;; 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_f_full) (read-case-sensitive #t) (teachpacks ((lib "image.ss" "teachpack" "2htdp"))) (htdp-settings #(#t constructor repeating-decimal #t #t none #f ((lib "image.ss" "teachpack" "2htdp")))))
; gcd : number number -> number
; finds greatest common divisor of two numbers
(define (mygcd a b) 
  (find-divisor (min a b) a b)
  )

(check-expect (mygcd 30 18) 6)
(check-expect (mygcd 25 21) 1)

; find-divisor : number number number -> number
; returns greatest common divisor of a and b starting at i
(define (find-divisor i a b)
  (cond [(and (zero? (remainder a i)) (zero? (remainder b i)))
         i]
        [else (find-divisor (- i 1) a b)])
  )

(check-expect (find-divisor 7 30 18) 6)
(check-expect (find-divisor 20 25 21) 1)

; clever-gcd : number number -> number
; finds gcd using Euclidean algorithm
(define (clever-gcd bigger smaller)
  (cond [(zero? smaller) bigger]
        [else (clever-gcd smaller (remainder bigger smaller))]))

;    A
;   / \
;  B   C
;  |\ / |
;  D  E F
;  \  | /
;     G

; a graph is :
; (make-graph list-of-symbols (symbol -> list-of-symbols))
(define-struct graph (nodes neighbor))

(define mygraph (make-graph '(a b c d e f)
                  (lambda (node)
                    (cond [(symbol=? node 'a) '(b c)]
                          [(symbol=? node 'b) '(d e)]
                          [(symbol=? node 'c) '(e f)]
                          [(member node '(d e f)) '(g)]
                          [(symbol=? node 'g) '()]))))