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when we tore the phone book in half.
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You can throw half of that phone book away as well.
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So thank you very much for finding us the number 50.
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So this is something that we did see, indeed, in week 0.
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And it's what we would generally call binary search.
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Or more generally, just a divide and conquer algorithm.
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But today, what we start to do is to assess
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just how much better this actually is.
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And how we can go about finding things more programmatically.
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So what Derek could have tried is what someone would generally
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call linear search.
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And as the name suggests, linear, meaning line,
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you can just kind of solve a problem from left to right.
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And indeed, while Derek did take a random approach,
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it would have been functionally equivalent
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for him simply to go left to right or right to left and find the number 50.
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It's indeed there.
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So let's introduce some pseudocode for this.
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And there is no one right way to implement pseudocode.
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Here is one of the most succinct ways I could come up
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with for expressing this kind of left to right approach.
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Or equivalently, right to left.
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For each element in the array, if element you're looking for return true.
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And so this is a very common paradigm in programming.
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Just say something generally, like for each element in an array.
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And the implication is that you would generally go left to right,
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but it's equivalent to go right to left.
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And if we indeed see at some location in that array
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that array of boxes, the element we're looking for, we can just return true.
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And yet, here I have return false.
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But the indentation, so to speak, is very different.
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Why have I aligned return false with the for loop
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here all the way on the left as opposed to it being aligned in the middle
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or one line deeper?
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Yeah.
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AUDIENCE: [INAUDIBLE].
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SPEAKER 1: Yeah.
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In order to denote that all of the indented elements
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are within the for loop.
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So it doesn't strictly matter how much you indent.
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And indeed, in some languages, C among them,
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it doesn't matter that you indent at all.
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But for the sake of good style and readability,
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we've indented this to convey to the human
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especially that this "if" is only applicable when you're inside
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of the for loop.
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This return is only applicable when you're inside of this "if" condition.
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And this return false really only happens
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as the very last step in this program if nothing else actually returns a value.
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So only if return true happens does this program say,
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yes, I found the element you're looking for.
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And you can think of this, therefore, as the sort of default case.
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Now, just to toss it out there, why would this be wrong?
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Let me go ahead and temporarily change this program
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to be a more familiar if/else block.
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So why is this seemingly logically fine?
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It's a valid puzzle piece if you will, a la scratch.
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But this program is now incorrect.
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Why?
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Yeah.
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AUDIENCE: [INAUDIBLE].
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SPEAKER 1: Once you hit it, it's automatically
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going to come out of the for loop when?
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Exactly.
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When will this come out of the for loop?
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AUDIENCE: [INAUDIBLE].
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SPEAKER 1: Good.
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So it's going to return false if the first element isn't
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what you're looking for.
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In so far as for each element in an array
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kind of implies that you should be looking from left to right
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or right to left, the first question you're
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asking yourself when looking in that first element
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is, is this the element you're looking for?
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If it is, great.
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You're going to return true.
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And your answer is correct.
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But if it's not the element you're looking
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for, you're executing else return false immediately saying no, the element
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I'm looking for is not here.
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But when really the only question you've asked is, is the element
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I'm looking for the very first in the array?
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And so, indeed, this would just be logically incorrect
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because you might as well not look at any of the array
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if you're only looking at that very first element.
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So not what we intended.
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So indeed, that original pseudocode is just fine.
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So alternatively, there's something called binary search, which
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Derek actually used intuitively for his second approach,
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where he was told in advance that the array is sorted numerically from left
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to right.
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This gives him more information, much like I had in week 0
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when I searched a phone book that I knew was alphabetical.
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And you can write this algorithm in any number of ways, too.
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I kind of borrowed the spirit of our Mike Smith algorithm from week 0
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and I proposed this.
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Look at the middle of the array.
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If element you're looking for return true.
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We just get lucky if it's smack dab in the middle of the array.
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Else if the element is to the left, because the element
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