rio-0.1.5.0: A standard library for Haskell

RIO.Set

Description

Set. Import as:

import qualified RIO.Set as Set
Synopsis

# Set type

data Set a #

A set of values a.

Instances

# Operators

(\\) :: Ord a => Set a -> Set a -> Set a infixl 9 #

O(m*log(n/m+1)), m <= n. See difference.

# 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?

lookupLT :: Ord a => a -> Set a -> Maybe a #

O(log n). Find largest element smaller than the given one.

lookupLT 3 (fromList [3, 5]) == Nothing
lookupLT 5 (fromList [3, 5]) == Just 3

lookupGT :: Ord a => a -> Set a -> Maybe a #

O(log n). Find smallest element greater than the given one.

lookupGT 4 (fromList [3, 5]) == Just 5
lookupGT 5 (fromList [3, 5]) == Nothing

lookupLE :: Ord a => a -> Set a -> Maybe a #

O(log n). Find largest element smaller or equal to the given one.

lookupLE 2 (fromList [3, 5]) == Nothing
lookupLE 4 (fromList [3, 5]) == Just 3
lookupLE 5 (fromList [3, 5]) == Just 5

lookupGE :: Ord a => a -> Set a -> Maybe a #

O(log n). Find smallest element greater or equal to the given one.

lookupGE 3 (fromList [3, 5]) == Just 3
lookupGE 4 (fromList [3, 5]) == Just 5
lookupGE 6 (fromList [3, 5]) == Nothing

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.

isProperSubsetOf :: Ord a => Set a -> Set a -> Bool #

O(n+m). Is this a proper subset? (ie. a subset but not equal).

# 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 :: Ord a => [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.

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

O(log n). Take while a predicate on the elements holds. The user is responsible for ensuring that for all elements j and k in the set, j < k ==> p j >= p k. See note at spanAntitone.

takeWhileAntitone p = fromDistinctAscList . takeWhile p . toList
takeWhileAntitone p = filter p


Since: containers-0.5.8

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

O(log n). Drop while a predicate on the elements holds. The user is responsible for ensuring that for all elements j and k in the set, j < k ==> p j >= p k. See note at spanAntitone.

dropWhileAntitone p = fromDistinctAscList . dropWhile p . toList
dropWhileAntitone p = filter (not . p)


Since: containers-0.5.8

spanAntitone :: (a -> Bool) -> Set a -> (Set a, Set a) #

O(log n). Divide a set at the point where a predicate on the elements stops holding. The user is responsible for ensuring that for all elements j and k in the set, j < k ==> p j >= p k.

spanAntitone p xs = (takeWhileAntitone p xs, dropWhileAntitone p xs)
spanAntitone p xs = partition p xs


Note: if p is not actually antitone, then spanAntitone will split the set at some unspecified point where the predicate switches from holding to not holding (where the predicate is seen to hold before the first element and to fail after the last element).

Since: containers-0.5.8

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.

splitRoot :: Set a -> [Set a] #

O(1). Decompose a set into pieces based on the structure of the underlying tree. This function is useful for consuming a set in parallel.

No guarantee is made as to the sizes of the pieces; an internal, but deterministic process determines this. However, it is guaranteed that the pieces returned will be in ascending order (all elements in the first subset less than all elements in the second, and so on).

Examples:

splitRoot (fromList [1..6]) ==
[fromList [1,2,3],fromList [4],fromList [5,6]]
splitRoot empty == []

Note that the current implementation does not return more than three subsets, but you should not depend on this behaviour because it can change in the future without notice.

Since: containers-0.5.4

# Indexed

lookupIndex :: Ord a => a -> Set a -> Maybe Int #

O(log n). Lookup the index of an element, which is its zero-based index in the sorted sequence of elements. The index is a number from 0 up to, but not including, the size of the set.

isJust   (lookupIndex 2 (fromList [5,3])) == False
fromJust (lookupIndex 3 (fromList [5,3])) == 0
fromJust (lookupIndex 5 (fromList [5,3])) == 1
isJust   (lookupIndex 6 (fromList [5,3])) == False

Since: containers-0.5.4

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: containers-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: containers-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

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

# 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

## Strict folds

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

O(n). A strict version of foldr. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

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

O(n). A strict version of foldl. Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.

# Min/Max

lookupMin :: Set a -> Maybe a #

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

Since: containers-0.5.9

lookupMax :: Set a -> Maybe a #

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

Since: containers-0.5.9

deleteMin :: Set a -> Set a #

O(log n). Delete the minimal element. Returns an empty set if the set is empty.

deleteMax :: Set a -> Set a #

O(log n). Delete the maximal element. Returns an empty set if the set is empty.

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.

# Conversion

## List

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.

## Ordered list

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.

# Debugging

showTree :: Show a => Set a -> String #

O(n). Show the tree that implements the set. The tree is shown in a compressed, hanging format.

showTreeWith :: Show a => Bool -> Bool -> Set a -> String #

O(n). The expression (showTreeWith hang wide map) shows the tree that implements the set. If hang is True, a hanging tree is shown otherwise a rotated tree is shown. If wide is True, an extra wide version is shown.

Set> putStrLn $showTreeWith True False$ fromDistinctAscList [1..5]
4
+--2
|  +--1
|  +--3
+--5

Set> putStrLn $showTreeWith True True$ fromDistinctAscList [1..5]
4
|
+--2
|  |
|  +--1
|  |
|  +--3
|
+--5

Set> putStrLn $showTreeWith False True$ fromDistinctAscList [1..5]
+--5
|
4
|
|  +--3
|  |
+--2
|
+--1

valid :: Ord a => Set a -> Bool #

O(n). Test if the internal set structure is valid.