Copyright | (c) Christoph Breitkopf 2011 |
---|---|

License | BSD-style |

Maintainer | chbreitkopf@gmail.com |

Stability | experimental |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell98 |

An implementation of maps from intervals to values. The key intervals may overlap, and the implementation contains efficient search functions for all keys containing a point or overlapping an interval. Closed, open, and half-open intervals can be contained in the same map.

The functions in this module are strict in both the keys and the values. If you need value-lazy maps, use Data.IntervalMap.Lazy instead. The IntervalMap type itself is shared between the lazy and strict modules, meaning that the same IntervalMap value can be passed to functions in both modules (although that is rarely needed).

An IntervalMap cannot contain duplicate keys - if you need to map a
key to multiple values, use a collection as the value type, for
example: `IntervalMap `

.*k* [*v*]

It is an error to insert an empty interval into a map. This precondition is not checked by the various construction functions.

Since many function names (but not the type name) clash with *Prelude*
names, this module is usually imported `qualified`

, e.g.

import Data.IntervalMap (IvMap) import qualified Data.IntervalMap as IvMap

It offers most of the same functions as `Map`

, but uses
`Interval`

*k* instead of just *k* as the key type. Some of the
functions need stricter type constraints to maintain the additional
information for efficient interval searching, for example
`fromDistinctAscList`

needs an `Ord`

*k* constraint. Also, some
functions differ in asymptotic performance (for example `size`

) or
have not been tuned for efficiency as much as their equivalents in
`Map`

(in particular the various set functions).

In addition, there are functions specific to maps of intervals, for example to search for all keys containing a given point or contained in a given interval.

To stay compatible with standard Haskell, this implementation uses a
fixed data type for intervals, and not a multi-parameter type
class. Thus, it's currently not possible to define e.g. a 2-tuple as
an instance of interval and use that map key. Instead, you must
convert your keys to `Interval`

.

The implementation is a red-black tree augmented with the maximum upper bound of all keys.

Parts of this implementation are based on code from the `Map`

implementation, (c) Daan Leijen 2002, (c) Andriy Palamarchuk 2008. The
red-black tree deletion is based on code from llrbtree by Kazu
Yamamoto. Of course, any errors are mine.

- data Interval a
- = IntervalCO !a !a
- | ClosedInterval !a !a
- | OpenInterval !a !a
- | IntervalOC !a !a

