你能解释一下这个Factorial函数是如何工作的吗？ [英] Can you explain how this Factorial function works?

问题描述

我理解a解决方案是：

function Factorial(number)
{
    if(number == 0 || number == 1){
        return 1;
    }

    return number * Factorial(number -1);

}

我想了解到底发生了什么。我理解当数字== 1时，到最后一部分一直在发生什么。

I want to understand what exactly is going on. I understand what is going on all the way to the last part when number == 1.

如果我们采用一个简单的例子说3！

If we were to take a simple example of say 3!

1. 3不等于0或1所以我们返回3 * Factorial（2）


2. 2不等于到0或1所以我们返回2 * Factorial（1）


3. 1等于1所以我们返回1

我们如何知道何时停止？事实是我们返回1告诉函数停止吗？

How do we know when to stop? Is it the fact that we return 1 that tells the function to stop?

如果是这样的话，为什么当我们第一次返回3 * Factorial时函数不会停止（ 2）？是因为它返回一个函数，所以它必须继续，直到它不再返回一个函数？

If that is the case, why does the function not stop when we first return 3 * Factorial(2)? Is it because it's returning a function so that it must continue until it no longer returns a function?

谢谢

推荐答案

我认为你必须理解阶乘的逻辑。

I think you have to understand the logic of factorial.

因此，factorial只是产品，用感叹号表示，即如果你写的话

So factorial is just products, indicated by an exclamation mark ie, if you write

 0! = 1
 1! = 1
 2! = 2*1
 3! = 3*2*1
 4! = 4*3*2*1
 5! = 5*4*3*2*1

希望您找到该模式，这样您就可以编写以上阶乘：

Hope you find the pattern, so you can write the above factorials as:

 0! = 1
 1! = 1
 2! = 2*1!
 3! = 3*2!
 4! = 4*3!
 5! = 5*4!

所以在你的函数中你使用的是类似的逻辑。

So in your function you are using the similar logic.

现在你的功能

if(number == 0 || number == 1)
{
   return 1;
}

以上逻辑涵盖前两种情况，即 0 ！和 1！和

The above logic is to cover the first two cases i.e, 0! and 1! And

return number * Factorial(number -1);

是剩下的数字。

所以你正在使用解决阶乘问题的递归技术。

So you are using the recursive technique of solving the factorial problem.

为了理解递归，让我们取一个数字5即ie，我们想要找到5的值！ 。

To understand recursion, lets take a number say 5 i.e., we want find the value of 5!.

然后首先你的函数将检查

Then first your function will check

if(number == 0 || number == 1)

不满足，然后移动到下一行即，

which is not satisfied, then it moves to the next line ie,

return number * Factorial(number -1); 

给出

5*Factorial(5-1) which is equal to 5*Factorial(4)

现在，在对您的Factorial函数的后续调用中，它将返回如下值：

Now on subsequent calls to your Factorial function it will return the value like below:

5*(4*Factorial(4-1)) which is equal to 5*(4*Factorial(3))
5*(4*(3*Factorial(3-1)) which is equal to 5*(4*(3*Factorial(2)))
5*(4*(3*(2*Factorial(2-1)))) which is equal to 5*(4*(3*(2*Factorial(1))))

现在当它返回阶乘（1）然后你的状况

Now when it returns factorial(1) then your condition

if(number == 0 || number == 1)

是满意的，因此您得到的结果为：

is satisfied and hence you get the result as:

5*4*3*2*1 = 120

旁注：

请注意，factrial仅用于正整数。

Beware that factrial is used only for positive integers.

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