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you're seeing in the middle is too big, then search the left half of the array.
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Else if the element is to the right, as it was in Derek's case,
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search the right half of the array, else return false.
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But there is no go-to instruction here.
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And there's no line numbers.
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Recall from week 0 when we searched for Mike Smith,
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I deliberately numbered all of the lines.
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And then I said, go back to step 2 or 3 I think it was.
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Here, I seem to be cutting a corner.
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I'm just kind of waving my hand and saying,
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search the left half of the list.
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Or, search the right half of the list.
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But what algorithm should we use in either of these cases?
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How do you search the left half of a list?
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How do you search the right half of a list?
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How do I do this?
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Well, where do I have an algorithm for searching?
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Well, we saw one a moment ago.
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I've already got in my toolkit, so to speak, linear search.
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So I could certainly use that.
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But sort of cyclically, or sort of confusingly,
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I also have this other seemingly fancier, faster algorithm
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called binary search.
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And yet, I'm in the middle of defining binary search with my pseudocode.
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And yet, here I am sort of trying to define myself with myself.
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You can't get away with this in English.
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If you're asked to define an English word
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and you use the word in the definition, usually a teacher or someone
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in a conversation will sort of verbally slap you on the wrist
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because you're not answering the question.
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And yet somehow in programming, you can get away with this.
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Somehow, you can get away with defining a problem with a solution like this,
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and then using that same solution inside of your solution
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because something is changing.
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This line here, search the left half of the array,
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and this line here, search right half of the array,
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is not equivalent to asking the same question again.
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Is this element in the array?
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What changes when I either search the left half or the right half that
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makes this acceptable?
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AUDIENCE: [INAUDIBLE].
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SPEAKER 1: What's that?
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AUDIENCE: [INAUDIBLE].
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SPEAKER 1: Yes.
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That's the key ingredient.
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In so far as search left half and search right half imply
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search in the same way, but search a smaller problem,
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this problem will eventually stop.
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You're not going to get stuck in an infinite loop so to speak.
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Because eventually-- you can't half something forever.
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You're eventually going to end up with one or zero elements.
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At which point, the answer's going to be no.
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Return false, it's not here per the else condition.
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But these sort of reflexive calls or inductive,
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or more properly here, recursive calls-- the new buzzword
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for today-- means for a function, or in this case pseudocode, to call itself.
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To use its own definition again and again
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and again, which is bad instinctively, unless you keep doing it
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on smaller and smaller problems.
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And so this is a general principle, actually,
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that we're going to be able to leverage ultimately, not only for searching but
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also, as we shall see, for sorting.
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So let's go ahead and let me share actually
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how this example went last year.
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We're fortunate to capture sort of memories on film.
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And I thought it would be fun to share this,
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when one of your predecessors in the class came up,
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was asked the exact same question, find us the number 50.
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But it didn't quite go as well as we hoped.
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Let's take a look at 2014.
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[AUDIO PLAYBACK]
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-All I want you to do now is to find for me and for us,
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really, the number 50 one step at a time.
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-Number 50?
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-The number 50.
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And you can reveal what's behind each of these doors
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simply by touching it with a finger.
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Damn it.
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[APPLAUSE]
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[END PLAYBACK]
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SPEAKER 1: OK.
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So that didn't really demonstrate anything that year.
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So we tried again, this time saying, all right, this time the array is sorted.
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What are you going to do this time if you want to find the same number 50,
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but the array is now sorted?
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I thought I'd share this.
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[AUDIO PLAYBACK]
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-The goal now is to also find us the number 50, but do it algorithmically.
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And tell us how you're going about it.
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And if you find it, you keep the movie.
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If you don't find it, you give it back.
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-Man. [INAUDIBLE].
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OK.
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So I'm going to check the ends first to determine if there's-- oh.
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[APPLAUSE]
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[END PLAYBACK]
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SPEAKER 1: OK, now I feel a little bad because clearly we
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used to give away movies and now we give away stress balls.
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But no one really has DVD players anymore, so it's OK probably.
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And then, let me share one other clip back from our SD days.
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