Maintainer | Jannis Harder <jannis@harderweb.de> |
---|

An implementation of integer sets with a constant time `translate`

operation, where `translate`

is defined to be

.
`translate`

x s = `map`

(+x) s

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

, e.g.

import Data.IntSet.Translatable (IntSet) import qualified Data.IntSet.Translatable as IntSet

This implementation is based on *Finger-Trees* storing differences
of consecutive entries of the ordered sequence of set elements.
With this representation, a translation of all elements can be
realized by changing only the leftmost element of the Finger-Tree
which is a constant time operation. Together with caching of the
accumulated differences most set operations can be implemented
efficiently too.

- data IntSet
- (\\) :: IntSet -> IntSet -> IntSet
- null :: IntSet -> Bool
- size :: IntSet -> Int
- member :: Int -> IntSet -> Bool
- notMember :: Int -> IntSet -> Bool
- empty :: IntSet
- singleton :: Int -> IntSet
- insert :: Int -> IntSet -> IntSet
- delete :: Int -> IntSet -> IntSet
- union :: IntSet -> IntSet -> IntSet
- unions :: [IntSet] -> IntSet
- difference :: IntSet -> IntSet -> IntSet
- intersection :: IntSet -> IntSet -> IntSet
- filter :: (Int -> Bool) -> IntSet -> IntSet
- partition :: (Int -> Bool) -> IntSet -> (IntSet, IntSet)
- split :: Int -> IntSet -> (IntSet, IntSet)
- splitMember :: Int -> IntSet -> (IntSet, Bool, IntSet)
- findMin :: IntSet -> Int
- findMax :: IntSet -> Int
- deleteMin :: IntSet -> IntSet
- deleteMax :: IntSet -> IntSet
- deleteFindMin :: IntSet -> (Int, IntSet)
- deleteFindMax :: IntSet -> (Int, IntSet)
- maxView :: IntSet -> Maybe (Int, IntSet)
- minView :: IntSet -> Maybe (Int, IntSet)
- map :: (Int -> Int) -> IntSet -> IntSet
- translate :: Int -> IntSet -> IntSet
- fold :: (Int -> b -> b) -> b -> IntSet -> b
- elems :: IntSet -> [Int]
- toList :: IntSet -> [Int]
- fromList :: [Int] -> IntSet
- toAscList :: IntSet -> [Int]
- fromAscList :: [Int] -> IntSet
- fromDistinctAscList :: [Int] -> IntSet

# Set type

# Operators

# Query

# Construction

delete :: Int -> IntSet -> IntSetSource

*O(log(n))*. Delete a value in the set. Returns the
original set when the value was not present.

# Combine

union :: IntSet -> IntSet -> IntSetSource

*O(m log(n */* m))* where *m<=n*. The union of two sets. *O(log m)*
if all elements of one set are larger than all elements of the
other set.

difference :: IntSet -> IntSet -> IntSetSource

*O(???)*. Difference between two sets.

intersection :: IntSet -> IntSet -> IntSetSource

*O(???)*. The intersection of two sets.

# Filter

filter :: (Int -> Bool) -> IntSet -> IntSetSource

*O(n)*. Filter all elements that satisfy some predicate.

partition :: (Int -> Bool) -> IntSet -> (IntSet, IntSet)Source

*O(n)*. Partition the set into two sets, one with all elements that satisfy
the predicate and one with all elements that don't satisfy the predicate.
See also `split`

.

split :: Int -> IntSet -> (IntSet, IntSet)Source

*O(log(min(i,n-i)))*. 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`

.

split 3 (fromList [1..5]) == (fromList [1,2], fromList [4,5])

splitMember :: Int -> IntSet -> (IntSet, Bool, IntSet)Source

*O(log(min(i,n-i)))*. Performs a `split`

but also returns whether the pivot
element was found in the original set.

# Min/Max

deleteFindMin :: IntSet -> (Int, IntSet)Source

*O(1)*. Delete and find the minimal element.

deleteFindMin set = (findMin set, deleteMin set)

deleteFindMax :: IntSet -> (Int, IntSet)Source

*O(1)*. Delete and find the maximal element.

deleteFindMax set = (findMax set, deleteMax set)

maxView :: IntSet -> Maybe (Int, IntSet)Source

*O(1)*. Retrieves the maximal key of the set, and the set
stripped of that element, or `Nothing`

if passed an empty set.

minView :: IntSet -> Maybe (Int, IntSet)Source

*O(1)*. Retrieves the minimal key of the set, and the set
stripped of that element, or `Nothing`

if passed an empty set.

# Map

map :: (Int -> Int) -> IntSet -> IntSetSource

*O(n*log(n))*.

is the set obtained by applying `map`

f s`f`

to each element of `s`

.

It's worth noting that the size of the result may be smaller if,
for some `(x,y)`

, `x /= y && f x == f y`

translate :: Int -> IntSet -> IntSetSource

*O(1)*. Add a constant value to all elements of the set.

translate x s == map (+x) s

# Fold

fold :: (Int -> b -> b) -> b -> IntSet -> bSource

*O(n)*. Fold over the elements of a set in an unspecified order.

sum set == fold (+) 0 set elems set == fold (:) [] set

# Conversion

## List

## Ordered list

fromAscList :: [Int] -> IntSetSource

*O(n)*. Build a set from an ascending list of elements.
*The precondition (input list is ascending) is not checked.*

fromDistinctAscList :: [Int] -> IntSetSource

*O(n)*. Build a set from an ascending list of distinct elements.
*The precondition (input list is strictly ascending) is not checked.*