例子:求2的平方根
| Guess |
Quotient |
Average |
| |
| 1 |
(2/1) = 2 |
((2 + 1)/2) = 1.5 |
| |
| 1.5 |
(2/1.5) = 1.3333 |
((1.3333 + 1.5)/2) = 1.4167 |
| |
| 1.4167 |
(2/1.4167) = 1.4118 |
((1.4167 + 1.4118)/2) = 1.4142 |
| |
| 1.4142 |
...
|
...
|
一.给出一个scheme的过程 (define (sqrt-iter guess x)
(if (good-enough? guess x)
guess
(sqrt-iter (improve guess x)
x)))
二.改进猜的数(x除以猜的数和猜的数的平均值
(define (average x y)
(/ (+ x y) 2)) (define (improve guess x)
(average guess (/ x guess)))
三.如何得到比较适合的值.这里做了一个假设,猜的值的平方减去x不小于0.001
(define (good-enough? guess x)
(< (abs (- (square guess) x)) 0.001))
注:如何用内部过程来使用上面的部分:
(define (sqrt x)
(define (good-enough? guess)
(define (square)
(* guess guess))
(< (abs (- (square) x)) 0.001))
(define (improve guess)
(define (average y)
(/ (+ guess y)
2))
(average (/ x guess)))
(define (sqrt-iter guess)
(if (good-enough? guess)
guess
(sqrt-iter (improve guess))))
(sqrt-iter 1.0))
|