問題2-39 (2.2.3 Sequences as Conventional Interfaces)

[tex:1\leq j

(define (square x) (* x x))

(define (smallest-divisor n)
  (find-divisor n 2))

(define (find-divisor n test-divisor)
  (cond ((> (square test-divisor) n) n)
	((divides? test-divisor n) test-divisor)
	(else (find-divisor n (+ test-divisor 1)))))

(define (divides? a b)
  (= (remainder b a) 0))

(define (prime? n)
  (= n (smallest-divisor n)))

まずは[tex: 1\leq j

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

これに対して、こんな風なunique-pairsをつくります。

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

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

実行結果はこうなるよ。

gosh> (unique-pairs 5)
((2 1) (3 1) (3 2) (4 1) (4 2) (4 3) (5 1) (5 2) (5 3) (5 4))

そしたら後はSICPに書いてあるprime-sum-pairsを置き換えればいいですね！

(use srfi-1)

(define (make-pair-sum pair)
  (list (car pair) (cadr pair) (+ (car pair) (cadr pair))))

(define (prime-sum? pair)
  (prime? (+ (car pair) (cadr pair))))

(define (prime-sum-pairs n)
  (map make-pair-sum
       (filter prime-sum?
	       (unique-pairs n))))

3つ組は最初の2つがi,jで、最後の値がi+jです。

gosh> (prime-sum-pairs 6)
((2 1 3) (3 2 5) (4 1 5) (4 3 7) (5 2 7) (6 1 7) (6 5 11))