SICP ex 1-27

最新推荐文章于 2016-05-14 14:08:09 发布

原创最新推荐文章于 2016-05-14 14:08:09 发布 · 271 阅读

0 ·

CC 4.0 BY-SA版权

本文通过Scheme语言实现了一个通用的filter-accumulate过程，用于计算特定条件下数值的累积结果。具体包括了给定范围内素数平方的累加及与指定数互质的数的乘积等数学问题。

由于ex1-27是对于26的改进,所以直接给出27

要求,之前的模板,其实我们可以采用filter-accumulate的更通用的模板来抽象(filter-accumulate combiner null-value predicate term a next b)

要求写出给定范围素数的平方的和，以及给定的n 给定范围内GCD(a,n)=1的积

(define (filter-accumulate combiner inti-value predicate term a next b)
	(define (iter count result)
		(if (= count b) result 
			(if (predicate count) (iter (next count) (combiner result (term count)))
				(iter (next count) result)
			)
		)
	)
	(iter a inti-value)
)

(define (f x) x)
(define (plus x) (+ x 1))
(define (Gcd a b)
	(define (reminder x y) (if (< x y) x (reminder (- x y) y)))
	(if (= b 0)  a  (Gcd b (reminder a b)))
)
(define (is-prime? n times)
	(define (fermat n)
		(define a (+ 2 (random (- n 2) ) ) )
		(define (expmod base Exp div)
			(define (reminder x y) (if (< x y) x (reminder (- x y) y)))
			(define (square x) (* x x) )
			(define (is-even? x) (= (reminder x 2) 0))	
			(cond ((= Exp 0) 1)
					((is-even? Exp) (reminder (square (expmod base (/ Exp 2) div) ) div ) )
					(else (reminder (* base (expmod base (- Exp 1) div) ) div ) ) ) 
		)
		(= (expmod a n n) a)
	)
	(cond ((= times 0) #t)
			((fermat n) (is-prime? n (- times 1)))
			(else #f))
)
(define (prime? n) (is-prime? n 5))
(define (square x) (* x x))
(define (test a)
	(= (Gcd a 17) 1)
)

(define (conditional-sum a b)
	(filter-accumulate + 0 prime? square a plus b)
)
(define (conditional-product a b)
	(filter-accumulate * 1 test f a plus b)
)