Added Welcome Back to Dr. Racket assignment.

welcome-back-to-dr-racket/main.rkt

@@ -0,0 +1,32 @@
+;; 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)))
+; List of Number -> String
+; Determines whether a list of 3 numbers is ascending or descending. Throws error if neither.
+(define (scending-how l)
+  (cond [(< (first l) (second l) (third l)) "ascending"]
+        [(> (first l) (second l) (third l)) "descending"]
+        [else (error "too complex")]))
+
+(check-expect (scending-how (list 1 2 3)) "ascending")
+(check-expect (scending-how (list 5 4 3)) "descending")
+(check-error (scending-how (list 1 0 3)))
+
+
+; Number, Number -> Number
+; Finds two positive numbers' greatest common denominator.
+(define (gcd2 a b)
+  (cond
+    [(= a 0) b]
+    [(= b 0) a]
+    [(= 0 (+ (modulo a 2) (modulo b 2))) (* 2 (gcd2 (/ a 2) (/ b 2)))]
+    [(= 0 (modulo b 2)) (gcd2 a (/ b 2))]
+    [(= 0 (modulo a 2)) (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)