SICP ex 1-27

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)
)