SICP笔记与习题-第一章

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习题1.3：

(define (sum2Greater a b c)  (cond ((and (< a b) (< a c)) (+ b c))        ((and (< b a) (< b c)) (+ a c))        ((and (< c a) (< c b)) (+ a b))))(define (sum2Bigger a b c)  (if (and (< a b) (< a c)) (+ b c)      (sum2Bigger b c a)))(sum2Greater 1 2 3)(sum2Bigger 1 2 3)

第一种方法是通过cond列举出三种情形并求和，第二种方法是利用if判断，并通过递归求和。

p14 牛顿法求平方根

#lang racket(define (square x) (* x x))(define (average x y) (/ (+ x y) 2))(define (abs x)  (if (< x 0) (- x)      x))(define (guess_enough guess x)  (< (abs (- (square guess) x)) 0.00001))(define (improve guess x)  (average guess (/ x guess)))(define (sqrt_iter guess x)  (if (guess_enough guess x)      guess      (sqrt_iter (improve guess x)            x)))(define (sqrt x)  (sqrt_iter 1 x))

调用时输入如(sqrt 2)即可。

习题1.7：

#lang racket(define (square x) (* x x))(define (average x y) (/ (+ x y) 2))(define (abs x)  (if (< x 0) (- x)      x))(define (improve guess x)  (average guess (/ x guess)))(define (guess_enough guess x)  (< (abs (- guess x)) 0.01))(define (sqrt_iter guess x)  (if (guess_enough guess (improve guess x))      guess      (sqrt_iter (improve guess x)            x)))(define (sqrt x)  (sqrt_iter 1 x))

习题1.8：

#lang racket(define (square x) (* x x))(define (abs x)  (if (< x 0) (- x)      x))(define (improve guess x)  (/ (+ (/ x (square guess)) (* 2 guess)) 3))(define (guess_enough guess x)  (< (abs (- guess x)) 0.001))(define (cbrt_iter guess x)  (if (guess_enough guess (improve guess x))      guess      (cbrt_iter (improve guess x)            x)))(define (cbrt x)  (cbrt_iter 1 x))

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