Data.IntervalMap.FingerTree

fingertree-0.1.1.0: Generic finger-tree structure, with example instances

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 | Safe
Language | Haskell98

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
- data IntervalMap 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

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.