and (Set String) is a set of strings.

Build

empty : Set a

Create an empty set.

singleton : comparable -> Set comparable

Create a set with one value.

insert : comparable -> Set comparable -> Set comparable

Insert a value into a set.

remove : comparable -> Set comparable -> Set comparable

Remove a value from a set. If the value is not found, no changes are made.

Query

isEmpty : Set a -> Bool

Determine if a set is empty.

member : comparable -> Set comparable -> Bool

Determine if a value is in a set.

size : Set a -> Int

Determine the number of elements in a set.

Combine

union : Set comparable -> Set comparable -> Set comparable

Get the union of two sets. Keep all values.

intersect : Set comparable -> Set comparable -> Set comparable

Get the intersection of two sets. Keeps values that appear in both sets.

diff : Set comparable -> Set comparable -> Set comparable

Get the difference between the first set and the second. Keeps values that do not appear in the second set.

Lists

toList : Set comparable -> List comparable

Convert a set into a list, sorted from lowest to highest.

fromList : List comparable -> Set comparable

Convert a list into a set, removing any duplicates.

Transform

map : (comparable -> comparable2) -> Set comparable -> Set comparable2

Map a function onto a set, creating a new set with no duplicates.

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

Fold over the values in a set, in order from lowest to highest.

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

Fold over the values in a set, in order from highest to lowest.

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

Create a new set consisting only of elements which satisfy a predicate.

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

Create two new sets; the first consisting of elements which satisfy a predicate, the second consisting of elements which do not.

module Set exposing
  ( Set
  , empty, singleton, insert, remove
  , isEmpty, member, size
  , foldl, foldr, map
  , filter, partition
  , union, intersect, diff
  , toList, fromList
  )

{-| A set of unique values. The values can be any comparable type. This
includes `Int`, `Float`, `Time`, `Char`, `String`, and tuples or lists
of comparable types.

Insert, remove, and query operations all take *O(log n)* time.

# Sets
@docs Set

# Build
@docs empty, singleton, insert, remove

# Query
@docs isEmpty, member, size

# Combine
@docs union, intersect, diff

# Lists
@docs toList, fromList

# Transform
@docs map, foldl, foldr, filter, partition

-}

import Basics exposing ((<|))
import Dict as Dict
import List as List


{-| Represents a set of unique values. So `(Set Int)` is a set of integers and
`(Set String)` is a set of strings.
-}
type Set t =
  Set_elm_builtin (Dict.Dict t ())


{-| Create an empty set.
-}
empty : Set a
empty =
  Set_elm_builtin Dict.empty


{-| Create a set with one value.
-}
singleton : comparable -> Set comparable
singleton k =
  Set_elm_builtin <| Dict.singleton k ()


{-| Insert a value into a set.
-}
insert : comparable -> Set comparable -> Set comparable
insert k (Set_elm_builtin d) =
  Set_elm_builtin <| Dict.insert k () d


{-| Remove a value from a set. If the value is not found, no changes are made.
-}
remove : comparable -> Set comparable -> Set comparable
remove k (Set_elm_builtin d) =
  Set_elm_builtin <| Dict.remove k d


{-| Determine if a set is empty.
-}
isEmpty : Set a -> Bool
isEmpty (Set_elm_builtin d) =
  Dict.isEmpty d


{-| Determine if a value is in a set.
-}
member : comparable -> Set comparable -> Bool
member k (Set_elm_builtin d) =
  Dict.member k d


{-| Determine the number of elements in a set.
-}
size : Set a -> Int
size (Set_elm_builtin d) =
  Dict.size d


{-| Get the union of two sets. Keep all values.
-}
union : Set comparable -> Set comparable -> Set comparable
union (Set_elm_builtin d1) (Set_elm_builtin d2) =
  Set_elm_builtin <| Dict.union d1 d2


{-| Get the intersection of two sets. Keeps values that appear in both sets.
-}
intersect : Set comparable -> Set comparable -> Set comparable
intersect (Set_elm_builtin d1) (Set_elm_builtin d2) =
  Set_elm_builtin <| Dict.intersect d1 d2


{-| Get the difference between the first set and the second. Keeps values
that do not appear in the second set.
-}
diff : Set comparable -> Set comparable -> Set comparable
diff (Set_elm_builtin d1) (Set_elm_builtin d2) =
  Set_elm_builtin <| Dict.diff d1 d2


{-| Convert a set into a list, sorted from lowest to highest.
-}
toList : Set comparable -> List comparable
toList (Set_elm_builtin d) =
  Dict.keys d


{-| Convert a list into a set, removing any duplicates.
-}
fromList : List comparable -> Set comparable
fromList xs = List.foldl insert empty xs


{-| Fold over the values in a set, in order from lowest to highest.
-}
foldl : (comparable -> b -> b) -> b -> Set comparable -> b
foldl f b (Set_elm_builtin d) =
  Dict.foldl (\k _ b -> f k b) b d


{-| Fold over the values in a set, in order from highest to lowest.
-}
foldr : (comparable -> b -> b) -> b -> Set comparable -> b
foldr f b (Set_elm_builtin d) =
  Dict.foldr (\k _ b -> f k b) b d


{-| Map a function onto a set, creating a new set with no duplicates.
-}
map : (comparable -> comparable2) -> Set comparable -> Set comparable2
map f s = fromList (List.map f (toList s))


{-| Create a new set consisting only of elements which satisfy a predicate.
-}
filter : (comparable -> Bool) -> Set comparable -> Set comparable
filter p (Set_elm_builtin d) =
  Set_elm_builtin <| Dict.filter (\k _ -> p k) d


{-| Create two new sets; the first consisting of elements which satisfy a
predicate, the second consisting of elements which do not.
-}
partition : (comparable -> Bool) -> Set comparable -> (Set comparable, Set comparable)
partition p (Set_elm_builtin d) =
  let
    (p1, p2) = Dict.partition (\k _ -> p k) d
  in
    (Set_elm_builtin p1, Set_elm_builtin p2)