sicp 习题 1.21 ~ 1.22

1.21

(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 (square n)
  (* n n))

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

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

(smallest-divisor 19999)
(prime? 19999)

1.22

(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 (square n)
  (* n n))

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

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

(define (start-prime-test n start-time)
  (if (prime? n)
      (report-prime (- (current-inexact-milliseconds) start-time))
      #f))

(define (report-prime elapsed-time)
  (display " *** ")
  (display elapsed-time))

(define (timed-prime-test n)
  (newline)
  (display n)
  (start-prime-test n (current-inexact-milliseconds)))

(define (search-for-primes from n)
  (cond ((= n 0) (newline) (display "finish") (newline))
        ((even? from) (search-for-primes (+ from 1) n))
        ((timed-prime-test from)
         (search-for-primes (+ from 2)
                            (- n 1)))
        (else (search-for-primes  (+ from 2) n))))
        
(search-for-primes 1000000 3)