- type IntervalMap k v = IntervalMap (Interval k) v
- (!) :: (Interval k e, Ord k) => IntervalMap k v -> k -> v
- (\\) :: (Interval k e, Ord k) => IntervalMap k a -> IntervalMap k b -> IntervalMap k a
- null :: Foldable t => forall a. t a -> Bool
- size :: IntervalMap k v -> Int
- member :: Ord k => k -> IntervalMap k v -> Bool
- notMember :: Ord k => k -> IntervalMap k v -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- findWithDefault :: Ord k => a -> k -> IntervalMap k a -> a
- containing :: Interval k e => IntervalMap k v -> e -> [(k, v)]
- intersecting :: Interval k e => IntervalMap k v -> k -> [(k, v)]
- within :: Interval k e => IntervalMap k v -> k -> [(k, v)]
- empty :: IntervalMap k v
- singleton :: k -> v -> IntervalMap k v
- insert :: (Interval k e, Ord k) => k -> v -> IntervalMap k v -> IntervalMap k v
- insertWith :: (Interval k e, Ord k) => (v -> v -> v) -> k -> v -> IntervalMap k v -> IntervalMap k v
- insertWithKey :: (Interval k e, Ord k) => (k -> v -> v -> v) -> k -> v -> IntervalMap k v -> IntervalMap k v
- insertLookupWithKey :: (Interval k e, Ord k) => (k -> v -> v -> v) -> k -> v -> IntervalMap k v -> (Maybe v, IntervalMap k v)
- delete :: (Interval k e, Ord k) => k -> IntervalMap k v -> IntervalMap k v
- adjust :: Ord k => (a -> a) -> k -> IntervalMap k a -> IntervalMap k a
- adjustWithKey :: Ord k => (k -> a -> a) -> k -> IntervalMap k a -> IntervalMap k a
- update :: (Interval k e, Ord k) => (a -> Maybe a) -> k -> IntervalMap k a -> IntervalMap k a
- updateWithKey :: (Interval k e, Ord k) => (k -> a -> Maybe a) -> k -> IntervalMap k a -> IntervalMap k a
- updateLookupWithKey :: (Interval k e, Ord k) => (k -> a -> Maybe a) -> k -> IntervalMap k a -> (Maybe a, IntervalMap k a)
- alter :: (Interval k e, Ord k) => (Maybe a -> Maybe a) -> k -> IntervalMap k a -> IntervalMap k a
- union :: (Interval k e, Ord k) => IntervalMap k a -> IntervalMap k a -> IntervalMap k a
- unionWith :: (Interval k e, Ord k) => (a -> a -> a) -> IntervalMap k a -> IntervalMap k a -> IntervalMap k a
- unionWithKey :: (Interval k e, Ord k) => (k -> a -> a -> a) -> IntervalMap k a -> IntervalMap k a -> IntervalMap k a
- unions :: (Interval k e, Ord k) => [IntervalMap k a] -> IntervalMap k a
- unionsWith :: (Interval k e, Ord k) => (a -> a -> a) -> [IntervalMap k a] -> IntervalMap k a
- difference :: (Interval k e, Ord k) => IntervalMap k a -> IntervalMap k b -> IntervalMap k a
- differenceWith :: (Interval k e, Ord k) => (a -> b -> Maybe a) -> IntervalMap k a -> IntervalMap k b -> IntervalMap k a
- differenceWithKey :: (Interval k e, Ord k) => (k -> a -> b -> Maybe a) -> IntervalMap k a -> IntervalMap k b -> IntervalMap k a
- intersection :: (Interval k e, Ord k) => IntervalMap k a -> IntervalMap k b -> IntervalMap k a
- intersectionWith :: (Interval k e, Ord k) => (a -> b -> c) -> IntervalMap k a -> IntervalMap k b -> IntervalMap k c
- intersectionWithKey :: (Interval k e, Ord k) => (k -> a -> b -> c) -> IntervalMap k a -> IntervalMap k b -> IntervalMap k c
- map :: (a -> b) -> [a] -> [b]
- mapWithKey :: (k -> a -> b) -> IntervalMap k a -> IntervalMap k b
- mapAccum :: (a -> b -> (a, c)) -> a -> IntervalMap k b -> (a, IntervalMap k c)
- mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> IntervalMap k b -> (a, IntervalMap k c)
- mapAccumRWithKey :: (a -> k -> b -> (a, c)) -> a -> IntervalMap k b -> (a, IntervalMap k c)
- mapKeys :: (Interval k2 e, Ord k2) => (k1 -> k2) -> IntervalMap k1 a -> IntervalMap k2 a
- mapKeysWith :: (Interval k2 e, Ord k2) => (a -> a -> a) -> (k1 -> k2) -> IntervalMap k1 a -> IntervalMap k2 a
- mapKeysMonotonic :: (Interval k2 e, Ord k2) => (k1 -> k2) -> IntervalMap k1 a -> IntervalMap k2 a
- foldr :: Foldable t => forall a b. (a -> b -> b) -> b -> t a -> b
