;; The first three lines of this file were inserted by DrScheme. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-advanced-reader.ss" "lang")((modname |31.3|) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #t #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp")))))
(define-struct node (left right))

;A binary-tree (bt) is either
;1. empty or
;2. (make-node l r)
;where l,r are binary-trees (bt).
;
;height-1 : bt -> number
;Determines the height (depth) of a binary tree using structural recursion.

(define (height-1 abt)
  (cond
    [(empty? abt) 0]
    [else (+ (max (height-1 (node-left abt))
                  (height-1 (node-right abt)))
             1)]))

;height-2 : bt -> number
;Determines the height (depth) of a binary tree using an accumulator.

(define (height-2 abt)
  (local ;; the accumulator represents the number of nodes passed in going from abt to bt0
    ((define (height-aux bt0 accumulator)
       (cond
         [(empty? bt0) accumulator]
         [else (max (height-aux (node-left bt0) (+ 1 accumulator))
                    (height-aux (node-right bt0) (+ 1 accumulator)))])))
    (height-aux abt 0)))

(define bt1 (make-node 
             (make-node 
              empty 
              (make-node empty empty)) 
             empty)) 
(height-1 bt1)
(height-2 bt1)