SICP练习题 1.7~1.8

1.7 mysqrt的改进

改善精度控制的细节, 判断如果连续两次迭代的猜测值相差很小, 就退出. 实验表明达到效果了, 大数和小数都得到了很大改善.

美中不足是我还不会用变量, get-guess-result方法被重复调用了.

(define (mysqrt x)

(define default-guess 1.0)
(define min-dx 0.000000001)

(define (get-guess-result guess )
(* guess guess))

(define (improve guess )
(/ (+ guess (/ x guess)) 2))

(define (goodguess? guess old-gruess)
(< (abs(- (/ (get-guess-result guess)
old-gruess )
1))
min-dx))

(define (sqrt-itor guess old-gruess)
(if (goodguess? guess old-gruess)
guess
(sqrt-itor (improve guess )
(get-guess-result guess ))))

(sqrt-itor default-guess x))

1.8 求立方根

求立方根实际上只需要替换improve函数和get-guess-result函数的实现, 其他代码相同. 我为了共享代码中的相同部分, 先重构了上面的代码, 做了一些抽象:

(define (gen-entire-surd-fun n )
;entire2/entire3

(define default-guess 1.0)
(define min-dx 0.000000001)

(define get-guess-result
(cond ((= n 2)
(lambda (guess )
(* guess guess)))
((= n 3)
(lambda (guess )
(* guess guess guess )))))

(define improve
(cond ((= n 2)
(lambda (guess x)
(/ (+ guess (/ x guess)) 2)))
((= n 3)
(lambda (guess x)
(/ (+ 	(/ x (* guess guess))
(* 2 guess)
)
3)))))

(define (goodguess? guess old-gruess)
(< (abs(- (/ (get-guess-result guess)
old-gruess )
1))
min-dx))

(define (entire-itor x guess old-gruess)
(if (goodguess? guess old-gruess)
guess
(entire-itor x (improve guess x )
(get-guess-result guess ))))

(lambda (x) (entire-itor x default-guess x)))

(define my-entire2 (gen-entire-surd-fun 2 ))
(define my-entire3 (gen-entire-surd-fun 3 ))

(write "hello, world, myentire sicp.1.8")
;(my-entire2 100000000000)
;(my-entire2 0.0000001)
;(my-entire3 100000000000)
;(my-entire3 0.0000001)

题外话, 熟悉了Lisp的写法, 感觉还是不错的, 简洁明了. 使用缩进能基本消除括号的烦恼. 进一步想, 如果直接使用缩进来控制代码结构, 那就变成Haskell和Python了. :D:D 但这样的风格似乎减弱了表达式和求值的思想.

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