Question

I’m having trouble getting used to the recursion in Haskell, is there anyway someone could explain to me how I would go about this.
I’ve looked at a bunch of other posts, but I can’t figure out how to do it.

I have my type as

data BST = MakeNode BST String BST
             | Empty              

I’m not sure how’d i’d examine every single combo of paths down the tree.

Answer 1

The trick to thinking about most recursive functions is simple: first consider the base case, then consider the recursive case.

The base case is usually trivial–when do you know the height of a tree without any additional calculations? When it has no children, of course! So the base case is:

height Empty = 0

That was pretty straightforward. Now the next question: what is the height of a binary tree with children?

Well, that’s also simple–it’s 1, for the current node, plus the height of the tallest subtree. So:

height MakeNode left _ right = 1 + max (height left) (height right)

(The _ just means we don’t care about the string in the node.)

And so we have a very simple function:

height :: BST -> Int
height Empty              = 0
height (BST left _ right) = 1 + max (height left) (height right)

I hope this clarifies the thought process of designing a recursive function.