[User] Please transcribe this text

[Assistant] I realized that I've left my final shots on the bench and they should have been with Fraser.


[User] Please transcribe this text

[Assistant] I don't want Mashef to end, and I'm just hoping, hoping that the flavors work.


[User] Please transcribe this text

[Assistant] I've still used them just because I wanted that final flavor there.


[User] Please transcribe this text

[Assistant] Then had a lucky break. You get a second life. But it came at a cost. The next leg, you are going to have to complete a speed bump.


[User] Please transcribe this text

[Assistant] Located on the Iberian peninsula, Portugal is the westernmost country of mainland Europe.


[User] Please transcribe this text

[Assistant] And it is from here that teams embark on the eighth leg of our race around the world.


[User] Please transcribe this text

[Assistant] Daniel and Ryan were the first to arrive. You boys are team number one.


[User] Please transcribe this text

[Assistant] So they will depart first at 7.51am.


[User] Please transcribe this text

[Assistant] Teams must now fly 3000 kilometers east to Dubrovnik, Croatia.


[User] Please transcribe this text

[Assistant] All teams are now on the same flight via Frankfurt to Dubrovnik, Croatia, due to arrive at 10.05pm.


[User] Please transcribe this text

[Assistant] City walls run for almost two kilometers and were intended to protect the Brubnik from attack.


[User] Please transcribe this text

[Assistant] Teams must take part in an ancient welcoming tradition by collecting two large stones and navigating the walls to the watchman's keep.


[User] Please transcribe this text

[Assistant] Old harbour. Teams will now make their way to the old harbour on the other side of the city, where they will sign up for one of three start times 15 minutes apart.


[User] Please transcribe this text

[Assistant] Teams who choose to perform the Fast Forward must make their way to this monastery. Once the Fast Forward has been completed by one team, it is out of play.


[User] Please transcribe this text

[Assistant] Teams who decide not to attempt the fast forward must search within the city walls for an ancient fountain where they will find their


[User] Please transcribe this text

[Assistant] A roadblock is a task only one team member may perform.


[User] Please transcribe this text

[Assistant] Fort Boca is one of the oldest preserved forts of its kind. In this roadblock, teams must abseil face forward down its impenetrable stone walls.


[User] Please transcribe this text

[Assistant] In this Fast Forward, teams must collect marked prayer cards from three of the city's many churches and deliver them to the local barber. Only when they deliver the prayer cards will teams discover the second part of the Fast Forward.


[User] Please transcribe this text

[Assistant] For men, a tonsure cut involves shaving the hair on the scalp leaving a round bald area. For women, a nun style haircut.


[User] Please transcribe this text

[Assistant] These teams must make their way to the other side of the Old City, to Fort St. John, where they will find their next clue.


[User] Please transcribe this text

[Assistant] Now we're going to take a look at ordered symbol table operations using the binary search tree data structure as the underlying implementation.


[User] Please transcribe this text

[Assistant] Suppose we wanted to find the minimum key in a binary search tree, or the maximum key. Well, just looking at one example, you can see almost immediately what to do.


[User] Please transcribe this text

[Assistant] To find the minimum, we move left from the root until we find a null key. That's where the smallest key in the data structure is. To find the maximum, we move right from the root until we find a null key.


[User] Please transcribe this text

[Assistant] So, just for example, let's take a look at the problem of computing the floor.


[User] Please transcribe this text

[Assistant] Uh, so what we want to find is, uh, so say we're, uh, seeking the floor of G. So that's the largest key, uh, in the data structure that is less than G. In this case, the answer is E.


[User] Please transcribe this text

[Assistant] So, let's just take a look at what we have to do in the tree, the path we have to take in the tree to figure that out.


[User] Please transcribe this text

[Assistant] Well, uh, so we're looking for the largest key that's less than G, uh, and we have S. Uh, well, that key's definitely going to be in the left subtree. Uh, it's not going to be bigger than S, because S is bigger than G, so we go to the left.


[User] Please transcribe this text

[Assistant] Uh, what's the largest key that's less than G in this, in this tree here? Well, it might be E, uh, but there's no way that it's to the left of E because those keys are all smaller than E and therefore smaller than G, so E's a candidate. Uh, but it might also be in the right.


[User] Please transcribe this text

[Assistant] So, uh, that's, uh, if k is, uh, equal to the key at the root, the floor of k is k. If k is less than the key at root, it's in the left subtree. That's the one we just did. Uh, if it's greater than the key at the root, the floor of k is in the right subtree if there is any key smaller than k in the right subtree.


[User] Please transcribe this text

[Assistant] And here's the code that does it, it's not that much code, it's just complicated code to understand. So, if we find our key that's the floor, if we're going to the left, we find the floor of the one on the left, and on the right, we have to do


[User] Please transcribe this text

[Assistant] A little bit of tricky code, uh, to make sure that, uh, we return, uh, the floor in the right subtree if there's some tree there. If there's, if there's no node there, then, uh, then, uh, we, we return, uh, the root itself.


[User] Please transcribe this text

[Assistant] Uh, so that's the implementation, but that code is definitely tricky. Uh, and there's similar code for ceiling.


[User] Please transcribe this text

[Assistant] Give us the seventh largest key. To facilitate implementing those operations, and also size, all we do is keep an extra field in each node, which is the number of the nodes in the subtree rooted at that node.


[User] Please transcribe this text

[Assistant] So this tree's got eight nodes in it, uh, this subtree has six nodes in it, uh, and so forth.


[User] Please transcribe this text

[Assistant] Uh, and those counts, uh, are going to not only enable us to immediately implement the size function, just return the count at the root, uh, but also they'll give us good implementations of rank and select. So let's look at those now. So we add a count field to every node.


[User] Please transcribe this text

[Assistant] And then to implement the size function, well, if it's null, we return zero. So a client might call us for null tree or an empty tree. Otherwise, we return x.count, which is the number of nodes in that, in that subtree by definition.


[User] Please transcribe this text

[Assistant] Uh, the way we maintain, there's a number of ways we can maintain the thing, but, uh, the one that will adopt uniformly because it adapts to more complicated situations is just before, uh, we're done.


[User] Please transcribe this text

[Assistant] With the put operation, uh, we'll, uh, say, okay, we've done all our work, uh, and before we return a pointer to the given subtree, uh, we're going to, uh.


