sicp 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 ")"))

 

(define (make-segment p1 p2)
  (cons p1 p2))

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

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

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

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

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

(define (midpoint-segment s)
  (make-point (/ (+ (x-point (start-segment s)) (x-point (end-segment s))) 2)
              (/ (+ (y-point (start-segment s)) (y-point (end-segment s))) 2)))

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

(define s (make-segment (make-point 1 5) (make-point 2 6)))
(print-point (midpoint-segment s))

 

结果：

(3/2, 11/2)