SICP 练习2.40 unique-pairs

Scheme实现素数求和

最新推荐文章于 2022-05-06 22:01:11 发布

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本文介绍了一个使用Scheme语言编写的程序，该程序通过定义多个辅助函数来找出指定范围内所有素数对，并计算这些素数对的和。文章首先定义了基本的数学运算和列表操作函数，接着实现了枚举区间、过滤、映射等高级函数，最终通过unique-pairs生成所有可能的素数对，并计算它们的总和。

我所做的只是把unique-pairs封装了一下

(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 (fliter predicate sequence)
  (cond ((null? sequence) '())
        ((predicate (car sequence))
         (cons (car sequence) (fliter predicate (cdr sequence))))
        (else (fliter predicate (cdr sequence)))))

(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)))

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

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

(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)))

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

(newline)
(display (prime-sum-pairs 6))