[User] Please transcribe this text

[Assistant] Take the size of what's on the left and the size of what's on the right and add one for us and that's going to be our count. So whether or not there was a new node added, we don't have to test for that.


[User] Please transcribe this text

[Assistant] This recursively takes care of the problem of maintaining the size in every node when there's a new node inserted. And it also handles more general situations as we'll see later on.


[User] Please transcribe this text

[Assistant] So that's how to maintain size. So now how do we implement rank? Well, it's a little like floor. It's an easy recursive algorithm, but there are three cases. So, let's look at the, at the three cases.


[User] Please transcribe this text

[Assistant] We're going to have a recursive algorithm, uh, for our given key. Uh, so let's, one of the easy ones is if our key is equal to, uh, the, if we're, to the, uh,


[User] Please transcribe this text

[Assistant] The key at the current node, uh, then the number of keys less than our key is the size of the left subtree of that node.


[User] Please transcribe this text

[Assistant] Uh, so if we're looking for, uh, the rank of E, say, how many keys are there less than E, uh, there's exactly two. That's by definition in the data structure, uh, that's the number of keys that are less than E.


[User] Please transcribe this text

[Assistant] Starting at the root, if we have the case where e is less than s.


[User] Please transcribe this text

[Assistant] Uh, so the rank of E in this whole tree is the same as the rank of E in the left subtree. So that's that case.


[User] Please transcribe this text

[Assistant] Uh, and then if we're going to the right, then we have to add one for the root and one for the left subtree of the root and then find the rank of us in the right. So that's an easy recursive algorithm for finding out the rank and it's definitely an instructive exercise to check that you believe that that method works.


[User] Please transcribe this text

[Assistant] The other thing we have to do, uh, is iteration. And iteration is a fundamental operation on tree structure, uh, and it's based on so-called in-order traversal. And that's also a simple recursive algorithm. Traverse the left subtree, uh, enqueue the key, traverse the right subtree.


[User] Please transcribe this text

[Assistant] So to iterate, we're going to maintain a queue of keys. And then we're going to call this recursive in order.


[User] Please transcribe this text

[Assistant] And that method, uh, is gonna add, uh, all the keys in the tree to the queue, uh, and then we'll just return that queue. And that's a, queue is an iterable data structure and the client can iterate that.


[User] Please transcribe this text

[Assistant] And in order, it's just a simple recursive method. Put everybody to the left on the cue, uh, then put the root on the cue, then put everybody to the right on the cue.


[User] Please transcribe this text

[Assistant] Uh, and to believe this method you just have to think recursively, uh, and prove by induction that, uh, this in-order method puts all the keys in the data structure on the queue, uh, in their natural order.


[User] Please transcribe this text

[Assistant] First it puts all the ones to the left in the queue. If that happens in their natural order, then the next thing that has to appear is the key at the root.


[User] Please transcribe this text

[Assistant] And then if the ones on the right go in their natural order, then by induction they're all in their natural order. That's a very simple implementation of an iterator for the symbol table with comparable keys.


[User] Please transcribe this text

[Assistant] Uh, so I have to again prove that property by induction and that's easy to do. The diagram at the right gives another simple way to look at it pictorially.


[User] Please transcribe this text

[Assistant] All the keys that are smaller on the left, we're going to put them out, and then we put the key at the root, and then we put all the keys on the right, uh, out in order, and then that key is going to have all those keys in order by induction.


[User] Please transcribe this text

[Assistant] So here's the operation summary for ordered symbol table. And the quick summary is that every one of those operations, well, ordered iteration is optimal, it just gets them in linear time.


[User] Please transcribe this text

[Assistant] And all the rest of them take time proportional to the height of the tree.


[User] Please transcribe this text

[Assistant] Now, if the keys are inserted in random order, we know that height by analysis is going to be proportional to log n.


[User] Please transcribe this text

[Assistant] Uh, or if it's some application where the order of insertion of the keys is well modeled by random order, uh, and that's not unusual at all. A binary search tree is a simple and extremely effective data structure that can support all of these operations quickly.


[User] Please transcribe this text

[Assistant] Much better than binary search in an ordered array, which is not dynamic and slow for insertion.


[User] Please transcribe this text

[Assistant] So that's a look at binary search tree implementations of ordered operations when keys are comparable.


[User] Please transcribe this text

[Assistant] Now we'll look at red-black BSTs, which is a simple data structure that allows us to implement two-three trees with very little extra code beyond the basic binary search tree code.


[User] Please transcribe this text

[Assistant] This is, and actually the version that we're looking at is called left-leaning red-black BSDs.


[User] Please transcribe this text

[Assistant] On a personal note, I wrote a research paper on this topic in 1979 with Leo Gibas. And we thought we pretty well understood these data structures at that time. And people around the world use them in implementing various different systems.


[User] Please transcribe this text

[Assistant] Uh, but just a few years ago, uh, for this course, uh, I found a much simpler implementation of red-black trees. Uh, and this is just a, a case study showing that there are simple algorithms still out there, uh, waiting to be discovered. And this is one of them that we're going to talk about.


[User] Please transcribe this text

[Assistant] And in order to get that done, uh, we just need a simple representation for three notes. So what we're gonna do is use internal left-leaning links, uh, to glue the three notes together.


[User] Please transcribe this text

[Assistant] So the larger of the two nodes in the three node will always be the root of a little binary search tree of size two for the three node.


[User] Please transcribe this text

[Assistant] Uh, and the link between the two nodes, the left link that links the larger key to the smaller one, uh, will color red. And that's to distinguish, uh, those links from the other links in the binary tree so that we can tell when we're, uh, inserting things, uh, which nodes are, uh, belong to three nodes and which ones don't.


[User] Please transcribe this text

[Assistant] Uh, and you can see from this transformation that, uh, it's easy to,


[User] Please transcribe this text

[Assistant] The middle link between a and b, those are the keys that are less than b and larger than a. So that takes two comparisons to get to them. The ones that are less than a, less than b, less than a, that's two comparisons for that. The ones that are greater than b are the right link of b.


[User] Please transcribe this text

[Assistant] So any two-three tree, uh, corresponds to a left-leaning red-black BST in this way. Just take the three nodes and, uh, split them into, uh, little binary search trees of size, uh, two held together by a red link.


