I'm working through some programing puzzles, and one of them was to find the sum
of all primes less the 2 million, the new math/number-theory collection (thanks
Neil) makes it easy:
#lang racket
(require math/number-theory)
;;takes about 4 seconds
(apply + (filter prime? (range 1 2000000)))
But I thought that spoiled the fun, and I was surely making racket work more
then necessary testing each number in the range, so I thought the Sieve of
Eratosthenes would be fast and fun:
#lang racket
;; Input: an integer n > 1
(define (sieve-of-eratosthenes n)
;; Let A be an array of Boolean values, indexed by integers 2 to n,
;; initially all set to true.
;; for i = 2, 3, 4, ..., √n :
;; when A[i] is true:
;; for j = i², i²+i, i²+2i, ..., n:
;; A[j] := false
(define A (make-vector n #t))
(for ([i (range 2 (sqrt n))])
(when (vector-ref A i)
(for ([p (range 0 n)])
#:break (> (+ (* i i) (* p i) 1) n)
(let ([j (+ (* i i) (* p i))])
(vector-set! A j #f)))))
;; Now all i such that A[i] is true are prime.
(filter number?
(for/list ([i (range 2 n)])
(when (vector-ref A i) i))))
;;takes about 17 seconds
(time (apply + (sieve-of-eratosthenes 2000000))
But it is dead slow....
Thanks,
Jordan
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