Solution of Lesson 0.4 Introduction to Racket from Northeastern University

lesson0.4-racket-intro.rkt

(require 2htdp/image)

; Ex 3:
; f->c : Real -> Real
; GIVEN: a temperature in degrees Fahrenheit as an argument
; RETURN: the equivalent temperature in degrees Celsius.
; Examples:
; (f->c 32)  => 0
; (f->c 100) => 37.7777777777....
(define (f->c x)
  (* (- x 32)
     (/ 5 9)))

(check-expect (f->c 32) 0)
(check-within (f->c 100) 37.7 10)



; tip : Real Real[0.0,1.0] -> Number
; GIVEN: the amount of the bill in dollars and the
; percentage of tip
; RETURNS: the amount of the tip in dollars.
; Examples:
; (tip 10 0.15) => 1.5
; (tip 20 0.17) => 3.4
(define (tip x y)
  (* x y))

(check-expect (tip 10 0.15) 1.5)
(check-expect (tip 20 0.17) 3.4)


; sq : Number -> Number
; RETURN: square of a given number
; Examples:
; (sq 4) => 16
; (sq 9) => 81
(define (sq x)
  (* x x))

(check-expect (sq 4) 16)
(check-expect (sq 9) 81)



; Ex 6:
; quadratic-root : Real Real Real -> Real
; GIVEN: 3 arguments of the quadratic equation
; RETURN: root of the corresponding quadratic equation
; Examples:
; (quadratic-root 1 0 -4) => 0
; (quadratic-root 1 -2 1) => 0
(define (quadratic-root a b c)
  (sqrt (/ (+ (- b)
              (sqrt (- (* b b) (* 4 a c))))
           (* 2 a))))

(check-within (quadratic-root 1 0 -4) 0 2)
(check-within (quadratic-root 1 -2 1) 0 2)


; Ex 7:
; circumference : Real -> Real
; GIVEN: the radius of a circle
; RETURNS: its circumference, using the fomula 2 * pi * r
; Examples:
; (circumference 1) => 2 * pi
; (circumference 0) => 0
(define (circumference r)
  (* 2 pi r))

(check-within (circumference 1) (* 2 pi) 4)
(check-expect (circumference 0) 0)


; Ex 8:
; circle-area : Real -> Real
; RETURNS: area of circle using given radius
; Examples:
; (circle-area 1) => pi
; (circle-area 5) => 78.53
; (circle-area 7) => 153.93
(define (circle-area r)
  (* pi r r))

(check-within (circle-area 1) pi 2)
(check-within (circle-area 5) 78.53 2)
(check-within (circle-area 7) 153.93 2)


; Ex 9:
; is-even? : Number -> Boolean
; RETURN: produce true if given number is even number otherwise false
; Examples:
; (is-even? 2) => true
; (is-even? 1) => false
; (is-even? 0) => true
(define (is-even? x)
  (= (remainder x 2) 0))

(check-expect (is-even? 2) true)
(check-expect (is-even? 1) false)
(check-expect (is-even? 0) true)


; Ex 10:
; sum-of-two-larger : Number Number Number -> Number
; RETURN: sum of the two larger numbers
; Examples:
; (sum-of-two-larger 10 20 30) => 50
; (sum-of-two-larger 5 1 3) => 8
(define (sum-of-two-larger x y z)
  (cond
    [(and (< x y) (< y z)) (+ y z)]
    [(and (< y x) (< x z)) (+ x z)]
    [(and (< z x) (< x y)) (+ x y)]
    [(and (< y x) (< y z)) (+ x z)]
    [(and (< z x) (< z y)) (+ x y)]
    [(and (< x y) (< z y)) (+ y z)]))

(check-expect (sum-of-two-larger 10 20 30) 50)
(check-expect (sum-of-two-larger 5 1 3) 8)
(check-expect (sum-of-two-larger 5 1 6) 11)
(check-expect (sum-of-two-larger 5 10 4) 15)
(check-expect (sum-of-two-larger 7 6 5) 13)
(check-expect (sum-of-two-larger 5 10 9) 19)


(define-struct point (x y))
;; A Point is a (make-point Number Number)
;; It represents a position on the screen
;; Interpretation:
;;   x = the x-coordinate on the screen (in pixel from the left).
;;   y = the y-coordinate on the screen (in pixel from the top).


; Ex 15:
(define-struct student (id name major))
;; A Student is a (make-student Number String String)
;; It represents a student data
;; Interpretation:
;;   id = the student id
;;   name = the student name
;;   major = the student major of study

(rectangle 2 4 "solid" "blue")
(rectangle 4 8 "solid" "blue")
(rectangle 8 16 "solid" "blue")
(rectangle 16 32 "solid" "blue")


; Ex 18:
; rec-sequence : Number -> Rectangle
; RETURN: return the nth rectangle in the sequence formula
; Examples:
; (rec-sequence 2) => (rectangle 4 8 "solid" "blue")
; (rec-sequence 4) => (rectangle 16 32 "solid" "blue")
(define (rec-sequence n)
  (rectangle (expt 2 n)
             (expt 2 (+ n 1))
             "solid"
             "blue"))

(check-expect (rec-sequence 2) (rectangle 4 8 "solid" "blue"))
(check-expect (rec-sequence 4) (rectangle 16 32 "solid" "blue"))