2.12

练习 2.12 请定义一个构造函数 make-center-percent，它以一个中心点和一个百分比为参数，产生出所需要的区间。你还需要定义选择函数 percent，通过它可以得到给定区间的百分数误差，选择函数 center 与前面定义的一样。

 
(define (make-interval a b) (cons a b))
(define upper-bound cdr)
(define lower-bound car)
(define (add-interval x y) 
  (make-interval (+ (lower-bound x) (lower-bound y))
                 (+ (upper-bound x) (upper-bound y))))
(define (sub-interval x y) (add-interval x (make-interval (- 0 (upper-bound y)) (- 0 (lower-bound y)))))
(define (subtract-interval x y)
  (define p1 (- (lower-bound x) (lower-bound y)))
  (define p2 (- (lower-bound x) (upper-bound y)))
  (define p3 (- (upper-bound x) (lower-bound y)))
  (define p4 (- (upper-bound x) (upper-bound y)))
​
  (make-interval (min p1 p2 p3 p4) (max p1 p2 p3 p4)))
​
(define (mul-interval x y)
  (define p1 (* (lower-bound x) (lower-bound y)))
  (define p2 (* (lower-bound x) (upper-bound y)))
  (define p3 (* (upper-bound x) (lower-bound y)))
  (define p4 (* (upper-bound x) (upper-bound y)))
​
  (make-interval (min p1 p2 p3 p4) (max p1 p2 p3 p4))
  )
​
(define int1 (make-interval 2 4))
(define int2 (make-interval 3 6))
(mul-interval int1 int2)
​x
 
(6 . 24)

在之前定义过的函数的基础上，很容易写出：

 
(define (make-center-percent center percent)
  (make-interval (- center (* center percent))
                 (+ center (* center percent))))
​
(define (center x) (/ (+ (lower-bound x) (upper-bound x)) 2))
​
(define (percent x)
  (/ (width x) (center x)))
​
(define int (make-center-percent 2 0.5))
int
 
(1 . 3)

 
(center int)
 
2

 
(define (width x) (/ (- (upper-bound x) (lower-bound x)) 2))
(percent int)
 
0.5