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)