- foldl :: Foldable t => forall b a. (b -> a -> b) -> b -> t a -> b
- foldrWithKey :: (k -> v -> a -> a) -> a -> IntervalMap k v -> a
- foldlWithKey :: (a -> k -> v -> a) -> a -> IntervalMap k v -> a
- elems :: IntervalMap k v -> [v]
- keys :: IntervalMap k v -> [k]
- keysSet :: Ord k => IntervalMap k v -> Set k
- assocs :: IntervalMap k v -> [(k, v)]
- toList :: IntervalMap k v -> [(k, v)]
- fromList :: (Interval k e, Ord k) => [(k, v)] -> IntervalMap k v
- fromListWith :: (Interval k e, Ord k) => (a -> a -> a) -> [(k, a)] -> IntervalMap k a
- fromListWithKey :: (Interval k e, Ord k) => (k -> a -> a -> a) -> [(k, a)] -> IntervalMap k a
- toAscList :: IntervalMap k v -> [(k, v)]
- toDescList :: IntervalMap k v -> [(k, v)]
- fromAscList :: (Interval k e, Eq k) => [(k, v)] -> IntervalMap k v
- fromAscListWith :: (Interval k e, Eq k) => (a -> a -> a) -> [(k, a)] -> IntervalMap k a
- fromAscListWithKey :: (Interval k e, Eq k) => (k -> a -> a -> a) -> [(k, a)] -> IntervalMap k a
- fromDistinctAscList :: Interval k e => [(k, v)] -> IntervalMap k v
- filter :: (a -> Bool) -> [a] -> [a]
- filterWithKey :: Interval k e => (k -> a -> Bool) -> IntervalMap k a -> IntervalMap k a
- partition :: Interval k e => (a -> Bool) -> IntervalMap k a -> (IntervalMap k a, IntervalMap k a)
- partitionWithKey :: Interval k e => (k -> a -> Bool) -> IntervalMap k a -> (IntervalMap k a, IntervalMap k a)
- mapMaybe :: Interval k e => (a -> Maybe b) -> IntervalMap k a -> IntervalMap k b
- mapMaybeWithKey :: Interval k e => (k -> a -> Maybe b) -> IntervalMap k a -> IntervalMap k b
- mapEither :: Interval k e => (a -> Either b c) -> IntervalMap k a -> (IntervalMap k b, IntervalMap k c)
- mapEitherWithKey :: Interval k e => (k -> a -> Either b c) -> IntervalMap k a -> (IntervalMap k b, IntervalMap k c)
- split :: (Interval i k, Ord i) => i -> IntervalMap i a -> (IntervalMap i a, IntervalMap i a)
- splitLookup :: (Interval i k, Ord i) => i -> IntervalMap i a -> (IntervalMap i a, Maybe a, IntervalMap i a)
- isSubmapOf :: (Ord k, Eq a) => IntervalMap k a -> IntervalMap k a -> Bool
- isSubmapOfBy :: Ord k => (a -> b -> Bool) -> IntervalMap k a -> IntervalMap k b -> Bool
- isProperSubmapOf :: (Ord k, Eq a) => IntervalMap k a -> IntervalMap k a -> Bool
- isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> IntervalMap k a -> IntervalMap k b -> Bool
- findMin :: IntervalMap k v -> (k, v)
- findMax :: IntervalMap k v -> (k, v)
- findLast :: Interval k e => IntervalMap k v -> (k, v)
- deleteMin :: (Interval k e, Ord k) => IntervalMap k v -> IntervalMap k v
- deleteMax :: (Interval k e, Ord k) => IntervalMap k v -> IntervalMap k v
- deleteFindMin :: (Interval k e, Ord k) => IntervalMap k v -> ((k, v), IntervalMap k v)
- deleteFindMax :: (Interval k e, Ord k) => IntervalMap k v -> ((k, v), IntervalMap k v)
- updateMin :: (Interval k e, Ord k) => (v -> Maybe v) -> IntervalMap k v -> IntervalMap k v
- updateMax :: (Interval k e, Ord k) => (v -> Maybe v) -> IntervalMap k v -> IntervalMap k v
- updateMinWithKey :: (Interval k e, Ord k) => (k -> v -> Maybe v) -> IntervalMap k v -> IntervalMap k v
- updateMaxWithKey :: (Interval k e, Ord k) => (k -> v -> Maybe v) -> IntervalMap k v -> IntervalMap k v
- minView :: (Interval k e, Ord k) => IntervalMap k a -> Maybe (a, IntervalMap k a)
- maxView :: (Interval k e, Ord k) => IntervalMap k a -> Maybe (a, IntervalMap k a)
- minViewWithKey :: (Interval k e, Ord k) => IntervalMap k a -> Maybe ((k, a), IntervalMap k a)
- maxViewWithKey :: (Interval k e, Ord k) => IntervalMap k a -> Maybe ((k, a), IntervalMap k a)
- valid :: (Interval i k, Ord i) => IntervalMap i v -> Bool
- height :: IntervalMap k v -> Int
- maxHeight :: Int -> Int
- showStats :: IntervalMap k a -> (Int, Int, Int)

