What is the most efficient implementation of arrays with functional updates?

Question

I need an array-like data structure with the fastest possible functional update. I\'ve seen a few different implementation of flexible arrays that provide me with this prope

Answer 1

I also needed functional arrays and felt on this SO question some days ago. I was not satisfied with the solution proposed by Gasche as creating a new array is a costly operation and I need to access older versions of array quite frequently (I plan to use this for an AI alpha/beta implementation playing on an array).

(When I say costly, I guess it is O(n*h) where h is the history size because in the worst case only one cell was updated repeatedly and it is needed to go through the whole update list for each cell. I also expect most of the cells not being updated when I need to reroute the array).

This is why I propose another approach, maybe I can get some feedback here. My idea is to store the array like in a B-Tree, except that as it is not mutable, I can access and update any value by index quite easily.

I wrote a small introduction on the project's repository : https://github.com/shepard8/ocaml-ptarray. The order is chosen so as to even depth and order of the tree, so I can get nice complexities depending only on the order for get/set operations, namely O(k^2).

With k = 10 I can store up to 10^10 values. Actually my arrays should not contain more than 200 values but this is to show how robust my solution is intended to be.

Any advice welcome!