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 m a k e − s e g m e n t make-segment make−segment and selectors s t a r t − s e g m e n t start-segment start−segment and e n d − s e g m e n t end-segment 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 x x coordinate and the y y y coordinate. Accordingly, specify a constructor m a k e − p o i n t make-point make−point and selectors x − p o i n t x-point x−point and $y-point $that define this representation. Finally, using your selectors and constructors, define a procedure m i d p o i n t − s e g m e n t midpoint-segment 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 ")"))
这道题目很简单，主要是为了检查我们是否理解了嵌套使用抽象数据结构的概念，有点像 Python 里的列表，每个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))
; 线段中点坐标就是起点和终点横纵坐标的平均值
(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)))))
; 设置线段起点为(3, 5)，终点为(7, 7)，中点应该为(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))
; 执行结果
(5, 6)
