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Find a number behind these doors.
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Now, unfortunately, you don't know in advance
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what numbers are behind those doors and where they are.
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Indeed, that's why the doors are closed.
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But you know that, say, the number 50 is somewhere behind those doors.
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So what do we do to actually find this?
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Well, let's go ahead and do this.
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Let me go ahead and summon up a brave volunteer if you would.
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There's a CS50 stress ball in it for you.
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OK, come on up.
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You want to come up on up over here?
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So we have not 8, but rather 7 doors here.
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Even easier.
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So 7/8 the size.
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And what's your name?
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AUDIENCE: Derek [INAUDIBLE].
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SPEAKER 1: Derek?
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OK.
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David, come on up.
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Nice to meet you.
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All right.
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So here we have 7 doors.
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And the goal at hand for you is to simply find the number 50.
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How do we find it?
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What are you going to do?
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AUDIENCE: [INAUDIBLE].
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SPEAKER 1: It's behind one of these doors, I think.
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AUDIENCE: All right.
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I'll just try a door?
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SPEAKER 1: Try a door.
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Not the door.
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So 16 turns up.
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OK.
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Stress ball gets one step away.
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Try another.
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42.
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Answer to life, the universe, and everything, but not this question.
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50.
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OK, very well done.
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So a round of applause if we could for Derek here.
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Very nicely done.
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OK.
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And let's pause for just a moment.
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What was the algorithm?
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What was the set of instructions that you used to find the number 50?
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AUDIENCE: Just try and see if I could find any sort of arrangement.
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But otherwise, try random doors.
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SPEAKER 1: OK.
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So try random doors.
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And indeed, given no additional information from me,
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that's the best you can do.
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Just try random doors.
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Or, if it's a little easier, just go left to right or right to left.
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But random is perfectly equivalent to all of those algorithms
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because you don't know anything necessarily a priori.
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So how about for two stress balls?
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Find the number 50 this time, but the additional ingredient
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is that we have taken the time in advance
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to sort the numbers behind these doors.
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Does that change your thinking in any way?
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AUDIENCE: Well, I don't know whether you're
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sorting increasing left or right.
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SPEAKER 1: Good.
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So good challenge.
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He doesn't know if we've sorted from left to right or right to left.
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Left to right.
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So generally, a computer scientist when he or she says "sorted"
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would say left to right.
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But reasonable question.
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AUDIENCE: Left to right increasing or decreasing?
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SPEAKER 1: Left to right increasing.
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Yes.
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It would be left to right in any way.
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16.
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Not 50.
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So what are you going to do?
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AUDIENCE: Well, let's see.
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I know these have to be less, so I can remove them.
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SPEAKER 1: Good.
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AUDIENCE: [INAUDIBLE].
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SPEAKER 1: 42 is still not 50.
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And to the right.
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Very well done for Derek.
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OK, come on.
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OK.
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They're less impressed that time.
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So what did you do, though, that second time that was actually more effective?
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I mean, frankly, at first glance it looks like this approach was just as
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fast or just as slow as your first approach
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because it still took you through steps.
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AUDIENCE: So what I did was since you told me that it was sorted left
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to right increasing, I decided to look at the middle number first
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and see whether it was greater than or less than--
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SPEAKER 1: Good
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AUDIENCE: --the target number.
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SPEAKER 1: Good.
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AUDIENCE: And since it was less than, I knew that all of these three values--
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SPEAKER 1: Wonderful.
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And indeed, are smaller by design.
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And so you can throw half of that problem away, much like in week 0
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