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Python Jumpstart by Building 10 Apps Transcripts

Chapter: App 8: File Searcher App

Lecture: Recursion factorial example

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So let's take a step back from application for a moment

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and just open this empty file called play for play around,

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where we can just play around with some ideas.

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We'll do this for recursion but we also do this for our generator methods later.

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Let's take a really simple case something like creating the factorial of a number.

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Now remember, factorials are sort of iterative processes

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the factorial written with like a number and an exclamation point right

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so like let's say 5! = 120

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and the way that you get that is you take 5*4*3*2*1

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and each step if I start here the thing I need to multiply is

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the number minus 1 times the rest of the factorial

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and then form here I need to multiply it by that smaller number minus 1

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times the rest of the factorial

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and I keep doing that until I get down to 1 and then I stop.

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So this turns out to be really easily modeled with this concept called recursion.

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So let's look at this in code

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and then we'll look at this conceptually

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and we'll go back and apply this to our searching app.

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So here we have this factorial function, empty,

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but it's going to return the number which is the factorial

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so here I have pre loaded the few, we'll compute 5, 3 and 11 factorial

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and these numbers grow tremendously large in a hurry.

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So remember the way you take the factorial,

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is you want to take the number in this case we are going to have n

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and we want to multiply it by the factorial of the smaller piece of the stuff to the right,

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and we kind of keep building that up and it turns out that

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we can say we want those factorial to be n times

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and we can call the same method within itself with different parameters,

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so for this step from here is just going to be whatever that is times 5,

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so n*factorial (n-1) now if we do it like this

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we are going to end up in a stack overflow situation,

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it's going to keep calling this function over and over and over

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until it just runs out of space.

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So once we get down to one we are going to stop

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and we just say 1! is defined to be 1,

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so we'll say something like if n is 1 return 1

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otherwise we are going to come down here and do this we'll just say

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return n*factorial (n-1) so let's run this,

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now this one this should be 120,

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this one I know should be 6, this one should be huge,

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I don't know what factorial of 11 is

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but I know it is much larger than you expect,

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so let's run this and see how it works.

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Awesome, 5! is 120, 3! is 6 and 11! is some big number,

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now we don't like to look at numbers like this, right,

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we like separators,

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so we can actually do that by putting colon comma on all of these,

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will make a difference on the small ones but on the larger one

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you can see we now have separated those with digit grouping.

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So this is a recursive algorithm, let's take a moment

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and look at this as it's one of our core concepts.