sicp每日一題[2.2]

Exercise 2.2

Consider the problem of representing line segments in a plane. Each segment is represented as a pair of points: a starting point and an ending point. Define a constructor make-segment and selectors start-segment and end-segment that define the representation of segments in terms of points. Furthermore, a point can be represented as a pair of numbers: the x coordinate and the y coordinate. Accordingly, specify a constructor make-point and selectors x-point and y-point that define this representation. Finally, using your selectors and constructors, define a procedure midpoint-segment that takes a line segment as argument and returns its midpoint (the point whose coordinates are the average of the coordinates of the endpoints). To try your procedures, you’ll need a way to print points:

(define (print-point p)
  (newline)
  (display "(")
  (display (x-point p))
  (display ",")
  (display (y-point p))
  (display ")"))

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這道題目很簡單，主要是為了檢查我們是否理解了巢狀使用抽象資料結構的概念，有點像 Python 裡的列表，每個列表元素也可以是列表。

(define (make-point x y)
  (cons x y))

(define (x-point p) (car p))

(define (y-point p) (cdr p))

(define (make-segment start end)
  (cons start end))

(define (start-segment segment)
  (car segment))

(define (end-segment segment)
  (cdr segment))

; 線段中點座標就是起點和終點橫縱座標的平均值
(define (midpoint-segment segment)
  (let ((start (start-segment segment))
        (end (end-segment segment)))
    (make-point (average (x-point start) (x-point end))
                (average (y-point start) (y-point end)))))


; 設定線段起點為(3, 5)，終點為(7, 7)，中點應該為(5, 6)
(define start (make-point 3 5))
(define end (make-point 7 7))
(define line (make-segment start end))
(print-point (midpoint-segment line))

; 執行結果
(5, 6)