range-set-list-0.1.2.0: Memory efficient sets with ranges of elements.

Data.RangeSet.Map

Description

A slightly less trivial implementation of range sets.

This is nearly identical to Data.RangeSet.List except for some important performance differences:

• Most query functions in this module are O(log n) rather than O(n), so may be much faster.
• Most composition functions have the same time complexity but a higher constant, so may be somewhat slower.

If you're mainly calling `member`, you should consider using this module, but if you're calling `union`, `deleteRange`, and other range manipulation functions as often as querying, you might stick with the list implementation.

This module is intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.

``` import Data.RangeSet.Map (RSet)
import qualified Data.RangeSet.Map as RSet```

The implementation of `RSet` is based on Data.Map.Strict.

Synopsis

# Range set type

data RSet a Source

Internally set is represented as sorted list of distinct inclusive ranges.

Instances

 Eq a => Eq (RSet a) Source Ord a => Ord (RSet a) Source Show a => Show (RSet a) Source (Ord a, Enum a) => Monoid (RSet a) Source NFData a => NFData (RSet a) Source (Ord a, Enum a) => Semigroup (RSet a) Source

# Operators

(\\) :: (Ord a, Enum a) => RSet a -> RSet a -> RSet a infixl 9 Source

O(n+m). See `difference`.

# Query

null :: RSet a -> Bool Source

O(1). Is this the empty set?

isFull :: (Eq a, Bounded a) => RSet a -> Bool Source

O(1). Is this the empty set?

size :: Enum a => RSet a -> Int Source

O(n). The number of the elements in the set.

member :: (Ord a, Enum a) => a -> RSet a -> Bool Source

O(log n). Is the element in the set?

notMember :: (Ord a, Enum a) => a -> RSet a -> Bool Source

O(log n). Is the element not in the set?

lookupLT :: (Ord a, Enum a) => a -> RSet a -> Maybe a Source

O(log n). Find largest element smaller than the given one.

lookupGT :: (Ord a, Enum a) => a -> RSet a -> Maybe a Source

O(log n). Find smallest element greater than the given one.

lookupLE :: Ord a => a -> RSet a -> Maybe a Source

O(log n). Find largest element smaller or equal to than the given one.

lookupGE :: Ord a => a -> RSet a -> Maybe a Source

O(log n). Find smallest element greater or equal to than the given one.

containsRange :: Ord a => (a, a) -> RSet a -> Bool Source

O(log n). Is the entire range contained within the set?

isSubsetOf :: Ord a => RSet a -> RSet a -> Bool Source

O(n+m). Is this a subset? `(s1 isSubsetOf s2)` tells whether `s1` is a subset of `s2`.

valid :: (Ord a, Enum a, Bounded a) => RSet a -> Bool Source

O(n). Ensure that a set is valid. All functions should return valid sets except those with unchecked preconditions: `fromAscList`, `fromNormalizedRangeList`

# Construction

O(1). The empty set.

full :: Bounded a => RSet a Source

O(1). The full set.

singleton :: a -> RSet a Source

O(1). Create a singleton set.

singletonRange :: Ord a => (a, a) -> RSet a Source

O(1). Create a continuos range set.

insert :: (Ord a, Enum a) => a -> RSet a -> RSet a Source

O(n). Insert an element in a set.

insertRange :: (Ord a, Enum a) => (a, a) -> RSet a -> RSet a Source

O(n). Insert a continuos range in a set.

delete :: (Ord a, Enum a) => a -> RSet a -> RSet a Source

/O(n). Delete an element from a set.

deleteRange :: (Ord a, Enum a) => (a, a) -> RSet a -> RSet a Source

/O(n). Delete a continuos range from a set.

# Combine

union :: (Ord a, Enum a) => RSet a -> RSet a -> RSet a Source

O(n*m). The union of two sets.

difference :: (Ord a, Enum a) => RSet a -> RSet a -> RSet a Source

O(n*m). Difference of two sets.

intersection :: (Ord a, Enum a) => RSet a -> RSet a -> RSet a Source

O(n*m). The intersection of two sets.

# Filter

split :: (Ord a, Enum a) => a -> RSet a -> (RSet a, RSet a) Source

O(log n). The expression (`split x set`) is a pair `(set1,set2)` where `set1` comprises the elements of `set` less than `x` and `set2` comprises the elements of `set` greater than `x`.

splitMember :: (Ord a, Enum a) => a -> RSet a -> (RSet a, Bool, RSet a) Source

O(log n). Performs a `split` but also returns whether the pivot element was found in the original set.

# Min/Max

findMin :: RSet a -> a Source

O(log n). The minimal element of a set.

findMax :: RSet a -> a Source

O(log n). The maximal element of a set.

# Complement

complement :: (Ord a, Enum a, Bounded a) => RSet a -> RSet a Source

O(n). Complement of the set.

# Conversion

elems :: Enum a => RSet a -> [a] Source

O(n*r). An alias of `toAscList`. The elements of a set in ascending order. r is the size of longest range.

toList :: Enum a => RSet a -> [a] Source

O(n*r). Convert the set to a list of elements (in arbitrary order). r is the size of longest range.

fromList :: (Ord a, Enum a) => [a] -> RSet a Source

O(n*log n). Create a set from a list of elements. Note that unlike Data.Set and other binary trees, this always requires a full sort and traversal to create distinct, disjoint ranges before constructing the tree.

fromAscList :: (Ord a, Enum a) => [a] -> RSet a Source

O(n). Create a set from a list of ascending elements. The precondition is not checked. You may use `valid` to check the result. Note that unlike Data.Set and other binary trees, this always requires a full traversal to create distinct, disjoint ranges before constructing the tree.

toAscList :: Enum a => RSet a -> [a] Source

O(n*r). Convert the set to an ascending list of elements.

toRangeList :: RSet a -> [(a, a)] Source

O(n). Convert the set to a list of range pairs.

fromRangeList :: (Ord a, Enum a) => [(a, a)] -> RSet a Source

O(n*log n). Create a set from a list of range pairs. Note that unlike Data.Set and other binary trees, this always requires a full sort and traversal to create distinct, disjoint ranges before constructing the tree.

fromRList :: RSet a -> RSet a Source

O(n). Convert a list-based `RSet` to a map-based `RSet`.

toRList :: RSet a -> RSet a Source

O(n). Convert a map-based `RSet` to a list-based `RSet`.

fromNormalizedRangeList :: [(a, a)] -> RSet a Source

O(n). Convert a normalized, non-adjacent, ascending list of ranges to a set. The precondition is not checked. In general you should only use this function on the result of `toRangeList` or ensure `valid` on the result.