了解分解函数 [英] Understanding factorize function
问题描述
请注意，这个问题包含一些破坏因素.
Note that this question contains some spoilers.
除数(包括1和数字本身)可以用质数(和幂)除数中的一个元素来计算."
"Number of divisors (including 1 and the number itself) can be calculated taking one element from prime (and power) divisors."
它执行此操作的(python)代码是num_factors = lambda x: mul((exp+1) for (base, exp) in factorize(x))(其中mul()是reduce(operator.mul, ...).)
The (python) code that it has doing this is num_factors = lambda x: mul((exp+1) for (base, exp) in factorize(x)) (where mul() is reduce(operator.mul, ...).)
它没有说明factorize的定义方式，我在理解它的工作方式时遇到了麻烦.它如何告诉您数量因素的数量?
It doesn't state how factorize is defined, and I'm having trouble understanding how it works. How does it tell you the number of factors of the number?
推荐答案
基本思想是，如果将一个因数分解为以下形式，则该形式实际上是标准形式:
The basic idea is that if you have a number factorized into the following form which is the standard form actually:
let p be a prime and e be the exponent of the prime:
N = p1^e1 * p2^e2 *....* pk^ek
现在，要知道N有多少个除数，我们必须考虑素数的每种组合.因此，您可能会说除数为:
Now, to know how many divisors N has we have to take into consideration every combination of prime factors. So you could possibly say that the number of divisors is:
e1 * e2 * e3 *...* ek
但是您必须注意，如果素数因子之一的标准形式的指数为零，那么结果也将为除数.这意味着，我们必须在每个指数上加一个，以确保我们将第i个p包含在零的幂中.这是一个使用数字12的示例-与问题编号:D
But you have to notice that if the exponent in the standard form of one of the prime factors is zero, then the result would also be a divisor. This means, we have to add one to each exponent to make sure we included the ith p to the power of zero. Here is an example using the number 12 -- same as the question number :D
Let N = 12
Then, the prime factors are:
2^2 * 3^1
The divisors are the multiplicative combinations of these factors. Then, we have:
2^0 * 3^0 = 1
2^1 * 3^0 = 2
2^2 * 3^0 = 4
2^0 * 3^1 = 3
2^1 * 3^1 = 6
2^2 * 3^1 = 12
我希望您现在明白为什么在计算除数时为什么要在指数上加一.
I hope you see now why we add one to the exponent when calculating the divisors.
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