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") 

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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