# re-export

Intervals with endpoints of type `a`

.

`Read`

and `Show`

use mathematical notation with square brackets for closed
and parens for open intervals.
This is better for human readability, but is not a valid Haskell expression.
Closed intervals look like a list, open intervals look like a tuple,
and half-open intervals look like mismatched parens.

IntervalCO !a !a | Including lower bound, excluding upper |

ClosedInterval !a !a | Closed at both ends |

OpenInterval !a !a | Open at both ends |

IntervalOC !a !a | Excluding lower bound, including upper |

# Map type

type IntervalMap k v = IntervalMap (Interval k) v Source

# Operators

(!) :: (Interval k e, Ord k) => IntervalMap k v -> k -> v infixl 9 Source

*O(log n)*. Lookup value for given key. Calls `error`

if the key is not in the map.

Use `lookup`

or `findWithDefault`

instead of this function, unless you are absolutely
sure that the key is present in the map.

(\\) :: (Interval k e, Ord k) => IntervalMap k a -> IntervalMap k b -> IntervalMap k a infixl 9 Source

Same as `difference`

.

# Query

null :: Foldable t => forall a. t a -> Bool

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

size :: IntervalMap k v -> Int Source

*O(n)*. Number of keys in the map.

Caution: unlike `size`

, which takes constant time, this is linear in the
number of keys!

member :: Ord k => k -> IntervalMap k v -> Bool Source

*O(log n)*. Does the map contain the given key? See also `notMember`

.

notMember :: Ord k => k -> IntervalMap k v -> Bool Source

*O(log n)*. Does the map not contain the given key? See also `member`

.

findWithDefault :: Ord k => a -> k -> IntervalMap k a -> a Source

*O(log n)*. The expression `(`

returns
the value at key `findWithDefault`

def k map)`k`

or returns default value `def`

when the key is not in the map.

findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'

## Interval query

containing :: Interval k e => IntervalMap k v -> e -> [(k, v)] Source

Return all key/value pairs where the key intervals contain the given point. The elements are returned in ascending key order.

*O(n)*, since potentially all keys could contain the point.
*O(log n)* average case. This is also the worst case for maps containing no overlapping keys.

intersecting :: Interval k e => IntervalMap k v -> k -> [(k, v)] Source

Return all key/value pairs where the key intervals overlap (intersect) the given interval. The elements are returned in ascending key order.

*O(n)*, since potentially all keys could intersect the interval.
*O(log n)* average case, if few keys intersect the interval.

within :: Interval k e => IntervalMap k v -> k -> [(k, v)] Source

Return all key/value pairs where the key intervals are completely inside the given interval. The elements are returned in ascending key order.

*O(n)*, since potentially all keys could be inside the interval.
*O(log n)* average case, if few keys are inside the interval.

# Construction

empty :: IntervalMap k v Source

*O(1)*. The empty map.

singleton :: k -> v -> IntervalMap k v Source

*O(1)*. A map with one entry.

## Insertion

insert :: (Interval k e, Ord k) => k -> v -> IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Insert a new key/value pair. If the map already contains the key, its value is
changed to the new value.

insertWith :: (Interval k e, Ord k) => (v -> v -> v) -> k -> v -> IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Insert with a function, combining new value and old value.

will insert the pair (key, value) into `insertWith`

f key value mp`mp`

if key does
not exist in the map. If the key does exist, the function will
insert the pair `(key, f new_value old_value)`

.

insertWithKey :: (Interval k e, Ord k) => (k -> v -> v -> v) -> k -> v -> IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Insert with a function, combining key, new value and old value.

will insert the pair (key, value) into `insertWithKey`

f key value mp`mp`

if key does
not exist in the map. If the key does exist, the function will
insert the pair `(key, f key new_value old_value)`

.
Note that the key passed to f is the same key passed to `insertWithKey`

.

insertLookupWithKey :: (Interval k e, Ord k) => (k -> v -> v -> v) -> k -> v -> IntervalMap k v -> (Maybe v, IntervalMap k v) Source

*O(log n)*. Combine insert with old values retrieval.

