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README
rbst: efficient randomized binary search trees
[RBST nodes](./images/rbst.png) [](LICENSE)
Efficient implementation of the Randomized Binary Search Trees data structure.
When to use this package?
Randomized Binary Search Trees are useful when you cannot make assumptions on the input distribution but you still need fast (logarithmic time complexity) insert
/lookup
/delete
/at
/union
/etc. operations. It is guaranteed efficient selfbalancing. Below you can find the table of time complexity for all operations (where n
is the size of the tree):
Operation  Time complexity  Description 

size 
O(1) 
Count elements in the tree 
height 
O(log n) w.h.p 
Height of the tree 
lookup 
O(log n) 
Access by key 
insert 
O(log n) 
Insert an element with the given key 
delete 
O(log n) 
Delete the element associated to the given key 
take 
O(log n) 
Take first ith elements 
drop 
O(log n) 
Drop first ith elements 
at 
O(log n) 
Access by index 
remove 
O(log n) 
Remove the ith element 
union 
O(m + n) 
Union of two trees 
intersection 
O(m + n) 
Intersection of two trees 
subtraction 
O(m + n) 
Subtraction of two trees 
difference 
O(m + n) 
Symmetric difference of two trees 
Usage example
>>> :set XOverlodadeLists
>>> import GHC.Exts
>>> import RBST
 Manually created
>>> let tree = insert 'a' 1
$ insert 'b' 2
$ insert 'c' 3
$ insert 'd' 4
$ insert 'e' 5
$ empty
 Using 'OverloadedLists'
>>> let tree = (fromList $ zip ['a'..'e'] [1..5]) :: RBST Char Int
>>> RBST.prettyPrint tree
('b',2) [5]
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('a',1) [1] ('d',4) [3]
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('c',3) [1] ('e',5) [1]
 Queries
>>> size tree
5
>>> lookup 'd'
Just 4
>>> lookup 'a' $ insert 'a' 7 tree
Just 7
>>> lookup 'd' (delete 'd' tree)
Nothing
How to use it
In order to start using rbst
in your project, you will need to set it up with the two easy steps:
 Add the dependency in your project's
.cabal
file:
builddepends: base ^>= 4.14
, rbst ^>= 0.0.0.0
 In the module where you wish to use
rbst
, add the (qualified) import:
import qualified RBST
Stack
If
rbst
is not available on your current Stackage resolver yet, you can still use it by adding the following in theextradeps
section of yourstack.yaml
file:extradeps:  rbst0.0.0.0
Then you can add it as a dependency in your
package.yaml
file as usual:library: dependencies:  rbst
Acknowledgement
To the authors C. Martinez and S. Roura.
To D. Kovanikov and his project implicit treap.
Icons designed by Freepik from www.flaticon.com.
*Note that all licence references and agreements mentioned in the rbst README section above
are relevant to that project's source code only.