;; 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-advanced-reader.ss" "lang")((modname week8_m_full) (read-case-sensitive #t) (teachpacks ((lib "image.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #t #t none #f ((lib "image.ss" "teachpack" "htdp")))))
; find-divisor : number number number -> number
; returns the greatest divisor of a and b less than i
(define (find-divisor i a b)
  (cond
    [(= i 1) 1]
    [else
     (cond
       [(and (zero? (remainder a i))
             (zero? (remainder b i))) i]
       [else (find-divisor (- i 1) a b)])]
   ))

(define (gcd-naive a b) (find-divisor (min a b) a b))

(check-expect (gcd-naive 15 5) 5)
(check-expect (gcd-naive 249 1577) 83)

(time (gcd-naive 11797640 11702559))

;(gcd larger smaller) = (gcd smaller (remainder larger smaller)

; gcd-clever : number number -> number
; returns gcd of two numbers, assuming larger is first
(define (gcd-clever bigger smaller)
  (cond[(zero? smaller) bigger]
  [else (gcd-clever smaller (remainder bigger smaller))]))


(check-expect (gcd-clever 15 5) 5)
(check-expect (gcd-clever 249 1577) 83)

(time (gcd-clever 11797640 11702559))

;(gcd-clever 15 5)
;(gcd-clever 5 0)
;(gcd-clever 0 0)
;(gcd-clever 0 0)


;; a graph is:
;;  (make-graph (listof symbol) (symbol -> (listof symbol)))
(define-struct graph (nodes neighbor))

;      A
;     /
;    /  
;   B    C
;   |\  /|
;   | \/ |
;   D E  F
;   \ | /
;    \|/
;     G
; (arrows pointing down)
(define mygraph (make-graph
 '(a b c d e f g)
  (lambda (node)
   (cond
    [(symbol=? node 'a) '(b)]
    [(symbol=? node 'b) '(d e)]
    [(symbol=? node 'c) '(e f)]
    [(member node '(d e f)) '(g)]
    [(symbol=? node 'g) '()]))))

; add-edge : graph symbol symbol -> graph
; returns graph with an edge from a to b
(define (add-edge g a b) (...))