[User] Please transcribe this text

[Assistant] But just look at the properties of, uh, looking at the properties of our left-leaning red-black BST, uh, you know, with reference to what we know about two-three trees. Uh, first of all, uh, no node has two red links connected to it.


[User] Please transcribe this text

[Assistant] Uh, cause the only red links are internal to three nodes and, uh, those have to have ex, external links or tree links connecting them to some other node.


[User] Please transcribe this text

[Assistant] Uh, every path from the root down to a null link has the same number of black links. Uh, that just follows directly from the corresponding property for two three trees. Uh, a left leaning red-black BST has perfect black balance.


[User] Please transcribe this text

[Assistant] Uh, and all the red links lean left. Uh, so given a BST with some of the links colored red that has those properties, uh, that's going to correspond to a 2-3 tree.


[User] Please transcribe this text

[Assistant] And that's a key property is this one to one correspondence between two three trees and left leaning red black trees. Given a two three tree, we saw how to do it. Given a, given a red black tree, we just make the red links horizontal and merge the nodes together to be three nodes.


[User] Please transcribe this text

[Assistant] So all of the operations that we're going to look at for red-black trees can be understood in terms of the corresponding operations on two-three trees.


[User] Please transcribe this text

[Assistant] Now, uh, the first and really one of the most critical observations is that search in a red-black BST is exactly the same as for an elementary BST. We just ignore the color.


[User] Please transcribe this text

[Assistant] Now it's going to be much faster because of better balance in the tree, but in terms of the code, we don't have to change the code at all. Our regular search code doesn't examine the color of a link, uh, and so we can just use it exactly as is.


[User] Please transcribe this text

[Assistant] And in fact, most of the other operations that we implemented on BSTs are also identical. They don't need the colors, but they can all benefit from the fact that the trees are much better balanced.


[User] Please transcribe this text

[Assistant] Regular BSTs involve some complicated code for floor and ceiling and rank and so forth. We don't have to change that code at all.


[User] Please transcribe this text

[Assistant] So, uh, first, uh, before we get to the code for insertion, we have to look at the red, uh, representation. Uh, we didn't actually have explicit representation of links. Uh, our links in trees are just references to nodes.


[User] Please transcribe this text

[Assistant] You could implement this by building explicit links, but an easier thing to do is to notice that every node is referenced by just one link in a tree.


[User] Please transcribe this text

[Assistant] Uh, the one from its parents. So you can put the color of a link in the node that it references.


[User] Please transcribe this text

[Assistant] Uh, and then if the link coming into a node is red, we set that to true.


[User] Please transcribe this text

[Assistant] Uh, so, uh, this simple thing just, uh, tests is a node red, uh, we consider all null nodes to be, uh, black, uh, null links to be black, we don't have red links dangling off, that'd be, uh, incomplete three nodes, uh, and, uh,


[User] Please transcribe this text

[Assistant] Uh, so, uh, in this tree, the color of h.left is red, the color of h.right is black, and so forth. Uh, so that's the way we represent colors, uh, by putting, uh, the color bit in the node for the color of the link that points to it.


[User] Please transcribe this text

[Assistant] Alright, so now there's a couple of elementary operations, uh, that we have to perform on red-black trees called rotations. Uh, and the idea is that during the construction of a tree or during an insertion operation, sometimes we wind up with red links that are leaning in the wrong direction.


[User] Please transcribe this text

[Assistant] So, we'll need what's called a left rotation. And the job of that operation is to take a right leaning red link that is there for whatever reason and reorient it to lean to the left.


[User] Please transcribe this text

[Assistant] Uh, so in this case we have the right link of E points to S, and S is red, so that's a right leaning red link. Uh, and so that's the before, and what we want to do is reorient things so that it leans to the left.


[User] Please transcribe this text

[Assistant] And again, that has to be a local operation that, uh, only changes a few links. And, uh, just from, uh, the diagram, uh, it's not difficult to see that, uh, this little bit of code will, uh, do the job.


[User] Please transcribe this text

[Assistant] Uh, and, uh, also whatever color, uh, H was, well, looks like it should be black, but actually the situation is where it could be red. Uh, then X is going to have that color because the link coming into H is going to be the link coming into, uh, X.


[User] Please transcribe this text

[Assistant] Uh, and then H's color is going to be black afterwards. And then we return X, uh, to link further up the tree, which happens during our standard recursive insert.


[User] Please transcribe this text

[Assistant] Now the property of this operation, uh, that's very important is it maintains a symmetric order. The keys between E and S are still there.


[User] Please transcribe this text

[Assistant] Uh, we just changed the way we get to them, uh, and the key's less than E and so forth. And also, uh, we maintained perfect black balance because we didn't change the black, uh, uh, height of anything, uh, by doing this transformation.


[User] Please transcribe this text

[Assistant] All those, uh, subtrees, those three subtrees are exactly the same, uh, relative to the top and bottom of the tree as they were before the rotation.


[User] Please transcribe this text

[Assistant] To get the insertion done properly, uh, we sometimes need to take a left leaning red link and temporarily make it lean right.


[User] Please transcribe this text

[Assistant] Uh, and so that's just the symmetric code to the code that we just did.


[User] Please transcribe this text

[Assistant] Uh, now, uh, again, now x is h dot left, uh, and uh, h dot left is going to be x dot right after the rotation. x's color is still going to be h's color, uh, and h's color is going to be red, uh, and the right rotation implements this.


[User] Please transcribe this text

[Assistant] Uh, sometimes during the insertion, we might wind up with a node, uh, that's got two red links coming out of it. That, that's, corresponds, uh, precisely to our temporary four node when we're doing two three trees.


[User] Please transcribe this text

[Assistant] And what we wanted to do with the temporary forward node was to split it and pass the center node up to the root.


[User] Please transcribe this text

[Assistant] Well you can see from this structure that we're all set to do that. Uh, all we need to do actually is not change any links, just change all the colors.


[User] Please transcribe this text

[Assistant] Uh, and so that is we change the link from E to A and from E to S to be black. That essentially splits the four node. Uh, and then we want to insert the E into its parent. Uh, and we just do that by changing its link to be red.


