90 lines
2.1 KiB
Scheme
90 lines
2.1 KiB
Scheme
(define (filter predicate sequence)
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(cond ((null? sequence) '())
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((predicate (car sequence))
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(cons (car sequence)
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(filter predicate (cdr sequence))))
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(else (filter predicate (cdr sequence)))))
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(define (accumulate op initial sequence)
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(if (null? sequence)
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initial
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(op (car sequence)
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(accumulate op initial (cdr sequence)))))
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(define (flatmap proc seq)
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(accumulate append '() (map proc seq)))
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;(define (prime-sum? pair)
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; (prime? (+ (car pair) (cadr pair))))
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(define (make-pair-sum pair)
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(list (car pair) (cadr pair) (+ (car pair) (cadr pair))))
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(define (smallest-divisor n)
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(find-divisor n 2))
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(define (square x) (* x x))
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(define (find-divisor n test-divisor)
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(cond ((> (square test-divisor) n) n)
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((divides? test-divisor n) test-divisor)
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(else (find-divisor n (+ test-divisor 1)))))
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(define (divides? a b)
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(= (remainder b a) 0))
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(define (prime? n)
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(= n (smallest-divisor n)))
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(define (permutations s)
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(if (null? s) ; empty set?
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(list '()) ; sequence containing empty set
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(flatmap (lambda (x)
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(map (lambda (p) (cons x p))
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(permutations (remove x s))))
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s)))
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(define (remove item sequence)
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(filter (lambda (x) (not (= x item)))
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sequence))
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(define (enumerate-interval low high)
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(if (> low high)
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'()
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(cons low (enumerate-interval (+ low 1) high))))
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(define (unique-pairs n)
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(flatmap
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(lambda (i)
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(map (lambda (j) (list i j))
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(enumerate-interval 1 (- i 1))))
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(enumerate-interval 1 n)))
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(define (prime-sum-pairs n)
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(map make-pair-sum
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(filter prime-sum? (unique-pairs n))))
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; 2.41
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(define (ordered-triples n)
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(flatmap
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(lambda (i)
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(flatmap
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(lambda (j)
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(map (lambda (k) (list i j k))
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(enumerate-interval 1 (- j 1))))
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(enumerate-interval 1 (- i 1))))
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(enumerate-interval 1 n)))
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(define (sum l)
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(if (null? l)
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0
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(+ (car l) (sum (cdr l)))))
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(define (triple-leq-n-sum-s n s)
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(filter (lambda (x) (= (sum x) s)) (ordered-triples n)))
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