练习 2.40

书本 83 页的第一段代码其实就是 unique-pairs 的定义：

(accumulate append
            '()
            (map (lambda (i)
                     (map (lambda (j) (list i j))
                          (enumerate-interval 1 (- i 1))))
                 (enumerate 1 n)))

不过书本给出的这段代码并没有使用 flatmap 函数，我们将那这段代码改成使用 flatmap 的版本就行了：

;;; 40-unique-pairs.scm

(load "p78-enumerate-interval.scm")
(load "p83-flatmap.scm")

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

测试：

1 ]=> (load "40-unique-pairs.scm")

;Loading "40-unique-pairs.scm"...
;  Loading "p78-enumerate-interval.scm"... done
;  Loading "p83-flatmap.scm"...
;    Loading "p78-accumulate.scm"... done
;  ... done
;... done
;Value: unique-pairs

1 ]=> (unique-pairs 4)

;Value 12: ((2 1) (3 1) (3 2) (4 1) (4 2) (4 3))

1 ]=> (unique-pairs 6)

;Value 13: ((2 1) (3 1) (3 2) (4 1) (4 2) (4 3) (5 1) (5 2) (5 3) (5 4) (6 1) (6 2) (6 3) (6 4) (6 5))

使用 unique-pairs 重定义 prime-sum-pairs

;;; 40-prime-sum-pairs.scm

(load "40-unique-pairs.scm")
(load "p83-prime-sum.scm")
(load "p83-make-pair-sum.scm")

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

测试：

1 ]=> (load "40-prime-sum-pairs.scm")

;Loading "40-prime-sum-pairs.scm"...
;  Loading "40-unique-pairs.scm"...
;    Loading "p78-enumerate-interval.scm"... done
;    Loading "p83-flatmap.scm"...
;      Loading "p78-accumulate.scm"... done
;    ... done
;  ... done
;  Loading "p83-prime-sum.scm"...
;    Loading "p33-prime.scm"...
;      Loading "p33-smallest-divisor.scm"... done
;    ... done
;  ... done
;  Loading "p83-make-pair-sum.scm"... done
;... done
;Value: prime-sum-pairs

1 ]=> (prime-sum-pairs 6)

;Value 11: ((2 1 3) (3 2 5) (4 1 5) (4 3 7) (5 2 7) (6 1 7) (6 5 11))

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