exercise2-66.lisp

(define (entry tree) (car tree))
(define (left-branch tree) (cadr tree))
(define (right-branch tree) (caddr tree))
(define (make-tree entry left right)
  (list entry left right))

(define (tree->list tree)
  (define (copy-to-list tree result-list)
    (if (null? tree)
      result-list
      (copy-to-list (left-branch tree)
                    (cons (entry tree)
                          (copy-to-list (right-branch tree)
                                        result-list)))))
  (copy-to-list 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)
                                            right-size)))
            (let ((right-tree (car right-result))
                  (remaining-elts (cdr right-result)))
              (cons (make-tree this-entry left-tree right-tree)
                    remaining-elts))))))))

(define (element-of-set? x set)
  (cond ((null? set) false)
        ((= x (entry set)) true)
        ((< x (entry set))
         (element-of-set? x (left-branch set)))
        ((> x (entry set))
         (element-of-set? x (right-branch set)))))

(define (lookup given-key set-of-records)
  (cond ((null? set) false)
        ((= given-key (key (entry set))) (entry set))
        ((< given-key (key (entry set)))
         (lookup given-key (left-branch set)))
        ((> given-key (key (entry set)))
         (lookup given-key (right-branch set)))))