我正在尝试使用来实现素数生成器埃拉托斯特尼筛法 http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes算法。我这样做只是为了尝试使用递归迭代器合并 https://stackoverflow.com/a/465043/862380实施筛子。
我所做的是这样的:
from itertools import count,islice,groupby
from heapq import merge
def primes3():
p = 2
yield p
sifter = (i*p for i in count(p))
s = next(sifter)
for p in count(p+1):
if p==s: # this p is sieved out
print('s: {}'.format(s))
s = next(sifter)
else:
yield p # this is prime
print('p: {}'.format(p))
sifter = (k for k, g in groupby(merge(sifter,(i*p for i in count(p))))) #add this serie to the sifter: p*p, p*(p+1), p*(p+2), ...
print(list(islice(primes3(),10)))
输出是:
p: 3
s: 4
p: 5
p: 6
p: 7
p: 8
p: 9
p: 10
p: 11
s: 12
[2, 3, 5, 6, 7, 8, 9, 10, 11, 13]
第一个要筛出的数是4
。但接下来是12
, not 6
本来应该如此。这是为什么?我用下面的代码检查了它:
>>> sifter = (i*2 for i in count(2))
>>> next(sifter)
4
>>> sifter = (k for k, g in groupby(merge(sifter,(i*3 for i in count(3)))))
>>> print(list(islice(sifter,20)))
[6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34]
因此,正如我们所看到的,在测试条件下,筛子会产生正确的结果。
我哪里出错了?我想这一定是一些我看不到的微不足道的事情。