## Delete/Update

delete :: (Interval k e, Ord k) => k -> IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Delete a key from the map. If the map does not contain the key,
it is returned unchanged.

adjust :: Ord k => (a -> a) -> k -> IntervalMap k a -> IntervalMap k a Source

*O(log n)*. Update a value at a specific key with the result of the provided function.
When the key is not
a member of the map, the original map is returned.

adjustWithKey :: Ord k => (k -> a -> a) -> k -> IntervalMap k a -> IntervalMap k a Source

*O(log n)*. Adjust a value at a specific key. When the key is not
a member of the map, the original map is returned.

update :: (Interval k e, Ord k) => (a -> Maybe a) -> k -> IntervalMap k a -> IntervalMap k a Source

updateWithKey :: (Interval k e, Ord k) => (k -> a -> Maybe a) -> k -> IntervalMap k a -> IntervalMap k a Source

*O(log n)*. The expression (

) updates the
value `updateWithKey`

f k map`x`

at `k`

(if it is in the map). If (`f k x`

) is `Nothing`

,
the element is deleted. If it is (

), the key `Just`

y`k`

is bound
to the new value `y`

.

updateLookupWithKey :: (Interval k e, Ord k) => (k -> a -> Maybe a) -> k -> IntervalMap k a -> (Maybe a, IntervalMap k a) Source

*O(log n)*. Lookup and update. See also `updateWithKey`

.
The function returns changed value, if it is updated.
Returns the original key value if the map entry is deleted.

alter :: (Interval k e, Ord k) => (Maybe a -> Maybe a) -> k -> IntervalMap k a -> IntervalMap k a Source

# Combine

## Union

union :: (Interval k e, Ord k) => IntervalMap k a -> IntervalMap k a -> IntervalMap k a Source

unionWith :: (Interval k e, Ord k) => (a -> a -> a) -> IntervalMap k a -> IntervalMap k a -> IntervalMap k a Source

*O(n+m)*. Union with a combining function.

unionWithKey :: (Interval k e, Ord k) => (k -> a -> a -> a) -> IntervalMap k a -> IntervalMap k a -> IntervalMap k a Source

*O(n+m)*. Union with a combining function.

unions :: (Interval k e, Ord k) => [IntervalMap k a] -> IntervalMap k a Source

unionsWith :: (Interval k e, Ord k) => (a -> a -> a) -> [IntervalMap k a] -> IntervalMap k a Source

The union of a list of maps, with a combining operation:
(

).`unionsWith`

f == `foldl`

(`unionWith`

f) `empty`

## Difference

difference :: (Interval k e, Ord k) => IntervalMap k a -> IntervalMap k b -> IntervalMap k a Source

*O(n+m)*. Difference of two maps.
Return elements of the first map not existing in the second map.

differenceWith :: (Interval k e, Ord k) => (a -> b -> Maybe a) -> IntervalMap k a -> IntervalMap k b -> IntervalMap k a Source

differenceWithKey :: (Interval k e, Ord k) => (k -> a -> b -> Maybe a) -> IntervalMap k a -> IntervalMap k b -> IntervalMap k a Source

## Intersection

intersection :: (Interval k e, Ord k) => IntervalMap k a -> IntervalMap k b -> IntervalMap k a Source

*O(n+m)*. Intersection of two maps.
Return data in the first map for the keys existing in both maps.
(

).`intersection`

m1 m2 == `intersectionWith`

`const`

m1 m2

intersectionWith :: (Interval k e, Ord k) => (a -> b -> c) -> IntervalMap k a -> IntervalMap k b -> IntervalMap k c Source

*O(n+m)*. Intersection with a combining function.

intersectionWithKey :: (Interval k e, Ord k) => (k -> a -> b -> c) -> IntervalMap k a -> IntervalMap k b -> IntervalMap k c Source

*O(n+m)*. Intersection with a combining function.

