sicp 习题 2.12 ~ 2.13

zhangle

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)