;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-intermediate-reader.ss" "lang")((modname lec14) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))
;; A Pittsburgh-road is either
;;  - empty
;;  - (make-branch Pittsburgh-road Pittsburgh-road sym)
(define-struct branch (left right sign))

;; metric : Pittsburgh-road num (num num -> num) -> num
;;  To count all the dead ends in pr
(define (metric pr base OP)
  (cond
    [(empty? pr) base]
    [(branch? pr) (OP (metric (branch-left pr) base OP)
                      (metric (branch-right pr) base OP))]))


;; Original:
;;; count-ends : Pittsburgh-road -> num
;;;  To count all the dead ends in pr
;(define (count-ends pr)
;  (cond
;    [(empty? pr) 1]
;    [(branch? pr) (+ (count-ends (branch-left pr))
;                     (count-ends (branch-right pr)))]))

;; count-ends : Pittsburgh-road -> num
;;  To count all the dead ends in pr
(define (count-ends pr)
  (metric pr 1 +))

(define big-pr
  (make-branch empty 
               (make-branch empty (make-branch empty empty 'left) 'right)
               'left))

(check-expect (count-ends empty) 1)
(check-expect (count-ends (make-branch empty empty 'left)) 2)
(check-expect (count-ends big-pr) 4)

;; Original:
;;; max-drive : Pittsburgh-road -> num
;;;  Max number of steps to drive one-way to read a dead end
;(define (max-drive pr)
;  (cond
;    [(empty? pr) 0]
;    [(branch? pr) (+ 1 (max (max-drive (branch-left pr))
;                            (max-drive (branch-right pr))))]))

;; max-plus-one : num num -> num
(define (max-plus-one a b)
  (+ 1 (max a b)))

(check-expect (max-plus-one 3 5) 6)

;; max-drive : Pittsburgh-road -> num
;;  Max number of steps to drive one-way to read a dead end
(define (max-drive pr)
  (metric pr 0 max-plus-one))
  
(check-expect (max-drive empty) 0)
(check-expect (max-drive (make-branch empty empty 'left)) 1)
(check-expect (max-drive big-pr) 3)