;; 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-beginner-reader.ss" "lang")((modname main) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f () #f)))
; Number a, Number b, Number c -> String
; Determines whether a list of 3 numbers is ascending or descending. Throws error if neither.
(define (scending-how a b c)
  (cond [(< a b c) "ascending"]
        [(> a b c) "descending"]
        [else (error "too complex")]))

(check-expect (scending-how 1 2 3) "ascending")
(check-expect (scending-how 5 4 3) "descending")
(check-error (scending-how 1 0 3))


; Number a, Number b -> Number
; Finds two positive numbers' greatest common denominator.
(define (gcd2 a b)
  (cond
    [(= a 0) b]
    [(= b 0) a]
    [(and (even? a) (even? b))
     (* 2 (gcd2 (/ a 2) (/ b 2)))]
    [(even? b) (gcd2 a (/ b 2))]
    [(even? a) (gcd2 (/ a 2) b)]
    [else(if (<= a b)
             (gcd2 a (- b a))
             (gcd2 b (- a b)))]))

(check-expect (gcd2 0 0) 0)
(check-expect (gcd2 100 0) 100)
(check-expect (gcd2 10 2) 2)
(check-expect (gcd2 10 10) 10)
(check-expect (gcd2 14 7) 7)
(check-expect (gcd2 288 64) 32)

; (gcd2 30 210)
; (* 2 (gcd2 15 105))
; (* 2 (gcd2 15 90))
; (* 2 (gcd2 15 45))
; (* 2 (gcd2 15 30))
; (* 2 (gcd2 15 15))
; (* 2 (gcd2 15 0))
; (* 2 15)
; 30