Copyright | (c) Dylan Simon, 2015 |
---|---|

License | MIT |

Safe Haskell | Safe |

Language | Haskell2010 |

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.

- data RSet a
- (\\) :: (Ord a, Enum a) => RSet a -> RSet a -> RSet a
- null :: RSet a -> Bool
- isFull :: (Eq a, Bounded a) => RSet a -> Bool
- size :: Enum a => RSet a -> Int
- member :: (Ord a, Enum a) => a -> RSet a -> Bool
- notMember :: (Ord a, Enum a) => a -> RSet a -> Bool
- lookupLT :: (Ord a, Enum a) => a -> RSet a -> Maybe a
- lookupGT :: (Ord a, Enum a) => a -> RSet a -> Maybe a
- lookupLE :: Ord a => a -> RSet a -> Maybe a
- lookupGE :: Ord a => a -> RSet a -> Maybe a
- containsRange :: Ord a => (a, a) -> RSet a -> Bool
- isSubsetOf :: Ord a => RSet a -> RSet a -> Bool
- valid :: (Ord a, Enum a, Bounded a) => RSet a -> Bool
- empty :: RSet a
- full :: Bounded a => RSet a
- singleton :: a -> RSet a
- singletonRange :: Ord a => (a, a) -> RSet a
- insert :: (Ord a, Enum a) => a -> RSet a -> RSet a
- insertRange :: (Ord a, Enum a) => (a, a) -> RSet a -> RSet a
- delete :: (Ord a, Enum a) => a -> RSet a -> RSet a
- deleteRange :: (Ord a, Enum a) => (a, a) -> RSet a -> RSet a
- union :: (Ord a, Enum a) => RSet a -> RSet a -> RSet a
- difference :: (Ord a, Enum a) => RSet a -> RSet a -> RSet a
- intersection :: (Ord a, Enum a) => RSet a -> RSet a -> RSet a
- split :: (Ord a, Enum a) => a -> RSet a -> (RSet a, RSet a)
- splitMember :: (Ord a, Enum a) => a -> RSet a -> (RSet a, Bool, RSet a)
- findMin :: RSet a -> a
- findMax :: RSet a -> a
- complement :: (Ord a, Enum a, Bounded a) => RSet a -> RSet a
- elems :: Enum a => RSet a -> [a]
- toList :: Enum a => RSet a -> [a]
- fromList :: (Ord a, Enum a) => [a] -> RSet a
- fromAscList :: (Ord a, Enum a) => [a] -> RSet a
- toAscList :: Enum a => RSet a -> [a]
- toRangeList :: RSet a -> [(a, a)]
- fromRangeList :: (Ord a, Enum a) => [(a, a)] -> RSet a
- fromRList :: RSet a -> RSet a
- toRList :: RSet a -> RSet a
- fromNormalizedRangeList :: [(a, a)] -> RSet a

# Range set type

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

# Operators

# Query

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 `

tells whether `isSubsetOf`

s2)`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

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

*O(1)*. Create a continuos range set.

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

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

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

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

# Combine

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 (

) is a pair `split`

x set`(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

# Complement

# 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

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.

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.