(define make-empty-tree
  (lambda () '()))

(define make-nonempty-tree
  (lambda (root left-subtree right-subtree)
    (list root left-subtree right-subtree)))

(define example-tree
  (make-nonempty-tree
   191
   (make-nonempty-tree 157
                       (make-empty-tree)
                       (make-empty-tree))
   (make-nonempty-tree 202
                       (make-nonempty-tree 200
                                           (make-empty-tree)
                                           (make-empty-tree))
                       (make-empty-tree))))

(define empty-tree? null?)

(define root car)

(define left-subtree cadr)

(define right-subtree caddr)

(define in?
  (lambda (value tree)
    (cond
     ((empty-tree? tree) #f)
     ((= value (root tree)) #t)
     ((< value (root tree)) (in? value (left-subtree tree)))
     (else ; the value must be greater than the root
      (in? value (right-subtree tree))))))

(define minimum
  (lambda (bst)  ; given that bst is nonempty
    (if (empty-tree? bst)
        (error "But you promised me.....")
        (if (empty-tree? (left-subtree bst))
            (root bst)
            (minimum (left-subtree bst))))))
  
(define successor-of-in-or
  (lambda (value bst if-none)
    (cond ((empty-tree? bst)
           if-none)
          ((<= (root bst) value)
           (successor-of-in-or value
                               (right-subtree bst)
                               if-none))
          (else
           (successor-of-in-or value
                               (left-subtree bst)
                               (root bst))))))