Procedures for sets implemented as (balanced) binary trees

Use the results of exercises 2.63 and 2.64 to give Θ(n) implementations of union-set and intersection-set for sets implemented as (balanced) binary trees.

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(define (make-tree entry left right)
  (list entry left right))

(define (left-branch tree) (cadr tree))

(define (entry tree) (car tree))

(define (right-branch tree) (caddr tree))

(define (list->tree elements)
  (car (partial-tree elements (length elements))))

(define (partial-tree elts n)
  (if (= n 0)
      (cons '() elts)
      (let ((left-size (quotient (- n 1) 2)))
        (let ((left-result (partial-tree elts left-size)))
          (let ((left-tree (car left-result))
                (non-left-elts (cdr left-result))
                (right-size (- n (+ left-size 1))))
            (let ((this-entry (car non-left-elts))
                  (right-result (partial-tree (cdr non-left-elts)
              (let ((right-tree (car right-result))
                    (remaining-elts (cdr right-result)))
                (cons (make-tree this-entry left-tree right-tree)

(define (tree->list-1 tree)
  (if (null? tree)
      (append (tree->list-1 (left-branch tree))
              (cons (entry tree)
                    (tree->list-1 (right-branch tree))))))

(define (tree->list-2 tree)
  (define (copy-to-list tree result-list)
    (if (null? tree)
        (copy-to-list (left-branch tree)
                      (cons (entry tree)
                            (copy-to-list (right-branch tree)
  (copy-to-list tree '()))

(define first (list->tree '(1 2 3 5)))

(define second (list->tree '(3 4 5 6)))

(check-equal? (tree->list-2 (intersection-set first second)) '(3 5))
(check-equal? (tree->list-2 (union-set first second)) '(1 2 3 4 5 6))