Lookup procedure

Implement the lookup procedure for the case where the set of records is structured as a binary tree, ordered by the numerical values of the keys.


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

(define (key entry) (car entry))

(define (entry tree) (car tree))

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

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

(define test-tree 
  (make-tree '(5 "Five") 
    (make-tree '(3 "Three") 
      (make-tree '(2 "Two") '() '())
      (make-tree '(4 "Four") '() '()))
    (make-tree '(8 "Eight") '() '())))


(check-equal? (lookup 5 test-tree) '(5 "Five"))
(check-equal? (lookup 2 test-tree) '(2 "Two"))
(check-equal? (lookup 6 test-tree) #f)
(check-equal? (lookup 8 test-tree) '(8 "Eight"))