;;
;; tree-in-class.scm
;;
;; representation :
;;   node : (name left branch)
;;

(define (new-node name left right)
  ;; same as (list name left right)
  (cons name (cons left (cons right '()))))

(define (new-leaf name)
  (new-node name '() '()))

(define (node-name node)
  (car node))

(define (node-left node)
  (car (cdr node)))  ;; same as cadr

(define (node-right node)
  (car (cdr (cdr node)))) ;; same as caddr

(define ABCDE
  (new-node 'A
            (new-leaf 'B')
            (new-node 'C'
                      (new-leaf 'D')
                      (new-leaf 'E'))))

(define (count-nodes tree)
  (if (null? tree)
      0
      (+ (count-nodes (node-left tree))
         (count-nodes (node-right tree))
         1)))

(printf "tree ABCDE has ~a nodes.\n"
        (count-nodes ABCDE))