sicp每日一题[2.77]

Exercise 2.77

Louis Reasoner tries to evaluate the expression (magnitude z) where z is the object shown in Figure 2.24. To his surprise, instead of the answer she gets an error message from apply-generic, saying there is no method for the operation magnitude on the types (complex). He shows this interaction to Alyssa P. Hacker, who says "The problem is that the complex-number selectors were never defined for complex numbers, just for polar and rectangular numbers. All you have to do to make this work is add the following to the complex package:"

复制代码
  (put 'real-part '(complex) real-part)
  (put 'imag-part '(complex) imag-part)
  (put 'magnitude '(complex) magnitude)
  (put 'angle '(complex) angle)

Describe in detail why this works. As an example, trace through all the procedures called in evaluating the expression (magnitude z) where z is the object shown in Figure 2.24. In particular, how many times is apply-generic invoked? What procedure is dispatched to in each case?


这道题我想的是先把代码跑起来,因为直接按题目提示添加了那4行代码还是会报错,最终能运行的代码如下:

复制代码
(define (install-rectangular-package)
  ;; internal procedures
  (define (real-part z) (car z))
  (define (imag-part z) (cdr z))
  (define (make-from-real-imag x y) (cons x y))
  (define (magnitude z)
    (sqrt (+ (square (real-part z))
             (square (imag-part z)))))
  (define (angle z)
    (atan (imag-part z) (real-part z)))
  (define (make-from-mag-ang r a)
    (cons (* r (cos a)) (* r (sin a))))
  ;; interface to the rest of the system
  (define (tag x) (attach-tag 'rectangular x))
  (put 'real-part '(rectangular) real-part)
  (put 'imag-part '(rectangular) imag-part)
  (put 'magnitude '(rectangular) magnitude)
  (put 'angle '(rectangular) angle)
  (put 'make-from-real-imag 'rectangular
       (lambda (x y) (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'rectangular
       (lambda (r a) (tag (make-from-mag-ang r a))))
  'done)

(define (install-polar-package)
  ;; internal procedures
  (define (magnitude z) (car z))
  (define (angle z) (cdr z))
  (define (make-from-mag-ang r a) (cons r a))
  (define (real-part z) (* (magnitude z) (cos (angle z))))
  (define (imag-part z) (* (magnitude z) (sin (angle z))))
  (define (make-from-real-imag x y)
    (cons (sqrt (+ (square x) (square y)))
          (atan y x)))
  ;; interface to the rest of the system
  (define (tag x) (attach-tag 'polar x))
  (put 'real-part '(polar) real-part)
  (put 'imag-part '(polar) imag-part)
  (put 'magnitude '(polar) magnitude)
  (put 'angle '(polar) angle)
  (put 'make-from-real-imag 'polar
       (lambda (x y) (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'polar
       (lambda (r a) (tag (make-from-mag-ang r a))))
  'done)

;; 复数
(define (install-complex-package)
  ;; imported procedures from rectangular and polar packages
  (define (make-from-real-imag x y)
    ((get 'make-from-real-imag 'rectangular) x y))
  (define (make-from-mag-ang r a)
    ((get 'make-from-mag-ang 'polar) r a))
  ;; internal procedures
  (define (add-complex z1 z2)
    (make-from-real-imag (+ (real-part z1) (real-part z2))
                         (+ (imag-part z1) (imag-part z2))))
  (define (sub-complex z1 z2)
    (make-from-real-imag (- (real-part z1) (real-part z2))
                         (- (imag-part z1) (imag-part z2))))
  (define (mul-complex z1 z2)
    (make-from-mag-ang (* (magnitude z1) (magnitude z2))
                       (+ (angle z1) (angle z2))))
  (define (div-complex z1 z2)
    (make-from-mag-ang (/ (magnitude z1) (magnitude z2))
                       (- (angle z1) (angle z2))))
  ;; interface to rest of the system
  (define (tag z) (attach-tag 'complex z))
  (put 'add '(complex complex)
       (lambda (z1 z2) (tag (add-complex z1 z2))))
  (put 'sub '(complex complex)
       (lambda (z1 z2) (tag (sub-complex z1 z2))))
  (put 'mul '(complex complex)
       (lambda (z1 z2) (tag (mul-complex z1 z2))))
  (put 'div '(complex complex)
       (lambda (z1 z2) (tag (div-complex z1 z2))))
  (put 'make-from-real-imag 'complex
       (lambda (x y) (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'complex
       (lambda (r a) (tag (make-from-mag-ang r a))))
  (put 'real-part '(complex) real-part)
  (put 'imag-part '(complex) imag-part)
  (put 'magnitude '(complex) magnitude)
  (put 'angle '(complex) angle)
  'done)