[User] Please transcribe this text

[Assistant] So that's flipping the colors, uh, and that's the way we split a temporary four node, uh, in a left-leaning red-black tree. And again, that's just flipping colors, uh, doesn't change any length, so it still, of course, maintains symmetric order and perfect black balance.


[User] Please transcribe this text

[Assistant] Then, uh, C, uh, is going to be, uh, less than E, greater than A, so it'll get added to the, as the right link of A. And every time we add a node, uh, we just, uh, create a red link to its parents, uh, and so that's changing the two node into a three node.


[User] Please transcribe this text

[Assistant] After we do the left rotate, we have a legal left-leaning red-black tree, and it exactly corresponds to, uh, that 2-3 tree. So the insertion of C gives us exactly what we'd want, the correspondence with the 2-3 tree.


[User] Please transcribe this text

[Assistant] We have to work through, uh, other cases that can arise, uh, but there's, uh, not too many, uh, so we'll work through them. And we have the basic operations left rotate, right rotate, and flip colors.


[User] Please transcribe this text

[Assistant] Uh, well, if it goes on the left, then we just make a red link and add it on and we're done. Uh, if it goes on the right, then we attach a new node with a red link on the right, but we have to rotate it to the left to make a legal three node.


[User] Please transcribe this text

[Assistant] Uh, so now let's look at a second warm-up. So say we have just, uh, two nodes in the tree. So it's a, we have two nodes, and that means it's a single three node.


[User] Please transcribe this text

[Assistant] If that's true, then we, uh, attach the new node with a red link as always, uh, and that gives us, uh, a temporary four node. And what we want to do is split that four node, uh, and in this case, since we're at the root, that's all, so that just flips the colors.


[User] Please transcribe this text

[Assistant] Uh, so that's inserting, uh, into a tree that's a single three node, uh, a node that's larger than both of them, a key that's larger than both of them, and we get, wind up with a four node. But let's look at the other two cases, and these, understanding these is crucial to understanding the whole algorithm.


[User] Please transcribe this text

[Assistant] Let's say the new key is smaller than both of the keys in our three node. We attach a new link, uh, at the left of the smaller node, uh, and now we've got a fine BST, but it has two red links in a row.


[User] Please transcribe this text

[Assistant] And that's, uh, something that's not allowed. So what we're gonna do is we're gonna rotate the top link to the right.


[User] Please transcribe this text

[Assistant] Uh, so, uh, that puts B at the root, and now it's got two red children. It reduces it to this case, and we flip the colors, and we have a single, uh, four-node, uh, sorry, a, a,


[User] Please transcribe this text

[Assistant] Uh, a red-black tree that's got three two nodes, uh, and no red links. Uh, same situation as before.


[User] Please transcribe this text

[Assistant] So we had a single temporary four note and we split it up into two two notes and I connected to a two note.


[User] Please transcribe this text

[Assistant] Uh, and comes out at this link here. Uh, again, we just add a red link, and now we have a BST with two red links along a path connected to A, and that's not allowed.


[User] Please transcribe this text

[Assistant] Uh, so, and that gives us this, and reduce it to the other situation that we had before. And then we wrote the, rotate the top link right, uh, and then we flip the colors.


[User] Please transcribe this text

[Assistant] So this one we use all three of our operations. Rotate left, rotate right, and flip the color. And that gets us an insertion into a tree that has, uh, from a tree that is a single three node to a tree that is three two nodes containing three keys.


[User] Please transcribe this text

[Assistant] And we do the rotations that we need, either, uh, one or two rotations to balance the temporary four node, and then we flip colors to pass the red link up one level, uh, and then, uh, we might need to rotate to that and to make that one lean left. So for example,


[User] Please transcribe this text

[Assistant] Uh, so that gives us a temporary four node that's not balanced, so we need to rotate the link from S to the right.


[User] Please transcribe this text

[Assistant] Uh, and that gives us now a temporary four node that is balanced. And again, these are all local transformations. It's not changing the rest of the tree.


[User] Please transcribe this text

[Assistant] If that gets passed up to a three node, then we have to continue moving up the tree and just treat it in the same way as we just treated inserting at the bottom.


[User] Please transcribe this text

[Assistant] We have a new red link appearing into some three node. Uh, there's the three cases that could happen. And here's, uh, an example.


[User] Please transcribe this text

[Assistant] So say we're inserting P into this left-leaning red-black tree. Uh, it goes to the right of M, so we get a temporary four-node that's got, uh, two red links. Uh, both children are red in that thing, so we want to flip the colors.


[User] Please transcribe this text

[Assistant] Uh, we flipped the colors, uh, and, uh, now our temporary four-note is up higher in the tree.


[User] Please transcribe this text

[Assistant] Uh, but it's not balanced, so we're going to have to do two rotations to make that balanced. Uh, first one, uh, is to make the bottom link left leaning. Uh, and then the second one is to make the top link right leaning, uh, so that we can have the temporary four node balanced.


[User] Please transcribe this text

[Assistant] Uh, and then the last thing we do is flip the colors and now that's the result of that insertion.


[User] Please transcribe this text

[Assistant] Uh, and that, uh, when happened to be at the root, if that red link, uh, were way down in the tree and there were another three node above it, we might have to do it again. Again, exactly as would happen in a 2-3 tree.


[User] Please transcribe this text

[Assistant] So let's do a demo of constructing a red-black BST from our standard set of keys.


[User] Please transcribe this text

[Assistant] Uh, so we start with a single key, uh, and now if we want to insert E, uh, it goes to the left, that's fine. That's a legal left leaning red-black tree. A would go to the left of E, uh, two lefts in a row, so we have to rotate S right.


[User] Please transcribe this text

[Assistant] Uh, and then we have to flip the colors. And that's a legal red-black BST.


[User] Please transcribe this text

[Assistant] Legal red-black BST. We want to insert H, uh, that goes to the left of R, two reds in a row, rotate the top.


[User] Please transcribe this text

[Assistant] Rotate the top, our temporary four node is balanced, flip colors. Uh, now we have a, uh, three node, but the, uh, red link is leaning right, so we have to rotate.


[User] Please transcribe this text

[Assistant] Uh, most of the operations are simple ones like this happening at the bottom. Insert P, uh, that goes to the right of M, that makes M a temporary 4-node that happens to be balanced, so flip the colors.


