Question

Hi I have been searching for some good information about how I can make a sorted binary tree datatype in F# but i cant find anything understandable. I have checked the example on msdn-page but i dont get it.

Answer 1

If you’re looking for an existing implementation, then the FSharpX library has quite a few data structures (including some trees) available. Although I do not think it has a straightforward implementation of a sorted binary tree. You can also access all the .NET collections from F#, but I don’t think .NET has a binary tree either. It has sorted list, which might be just fine for you, depending on what you’re trying to do.

If you want to implement your own, then you need to start by defining a data type to represent the tree:

type SortedTree<'T when 'T : comparison> =
  | Node of SortedTree<'T> * 'T * SortedTree<'T>
  | Leaf of 'T

The Node element means that all values on the left are smaller than the value stored in the node and all greater (or equal) values are on the right. I added a constraint 'T : comparison which means that you can only create tree of comparable elements (this is needed in the implementation to sort the tree).

Implementing all the common tree operations is going to be quite a lot of work, but a simple attempt at insertion (that does not keep the tree ballanced in any way) looks like this:

let rec insert element tree = 
  match tree with
  | Leaf v when element < v -> Node(Leaf element, v, Leaf v)
  | Leaf v -> Node(Leaf v, element, Leaf element)
  | Node(left, key, right) when element < key -> Node(insert element left, key, right)
  | Node(left, key, right) -> Node(left, key, insert element right)

The pattern matching handles 4 interesting cases: When the tree is Leaf, you need to build a new node with the new element either on the left or on the right. When the tree is Node, then you want to insert to the left or right, depending on the value of the key.