Module Bt2

type (+'a, +'b) t = private
  1. | Leaf
  2. | Node of int * ('a, 'b) t * 'a * 'b * ('a, 'b) t
    (*

    Node(size, l, x, r) where:

    • size is the number of elements in the tree,
    • l is the left sub-tree
    • x is a user-defined value
    • r is the right sub-tree.

    Trees are guaranteed balanced by construction, the depth of all branches is O(log size).

    *)

Type of balanced trees with two custom values (more efficient than a pair)

val leaf : ('a, 'b) t

Leaf constructor, the empty tree

val node : ('a, 'b) t -> 'a -> 'b -> ('a, 'b) t -> ('a, 'b) t

Smart Node constructor, ensuring that the resulting tree is balanced and has the appropriate size.

Cost of node l x r is expected to be O(log |size l - size r|) amortized, i.e proportional to the logarithm of the disbalance. In particular, if l and r are similarly-sized, it operates in constant time on average. NOT PROVEN

User-values can be moved in different subtrees of the result, but the ordering is preserved (so data stay correct if the operation applied on values is associative or the relation expected between them is transitive).

Convenience functions

val size : ('a, 'b) t -> int

Accessor to the size

val join : ('a, 'b) t -> ('a, 'b) t -> ('a, 'b) t

Concatenate two trees. Cost of join l r is O(log (min size l size r)). NOT PROVEN

val rank : int -> ('a, 'b) t -> 'a * 'b

Return the n'th node in tree order