Data.IntervalMap.FingerTree

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.

Intervals

data Interval v

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

Constructors

Interval v v

Lower and upper bounds of the interval.

Instances

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

low :: Interval v -> v

Lower bound of the interval

high :: Interval v -> v

Upper bound of the interval

point :: v -> Interval v

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

Interval maps

data IntervalMap v a

Map of closed intervals, possibly with duplicates.

Instances

Functor (IntervalMap v)

Methods

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

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

Foldable (IntervalMap v)

Values in lexicographical order of intervals.

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)

Traverse the intervals in lexicographical order.

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)

(Eq v, Eq a) => Eq (IntervalMap v a)

Methods

(==) :: IntervalMap v a -> IntervalMap v a -> Bool

(/=) :: IntervalMap v a -> IntervalMap v a -> Bool

(Ord v, Ord a) => Ord (IntervalMap v a)

Lexicographical ordering

Methods

compare :: IntervalMap v a -> IntervalMap v a -> Ordering

(<) :: IntervalMap v a -> IntervalMap v a -> Bool

(<=) :: IntervalMap v a -> IntervalMap v a -> Bool

(>) :: IntervalMap v a -> IntervalMap v a -> Bool

(>=) :: IntervalMap v a -> IntervalMap v a -> Bool

max :: IntervalMap v a -> IntervalMap v a -> IntervalMap v a

min :: IntervalMap v a -> IntervalMap v a -> IntervalMap v a

(Show v, Show a) => Show (IntervalMap v a)

Methods

showsPrec :: Int -> IntervalMap v a -> ShowS

show :: IntervalMap v a -> String

showList :: [IntervalMap v a] -> ShowS

Ord v => Semigroup (IntervalMap v a)

union.

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)

empty and union.

Methods

mempty :: IntervalMap v a

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

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

empty :: Ord v => IntervalMap v a

O(1). The empty interval map.

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

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

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

O(log n). Insert an interval and associated value 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

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)]

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)]

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)]

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

Extraction

bounds :: Ord v => IntervalMap v a -> Maybe (Interval v)

O(1). bounds m returns Nothing if m is empty, and otherwise Just i, where i is the smallest interval containing all the intervals in the map.

leastView :: Ord v => IntervalMap v a -> Maybe ((Interval v, a), IntervalMap v a)

O(1). leastView m returns Nothing if m is empty, and otherwise Just ((i, x), m'), where i is the least interval, x is the associated value, and m' is the rest of the map.

splitAfter :: Ord v => v -> IntervalMap v a -> (IntervalMap v a, IntervalMap v a)

O(log(min(i,n-i))). splitAfter k m returns a pair of submaps, one consisting of intervals whose lower bound is less than or equal to k, and the other of those whose lower bound is greater.