项目Euler - 这个haskell代码如此之快？

I'm working on problem 401 in project euler, I coded up my solution in python but it's going to take a few days to run, obviously I'll need to speed it up or use a different approach. I came across a solution in Haskell that looks almost identical to my python solution but completes almost instantaneously.

我正在研究项目euler中的问题401，我在python中编写了我的解决方案，但它需要几天才能运行，显然我需要加快速度或使用不同的方法。我在Haskell中遇到了一个与我的python解决方案几乎完全相同的解决方案，但几乎是瞬间完成的。

Can someone explain how it is so fast? (I AM NOT ASKING FOR HELP OR SOLUTIONS TO PROBLEM 401)

有人可以解释它是如此之快吗？（我不是要求帮助或解决问题401）

divisors n = filter (\x -> n `mod` x == 0) [1..(n`div`2)] ++ [n]
sigma2 n = sum $ map (\x -> x * x) (divisors n)
sigma2big n = sum $ map (sigma2)[1..n]
let s2b = sigma2big 10^15
putStrLn ("SIGMA2(10^15) mod 10^9 is " ++ (show (mod s2b 10^9)))

From my understanding it is just using trial division to generate a list of divisors, squaring and summing them, and then summing the results from 1 to n.

根据我的理解，它只是使用试验除法生成一个除数列表，对它们进行平方和求和，然后将结果从1加到n。

EDIT: forgot my python code

编辑：忘了我的python代码

from time import clock


def timer(function):

    def wrapper(*args, **kwargs):
        start = clock()
        print(function(*args, **kwargs))
        runtime = clock() - start
        print("Runtime: %f seconds." % runtime)

    return wrapper


@timer
def find_answer():
    return big_sigma2(10**15) % 10**9

def get_divisors(n):
    divs = set()
    for i in range(1, int(sqrt(n)) + 1):
        if n % i == 0:
            divs.add(i)
            divs.add(n // i)
    return divs

def sigma2(n):
    return sum(map(lambda x: x**2, get_divisors(n)))

def big_sigma2(n):
    total = 0
    for i in range(1, n + 1):
        total += sigma2(i)
    return total

if __name__ == "__main__":
    find_answer()

2 个解决方案

#1

Prelude> sigma2big 1000
401382971
(0.48 secs, 28491864 bytes)

Prelude> sigma2big 10^3
103161709
(0.02 secs, 1035252 bytes)

Prelude> (sigma2big 10)^3
103161709

function precedence (shh...)

功能优先（嘘......）

#2

Make sure you are using Integer for your calculations and not Int since 10^15 will overflow an Int value.

确保您使用Integer进行计算而不是Int，因为10 ^ 15将溢出Int值。

If you change:

如果你改变：

let s2b = sigma2big 10^15

to:

至：

let s2b = sigma2big (10^15 :: Integer)

the Haskell code runs out of memory in ghci and I didn't bother to wait for it to complete when running the compiled version.

Haskell代码在ghci中耗尽了内存，在运行编译版本时我没有等待它完成。

#1

Prelude> sigma2big 1000
401382971
(0.48 secs, 28491864 bytes)

Prelude> sigma2big 10^3
103161709
(0.02 secs, 1035252 bytes)

Prelude> (sigma2big 10)^3
103161709