[User] Please transcribe this text

[Assistant] Look at the, uh, implementation for, of the code for inserting into a left-leaning red-black tree.


[User] Please transcribe this text

[Assistant] And the key to understanding this code is to realize that the same code handles all of the cases. And the way that it works is we're always reducing one case to another. We got this most complicated case. We did a left rotate on the bottom node.


[User] Please transcribe this text

[Assistant] That transformed to this case where they're both leaning left. And then we did a right rotate on the top node and that transformed to the case where our temporary four node is balanced. And then we flipped colors on that.


[User] Please transcribe this text

[Assistant] So in gray is our standard insertion code for binary search trees. And remember, we took some pains to think about the recursive implementation where when we go down a link,


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[Assistant] We replace that link by whatever the recursive routine gives us back.


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[Assistant] Because in this implementation for left-leaning red-black trees, we're going to return the link whenever we're done, and then that'll get that link installed up in the node above, whether it be left or right.


[User] Please transcribe this text

[Assistant] Do not use this recursive strategy. Wind up having, uh, lots of cases depending on whether, uh, left or right or double rotate to the left or double rotate to the right.


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[Assistant] I can be critical of this code because my own code was this way for the first three editions of the book. It was only in this edition that we figured out how to make the code this simple.


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[Assistant] Okay, so what are the things that have to be done? Let's just check.


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[Assistant] When we insert a new node, all we want to do is create a new node with the given, associating the given value with the given key as before. But now we just make that node red. So that's adding a new node with a red link at the bottom.


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[Assistant] Uh, and then we do the comparisons as, as before, uh, and that, and that's all fine. Now when it's returned, uh, then that's the point at which, uh, we're going to check, uh, whether, uh,


[User] Please transcribe this text

[Assistant] Is, uh, H dot right, uh, is red, uh, so that means that the right link of H is leaning the wrong way. H is a three node leaning the wrong way.


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[Assistant] So that would be, in this case here, we'd rotate it left and reduce it to that one.


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[Assistant] Or, uh, in, uh, in the case when, uh, we're just inserting a new node and it's, uh, turns out to be, uh, the right, uh, red link, uh, attached to a black one.


[User] Please transcribe this text

[Assistant] So that handles that case. Uh, now if, uh, H dot left is red and H dot left dot left is also red, uh, that's this case here, uh, where we have two left leaning, uh, red links. And then in that case, we just, uh, rotate the top one right, uh, and that brings us to this one.


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[Assistant] So notice that we're in this case, we do this rotation first, we're on this node, and then that returns when we come up to deal with the situation on this node after the return, and then we do that rotation.


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[Assistant] And then after that rotation, or if there were no rotations at all, if the insertion happened over here, then we test and flip the colors.


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[Assistant] It's a little mind-bending at first because of the recursive structure, uh, but it won't take you long to convince yourself that, uh, this little bit of extra code, uh, completes the implementation of left-leaning red-black trees. Quite remarkable, actually. So let's look at a visualization.


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[Assistant] This is a balanced tree getting, uh, constructed, uh, in the worst case where everything that comes in, uh, is in ascending order.


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[Assistant] A regular binary search tree would just be all strung out in a single line and wouldn't have quadratic time for this input. But a left leaning red-black tree actually, whenever it becomes a power of two, is completely balanced, as you can see from this example.


[User] Please transcribe this text

[Assistant] Uh, and what about descending order? Well, it's left leaning and the process is a little bit different. And, uh, sometimes the left path can get long, but not that long. Uh, the worst that can happen is that it alternates, uh, red and black.


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[Assistant] Uh, and then after it gets to that worst case, uh, it also, uh, winds up being completely balanced when we have a power of two. Interesting to think just, just about this case and to prove to yourself that it's always going to be perfectly balanced when it's descending.


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[Assistant] The tree stays very balanced. It's guaranteed that the longest path, which is alternating red and black, can be no more than twice as long as the shortest path, which is all blacks.


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[Assistant] Uh, so easy to prove by correspondence with two three trees that the height is guaranteed to be less than two log base two n. Every search in a left leaning red black tree is guaranteed to take less than two log base two of n.


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[Assistant] Uh, and actually in typical applications, uh, with, uh, any kind of, uh, randomness or even, uh, if there's a lot of order, uh, it's difficult to find situations, uh, orders of keys that, uh, build trees that height is bigger than actually one log n.


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[Assistant] Uh, so that, uh, completes our, uh, summary for symbol table implementations. Uh, with red-black BSTs, uh, we have full code, uh, it's the regular BST code with a couple of lines, uh, adding the calls on the basic operations to rotate right, rotate left.


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[Assistant] Uh, in color flip, and we get guaranteed logarithmic performance, uh, not just for search, insert, uh, and delete. Delete code is a bit more complicated, uh, but it's, uh, on the book side and in the book.


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[Assistant] Uh, but also, since it's the compare to interface, and since it's a binary tree representation, uh, all the other comparable operations, uh, extended operations for ordered symbol tables, uh, are going to be implemented and take time proportional to log in.


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[Assistant] A lot of people ask why did we use the name red-black. Well, we invented this data structure, this way of looking at balanced trees at Xerox PARC.


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[Assistant] Uh, which was the home of the personal computer and many other innovations that we live with today, including a graphic user interface and ethernet and object oriented programming and many other things. But one of the things that was invented there was laser printing.


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[Assistant] And we were very excited to have nearby a color laser printer that could print things out in color. And out of the colors, the red looked the best. So that's why we picked the color red, to distinguish red links, the types of links in three nodes.


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[Assistant] Uh, and the provider, uh, implemented the database using red-black BSTs for search and insert.


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[Assistant] Now, our, uh, original paper on red-black trees, uh, was, uh, the way the paper was laid out, it turned out that the delete, uh, implementation happened, uh, to be placed after all the references, so a lot of people didn't see the delete implementation.


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[Assistant] Representation. So, uh, it was more complicated and involved a lot more cases and so usually not all the cases were put in the textbooks. So, uh, people found deletion more difficult. In fact, that's what led to, led me to, eh, analyze the situation and come up with the left-leaning variant.


