ex2.66-loopup-with-binary-tree.scm

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


(define key car)
(define value cadr)

(define (lookup given-key set-of-records)
  (cond ((null? set-of-records) '())
        ((equal? given-key (key (entry set-of-records))) (value (entry set-of-records)))
        ((< given-key (key (entry set-of-records))) (lookup given-key (left-branch set-of-records)))
        ((> given-key (key (entry set-of-records))) (lookup given-key (right-branch set-of-records)))))


(lookup 4 (list->tree '((1 "alpha") (2 "non") (3 "negative") (4 "are") (5 "str"))))