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 higher bound.

Constructors

Interval

Fields

low :: v

high :: v

Instances

Eq v => Eq (Interval v)

Ord v => Ord (Interval v)

Show v => Show (Interval v)

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. The Foldable and Traversable instances process the intervals in lexicographical order.

Instances

Functor (IntervalMap v)

Foldable (IntervalMap v)

Traversable (IntervalMap v)

Ord v => Monoid (IntervalMap v a)

empty and union.

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 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.