(define (make-complex-from-real-imag x y)
  ((get 'make-from-real-imag 'complex) x y))
(define (make-complex-from-mag-ang r a)
  ((get 'make-from-mag-ang 'complex) r a))

(define (real-part z) (apply-generic 'real-part z)) 
(define (imag-part z) (apply-generic 'imag-part z)) 
(define (magnitude z) (apply-generic 'magnitude z)) 
(define (angle z) (apply-generic 'angle z))

(install-rectangular-package)
(install-polar-package)
(install-complex-package)


(define z (make-complex-from-real-imag 3 4))
(magnitude z)

; 结果如下
5.000000000053722

这里要注意2点,一个是要安装这几个包,另一个是在安装这些包之前需要加上 (define (magnitude z) (apply-generic 'magnitude z)),不然会报错。

执行 (magnitude z) 的函数调用依次是:

复制代码
(magnitude z)
(magnitude '(complex rectangular 3 . 4))
(apply-generic 'magnitude '(complex rectangular 3 . 4))
(get 'magnitude '(complex))
(apply magnitude (map contents '((complex rectangular 3 . 4))))

(magnitude '(rectangular 3 . 4))
(apply-generic 'magnitude '(rectangular 3 . 4))
(get 'magnitude '(rectangular))
(apply magnitude-rectangular (map contents '((rectangular 3 . 4))))
(magnitude-rectangular '(3 . 4))
5

为了看得更清楚,这里用 magnitude-rectangular 表示 install-rectangular-package 包中的 magnitude 过程。可以看出,在上面的过程中,一共调用了2次 apply-generic,第一次它根据 complex 和 magnitude 去寻找 install-complex-package 包中对应的过程;第二次它根据 rectangular 和 magnitude 找到了 install-rectangular-package 包中的 magnitude 过程。

相关推荐
珹洺1 小时前
C++从入门到实战(十)类和对象(最终部分)static成员,内部类,匿名对象与对象拷贝时的编译器优化详解
java·数据结构·c++·redis·后端·算法·链表
写bug的小屁孩1 小时前
移动零+复写零+快乐数+盛最多水的容器+有效三角形的个数
c++·算法·双指针
飞川撸码1 小时前
【LeetCode 热题100】208:实现 Trie (前缀树)(详细解析)(Go语言版)
算法·leetcode·golang·图搜索算法
这就是编程2 小时前
自回归模型的新浪潮?GPT-4o图像生成技术解析与未来展望
人工智能·算法·机器学习·数据挖掘·回归
羑悻的小杀马特2 小时前
【狂热算法篇】探寻图论幽径:Bellman - Ford 算法的浪漫征程(通俗易懂版)
c++·算法·图论·bellman_ford算法
Fantasydg5 小时前
DAY 31 leetcode 142--链表.环形链表
算法·leetcode·链表
basketball6166 小时前
C++ STL常用算法之常用排序算法
c++·算法·排序算法
qystca6 小时前
蓝桥云客 岛屿个数
算法·dfs·bfs
什码情况7 小时前
回文时间 - 携程机试真题题解
数据结构·python·算法·华为od·机试
lwewan8 小时前
26考研——栈、队列和数组_数组和特殊矩阵(3)
数据结构·笔记·考研·算法