sicp习题试解 (2.12)

; ======================================================================

;

; Structure and Interpretation of Computer Programs

; (trial answer to excercises)

;

; 计算机程序的构造和解释(习题试解)

;

; created: code17 05/30/05

; modified:

; (保持内容完整不变前提下，可以任意转载)

; ======================================================================

;; SICP No.2.12

;; 唯一的注意事项是符号，

;; 比如当c小于0时，make-center-percent定义中make-interval中两个操作数的先后

;; 以及如何保证percent函数的输出始终是正的。

(define (make-center-percent c p)

(if (or (< p 0) (> p 1))

(error "Percentage x should satisfy 0 <= x <= 1")

(let ((a (* c (+ 1.0 p)))

(b (* c (- 1.0 p))))

(make-interval (min a b) (max a b)))))

(define (center i)

(/ (+ (lower-bound i) (upper-bound i)) 2.0))

(define (percent i)

(let ((l (lower-bound i))

(u (upper-bound i)))

(/ (- u l) (abs (+ u l)))))

;; Test-it:

;; Welcome to MzScheme version 209, Copyright (c) 2004 PLT Scheme, Inc.

;; ;; .............

;;

;; > (make-center-percent -20.0 0.1)

;; (-22.0 . -18.0)

;; > (define v (make-center-percent -20.0 0.1))

;; > (center v)

;; -20.0

;; > (percent v)

;; 0.1