Name: 遞歸導論（數據結構與算法#6 (Introduction to Recursion (Data Structures & Algorithms #6))
Uploaded: 2021-01-14T10:19:50.000Z
Duration: 22 min 37 s
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現在進行式

祈使句型

So in computer science, recursion is a way of solving

a problem, by having a function calling itself

First of all, let's think about factorials, and let's just quickly

review factorials here. If you're given a

So I'm just gonna give you a few examples here

zero factorial? It's actually defined to be one

and you might say why is that? But you know

This (inaudible) is just how it is defined, and let's just

say here, we're trying to write a function called

a positive integer or zero as its argument

and return this n factorial. Now let's say

we wanna write this function using Recursion

How can we do that? To solve this problem

we need to actually examine this equation and

a little bit more detail. Okay so I brought that

equation over here and like we saw earlier

and so on times three times two times one

I want you to see this equation, I want you to look at

and that might be more obvious if I write this separately here

n minus one times n minus times and so on

times three times two times one. So this whole thing

so you might say "well we can rewrite n factorial

this new equation is mostly correct but it's not

a complete definition of factorials. Let's see why

Let's say if you plug(?) in two to n right here

so two times one factorial is two and that's correct

It's still good because you'll get one factorial

one minus one factorial which is zero factorial

and zero factorial is one as we saw earlier

and this is correct. But as soon as you plug in

zero here, it breaks. Let's see how that works

which is minus one factorial, and minus one factorial

or equal to one, but it doesn't work for zero

so actually for this definition to be complete

for factorials, we need to write n factorial

so here we're gonna write n factorial is equal

this is actually a complete definition of

and zero. So let's just quickly see how we can

to find the factorial of any positive integer

two ways of answering that question. The first one would be

to use the old definition and then the second way

would be to use this new definition. And let's

we're gonna use this new definition later to write a

ask ourselves, what's three factorial? Well three is

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遞歸導論（數據結構與算法#6 (Introduction to Recursion (Data Structures & Algorithms #6))

equivalent

obvious

positive

separate