exam14.2.3

;; mht created on Nov 17, 2011

;; data definition :
(define-struct node (ssn name left right))
;; A binary-tree (short : BT) is either
;; 1. false; or
;; 2. (make-node soc pn lft rgt)
;; shere soc is a number, pn js a symbol, and lft and rgt are BTs.

;; A binary-search-tree (short: BST) is a BT:
;; 1. false is always a BST;
;; 2. (make-node soc pn lft rgt) is a BST if
;;    a. lft and rgt are BSTs;
;;    b. all ssn numbers in lft are smaller than soc, and
;;    c. all ssn numbers in rgt are larger than soc.

;; examples
;(make-node 15 'd false (make-node 24 'i false false))

;; Draw a tree:
(define treeA
  (make-node 63 'a
           (make-node 29 'b
                      (make-node 15 'c
                                 (make-node 10 'd false false)
                                 (make-node 24 'e false false))
                      false)
           (make-node 89 'f
                      (make-node 77 'g false false)
                      (make-node 95 'h false
                                 (make-node 99 'i false false)))))


;; inorder : BT -> list-of-numbers
;; to produce a list of all the ssn in a-bt
(define (inorder a-bt)
  (cond
    [(false? a-bt) empty]
    [else
     (append
      (cons (node-ssn a-bt) empty)
      (inorder (node-left a-bt))
      (inorder (node-right a-bt)))]))

;; test
(inorder treeA)