# Traversal

## Map

map :: (a -> b) -> [a] -> [b]

`map`

`f xs`

is the list obtained by applying `f`

to each element
of `xs`

, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]

mapWithKey :: (k -> a -> b) -> IntervalMap k a -> IntervalMap k b Source

*O(n)*. Map a function over all values in the map.

mapAccum :: (a -> b -> (a, c)) -> a -> IntervalMap k b -> (a, IntervalMap k c) Source

*O(n)*. The function `mapAccum`

threads an accumulating
argument through the map in ascending order of keys.

let f a b = (a ++ b, b ++ "X") mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])

mapAccumWithKey :: (a -> k -> b -> (a, c)) -> a -> IntervalMap k b -> (a, IntervalMap k c) Source

*O(n)*. The function `mapAccumWithKey`

threads an accumulating
argument through the map in ascending order of keys.

let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X") mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])

mapAccumRWithKey :: (a -> k -> b -> (a, c)) -> a -> IntervalMap k b -> (a, IntervalMap k c) Source

*O(n)*. The function `mapAccumRWithKey`

threads an accumulating
argument through the map in descending order of keys.

mapKeys :: (Interval k2 e, Ord k2) => (k1 -> k2) -> IntervalMap k1 a -> IntervalMap k2 a Source

*O(n log n)*.

is the map obtained by applying `mapKeys`

f s`f`

to each key of `s`

.

The size of the result may be smaller if `f`

maps two or more distinct
keys to the same new key. In this case the value at the smallest of
these keys is retained.

mapKeysWith :: (Interval k2 e, Ord k2) => (a -> a -> a) -> (k1 -> k2) -> IntervalMap k1 a -> IntervalMap k2 a Source

*O(n log n)*.

is the map obtained by applying `mapKeysWith`

c f s`f`

to each key of `s`

.

The size of the result may be smaller if `f`

maps two or more distinct
keys to the same new key. In this case the associated values will be
combined using `c`

.

mapKeysMonotonic :: (Interval k2 e, Ord k2) => (k1 -> k2) -> IntervalMap k1 a -> IntervalMap k2 a Source

*O(n)*.

, but works only when `mapKeysMonotonic`

f s == `mapKeys`

f s`f`

is strictly monotonic.
That is, for any values `x`

and `y`

, if `x`

< `y`

then `f x`

< `f y`

.
*The precondition is not checked.*

## Fold

foldrWithKey :: (k -> v -> a -> a) -> a -> IntervalMap k v -> a Source

*O(n)*. Fold the keys and values in the map using the given right-associative
binary operator, such that

.`foldrWithKey`

f z == `foldr`

(`uncurry`

f) z . `toAscList`

foldlWithKey :: (a -> k -> v -> a) -> a -> IntervalMap k v -> a Source

*O(n)*. Fold the keys and values in the map using the given left-associative
binary operator, such that

.`foldlWithKey`

f z == `foldl`

(\z' (kx, x) -> f z' kx x) z . `toAscList`

# Conversion

elems :: IntervalMap k v -> [v] Source

*O(n)*. List of all values in the map, in ascending order of their keys.

keys :: IntervalMap k v -> [k] Source

*O(n)*. List of all keys in the map, in ascending order.

keysSet :: Ord k => IntervalMap k v -> Set k Source

*O(n)*. Set of the keys.

assocs :: IntervalMap k v -> [(k, v)] Source

Same as `toAscList`

.

## Lists

toList :: IntervalMap k v -> [(k, v)] Source

*O(n)*. The list of all key/value pairs contained in the map, in no particular order.

fromList :: (Interval k e, Ord k) => [(k, v)] -> IntervalMap k v Source

*O(n log n)*. Build a map from a list of key/value pairs. See also `fromAscList`

.
If the list contains more than one value for the same key, the last value
for the key is retained.

fromListWith :: (Interval k e, Ord k) => (a -> a -> a) -> [(k, a)] -> IntervalMap k a Source

*O(n log n)*. Build a map from a list of key/value pairs with a combining function. See also `fromAscListWith`

.

fromListWithKey :: (Interval k e, Ord k) => (k -> a -> a -> a) -> [(k, a)] -> IntervalMap k a Source

*O(n log n)*. Build a map from a list of key/value pairs with a combining function. See also `fromAscListWith`

.