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[Assistant] But they still thought that it should be balanced and it shouldn't matter much. And they had a complex error recovery process that got triggered if the height limit got too big.


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[Assistant] Uh, and they rebuilt the whole tree and, uh, and then because of the way they did this deletion, well, the end of the story was that, uhm,


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[Assistant] They had extended, the client had extended outage because the, uh, implementer, uh, didn't use the, uh, full algorithm. Uh, and there was a lawsuit, uh, and, uh, some legal testimony, uh, and, uh, happy to report that the, uh, uh,


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[Assistant] It was clear that Hibid dilution was the problem, uh, once the expert analyzed it, uh, and the expert witness, who's a colleague of mine, said, uh, if implemented properly, the height of a red-black BST within keys is at most 2 log n.


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[Assistant] And that douchebag will be here any minute now. Up there here anyway.


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[Assistant] You wanna know how Rhonda's planning on paying me? With YOUR bounty suckers!


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[Assistant] Chapter 6. There and back again.


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[Assistant] In the evening, Aladdin and his friends finished hunting and began to go home. Suddenly, a friend said, Aladdin, look, the Sultan's men are coming with swords in their hands. What do they want? I don't know, Aladdin answered. When the Sultan's men arrived, they said,


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[Assistant] Aladdin, we must take you to the Sultan. He's very angry. Why? asked Aladdin, but the men could not tell him. In his palace,


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[Assistant] The Sultan took Aladdin to a window.


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[Assistant] Where is your palace? He cried angrily. And where is my daughter? Answer me! Aladdin looked out of the window.


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[Assistant] There was only the ground and the sky, no palace, no gardens, nothing. He closed his eyes, opened them and looked again, and he had no answer for the Sultan. It's black magic. I always said that.


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[Assistant] The vizier said quietly in the Sultan's ear, Your Majesty.


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[Assistant] Aladdin put his head at the Sultan's feet. Kill me now!


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[Assistant] I do not want to live without Badur al-Budur. There were tears in his eyes.


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[Assistant] Find her in forty days or you'll die, the sultan said. I hear and obey, your majesty, Aladdin answered. But without his magic lamp, what could Aladdin do? He went out from the city and


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[Assistant] He saw the magician's ring on his little finger. He began to rub it. Whoosh!


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[Assistant] Out of the blue smoke came the Ginny of the Ring.


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[Assistant] What is your wish, Master? he asked.


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[Assistant] Find my wife and bring her back to me. Answered Aladdin. Please. Master, I cannot do that.


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[Assistant] The Ginny of the Lamp took the Princess away.


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[Assistant] It is many, many miles from Arabia to Morocco.


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[Assistant] But Aladdin was there in a second. And there was his palace, in front of him. He went into the gardens and looked up at the windows. Badur al-Budur, he cried, are you there? In the palace, Badur al-Budur heard him. Is that Aladdin, she thought.


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[Assistant] For the first time in many days, Aladdin smiled. Come up quickly, the princess called. The magician is not here now.


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[Assistant] Her slave girl ran down and opened a little door into the gardens.


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[Assistant] Aladdin ran up to the princess's rooms and in a second she was in his arms. Oh my love, the princess said, a bad man carried me here, a magician. His name is, his name is Abanaza and I am going to kill him, said Aladdin. Tell me, does he have my old lamb?


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[Assistant] Yes, Badur al-Budur said, he always carries it with him. I know about its magic now, because he told me. Oh, why did I give it away? Listen, my love, said Aladdin.


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[Assistant] I'm going to give you some sleeping powder. When he comes here again, you must give him a drink and put the powder in it. When he is asleep, I can kill him. Don't be afraid.


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[Assistant] What is your wish, master? said the jinnie of the ring. Bring me some sleeping powder, said Aladdin. To hear is to obey. In a second.


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[Assistant] The Ginny was back with some sleeping powder.


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[Assistant] Then Aladdin and the Princess waited for Abanaza. In the evening, they heard him on the stairs. Don't be afraid, Aladdin said quietly to his wife. I am in the next room and can be with you in a second. He went quickly into the next room and stood behind the door.


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[Assistant] Abanaza opened the door of Badur al-Budur's room and came in. He smiled.


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[Assistant] You are more beautiful every day, Badur al-Budur, he said.


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[Assistant] That good-for-nothing Aladdin is dead now. You must marry me. You can have gold, jewels,


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[Assistant] For the first time, the princess smiled at Abanaza. Why not? she said.


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[Assistant] You are a rich man and I am happy here. Yes. Let's drink to that.


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[Assistant] And she gave him a tall gold cup with the drink and the powder in it. Let us drink from one cup, Abanaza, she said and smiled at him. You first, then me. In my country,


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[Assistant] New husbands and wives always do this.


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[Assistant] To Badur al-Budur.


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[Assistant] The most beautiful woman in Morocco, Abanaza said happily, and my wife.


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[Assistant] He looked into Badur al-Budur's eyes and began to drink.


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[Assistant] Very afraid, the princess watched him. But it was a good sleeping powder. And after five seconds, Abanaz's eyes closed and he was asleep.


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[Assistant] The princess ran to the door of the next room. Quick, Aladdin, she called.


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[Assistant] Aladdin ran in with his sword and saw the sleeping magician. Well done, my love, he said. Now, go into the next room and do not watch.


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[Assistant] Badur al-Budur ran to the next room and closed the door.


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[Assistant] Aladdin put his hand in Abanaza's pocket and took out the lamp.


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[Assistant] He put it carefully into the pocket of his coat and then stood up.


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[Assistant] And Abanaza never opened his eyes again. The princess came back into the room and ran to Aladdin. He took her in his arms. The magician is dead, he said. And now we can go home. He began to rub the lamp. Whoosh.


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[Assistant] Fire and red smoke came from the lamp. The Princess watched, afraid. I am here, Master, said the Ginny of the lamp.


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[Assistant] Carry this palace, Badr al-Budur, and me back to our city in Arabia.


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[Assistant] But leave that dog Abanaza here.


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[Assistant] To hear is to obey, said the Ginny.


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[Assistant] When the Sultan looked out of his window and saw Aladdin's palace again, he was a happy man.


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[Assistant] Aladdin and Badur al-Budur lived happily in their palace.


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[Assistant] They lived for many years and had many children.


