46 lines
1.4 KiB
Racket
46 lines
1.4 KiB
Racket
;; The first three lines of this file were inserted by DrRacket. They record metadata
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;; about the language level of this file in a form that our tools can easily process.
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#reader(lib "htdp-beginner-reader.ss" "lang")((modname main) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f () #f)))
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; Number a, Number b, Number c -> String
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; Determines whether a list of 3 numbers is ascending or descending. Throws error if neither.
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(define (scending-how a b c)
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(cond [(< a b c) "ascending"]
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[(> a b c) "descending"]
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[else (error "too complex")]))
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(check-expect (scending-how 1 2 3) "ascending")
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(check-expect (scending-how 5 4 3) "descending")
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(check-error (scending-how 1 0 3))
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; Number a, Number b -> Number
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; Finds two positive numbers' greatest common denominator.
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(define (gcd2 a b)
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(cond
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[(= a 0) b]
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[(= b 0) a]
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[(and (even? a) (even? b))
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(* 2 (gcd2 (/ a 2) (/ b 2)))]
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[(even? b) (gcd2 a (/ b 2))]
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[(even? a) (gcd2 (/ a 2) b)]
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[else(if (<= a b)
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(gcd2 a (- b a))
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(gcd2 b (- a b)))]))
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(check-expect (gcd2 0 0) 0)
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(check-expect (gcd2 100 0) 100)
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(check-expect (gcd2 10 2) 2)
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(check-expect (gcd2 10 10) 10)
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(check-expect (gcd2 14 7) 7)
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(check-expect (gcd2 288 64) 32)
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; (gcd2 30 210)
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; (* 2 (gcd2 15 105))
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; (* 2 (gcd2 15 90))
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; (* 2 (gcd2 15 45))
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; (* 2 (gcd2 15 30))
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; (* 2 (gcd2 15 15))
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; (* 2 (gcd2 15 0))
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; (* 2 15)
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; 30
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