Some implementations in OCaml of the Union/Find algorithm

All modules implementing Union/Find can be coerced by the same signature Partition.S.

Note the function alias which is equivalent to equiv, but not symmetric: alias x y means that x is an alias of y, which translates in the present context as x not being the representative of the equivalence class containing the equivalence between x and y. The function alias is useful when managing aliases during the static analyses of programming languages, so the representatives of the classes are always the original object.

The module PartitionMain tests each with the same equivalence relations.

Partition0.ml

This is a naive, persistent implementation of Union/Find featuring an asymptotic worst case cost of O(n^2).

Partition1.ml

This is a persistent implementation of Union/Find with height-balanced forests and without path compression, featuring an asymptotic worst case cost of O(n*log(n)).

Partition2.ml

This is an alternate version of Partition1.ml, using a different data type.

Partition3.ml

This is a destructive implementation of Union/Find with height-balanced forests but without path compression, featuring an asymptotic worst case of O(n*log(n)). In practice, though, this implementation should be faster than the previous ones, due to a smaller multiplicative constant term.