Copyright	(c) Ross Paterson 2008
License	BSD-style
Maintainer	R.Paterson@city.ac.uk
Stability	experimental
Portability	non-portable (MPTCs and functional dependencies)
Safe Haskell	None
Language	Haskell2010

HaskellWorks.Data.IntervalMap.FingerTree

Contents

Intervals
Interval maps
Searching

Description

Interval maps implemented using the FingerTree type, following section 4.8 of

Ralf Hinze and Ross Paterson, "Finger trees: a simple general-purpose data structure", Journal of Functional Programming 16:2 (2006) pp 197-217. http://staff.city.ac.uk/~ross/papers/FingerTree.html

An amortized running time is given for each operation, with n referring to the size of the priority queue. These bounds hold even in a persistent (shared) setting.

Note: Many of these operations have the same names as similar operations on lists in the Prelude. The ambiguity may be resolved using either qualification or the hiding clause.

Synopsis

data Interval v = Interval {
- low :: v
- high :: v
}
point :: v -> Interval v
newtype IntervalMap v a = IntervalMap (FingerTree (IntInterval v) (Node v a))
empty :: Ord v => IntervalMap v a
singleton :: Ord v => Interval v -> a -> IntervalMap v a
insert :: Ord v => Interval v -> a -> IntervalMap v a -> IntervalMap v a
union :: Ord v => IntervalMap v a -> IntervalMap v a -> IntervalMap v a
search :: Ord v => v -> IntervalMap v a -> [(Interval v, a)]
intersections :: Ord v => Interval v -> IntervalMap v a -> [(Interval v, a)]
dominators :: Ord v => Interval v -> IntervalMap v a -> [(Interval v, a)]

Intervals

data Interval v Source #

A closed interval. The lower bound should be less than or equal to the higher bound.

Constructors

Interval
Fields low :: v high :: v

Instances

Instances details

Eq v => Eq (Interval v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods (==) :: Interval v -> Interval v -> Bool # (/=) :: Interval v -> Interval v -> Bool #
Ord v => Ord (Interval v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods compare :: Interval v -> Interval v -> Ordering # (<) :: Interval v -> Interval v -> Bool # (<=) :: Interval v -> Interval v -> Bool # (>) :: Interval v -> Interval v -> Bool # (>=) :: Interval v -> Interval v -> Bool # max :: Interval v -> Interval v -> Interval v # min :: Interval v -> Interval v -> Interval v #
Show v => Show (Interval v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods showsPrec :: Int -> Interval v -> ShowS # show :: Interval v -> String # showList :: [Interval v] -> ShowS #
Generic (Interval v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Associated Types type Rep (Interval v) :: Type -> Type # Methods from :: Interval v -> Rep (Interval v) x # to :: Rep (Interval v) x -> Interval v #
NFData v => NFData (Interval v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods rnf :: Interval v -> () #
type Rep (Interval v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree type Rep (Interval v) = D1 ('MetaData "Interval" "HaskellWorks.Data.IntervalMap.FingerTree" "hw-fingertree-0.1.2.1-7DVjKwK8BqoETwS3vQ6f1i" 'False) (C1 ('MetaCons "Interval" 'PrefixI 'True) (S1 ('MetaSel ('Just "low") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 v) :*: S1 ('MetaSel ('Just "high") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 v)))

point :: v -> Interval v Source #

An interval in which the lower and upper bounds are equal.

Interval maps

newtype IntervalMap v a Source #

Map of closed intervals, possibly with duplicates. The Foldable and Traversable instances process the intervals in lexicographical order.

Constructors

IntervalMap (FingerTree (IntInterval v) (Node v a))

Instances

Instances details

Functor (IntervalMap v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods fmap :: (a -> b) -> IntervalMap v a -> IntervalMap v b # (<$) :: a -> IntervalMap v b -> IntervalMap v a #
Foldable (IntervalMap v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods fold :: Monoid m => IntervalMap v m -> m # foldMap :: Monoid m => (a -> m) -> IntervalMap v a -> m # foldMap' :: Monoid m => (a -> m) -> IntervalMap v a -> m # foldr :: (a -> b -> b) -> b -> IntervalMap v a -> b # foldr' :: (a -> b -> b) -> b -> IntervalMap v a -> b # foldl :: (b -> a -> b) -> b -> IntervalMap v a -> b # foldl' :: (b -> a -> b) -> b -> IntervalMap v a -> b # foldr1 :: (a -> a -> a) -> IntervalMap v a -> a # foldl1 :: (a -> a -> a) -> IntervalMap v a -> a # toList :: IntervalMap v a -> [a] # null :: IntervalMap v a -> Bool # length :: IntervalMap v a -> Int # elem :: Eq a => a -> IntervalMap v a -> Bool # maximum :: Ord a => IntervalMap v a -> a # minimum :: Ord a => IntervalMap v a -> a # sum :: Num a => IntervalMap v a -> a # product :: Num a => IntervalMap v a -> a #
Traversable (IntervalMap v) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods traverse :: Applicative f => (a -> f b) -> IntervalMap v a -> f (IntervalMap v b) # sequenceA :: Applicative f => IntervalMap v (f a) -> f (IntervalMap v a) # mapM :: Monad m => (a -> m b) -> IntervalMap v a -> m (IntervalMap v b) # sequence :: Monad m => IntervalMap v (m a) -> m (IntervalMap v a) #
Generic (IntervalMap v a) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Associated Types type Rep (IntervalMap v a) :: Type -> Type # Methods from :: IntervalMap v a -> Rep (IntervalMap v a) x # to :: Rep (IntervalMap v a) x -> IntervalMap v a #
Ord v => Semigroup (IntervalMap v a) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods (<>) :: IntervalMap v a -> IntervalMap v a -> IntervalMap v a # sconcat :: NonEmpty (IntervalMap v a) -> IntervalMap v a # stimes :: Integral b => b -> IntervalMap v a -> IntervalMap v a #
Ord v => Monoid (IntervalMap v a) Source #	`empty` and `union`.
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods mempty :: IntervalMap v a # mappend :: IntervalMap v a -> IntervalMap v a -> IntervalMap v a # mconcat :: [IntervalMap v a] -> IntervalMap v a #
(NFData a, NFData v) => NFData (IntervalMap v a) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree Methods rnf :: IntervalMap v a -> () #
type Rep (IntervalMap v a) Source #
Instance details Defined in HaskellWorks.Data.IntervalMap.FingerTree type Rep (IntervalMap v a)

empty :: Ord v => IntervalMap v a Source #

O(1). The empty interval map.

singleton :: Ord v => Interval v -> a -> IntervalMap v a Source #

O(1). Interval map with a single entry.

insert :: Ord v => Interval v -> a -> IntervalMap v a -> IntervalMap v a Source #

O(log n). Insert an interval into a map. The map may contain duplicate intervals; the new entry will be inserted before any existing entries for the same interval.

union :: Ord v => IntervalMap v a -> IntervalMap v a -> IntervalMap v a Source #

O(m log (n/m)). Merge two interval maps. The map may contain duplicate intervals; entries with equal intervals are kept in the original order.

Searching

search :: Ord v => v -> IntervalMap v a -> [(Interval v, a)] Source #

O(k log (n/k)). All intervals that contain the given point, in lexicographical order.

intersections :: Ord v => Interval v -> IntervalMap v a -> [(Interval v, a)] Source #

O(k log (n/k)). All intervals that intersect with the given interval, in lexicographical order.

dominators :: Ord v => Interval v -> IntervalMap v a -> [(Interval v, a)] Source #

O(k log (n/k)). All intervals that contain the given interval, in lexicographical order.