## Ordered lists

toAscList :: IntervalMap k v -> [(k, v)] Source

*O(n)*. The list of all key/value pairs contained in the map, in ascending order of keys.

toDescList :: IntervalMap k v -> [(k, v)] Source

*O(n)*. The list of all key/value pairs contained in the map, in descending order of keys.

fromAscList :: (Interval k e, Eq k) => [(k, v)] -> IntervalMap k v Source

*O(n)*. Build a map from an ascending list in linear time.
*The precondition (input list is ascending) is not checked.*

fromAscListWith :: (Interval k e, Eq k) => (a -> a -> a) -> [(k, a)] -> IntervalMap k a Source

*O(n)*. Build a map from an ascending list in linear time with a combining function for equal keys.
*The precondition (input list is ascending) is not checked.*

fromAscListWithKey :: (Interval k e, Eq k) => (k -> a -> a -> a) -> [(k, a)] -> IntervalMap k a Source

*O(n)*. Build a map from an ascending list in linear time with a combining function for equal keys.
*The precondition (input list is ascending) is not checked.*

fromDistinctAscList :: Interval k e => [(k, v)] -> IntervalMap k v Source

*O(n)*. Build a map from an ascending list of elements with distinct keys in linear time.
*The precondition is not checked.*

# Filter

filter :: (a -> Bool) -> [a] -> [a]

`filter`

, applied to a predicate and a list, returns the list of
those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

filterWithKey :: Interval k e => (k -> a -> Bool) -> IntervalMap k a -> IntervalMap k a Source

*O(n)*. Filter keys/values satisfying a predicate.

partition :: Interval k e => (a -> Bool) -> IntervalMap k a -> (IntervalMap k a, IntervalMap k a) Source

*O(n)*. Partition the map according to a predicate. The first
map contains all elements that satisfy the predicate, the second all
elements that fail the predicate. See also `split`

.

partitionWithKey :: Interval k e => (k -> a -> Bool) -> IntervalMap k a -> (IntervalMap k a, IntervalMap k a) Source

*O(n)*. Partition the map according to a predicate. The first
map contains all elements that satisfy the predicate, the second all
elements that fail the predicate. See also `split`

.

mapMaybe :: Interval k e => (a -> Maybe b) -> IntervalMap k a -> IntervalMap k b Source

*O(n)*. Map values and collect the `Just`

results.

mapMaybeWithKey :: Interval k e => (k -> a -> Maybe b) -> IntervalMap k a -> IntervalMap k b Source

*O(n)*. Map keys/values and collect the `Just`

results.

mapEither :: Interval k e => (a -> Either b c) -> IntervalMap k a -> (IntervalMap k b, IntervalMap k c) Source

mapEitherWithKey :: Interval k e => (k -> a -> Either b c) -> IntervalMap k a -> (IntervalMap k b, IntervalMap k c) Source

split :: (Interval i k, Ord i) => i -> IntervalMap i a -> (IntervalMap i a, IntervalMap i a) Source

*O(n)*. The expression (

) is a pair `split`

k map`(map1,map2)`

where
the keys in `map1`

are smaller than `k`

and the keys in `map2`

larger than `k`

.
Any key equal to `k`

is found in neither `map1`

nor `map2`

.

splitLookup :: (Interval i k, Ord i) => i -> IntervalMap i a -> (IntervalMap i a, Maybe a, IntervalMap i a) Source

*O(n)*. The expression (

) splits a map just
like `splitLookup`

k map`split`

but also returns

.`lookup`

k map

# Submap

isSubmapOf :: (Ord k, Eq a) => IntervalMap k a -> IntervalMap k a -> Bool Source

*O(n+m)*. This function is defined as (

).`isSubmapOf`

= `isSubmapOfBy`

(==)

isSubmapOfBy :: Ord k => (a -> b -> Bool) -> IntervalMap k a -> IntervalMap k b -> Bool Source

