Question

I am currently building my binary tree in F#, and I’m almost finished. I’m on the last assignment of this task, where I am supposed to make a string representation of the binary tree. Meaning that the tree should be presented like this:

Example: ("node" "value" ("node" "value" "Empty" "Empty") Empty) <- A tree with a rootnode that has a left subtree with a node that has two empty subtrees, and an empty right subtree.

My tree looks like this:

 type Btree<'a when 'a: comparison> = 
 |Node of  'a * Btree<'a> *Btree<'a> 
 |Leaf of 'a 
 |EmptyTree 

This is how far I’ve gotten:

let rec treeToString bintree = 
    match bintree with
    |EmptyTree -> "Empty" //Check if the tree is empty
    |Node(inner, left, right) when inner = 0 -> "Empty"
    |Leaf x-> "Node"+x.ToString() //Returns "Node" and its value
    |Node(inner, left, right) when inner <> 0-> treeToString left //Need some kind of output here, but what?
    |Node(inner, left, right) when inner <> 0->treeToString right

My method only returns one value, so the actual problem with my solution is getting the recursive part right.

So my question is: What am I doing wrong here?

Answer 1

The union case Leaf of 'a is redundant because Leaf(a) can be modelled by Node(a, Empty, Empty). Type declaration could be simplified to:

type BinTree<'a when 'a: comparison> = 
    | Empty 
    | Node of 'a * BinTree<'a> * BinTree<'a>

From the output sample ("node" "value" ("node" "value" "Empty" "Empty") Empty), you should display values of node elements first, then display left branches and right branches recursively:

let rec treeToString bintree = 
    match bintree with
    | Empty -> "Empty"
    | Node(value, left, right) -> 
      sprintf "(Node %O %s %s)" value (treeToString left) (treeToString right)

You can push this further by overriding ToString() method

type BinTree<'a> with
override x.ToString() = treeToString x

so that the type works with sprintf "%O" bintree and the like.