《计算机程序的构造和解释》学习笔记 1

课程来源

基本

lambda

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(define square (lambda (x) (* x x)))
(define (square x) (* x x))

一样的。

牛顿法平方根:

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(define (sqrt x)
(define (average x y) (/ (+ x y) 2.0))
(define (improve guess) (average guess (/ x guess)))
(define (good-enough? guess) (< (abs (- (* guess guess) x)) 0.0000000001))
(define try (lambda (guess)
(if (good-enough? guess)
guess
(try (improve guess)))))
(try 1))

高阶函数:函数当成变量

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;通用sum,求a到b term(a) 的和,步长为next(a)
(define (sum term a next b)
(if (> a b)
0
(+ (term a) (sum term (next a) next b))))

;从a加到b
(define (sum-int a b)
(define (indentity a) a)
(define (plus-one a) (+ 1 a))
(sum indentity a plus-one b))

(sum-int 1 10)

牛顿法求解

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#lang sicp

(define tolerance 0.000001)
(define dx 0.000001)

;找出f(x)不动点
(define (fixed-point f first-guess)
(define (close-enough? x y)
(< (abs (- x y)) tolerance))
(define (try guess)
(let ((next (f guess)))
(if (close-enough? guess next)
next
(try next))))
(try first-guess))

;求出g(x)导数
(define (deriv g)
(lambda (x) (/ (- (g (+ x dx)) (g x)) dx)))

;g(x)=0的解是f(x)=x-g(x)/dg(x)的一个不动点,下面的就是f(x)
(define (newton-transform g)
(lambda (x)
(- x (/ (g x) ((deriv g) x)))))

;牛顿法求出g(x)=0的解
(define (newton-method g guess)
(fixed-point (newton-transform g) guess))

(define (g x) (+ (* x x) (* 2 x) 1))

(newton-method g 1)

自己的 cons,car 和 cdr

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#lang sicp
(define (my-cons x y)
(lambda (pick)
(cond ((= pick 1) x)
((= pick 2) y))))

(define (my-car p) (p 1))

(define (my-cdr p) (p 2))

(my-cdr (my-cons 2 3))

自己的 map:

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#lang sicp
(define (my-map p l)
(if (null? l)
nil
(cons (p (car l)) (my-map p (cdr l)))))

(my-map (lambda (x) (* x x)) (list 1 2 3 4))

符号数据

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(list 'a 'b)
=> (a b)

(cdr '(b c))
=> (c)

其实 '(a b c) 就相当于 (quote (a b c))。以后可以用 '() 来代替 nil 了。

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