rbst: efficient randomized binary search trees

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 self-balancing. 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 i-th elements
drop	O(log n)	Drop first i-th elements
at	O(log n)	Access by index
remove	O(log n)	Remove the i-th 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]
                 ╱╲
                ╱  ╲
               ╱    ╲
              ╱      ╲
             ╱        ╲
            ╱          ╲
           ╱            ╲
          ╱              ╲
         ╱                ╲
('a',1) [1]       ('d',4) [3]
                       ╱╲
                      ╱  ╲
                     ╱    ╲
                    ╱      ╲
                   ╱        ╲
                  ╱          ╲
            ('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:

1. Add the dependency in your project's .cabal file:

    build-depends: base ^>= 4.14
                 , rbst ^>= 0.0.0.0

2. In the module where you wish to use rbst, add the (qualified) import:

   import qualified RBST

Stack

1. If rbst is not available on your current Stackage resolver yet, you can still use it by adding the following in the extra-deps section of your stack.yaml file:

   extra-deps:
     - rbst-0.0.0.0

2. 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.

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