SICP 习题2.9 区间宽度

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原创最新推荐文章于 2026-07-11 14:23:40 发布 599 阅读 AI 写同款· GEO 优化 ›

学好机器学习必会的统计学知识（第二篇）引言在机器学习应用中，我们不可能离开数据。没有了数据，机器学习算法就像没有了灵魂。更好地理解数据，可以使我们把它更好地应用在机器学习上。在这篇文章中，我会介绍一些在统计学中，理解数据的一些重要概念，从而使大家更准确地操作数据，玩转数据。注意：在这篇文章中会涉及到很多名词和定义，我就直接用英文了，因为这更加容易理解，翻译成汉语以后会让人更加混乱了。Populations and Parameters 阅读详情

可以看出add和sub之后的区间是之前两个区间的区间宽度之和，而mul和div是不确定的。

(define (add-interval x y)
  (make-interval (+ (lower-bound x) (lower-bound y))
         (+ (upper-bound x) (upper-bound y))))

(define (mul-interval x y)
  (let ((p1 (* (lower-bound x) (lower-bound y)))
    (p2 (* (lower-bound x) (upper-bound y)))
    (p3 (* (upper-bound x) (lower-bound y)))
    (p4 (* (upper-bound x) (upper-bound y))))
    (make-interval (min p1 p2 p3 p4)
           (max p1 p2 p3 p4))))

(define (div-interval x y)
  (mul-interval x 
        (make-interval (/ 1.0 (lower-bound y))
                   (/ 1.0 (upper-bound y)))))

(define (sub-interval x y)
  (make-interval (- (lower-bound x) (upper-bound y))
         (- (upper-bound x) (lower-bound y))))

(define (width-interval z)
  (/ (- (upper-bound z) (lower-bound z)) 2.0))

(define make-interval cons)
(define lower-bound car)
(define upper-bound cdr)

(define print-interval
  (lambda (z)
    (newline)
    (display (lower-bound z))
    (display " ~ ")
    (display (upper-bound z))))

(define a (make-interval 1 2))
(define b (make-interval 3 4))
(newline)
(display "a : ")
(display (width-interval a))
(newline)
(display "b : ")
(display (width-interval b))

(print-interval (add-interval a b))
(newline)
(display "add : ")
(display (width-interval (add-interval a b)))

(print-interval (mul-interval a b))
(newline)
(display "mul : ")
(display (width-interval (mul-interval a b)))

(print-interval (div-interval a b))
(newline)
(display "div : ")
(display (width-interval (div-interval a b)))

(print-interval (sub-interval a b))
(newline)
(display "sub : ")
(display (width-interval (sub-interval a b)))