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[Assistant] But Aladdin always carried the magic lamp with him day and night.


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[Assistant] Just about a year ago now, we first heard of a new potentially dangerous coronavirus. And now, in some ways, it feels like we know it all too well. And we do know a lot more than you'd expect only a year in. But there are also some big, enduring mysteries, including these three. First up, why some people get


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[Assistant] That people who breathe in more are more likely to get really sick. This has proven difficult to study in the past, but thanks to modern medical science, we might finally be able to figure out if it's true.


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[Assistant] For COVID-19 and other diseases. So that's one thing researchers are planning to look into more this year. But another is genetics. Immunologists have long suspected that people can be born with a tendency to have particularly mild or severe symptoms to a given infectious disease. And they've already linked some genetic variants to differences in immune function that may explain why some people end up in the ICU with COVID-19. Like, in an October 2020 study in Science,


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[Assistant] Intel that could help us predict how sick a person is likely to get and figure out the best drugs for them. There's also mounting evidence that problematic antibodies play a role in all this. Antibodies are normally helpful immune proteins that latch onto pathogens and, ideally, neutralize them.


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[Assistant] But sometimes, they misbehave and attack the person's healthy tissues instead. And in some people, the virus that causes COVID-19 seems to trigger the formation of these self-attacking antibodies.


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[Assistant] Like, ones that attack serum proteins, leading to sticky blood that clots too easily. Or ones that attack those important type 1 interferons, which causes basically the same problem as mutations in those genes. And there's also something weird going on with neutralizing antibodies. Those are the kind that we usually want, as they, well,


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[Assistant] neutralize pathogens and help a person fend them off. But a November 2020 study in the journal Nature Immunology found that adults with severe COVID-19


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[Assistant] Allowing their bodies to spot this virus and kick it out fast, before really ramping up antibody production. And confirming this could point towards ways of helping us grownups. But it could also be that neutralizing antibodies just aren't as helpful as we think, for reasons that are currently unknown.


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[Assistant] Next, antibodies also play a key role in our second big question that scientists will continue to investigate this year.


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[Assistant] How long immunity to COVID-19 lasts? With some viruses, surviving an infection confers lifelong immunity.


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[Assistant] The body essentially learns to spot it and eliminate it fast if it ever shows up again. But with other related cold-causing coronaviruses, you can get reinfected in a matter of months. Where COVID-19 falls on this spectrum isn't clear. One way scientists can get a hint at how long immunity lasts is by looking at how long neutralizing antibodies stick around.


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[Assistant] But those are even more of a black box. Understanding immunity to COVID-19 is important because it can help us develop better treatments, and it might even give us clues as to how effective or enduring vaccinations may be.


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[Assistant] And lastly, researchers are hoping 2021 will shed some light on the long-term effects of COVID-19. Already, we've seen the emergence of long haulers.


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[Assistant] People whose fatigue, pain, and heart and lung issues continue for months after they've gotten over their initial infections. Other people who have recovered report experiencing brain fog, continued loss of taste and smell,


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[Assistant] But it just hasn't been long enough for scientists to observe what happens to most people more than a few months post-infection. So until we get more data, we won't know how common any of this will be, or when or if these lasting symptoms will go away. And on top of lingering symptoms,


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[Assistant] COVID infections may have knock-on effects, like triggering or exacerbating chronic health conditions. For instance, some experts are worried that inflammation and other impacts on organs could contribute to brain deterioration.


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[Assistant] Thank you for watching this episode of SciShow News. We'll be here every Friday this year to keep you up to date on the newest scientific discoveries


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[Assistant] Coronavirus-related or not. Every other day of the week, we'll tell you something new about the way this amazing world we live in works. And you can keep up with all of our episodes by clicking that subscribe button and ringing the notification bell. From all of us here at SciShow, we hope you have a healthy and happy new year.


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[Assistant] There are many contenders for the title, at least a couple emanating as it happens from the same Yorkshire parsonage in the same year, but Jane Eyre has a claim to be the most popular single novel of the High Victorian period. That is to say, the most perennially and long-lastingly popular.


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[Assistant] It's also, one is reliably informed, the most prescribed English novel in Taiwanese schools. Apparently in South Korea, Wuthering Heights is preferred.


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[Assistant] Now, there are a number of reasons for this preeminence.


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[Assistant] Not least, of course, the fact that Jane Eyre is superbly exciting. It's a rattling good tale with suspense, surprise, and what the Victorians call tremendous scenes. I mean, can anyone?


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[Assistant] Who has read the, the novel Ever Forget That, the dreadful secret that lies hidden in the attic floor of Thornfield Hall. One of those tremendous scenes which we'll be looking at in, in shuddering detail a little later.


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[Assistant] These are some of the things which have made Jane Eyre perennially popular and much beloved. It's typically the first full-length Victorian novel that young people read and very often it hooks them on the genre for life, I'm glad to say.


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[Assistant] But what has made Jane Eyre so significant and such an important novel to us today is, quite simply, it's heroin. She's unlike any other heroine of the period.


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[Assistant] Jane is not terribly pretty. Plain is her too hard turn for herself. Little girl.


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[Assistant] Then an adolescent, then a young woman, and finally a mature, grown woman, who by sheer force of intelligence, high morality, indomitable pluck, and energy, makes her way in what D.H. Lawrence called the man's world.


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[Assistant] One could put that another way. She makes her way in spite of a man's world. Now, it's never been an easy thing to do, and it's rarely been harder than in the mid-19th century to do what Plain Jane did.


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[Assistant] It was, remember, a period when women did not have the vote. They wouldn't have it for another 70 years. They did not have equal property rights with men, even ownership of the children they bore. They would not have those maternal rights for 40 years. They did not have equal divorce rights. They wouldn't have those for 10 years.


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[Assistant] We're typically disposed of, women were typically disposed of by their male custodians, first fathers, then husbands, sometimes brothers, as a higher kind of chattel, chattel or concubine.


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[Assistant] I have many favorite moments in Jane Eyre, but near the top is that when Jane discovers the awful prisoner in the attic, Mrs. Rochester that is, and Rochester offers, marriage now being off the menu of course, because it would be bigamous, he offers to make Jane his mistress. In his mind it's the same thing.


