用python解决euler问题

Question

我是编程新手。我正在解决Project Euler Question 12：

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

1: 1 3: 1,3 6: 1,2,3,6 10: 1,2,5,10 15: 1,3,5,15 21: 1,3,7,21 28: 1,2,4,7,14,28 We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

我的解决方案是：

import math  
k=0  
count=0  
for i in range (1,100000):   
    k+=i  
    a=int(math.sqrt(k))+1
    count=0
    for j in range (1,a):  
        n=a%j  
        if n==0:  
           count=count+1  
           count*=2  
           if count>500:  
              print'',count  
              break

对于count>100和小于100的数字，它会很快给出输出， 但对于500人来说，这需要很长时间。如何缩短执行时间？你知道吗

Answer 1

i=0
count = 0
while count < 501:
    i+=1
    count = 0
    tNum = (i*(i + 1)) / 2
    y=int(tNum**0.5)
    for j in range(1,y + 1):
        if tNum % j==0 :
            count+=2
        if y ** 2 == tNum:
            count-=1
print(tNum)

Answer 2

只能使用奇数。你知道吗

for j in range (1,a, 2):

应该快一倍。你知道吗

您还可以将所有已知的素数保存到一个列表中，并且只通过该列表以%进行测试。你知道吗