sicp練習問題2.12~2.13

2.12

(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 (lower-bound y)) (- 0 (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)
  (let ((product-y (* (lower-bound y) (upper-bound y))))
    (if (< product-y 0)
        (display "illegal number")
        (mul-interval x 
                      (make-interval (/ 1.0 (upper-bound y)) (/ 1.0 (lower-bound y)))))))

(define (make-interval a b) (cons a b))

(define (lower-bound x) (car x))

(define (upper-bound x) (cdr x))

(define (interval-width interval)
  (/ (- (upper-bound interval) (lower-bound interval)) 2))

(define (oper-interval-width v1 v2)
  (let ((w1 (interval-width v1))
        (w2 (interval-width v2)))
    (lambda(x) (x w1 w2))))

(define (make-center-width c w)
  (make-interval (- c w) (+ c w)))

(define (center i)
  (/ (+ (lower-bound i) (upper-bound i)) 2))

(define (width i)
  (/ (- (upper-bound i) (lower-bound i)) 2))

(define (make-center-percent c p)
  (make-interval (- c (* c (/ p 100))) (+ c (* c (/ p 100)))))

(define (percent i)
  (* 100 (/ (width i) (center i))))

(define interval-1 (make-center-percent 10 2))

(center interval-1)
(percent interval-1)

2.13

(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 (lower-bound y)) (- 0 (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)
  (let ((product-y (* (lower-bound y) (upper-bound y))))
    (if (< product-y 0)
        (display "illegal number")
        (mul-interval x 
                      (make-interval (/ 1.0 (upper-bound y)) (/ 1.0 (lower-bound y)))))))

(define (make-interval a b) (cons a b))

(define (lower-bound x) (car x))

(define (upper-bound x) (cdr x))

(define (interval-width interval)
  (/ (- (upper-bound interval) (lower-bound interval)) 2))

(define (oper-interval-width v1 v2)
  (let ((w1 (interval-width v1))
        (w2 (interval-width v2)))
    (lambda(x) (x w1 w2))))

(define (make-center-width c w)
  (make-interval (- c w) (+ c w)))

(define (center i)
  (/ (+ (lower-bound i) (upper-bound i)) 2))

(define (width i)
  (/ (- (upper-bound i) (lower-bound i)) 2))

(define (make-center-percent c p)
  (make-interval (- c (* c (/ p 100))) (+ c (* c (/ p 100)))))

(define (percent i)
  (* 100 (/ (width i) (center i))))

(define interval-1 (make-center-percent 10 0.01))

(define interval-2 (make-center-percent 20 0.03))

(define interval-3 (mul-interval interval-1 interval-2))

(percent interval-3)


(define (par1 r1 r2)
  (div-interval (mul-interval r1 r2)
                (add-interval r1 r2)))

(define (par2 r1 r2)
  (let ((one (make-interval 1 1)))
    (div-interval one (add-interval (div-interval one r1)
                                    (div-interval one r2)))))

(define r1 (make-center-percent 10 0.01))

(define r2 (make-center-percent 20 0.02))

(define r3 (par1 r1 r2))

(define r4 (par2 r1 r2))

(lower-bound r3)
(upper-bound r3)

(lower-bound r4)
(upper-bound r4)