SICP学习笔记(2)

牛顿法求根

;The first program
(define (abs x) ( if(< x 0) (- x) x ))
(define (square x) (* x x) )
(define (average x y) (/ (+ x y) 2))
(define (improve guess x)(average guess (/ x guess)))
(define (good-enough? guess x) (< (abs (- (square guess) x))0.0001))
(define (sqrt_iter guess x) ( if(good-enough? guess x) guess (sqrt_iter (improve guess x) x)))
(define (sqrt x) (sqrt_iter 1.0 x) )

练习1.7:改变good-enough的内容,改为监视两次猜测的变化值相对于猜测值的比率.

(define (good-enough? guess x) (< (abs(/ (- (improve guess x) guess) guess)) 0.001) )

练习1.8：求解立方根,只要改动improve即可

(define (improve guess x)(/ (+ (/ x (square guess)) (* 2 guess)) 3))

块结构,将所有的辅助函数隐藏到sqrt里面,类似于一个封装.

(define (sqrt x) (define (abs x) ( if(< x 0) (- x) x )) (define (square x) (* x x) ) (define (average x y) (/ (+ x y) 2)) ;(define (improve guess x)(average guess (/ x guess))) (define (improve guess x)(/ (+ (/ x (square guess)) (* 2 guess)) 3)) (define (good-enough? guess x) (< (abs(/ (- (improve guess x) guess) guess)) 0.001) ) (define (sqrt_iter guess x) ( if(good-enough? guess x) guess (sqrt_iter (improve guess x) x))) (sqrt_iter 1.0 x))