Re: [Caml-list] Choosing a random element in a Map or a Set

[Francois Berenger <mlists@ligand.eu>]

On 18/03/2021 20:10, Nicolas Barnier wrote:
> Hi Jean-Marc,
> 
> Le 18/03/2021 à 10:44, jean-marc.alliot@irit.fr a écrit :
>> I am trying to take a random element from a Map or a Set.
>> 
>> Currently, I generate one random int between 1 et Card(map), and I 
>> iter
>> until I reach this element. The solution is in O(n) which is not 
>> great...
>> 
>> I was about to code the following solution: take the current Map code
>> and add a function which follows the balanced binary tree from the 
>> root
>> and takes randomly a left or right turn at each node until we reach a
>> leaf (we only need to generate one random int and use its binary
>> representation to choose the left or right direction at each node). 
>> This
>> should be in O(log(n))
>> 
>> Before I start coding like an idiot:
>> 1) Is there another, more intelligent, solution?
> 
> If using a Map or a Set is not compulsory, you can design a data 
> structure
> supporting insert, delete, search and random element in constant 
> amortized
> time with an extensible array and a hash-table as explained here:

Just FTR, a skip list would allow all the set operations, plus an 
efficient random
access operation and element rank.

Pugh, William. (1990). A skip list cookbook.

I am not aware of an OCaml implementation with all the interesting
operations though.

> https://www.geeksforgeeks.org/design-a-data-structure-that-supports-insert-delete-search-and-getrandom-in-constant-time/
> 
> I don't know if there are any good implementation of (Python-like)
> extensible arrays in a widespread OCaml library, but François Pottier
> published one as part of another superb data structure (union-find):
> 
> https://gitlab.inria.fr/fpottier/unionfind/-/blob/master/src/StoreVector.ml
> 
> You may want to adjust the ratio (2 here) by which the array is resized 
> when
> necessary.
> 
> Hope this helps,
> 
> -- Nicolas