SICP学习笔记 1.1.7 实例:使用牛顿法求平方根

 

   练习1.6

    应用序会对

 

(define (sqrt-iter guess x)
  (new-if (good-enough guess x)
	  guess
	  (sqrt-iter (improve guess x) x)))

 

    的new-if中的else-clause(即(sqrt-iter (improve guess x) x))进行展开，而sqrt-iter使用了递归，因此将进入死循环

 

    练习1.7

    在被求值的数很小或很大时，因为变化程度很小会导致程序进入死循环

    修改后的程序如下:

 

(define (square x)
  (* x x))
(define (myabs x)
  (if (< x 0) (- x) x))
(define (good-enough oguess nguess)
  (< (/ (myabs (- (square oguess) (square nguess))) (square oguess)) 0.001))
(define (average x y)
  (/ (+ x y) 2))
(define (improve guess x)
  (average guess (/ x guess)))
(define (sqrt-iter oguess nguess x)
  (if (good-enough oguess nguess)
      nguess
      (sqrt-iter nguess (improve nguess x) x)))
(define (sqrt x)
  (sqrt-iter x 1.0 x))

 

  练习1.8

 

(define (square x) (* x x))
(define (cube x) (* x x x))
(define (myabs x)
  (if (< x 0) (- x) x))
(define (good-enough oguess nguess)
  (< (/ (myabs (- (cube oguess) (cube nguess))) (cube oguess)) 0.001))
(define (improve guess x)
  (/ (+ (/ x (square guess)) (* 2 guess)) 3))
(define (cube-root-iter oguess nguess x)
  (if (good-enough oguess nguess)
      nguess
      (cube-root-iter nguess (cube-improve nguess x) x)))
(define (cube-root x)