sicp每日一题[2.3]

Exercise 2.3

Implement a representation for rectangles in a plane. (Hint: You may want to make use of Exercise 2.2.) In terms of your constructors and selectors, create procedures that compute the perimeter and the area of a given rectangle. Now implement a different representation for rectangles. Can you design your system with suitable abstraction barriers, so that the same perimeter and area procedures will work using either representation?

首先借用 Exercise 2.2 的函数来表示矩形，我们已经有了线段的表示方法，那矩形就是2组平行且相等的线段，且邻边垂直。为了简朴起见，把矩形左下角的顶点坐标设为(0, 0)，且一条边落在 x 轴上。然后接纳矩形左边的那条边和对角线交点坐标来确定一个矩形，同样为了简便起见，把交点坐标设为(0, 0)。可以看出 make-point, x-point, y-point; make-segment, start-segment, end-segment; make-rect, make-rect-by-meeting-point; get-line-length, get-perimeter, get-area 是四层不同的函数，某一层的函数实现逻辑的改变，不会影响到其他层的调用。

1. ; 用左下的顶点和经过该顶点的两条邻边来确定一个矩形，为简单起见，左下的顶点坐标设为(0, 0)
2. ; length, width 分别表示矩形的长和宽
3. (define (make-rect length width)
4.   (let ((left-bottom (make-point 0 0)))
5.     (cons (make-segment left-bottom (make-point (car left-bottom) (+ (cdr left-bottom) width)))    ; 竖直的那条边
6.           (make-segment left-bottom (make-point (+ (car left-bottom) length) (cdr left-bottom))))))    ; 水平的那条边
8. ; 用矩形的对角线交点和左边的边来确定一个矩形,为简单起见,对角线交点坐标设为(0, 0)
9. ; left-line 表示左边的边
10. (define (make-rect-by-meeting-point left-line)
11.   (cons left-line (make-segment (start-segment left-line) (make-point (- 0 (x-point (start-segment left-line)))
12.                                                                       (y-point (start-segment left-line))))))
14. ; 用两点间距离公式 d = sqrt(x^2 + y^2) 计算线段的长度
15. (define (get-line-length segment)
16.   (sqrt (+ (square (- (x-point (end-segment segment))
17.                       (x-point (start-segment segment))))
18.            (square (- (y-point (end-segment segment))
19.                       (y-point (start-segment segment)))))))
21. ; 计算矩形的周长
22. (define (get-perimeter rect)
23.   (* 2 (+ (get-line-length (car rect))
24.           (get-line-length (cdr rect)))))
26. ; 计算矩形的面积
27. (define (get-area rect)
28.   (* (get-line-length (car rect))
29.      (get-line-length (cdr rect))))
32. ; 设置一个长为7宽为5的矩形
33. (define test-rect1 (make-rect 7 5))
35. (display "矩形test-rect1周长为：")
36. (display (get-perimeter test-rect1))
37. (newline)
38. (display "矩形test-rect1面积为:")
39. (display (get-area test-rect1))
40. (newline)
42. ; 设置一个长为7宽为5的矩形
43. (define A (make-point -3.5 -2.5))
44. (define B (make-point -3.5 2.5))
45. (define left-line (make-segment A B))
46. (define test-rect2 (make-rect-by-meeting-point left-line))
47. (display "矩形test-rect2周长为:")
48. (display (get-perimeter test-rect2))
49. (newline)
50. (display "矩形test-rect2面积为:")
51. (display (get-area test-rect2))
52. (newline)
54. ; 执行结果
55. 矩形test-rect1周长为：24.000000282646763
56. 矩形test-rect1面积为:35.00000070672435
57. 矩形test-rect2周长为:24.000000282646763
58. 矩形test-rect2面积为:35.00000070672435

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