sicp每日一题[2.58]

合集 - sicp(77)
1.sicp每日一题[1.42]2.sicp每日一题[1.43]3.sicp每日一题[1.44]4.sicp每日一题[1.45]5.sicp每日一题[1.46]6.sicp每日一题[2.1]7.sicp每日一题[2.2]8.sicp每日一题[2.3]9.sicp每日一题[2.4]10.sicp每日一题[2.5]11.sicp每日一题[2.6]12.sicp每日一题[2.7]13.sicp每日一题[2.8]14.sicp每日一题[2.9]15.sicp每日一题[2.11]16.sicp每日一题[2.10]17.sicp每日一题[2.12]18.sicp每日一题[2.13-2.16]19.sicp每日一题[2.17]20.sicp每日一题[2.18]21.sicp每日一题[2.19]22.sicp每日一题[2.20]23.sicp每日一题[2.21]24.sicp每日一题[2.22-2.23]25.sicp每日一题[2.24-2.27]26.sicp每日一题[2.28]27.sicp每日一题[2.29]28.sicp每日一题[2.30]29.sicp每日一题[2.31]30.sicp每日一题[2.32]31.sicp每日一题[2.33]32.sicp每日一题[2.34]33.sicp每日一题[2.35]34.sicp每日一题[2.36-2.37]35.sicp每日一题[2.38-2.39]36.sicp每日一题[2.40]37.sicp每日一题[2.41]38.sicp每日一题[2.42]39.sicp每日一题[2.43]40.sicp每日一题[2.44]41.sicp每日一题[2.45]42.sicp每日一题[2.46]43.sicp每日一题[2.47]44.sicp每日一题[2.48]45.sicp每日一题[2.49]46.sicp每日一题[2.50]47.sicp每日一题[2.51]48.sicp每日一题[2.52]49.sicp每日一题[2.53-2.55]50.sicp每日一题[2.56]51.sicp每日一题[2.57]
52.sicp每日一题[2.58]
53.sicp每日一题[2.59]54.sicp每日一题[2.60]55.sicp每日一题[2.61]56.sicp每日一题[2.62]57.sicp每日一题[2.63-2.64]58.sicp每日一题[2.65]59.sicp每日一题[2.66]60.sicp每日一题[2.67-2.68]61.sicp每日一题[2.69]62.sicp每日一题[2.70]63.sicp每日一题[2.71]64.sicp每日一题[2.72]65.sicp每日一题[2.73]66.sicp每日一题[2.74]67.sicp每日一题[2.75]68.sicp每日一题[2.76]69.sicp每日一题[2.77]70.sicp每日一题[2.78]71.sicp每日一题[2.79]72.sicp每日一题[2.80]73.sicp每日一题[2.81]74.sicp每日一题[2.82]75.sicp每日一题[2.83]76.sicp每日一题[2.84]77.sicp每日一题[2.85-2.86]
收起

Exercise 2.58

Suppose we want to modify the differentiation program so that it works with ordinary mathematical notation, in which + and * are infix rather than prefix operators. Since the differentiation program is defined
in terms of abstract data, we ca modify it to work with different representations of expressions solely by changing the predicates, selectors, and constructors that define the representation of the algebraic
expressions on which the differentiator is to operate.

a. Show how to do this in order to differentiate algebraic expressions presented in infix form, such as (x + (3 * (x + (y + 2)))). To simplify the task, assume that + and * always take two arguments and that
expressions are fully parenthesized.
b. The problem becomes substantially harder if we allow standard algebraic notation, such as (x + 3 * (x + y + 2)), which drops unnecessary parentheses and assumes that multiplication is done before addition.
Can you design appropriate predicates, selectors, and constructors for this notation such that our derivative program still works?

这道题乍一看很棘手，但是仔细一想其实挺简单的，只要把构造函数和选择器里 + 和 * 的位置改一下就行了，还有原来的前缀表示法要多加一个 + 或 *，现在也可以直接省略掉了。

(define (make-sum a1 a2)
  (cond ((=number? a1 0) a2)
        ((=number? a2 0) a1)
        ((and (number? a1) (number? a2)) (+ a1 a2))
        (else (list a1 '+ a2))))

(define (sum? x) (and (pair? x) (eq? (cadr x) '+)))

(define (addend s) (car s))

(define (augend s)
  (let ((last (cddr s)))
    (if (null? (cdr last))
        (car last)
        last)))

(define (make-product m1 m2)
  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
        ((=number? m1 1) m2)
        ((=number? m2 1) m1)
        ((and (number? m1) (number? m2)) (* m1 m2))
        (else (list m1 '* m2))))

(define (product? x) (and (pair? x) (eq? (cadr x) '*)))

(define (multiplier p) (car p))

(define (multiplicand p)
    (let ((last (cddr p)))
    (if (null? (cdr last))
        (car last)
        last)))


(deriv '(x + (3 * (x + (y + 2)))) 'x)
(deriv '(x + 3 * (x + y + 2)) 'x)

; 执行结果
4
4
posted @   再思即可  阅读(17)  评论(0)  编辑  收藏  举报
相关博文：
· sicp每日一题[2.57]
· sicp每日一题[2.56]
· leetcode 227. Basic Calculator II
· 2019北航夏令营机试 T2 复杂计算器
· P1175-表达式的转换
阅读排行：
· DeepSeek 开源周回顾「GitHub 热点速览」
· 物流快递公司核心技术能力-地址解析分单基础技术分享
· .NET 10首个预览版发布：重大改进与新特性概览！
· AI与.NET技术实操系列（二）：开始使用ML.NET
· 单线程的Redis速度为什么快？
点击右上角即可分享
微信分享提示
AI FOR CODE 大赛