練習2 11 練習2 20

1.練習2.11

(define (mul-interval x y)

(let ((x1 (lower-bound x))
(x2 (upper-bound x))
(y1 (lower-bound y))
(y2 (upper-bound y)))
(let
((zzx (and (>= x1 0) (>= x2 0)))
(zzy (and (>= y1 0) (>= y2 0)))
(fzx (and (< x1 0) (>= x2 0)))
(fzy (and (< y1 0) (>= y2 0)))
(ffx (and (< x1 0) (< x2 0)))
(ffy (and (< y1 0) (< y2 0))))
(cond (zzy (cond (zzx (make-interval (* x1 y1) (* x2 y2)))
(fzx (make-interval (* x1 y2) (* x2 y2)))
(ffx (make-interval (* x1 y2) (* x2 y1)))))
(fzy (cond (zzx (make-interval (* x2 y1) (* x2 y2)))
(fzx (make-interval (min (* x1 y2) (* x2 y1))
(max (* x1 y1) (* x2 y2))))
(ffx (make-interval (* x1 y2) (* x1 y1)))))
(ffy (cond (zzx (make-interval (* x2 y1) (* x1 y2)))
(fzx (make-interval (* x2 y1) (* x1 y1)))
(ffx (make-interval (* x2 y2) (* x1 y1)))))))))

(define (mul-interval x y)

(let ((x1 (lower-bound x))
(x2 (upper-bound x))
(y1 (lower-bound y))
(y2 (upper-bound y)))
(let
((zzx (and (>= x1 0) (>= x2 0)))
(zzy (and (>= y1 0) (>= y2 0)))
(fzx (and (< x1 0) (>= x2 0)))
(fzy (and (< y1 0) (>= y2 0)))
(ffx (and (< x1 0) (< x2 0)))
(ffy (and (< y1 0) (< y2 0))))
(cond (zzy (cond (zzx (make-interval (* x1 y1) (* x2 y2)))
(fzx (make-interval (* x1 y2) (* x2 y2)))
(ffx (make-interval (* x1 y2) (* x2 y1)))))
(fzy (cond (zzx (make-interval (* x2 y1) (* x2 y2)))
(fzx (make-interval (min (* x1 y2) (* x2 y1))
(max (* x1 y1) (* x2 y2))))
(ffx (make-interval (* x1 y2) (* x1 y1)))))
(ffy (cond (zzx (make-interval (* x2 y1) (* x1 y2)))
(fzx (make-interval (* x2 y1) (* x1 y1)))
(ffx (make-interval (* x2 y2) (* x1 y1)))))))))

中文的翻譯太差了，句中的「兩個被乘區間的誤差」應該是「被乘區間的百分比誤差」吧，很生氣。。。

4.練習2.14

5.練習2.15

因為引入的誤差少，所以更精確

6.練習2.16

設計一種好難啊

7.練習2.17

(define (last-pair items)

(let ((len (length items)))
(define (last-pair-iter item tmplen)
(if (= tmplen 1)
item
(last-pair-iter (cdr item) (- tmplen 1))))
(last-pair-iter items len)))

(define (reverse items)

(define (reverse-iter tmpitems result)
(if (null? tmpitems)
result
(reverse-iter (cdr tmpitems)
(cons (car tmpitems) result))))
(reverse-iter items '()))

(define (first-denomination list1)

(car list1))
(define (except-first-denomination list1)
(cdr list1))
(define (no-more? list1)
(null? list1))

(define (same-parity . other)

(define (even-number? number)
(= (remainder number 2) 0))
(define (same-parity-recur even items)
(if (null? items)
'()(let ((now-even (even-number? (car items)))
(next (same-parity-recur even (cdr items))))
(if (or (and even now-even)
(and (not even) (not now-even)))
(cons (car items) next)
next))))
(let ((evenodds (even-number? (car other))))
(same-parity-recur evenodds other)))

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