【SICP练习】44 练习2.3
练习2.3
我们并不必急于写出点什么，先来回过头看看书吧。第56页说到了一种称为按愿望思维的强有力的综合策略。在这道题里，我们就可以假设已经写好了能够表示矩形的代码，以及能够求矩形长和宽的函数。
于是像先定义出add-rat一样，我们先定义出求矩形的周长和面机的函数。
(define(get-perimeter x)
(let ((length (rectangle-length x))
(width (rectangle-width x)))
(* 2 (+ length width))))
(define(get-area x)
(* (rectangle-length x) (rectangle-widthx)))
啊哈，书上要求用2中方式来表示矩形。我先来说说比较难看的一种表示方式，我一开始想到的下面那一种。
(define(make-ractangle rec-length-1 rec-length-2 rec-width-1 rec-width-2)
(cons (cons rec-length-1 rec-length-2)
(cons rec-width-1 rec-width-2)))
(define(rec-len-1 x)
(car (car x))
(define(rec-len-2 x)
(cdr (car x))
(define(rec-wid-1 x)
(car (cdr x))
(define(rec-wid-2 x)
(cdr (cdr x))
如书上所说，我们还要加载一下练习2.2中的代码。然后我们就可以开始构造矩形了。
(definelen-1 (make-segment (make-point 0 0)
(make-point 5 0)))
(definelen-2 (make-segment (make-point 0 4)
(make-point 5 4)))
(definewid-1 (make-segment (make-point 0 0)
(make-point 0 4)))
(definewid-2 (make-segment (make-point 5 0)
(make-point 5 4)))
(definerectangle-first (make-rectangle len-1 len-2 wid-1 wid-2))
这样打印出来的肯定是很混乱的，估计是一大堆括号的嵌套。所以还是要想书中那样自己写一个打印的函数。这里也要加载前面的print-point函数。
(define(print-rec x)
(let ((l1 (len-1 x))
(l2 (len-2 x))
(w1 (wid-1 x))
(w2 (wid-2 x)))
(newline)
(display “Length-1: “)
(print-point (start-segment l1))
(print-point (end-segment l1))
(newline)
(display “Length-2: “)
(print-point (start-segment l2))
(print-point (end-segment l2))
(newline)
(display “Width-1: “)
(print-point (start-segment w1))
(print-point (end-segment w1))
(newline)
(display “Width-1: “)
(print-point (start-segment w2))
(print-point (end-segment w2))
现在打印出来的就比较直观了。
(print-rec rectangle-first)
Length-1:
(0,0)
(5,0)
Length-2:
(0,4)
(5,4)
Width-1:
(0,0)
(0,4)
Width-2
(5,0)
(5,4)
下面我们还需要函数来计算长和宽。
(define (get-length x)
(let((length (len-1 x)))
(let ((start (start-segment length))
(end (end-segment length)))
(- (x-point end) (x-point start)))))
(define (get-width x)
(let((width (wid-1 x)))
(let ((start (start-segment width))
(end (end-segment width)))
(- (y-point end) (y-point start)))))
下面就可以来计算长和宽了，试试吧。
(get-perimeter rectangle-first)
;Value: 18
(get-area rectangle-fist)
;Value: 20
这种方式真是麻烦，谁会一开始想到这种呢，还是用两条线段简单啊，反正是矩形又不是菱形。
(define (make-ractangle length width)
(cons length width))
(define (rec-len x)
(car x))
(define (rec-wid x)
(cdr x))
(define (get-length x)
(let((length (rec-len x)))
(let ((start (start-segment length))
(end (end-segment length)))
(- (x-point end) (x-point start)))))
(define (get-width x)
(let((width (rec-wid x)))
(let ((start (start-segment width))
(end (end-segment width)))
(- (y-point end) (y-point start)))))
现在来创建矩形也很简单了。
(define len (make-segment (make-point 00)
(make-point 5 0)))
(define wid (make-segment (make-point 00)
(make-point 4 0)))
(define rectangle-second(make-rectangle len wid))