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And what's happening here?
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This is like me walking across the audience again and again
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and again and again.
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You don't see any of this bubbling effect,
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but you do see the smallest element being selected again
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and again and again.
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So we're kind of cleaning up that mess one step at a time.
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It's still going to take some steps, but you can perhaps
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see it a little better and a little faster here.
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And spoiler alert, when we skip forward to the end, that's what it looks like.
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If we now randomize it one last time and do insertion sort,
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this one kind of feels and looks different.
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It's kind of mostly fixing things, but then it
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kind of goes in and fills in the gaps.
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Because indeed, it's moving forward one at a time, grabbing the element,
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and then shifting the element as needed to make room for whatever number
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it's encountered.
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So that's why sometimes it only takes a few steps
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because you find where it belongs.
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That time it took a while to find the space that it belongs.
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But generally, the list is getting more and more sorted.
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And once we do get to the very end, this one
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we can actually feel being a little faster.
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Which isn't necessarily a testament to it being fundamentally better.
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All of these remain on the order of n squared steps.
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And now indeed, it's starting to drag, kind of like our blue books.
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And now we're actually complete.
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But what if we were to compare these things?
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Bubble sort on the left, selection sort in the middle,
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and then a third algorithm that we've not seen this time called merge sort.
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So insertion sort is roughly the same as all of these.
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So this visualization lets us try three.
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To start this, I have to click on them.
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So there's a little bit of a fudge factor
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here where I have to click on all three programs quickly in succession
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to see them.
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But let's see if we can't do fundamentally better.
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Merge sort is our new friend on the right.
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Oh my god.
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And these are different visualizations, but they're the same algorithms.
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And it's not that they're just poorly implemented.
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It's arguably that they're poorly designed.
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They are all correct, but merge sort clearly
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seems to have some upsides over selection sort.
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And if you'll take it on faith for now, just because we can only fit three
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on the screen, insertion sort, too.
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You see the bigger elements bubbling up to the top.
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You see us selecting.
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Again, it turns out this person implemented selection sort
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by selecting the biggest element.
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But that's fundamentally equivalent to selecting the smallest element.
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And that's because you can see them all stacking here in this way.
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But my god, I wonder, can me start this again?
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Let's try.
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Let's see if we can lap it.
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Come on.
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Come on.
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Come on.
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Come on.
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Oh, so close.
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All right.
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Had I not talked as much.
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So merge sort.
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Where is this magical algorithm?
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What are we actually doing wasting time on these other things?
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Well, let's consider exactly that, but we need sort of a secret ingredient.
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And let me revisit Mike Smith for just a moment.
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So you'll recall, this was the pseudocode
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that we had from Mike Smith in week 0.
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And we decided when Mike is earlier in the book
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or when Mike is later in the book, to just go to an earlier step.
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Thereby, inducing some kind of loop.
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But suppose we changed that language to be this instead.
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Don't go to a specific line number.
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Don't go to some earlier step.
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But just more generally, say, search for Mike
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in the left half of the book or search for Mike in the right half of the book.
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This is borrowing an idea that I proposed a moment ago when
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we were searching for something else.
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And what word did we ascribe to this kind
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of approach of this cyclical use of your own definition?
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Yeah.
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AUDIENCE: [INAUDIBLE].
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SPEAKER 1: Recursion.
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So recursion is actually this secret ingredient
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that we can leverage, both intuitively and in code,
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to implement this new and improved fourth algorithm, merge sort.
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And indeed, this we'll use demonstrative of a class of algorithms
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that doesn't behave in quite the same way fundamentally as selection
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sort, insertion sort, and bubble sort.
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Indeed, you can do better than big O of n squared.
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You can do much better, as you felt a moment ago with visualization.
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And merge sort is one such algorithm with which we can do that.
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And amazingly, the pseudocode code is this simple.
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When you're given n elements, if n is less than 2, just return.
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If you have fewer than 2 elements, the list is of size 1, which is sorted,
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or size 0, which is also meaninglessly sorted.
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So you're done.
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So that's kind of a base case, like a default scenario.
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Let's just make sure that no matter what, we eventually
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