项目Euler 12-两个代码的性能差异

我最近开始学习python,为了熟悉这些概念,我开始解决euler问题。我一直在努力解决 Euler's problem number 12 但是,我的代码运行了很长一段时间(超过10分钟,并且仍在运行)。我上网查了一下,运行了这段代码,令人惊讶的是只花了11秒。但我无法理解两者之间的区别。非常感谢有人能帮我理解

我的代码第1章:

from time import time
import math

def divisors(n):
    n = int(n)
    sqrt = int(math.sqrt(n))
    result = sum(2 for i in range(1, sqrt+1) if n%i == 0)
    for i in range(1, n+1):
        if i**2 == n:
            result = result - 1
    return result
i = 1
num = 0
a = 0
t = time()
while a < 500:
    num = num+i
    print(num, i)
    i = i+1
    a = divisors(num)
print(a)
tt = time() - t
print(tt)

我的代码2

from time import time
import math

def divisors(n):
    n = int(n)
    sqrt = int(math.sqrt(n))
    for i in range(1, n+1):
        result = sum(2
                     for i in range(1, sqrt+1) if n%i == 0)
        if i**2 == n:
            result = result - 1
    return result

i = 1
num = 0
a = 0
t = time()
while a < 500:
    num = num+i
    print(num, i)
    i = i+1
    a = divisors(num)
print(a)
tt = time() - t
print(tt)

用了11秒的代码:

import math
from time import time
t = time()
def divisors(n):
    number_of_factors = 0
    for i in range(1, int(math.ceil(math.sqrt(n)))):
        if n % i == 0:
            number_of_factors +=2
        else:
            continue
    return number_of_factors

x=1
for y in range(2,1000000):
    x += y
    if divisors(x) >= 500:
        print x
        break
tt = time()-t
print tt