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問題2.41

(define (unique-trio n)
  (flatmap (lambda (i)
                   (flatmap (lambda (j)
                                    (map (lambda (k) (list i j k))
                                         (enumerate-interval 1 (- j 1))))
                            (enumerate-interval 1 (- i 1))))
           (enumerate-interval 1 n)))

(define (sum-of-trio trio)
  (+ (car trio) (cadr trio) (cadr (cdr trio))))

(define (equal-sum-of-trio n s)
  (filter (lambda (x) (= (sum-of-trio x) s)) (unique-trio n)))

(unique-trio 6)
gosh> ((3 2 1) (4 2 1) (4 3 1) (4 3 2) (5 2 1) (5 3 1) (5 3 2) (5 4 1) (5 4 2) (5 4 3) (6 2 1) (6 3 1) (6 3 2) (6 4 1) (6 4 2) (6 4 3) (6 5 1) (6 5 2) (6 5 3) (6 5 4))
(equal-sum-of-trio 6 6)
gosh> ((3 2 1))
(equal-sum-of-trio 6 8)
gosh> ((4 3 1) (5 2 1))
(equal-sum-of-trio 6 12)
gosh> ((5 4 3) (6 4 2) (6 5 1))
(equal-sum-of-trio 6 15)
gosh> ((6 5 4))
(equal-sum-of-trio 6 16)
gosh> ()

上記手続きで利用している他の手続き

(define (filter predicate sequence)
  (cond ((null? sequence) ())
        ((predicate (car sequence))
         (cons (car sequence)
               (filter predicate (cdr sequence))))
        (else (filter predicate (cdr sequence)))))

(define (accumulate op initial sequence)
  (if (null? sequence)
      initial
      (op (car sequence)
          (accumulate op initial (cdr sequence)))))

(define (enumerate-interval low high)
  (if (> low high)
      ()
      (cons low (enumerate-interval (+ low 1) high))))

(define (flatmap proc seq)
  (accumulate append () (map proc seq)))

計算機プログラムの構造と解釈

posted with amazlet at 08.11.07

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