77 lines
1.8 KiB
Scheme
77 lines
1.8 KiB
Scheme
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(define (sqrt x)
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(define (average x y) (/ (+ x y) 2))
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(define (square x) (* x x))
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(define (good-enough? guess)
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(< (abs (- (square guess) x)) 0.00001))
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(define (improve guess)
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(average guess (/ x guess)))
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(define (sqrt-iter guess)
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(if (good-enough? guess)
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guess
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(sqrt-iter (improve guess))))
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(sqrt-iter 1.0))
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;(define (factorial n)
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; (if (= n 1) 1 (* n (factorial (- n 1)))))
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(define (factorial n)
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(define (fact-iter product counter max-count)
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(if (> counter max-count)
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product
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(fact-iter (* counter product)
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(+ counter 1)
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max-count)))
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(fact-iter 1 1 n))
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(define (A x y)
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(cond ((= y 0) 0)
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((= x 0) (* 2 y))
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((= y 1) 2)
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(else (A (- x 1)
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(A x (- y 1))))))
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;(define (fib n)
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; (cond ((= n 0) 0)
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; ((= n 1) 1)
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; (else (+ (fib(- n 1))
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; (fib(- n 2))))))
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(define (fib n)
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(define (fib-iter a b count)
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(if (= count 0)
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b
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(fib-iter (+ a b) a (- count 1))))
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(fib-iter 1 0 n))
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(define (count-change amount)
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(define (first-denomination kinds-of-coins)
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(cond ((= kinds-of-coins 1) 1)
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((= kinds-of-coins 2) 5)
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((= kinds-of-coins 3) 10)
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((= kinds-of-coins 4) 25)
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((= kinds-of-coins 5) 50)))
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(define (cc amount kinds-of-coins)
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(cond ((= amount 0) 1)
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((or (< amount 0)
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(= kinds-of-coins 0))
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0)
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(else
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(+ (cc amount (- kinds-of-coins 1))
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(cc (- amount (first-denomination kinds-of-coins))
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kinds-of-coins)))))
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(cc amount 5))
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(define (ptri n)
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(if (< n 3) n
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(+
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(ptri (- n 1))
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(+ (* (ptri (- n 2)) 2)
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(* (ptri (- n 3)) 3)))))
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