Text.Trifecta.Util.IntervalMap

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://www.soi.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.

Unlike Data.IntervalMap.FingerTree, this version sorts things so that the largest interval from a given point comes first. This way if you have nested intervals, you get the outermost interval before the contained intervals.

Intervals

data Interval v

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

Constructors

Interval

Fields

• low :: v
• high :: v

Instances

Functor Interval

Methods

fmap :: (a -> b) -> Interval a -> Interval b

(<$) :: a -> Interval b -> Interval a

Foldable Interval

Methods

fold :: Monoid m => Interval m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Interval a -> a

foldl1 :: (a -> a -> a) -> Interval a -> a

toList :: Interval a -> [a]

null :: Interval a -> Bool

length :: Interval a -> Int

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

maximum :: Ord a => Interval a -> a

minimum :: Ord a => Interval a -> a

sum :: Num a => Interval a -> a

product :: Num a => Interval a -> a

Traversable Interval

Methods

traverse :: Applicative f => (a -> f b) -> Interval a -> f (Interval b)

sequenceA :: Applicative f => Interval (f a) -> f (Interval a)

mapM :: Monad m => (a -> m b) -> Interval a -> m (Interval b)

sequence :: Monad m => Interval (m a) -> m (Interval a)

(Ord v, Monoid v) => Reducer v (Interval v)

Methods

unit :: v -> Interval v

snoc :: Interval v -> v -> Interval v

cons :: v -> Interval v -> Interval v

Eq v => Eq (Interval v)

Methods

(==) :: Interval v -> Interval v -> Bool

(/=) :: Interval v -> Interval v -> Bool

Ord v => Ord (Interval v)

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)

Methods

showsPrec :: Int -> Interval v -> ShowS

show :: Interval v -> String

showList :: [Interval v] -> ShowS

Ord v => Semigroup (Interval v)

Methods

(<>) :: Interval v -> Interval v -> Interval v

sconcat :: NonEmpty (Interval v) -> Interval v

stimes :: Integral b => b -> Interval v -> Interval v

FunctorWithIndex (Interval v) (IntervalMap v)

Methods

imap :: (Interval v -> a -> b) -> IntervalMap v a -> IntervalMap v b

imapped :: (Indexable (Interval v) p, Settable f) => p a (f b) -> IntervalMap v a -> f (IntervalMap v b)

FoldableWithIndex (Interval v) (IntervalMap v)

Methods

ifoldMap :: Monoid m => (Interval v -> a -> m) -> IntervalMap v a -> m

ifolded :: (Indexable (Interval v) p, Contravariant f, Applicative f) => p a (f a) -> IntervalMap v a -> f (IntervalMap v a)

ifoldr :: (Interval v -> a -> b -> b) -> b -> IntervalMap v a -> b

ifoldl :: (Interval v -> b -> a -> b) -> b -> IntervalMap v a -> b

ifoldr' :: (Interval v -> a -> b -> b) -> b -> IntervalMap v a -> b

ifoldl' :: (Interval v -> b -> a -> b) -> b -> IntervalMap v a -> b

TraversableWithIndex (Interval v) (IntervalMap v)

Methods

itraverse :: Applicative f => (Interval v -> a -> f b) -> IntervalMap v a -> f (IntervalMap v b)

itraversed :: (Indexable (Interval v) p, Applicative f) => p a (f b) -> IntervalMap v a -> f (IntervalMap v b)

Interval maps

newtype IntervalMap v a

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

Constructors

IntervalMap

Fields

• runIntervalMap :: FingerTree (IntInterval v) (Node v a)

Instances

Functor (IntervalMap v)

Methods

fmap :: (a -> b) -> IntervalMap v a -> IntervalMap v b

(<$) :: a -> IntervalMap v b -> IntervalMap v a

Foldable (IntervalMap v)

Methods

fold :: Monoid m => IntervalMap v m -> 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)

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)

FunctorWithIndex (Interval v) (IntervalMap v)

Methods

imap :: (Interval v -> a -> b) -> IntervalMap v a -> IntervalMap v b

imapped :: (Indexable (Interval v) p, Settable f) => p a (f b) -> IntervalMap v a -> f (IntervalMap v b)

FoldableWithIndex (Interval v) (IntervalMap v)

Methods

ifoldMap :: Monoid m => (Interval v -> a -> m) -> IntervalMap v a -> m

ifolded :: (Indexable (Interval v) p, Contravariant f, Applicative f) => p a (f a) -> IntervalMap v a -> f (IntervalMap v a)

ifoldr :: (Interval v -> a -> b -> b) -> b -> IntervalMap v a -> b

ifoldl :: (Interval v -> b -> a -> b) -> b -> IntervalMap v a -> b

ifoldr' :: (Interval v -> a -> b -> b) -> b -> IntervalMap v a -> b

ifoldl' :: (Interval v -> b -> a -> b) -> b -> IntervalMap v a -> b

TraversableWithIndex (Interval v) (IntervalMap v)

Methods

itraverse :: Applicative f => (Interval v -> a -> f b) -> IntervalMap v a -> f (IntervalMap v b)

itraversed :: (Indexable (Interval v) p, Applicative f) => p a (f b) -> IntervalMap v a -> f (IntervalMap v b)

Ord v => Measured (IntInterval v) (IntervalMap v a)

Methods

measure :: IntervalMap v a -> IntInterval v

Ord v => Monoid (IntervalMap v a)

Methods

mempty :: IntervalMap v a

mappend :: IntervalMap v a -> IntervalMap v a -> IntervalMap v a

mconcat :: [IntervalMap v a] -> IntervalMap v a

Ord v => HasUnion (IntervalMap v a)

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.

Methods

union :: IntervalMap v a -> IntervalMap v a -> IntervalMap v a

Ord v => HasUnion0 (IntervalMap v a)

Methods

empty :: IntervalMap v a

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

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

insert :: Ord v => v -> v -> a -> IntervalMap v a -> IntervalMap v a

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.

Searching

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

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

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

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

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

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

Prepending an offset onto every interval in the map

offset :: (Ord v, Monoid v) => v -> IntervalMap v a -> IntervalMap v a

O(n). Add a delta to each interval in the map

The result monoid

data IntInterval v

Constructors

NoInterval

IntInterval (Interval v) v

Instances

Ord v => Monoid (IntInterval v)

Methods

mempty :: IntInterval v

mappend :: IntInterval v -> IntInterval v -> IntInterval v

mconcat :: [IntInterval v] -> IntInterval v

Ord v => Measured (IntInterval v) (IntervalMap v a)

Methods

measure :: IntervalMap v a -> IntInterval v

fromList :: Ord v => [(v, v, a)] -> IntervalMap v a