Learn how to recursively compute the factorial of integer n.

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Recursive computation of factorials

This example is a slight cliché, but it is still a good illustration of both the beauty and pitfalls of recursion.

The factorial of an integer, nn, is the product of all the integers between 11 and nn. For example, six factorial (usually written 6!6!) is:

654321=7206*5*4*3*2*1 = 720

Now, as we said in the introduction, the obvious way to do this is with a loop. But there is an alternative, “cleverer” way, using recursion.

We can make a simple observation that 6!6! is actually 65!6*5!. And 5!5! is 54!5*4! and so on. So, we can calculate n!n! without ever explicitly calculating a factorial at all. We just keep relying on smaller and smaller factorials without ever calculating them.

Of course, you must stop somewhere – we know that 1!1! is 11.

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