Project Euler每帖一题（006）

最新推荐文章于 2019-01-21 21:47:40 发布

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最新推荐文章于 2019-01-21 21:47:40 发布

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分类专栏： Python 算法文章标签： Python

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本文探讨了前一百个自然数的平方和与和的平方之间的差异，并提供了两种Python实现方式：一种通过循环计算，另一种利用数学公式简化计算过程。

题目：
[quote]
The sum of the squares of the first ten natural numbers is,

12 + 22 + ... + 102 = 385
The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)2 = 552 = 3025
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
[/quote]

我的python代码：


sum_sq = 0
sq_sum = 0
for i in range(100):
    sum_sq += (i + 1) ** 2
    sq_sum += (i + 1)
print sq_sum ** 2 - sum_sq

看了别人写的，看来把它化简成公式更简单：
[quote]
(1 + 2 + ... + n)^2 = n^2 * (n+1)^2 * 1/4

1^2 + 2^2 + ... + n^2 = n * (n+1) * (2n+1) * 1/6
[/quote]

code:


sum_sq = 0
sq_sum = 0
n = 100
sum_sq += n * (n + 1) * (2 * n + 1) / 6
sq_sum += ((n ** 2) * (n + 1) ** 2) / 4
print sq_sum - sum_sq