functional programming - Simple non-optimal unionfind in OCaml

Question

I wrote a OCaml program for union find algorithm. This algorithm I wrote is not optimal and is the simplest version.

I put my OCaml code here because I am not sure whether this code is good enough or not (despite of the algorithm itself), although this code can run without errors.

This is the first time I wrote a complete working thing after I started to learn OCaml, so please help me by reviewing it.

Useful suggestions will help me improving my OCaml skills. Thanks

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type union_find = {id_ary : int array; sz_ary : int array};;

let create_union n = {id_ary = Array.init n (fun i -> i); 
                  sz_ary = Array.init n (fun i -> 1)};;

let union u p q = 
  let rec unionfy id_ary i = 
    let vp = id_ary.(p) in
    let vq = id_ary.(q) in
    if i < Array.length id_ary then begin 
      if i != q && id_ary.(i) = vp then id_ary.(i) <- vq;
      unionfy id_ary (i + 1)
    end 
    else print_string "end of union
"
  in
  unionfy u.id_ary 0;;

let is_connected u p q = u.id_ary.(p) = u.id_ary.(q);;

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First of all,

Am I creating the data structure of union (as in union find) correctly?

Should I include two arrays inside or is there any better way?

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Second,

I am using array in this code, but array is mutable which is not that good for fp right?

Is there a way to avoid using array?

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Finally,

Overall, is this piece of code good enough?

Anything can be improved?

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P.S. I am not using OCaml's object oriented bit yet, as I haven't learnt to that part.

Answer 1

Some comments on the code:

• You don't seem to use sz_ary for anything.

• Your code iterates through the whole array for each union operation. This is not correct for the standard (Tarjan) union-find. For a linear number of union operations your code produces a quadratic solution. Wikipedia has the standard algorithm: Disjoint-set Data Structure.

To answer your second question: as far as I know, union-find is one of the algorithms for which there's no known functional (immutable) solution with the same complexity as the best imperative solution. Since an array is simply a map from integers to values, you could always translate any array-based solution into an immutable one using maps. As far as I've been able to determine, this would match the best known solution in asymptotic complexity; i.e., it would add an extra factor of log n. Of course there would also be a constant factor that might be large enough to be a problem.

I've implemented union-find a few times in OCaml, and I've always chosen to do it using mutable data. However, I haven't used arrays. I have a record type for my basic objects, and I use a mutable field in each record to point to its parent object. To do path compression, you modify the parent pointer to point to the current root of the tree.