*O(n+m)*.
The expression (

) returns `isSubmapOfBy`

f t1 t2`True`

if
all keys in `t1`

are in tree `t2`

, and `f`

returns `True`

when
applied to their respective values.

isProperSubmapOf :: (Ord k, Eq a) => IntervalMap k a -> IntervalMap k a -> Bool Source

*O(n+m)*. Is this a proper submap? (ie. a submap but not equal).
Defined as (

).`isProperSubmapOf`

= `isProperSubmapOfBy`

(==)

isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> IntervalMap k a -> IntervalMap k b -> Bool Source

*O(n+m)*. Is this a proper submap? (ie. a submap but not equal).
The expression (

) returns `isProperSubmapOfBy`

f m1 m2`True`

when
`m1`

and `m2`

are not equal,
all keys in `m1`

are in `m2`

, and when `f`

returns `True`

when
applied to their respective values.

# Min/Max

findMin :: IntervalMap k v -> (k, v) Source

*O(log n)*. Returns the smallest key and its associated value.
Calls `error`

if the map is empty.

findMax :: IntervalMap k v -> (k, v) Source

*O(log n)*. Returns the largest key and its associated value.
Calls `error`

if the map is empty.

findLast :: Interval k e => IntervalMap k v -> (k, v) Source

Returns the key with the largest endpoint and its associated value. If there is more than one key with that endpoint, return the rightmost.

*O(n)*, since all keys could have the same endpoint.
*O(log n)* average case.

deleteMin :: (Interval k e, Ord k) => IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Remove the smallest key from the map. Return the empty map if the map is empty.

deleteMax :: (Interval k e, Ord k) => IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Remove the largest key from the map. Return the empty map if the map is empty.

deleteFindMin :: (Interval k e, Ord k) => IntervalMap k v -> ((k, v), IntervalMap k v) Source

*O(log n)*. Delete and return the smallest key.

deleteFindMax :: (Interval k e, Ord k) => IntervalMap k v -> ((k, v), IntervalMap k v) Source

*O(log n)*. Delete and return the largest key.

updateMin :: (Interval k e, Ord k) => (v -> Maybe v) -> IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Update or delete value at minimum key.

updateMax :: (Interval k e, Ord k) => (v -> Maybe v) -> IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Update or delete value at maximum key.

updateMinWithKey :: (Interval k e, Ord k) => (k -> v -> Maybe v) -> IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Update or delete value at minimum key.

updateMaxWithKey :: (Interval k e, Ord k) => (k -> v -> Maybe v) -> IntervalMap k v -> IntervalMap k v Source

*O(log n)*. Update or delete value at maximum key.

minView :: (Interval k e, Ord k) => IntervalMap k a -> Maybe (a, IntervalMap k a) Source

*O(log n)*. Retrieves the value associated with minimal key of the
map, and the map stripped of that element, or `Nothing`

if passed an
empty map.

maxView :: (Interval k e, Ord k) => IntervalMap k a -> Maybe (a, IntervalMap k a) Source

*O(log n)*. Retrieves the value associated with maximal key of the
map, and the map stripped of that element, or `Nothing`

if passed an
empty map.

minViewWithKey :: (Interval k e, Ord k) => IntervalMap k a -> Maybe ((k, a), IntervalMap k a) Source

*O(log n)*. Retrieves the minimal (key,value) pair of the map, and
the map stripped of that element, or `Nothing`

if passed an empty map.

minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a") minViewWithKey empty == Nothing

maxViewWithKey :: (Interval k e, Ord k) => IntervalMap k a -> Maybe ((k, a), IntervalMap k a) Source

*O(log n)*. Retrieves the maximal (key,value) pair of the map, and
the map stripped of that element, or `Nothing`

if passed an empty map.

# Debugging

valid :: (Interval i k, Ord i) => IntervalMap i v -> Bool Source

Check red-black-tree and interval search augmentation invariants. For testing/debugging only.

# Testing

height :: IntervalMap k v -> Int Source

The height of the tree. For testing/debugging only.