implementing binary search tree in scheme

Question

Functions in scheme/racket. Working on a few functions using a binary search tree. I have already defined helper functions to be:

;; returns value of node
(define (value node)
    (if (null? node) '()
        (car node)))

;; returns left subtree of node
(define (left node)
    (if (null? node) '()
    (cadr node)))

;; returns right subtree of node
(define (right node)
    (if (null? node) '()
    (caddr node)))

and I am trying to write a function size that takes a tree as a parameter and returns the number of non-null nodes in the given tree

Answer 1

It seems you're very close. Try this (untested):

(define (size tree)
  (if (null? tree) 0
      (+ 1 (size (left tree)) (size (right tree)))))

Though, personally, I would much rather prefer to use #f as the null value, rather than '() . In that case, use not instead of null? in the first line.

Answer 2

Just an alternative!! You could have used structs, which would reduce the work of writing the three functions...

(struct node (val left right) #:transparent)
(struct null-tree ())

and directly write the above function using in-built functions for a struct, ie a predicate and parameter accessors.

(define (size tree)
  (if (null-tree? tree) 0
    (+ 1 (size (left tree)) (size (right tree)))))