这是对Project Euler Problem 49的一次(略显凌乱的)尝试。
我应该直截了当地说,这deque
不是一个好的选择!我的想法是缩小质数集以测试成员资格会导致循环加速。然而,当我意识到我应该使用 a set
(而不用担心删除元素)时,我得到了 60 倍的加速。
from collections import deque
from itertools import permutations
from .sieve import sieve_of_erastothenes # my own implementation of the Sieve of Erastothenes
primes = deque(prime for prime in sieve_of_erastothenes(10000) if prime > 1000 and prime != 1487) # all four-digit primes except 1487
try:
while True:
prime = primes.popleft() # decrease the length of primes each time to speed up membership test
for inc in xrange(1,10000 + 1 - (2 * prime)): # this limit ensures we don't end up with results > 10000
inc1 = prime + inc
inc2 = prime + 2*inc
if inc1 in primes and inc2 in primes:
primestr = str(prime)
perms = set(''.join(tup) for tup in permutations(primestr)) # because permutations() returns tuples
inc1str = str(inc1)
inc2str = str(inc2)
if inc1str in perms and inc2str in perms:
print primestr + inc1str + inc2str
raise IOError # I chose IOError because it's unlikely to be raised
# by anything else in the block. Exceptions are an easy
# way to break out of nested loops.
except IOError:
pass
无论如何,在我想使用 a 之前set
,我在 Pypy 中进行了尝试。我发现结果相当令人惊讶:
$ time python "problem49-deque.py"
296962999629
real 1m3.429s
user 0m49.779s
sys 0m0.335s
$ time pypy-c "problem49-deque.py"
296962999629
real 5m52.736s
user 5m15.608s
sys 0m1.509s
为什么 Pypy 在这段代码上要慢五倍以上?我猜 Pypy 的版本deque
是罪魁祸首(因为它在set
版本上运行得更快),但我不知道为什么会这样。