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Exercise_2_11.rkt
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Exercise_2_11.rkt
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#lang racket/base
(define (make-interval a b) (cons a b))
(define (upper-bound interval)
(max (car interval) (cdr interval)))
(define (lower-bound interval)
(min (car interval) (cdr interval)))
(define (add-interval x y)
(make-interval (+ (lower-bound x) (lower-bound y))
(+ (upper-bound x) (upper-bound y))))
(define (sub-interval a b)
(add-interval
a
(make-interval
(- (lower-bound b))
(- (upper-bound b)))))
(define (mul-interval x y)
(let ([lx (lower-bound x)]
[ux (upper-bound x)]
[ly (lower-bound y)]
[uy (upper-bound y)])
(cond [(and (positive? lx)
(positive? ux)
(positive? ly)
(positive? uy))
(make-interval (* lx ly) (* ux uy))]
[(and (negative? lx)
(negative? ux)
(negative? ly)
(negative? uy))
(make-interval (* ux uy) (* lx ly))]
[(and (positive? lx)
(positive? ux)
(negative? ly)
(negative? uy))
(make-interval (* ux ly) (* lx uy))]
[(and (negative? lx)
(negative? ux)
(positive? ly)
(positive? uy))
(make-interval (* lx uy) (* ux ly))]
[(and (positive? lx)
(positive? ux)
(negative? ly)
(positive? uy))
(make-interval (* ux ly) (* ux uy))]
[(and (negative? lx)
(positive? ux)
(positive? ly)
(positive? uy))
(make-interval (* lx uy) (* ux uy))]
[(and (negative? lx)
(positive? ux)
(negative? ly)
(positive? uy))
(make-interval (min (* lx uy) (* ux ly)) (max (* ux uy) (* lx ly)))]
[(and (negative? lx)
(positive? ux)
(negative? ly)
(negative? uy))
(make-interval (* ux ly) (* lx ly))]
[(and (negative? lx)
(negative? ux)
(negative? ly)
(positive? uy))
(make-interval (* lx uy) (* lx ly))])))
(define a (make-interval -3 -4))
(define b (make-interval -1 -1))
(mul-interval a b)
; '(3 . 4)