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[Assistant] Jane pictures him as a pasha, an oriental potentate with his harem. Mistress, wife, what's the difference to him? She runs away, it's a big difference to her. He's mystified.


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[Assistant] The feminism at the heart of Jane Eyre is summed up in four words which are found famously at the novel's conclusion. Reader, I married him.


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[Assistant] Not, you'll note, Reader He Married Me, nor even Reader We Got Married.


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[Assistant] As the syntax and the transitive verb insist, it is Jane who is in charge.


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[Assistant] Women received, accepted, or graciously declined offers. It was men who did the marrying. Much of what we


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[Assistant] Now think of as, as feminist thinking can be located thematically, if not as articulate theory, in the adventures of Jane Eyre on her passage through life. On that question, through life, there's another relevant point about the kind of novel which Jane Eyre is.


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[Assistant] The mid-Victorian novelists, Charlotte among them, became fascinated by a form of narrative that has no English description and is covered by the German loanword Bildungsroman. It translates into English as portrait novel.


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[Assistant] Or more precisely, the life story portrait from childhood through a series of trials to maturity. A full length portrait, that is. One thinks of novels like David Copperfield's The Mill on the Floss by George Eliot, Great Expectations by Dickens again.


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[Assistant] What these novels have in common is a long narrative through many years of the hero or heroine's life.


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[Assistant] Like Dickens in Copperfield and Great Expectations, Charlotte Bronte told her Bildungsroman, Jane Eyre, autobiographical. There's another German term for that, but we'll call it I-noration. As for example, in Reader, I married him, rather than she married Rochester.


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[Assistant] As later more self-consciously artistic novelists, such as Henry James argued, eye narration can be somewhat crude. It ties down the point of view to one set of eyes, one consciousness, and it renders suspense.


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[Assistant] Writing the past tense, the I must know how things will turn out. Artificial and factitious. But I-noration has what Charlotte Bronte particularly wanted. Force and urgency. What one could call I-ness. It's high impact.


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[Assistant] Charlotte, born in 1816, was the eldest of the Bronte sisters. She also lived longest of all the six children, which was, alas, not very long. She died at the age of 39.


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[Assistant] Unlike her two writing sisters, Emily and Anne, she was granted sufficient years to build up a body of fiction, what we call an erve.


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[Assistant] Some five full-length novels and a quantity of lyric verse.


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[Assistant] Her most famous novel, Jane Eyre, is her first published. It has all the vitality and many of the imperfections of debut fiction. While on the subject of life stories, some family background.


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[Assistant] When Charlotte was four, her father, the Reverend Bronte, a remarkable man as you'll recall from the Wuthering Heights Lecture, was appointed perpetual, i.e. tenured, curate at Howarth in Yorkshire.


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[Assistant] The Parsonage in this large North England village, a region generally enriched by the Industrial Revolution, was a comfortable, sprawling, highly respectable place for a young girl to grow up.


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[Assistant] The personage at Haworth would be Charlotte's domestic centre throughout almost all her life.


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[Assistant] It's worth noting, perhaps, what is not evident when one looks at pictures of the, the Howarth, uh, past age, which is now, incidentally, uhm, the Bronte Museum.


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[Assistant] The passage was very close to the church graveyard. The Bronte children would have seen coffins and funerals as part of their everyday existence. And all the Bronte sisters lie in that churchyard now.


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[Assistant] What the effect on impressionable young women was, impressionable young girls.


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[Assistant] Was a, a, a, of seeing a parade of corpses at their own age very often during the regular cholera epidemics of the 1830s and 1840s can only be imagined.


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[Assistant] Yorkshire, the natural landscape of that majestically bleak, windswept and more dominated county, the largest in England, did not mean as much to Charlotte as to her more romantically inclined sister, Emily.


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[Assistant] But the Anglican church, and remember that the parsonage is next to the church and next to the graveyard, the Anglican church did mean a lot. The last words in Jane Eyre, it's often forgotten are


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[Assistant] You've read the novel, can you recall? The last words are, Jesus Christ. Piously uttered.


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[Assistant] The novel ends not with the Sanson-like Edward Rochester, the maimed Superman who makes Jane


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[Assistant] At last his wife, but with a Christian missionary, St John Rivers, who wanted to make Jane his wife, but denied that fulfillment, went off to India to convert that reluctant nation to Christianity. He, St John Rivers, the ordained Anglican clergyman, it is who owns those last words, Jesus Christ.


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[Assistant] Charlotte, we may guess, was much more the parson's daughter than Emily was. Now, Charlotte's father was not a conventional priest.


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[Assistant] The household that Haworth cannot have been easy for the Reverend Patrick Bronte to manage, patriarch that he was, and if we credit Charlotte's biographer, Mrs. Gascoil, he was given to firing a pistol around the house in moments of stress.


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[Assistant] There was a brood of young, fearsomely precocious, intelligent wayward children. Five daughters and a son.


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[Assistant] You know, one genius would strain most families. Four is, is, is, is a domestic nuclear situation.


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[Assistant] And particularly Wayward was the son of the highest bramble, much of whose wild character, dissipation, and sexual amorality feeds one may conjecture into Rochester and Heathcliff.


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[Assistant] Charlotte's mother died when the little girl was only five. None of the children knew her really well, nor was there any softening maternal influence in their lives. Jane Eyre, you will record, is a motherless child.


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[Assistant] Now the eldest four of the Bronte girls were sent to the clergy daughter's school at Cowenbridge in Lancashire. As the name indicates, it was a charitable institution. And as Charlotte would later portray it as Lowood in Jane Eyre, the place was scarcely more humane than Do The Boys Hall in Dickens's novel, Nicholas Nickleby.


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[Assistant] Think Victorian Hardship and Cowenbridge will be very high on the list.


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[Assistant] The hardships of Cambridge directly led to the death of some of the Bronte daughters and certainly the bad health of those who were unlucky enough to be enrolled there.


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[Assistant] Now we're free to hate that school as cordially as did the two Brontes. Three Brontes, but two of them depicted it. Not least for the novels they robbed us of by shortening the sisters' lives, but because in fact they inflicted hardship on children.


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[Assistant] The Victorians, as we saw with Dickens, were becoming very alive to the fact that children could suffer, and that children's suffering should be, where possible, minimized.


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[Assistant] Back at the Parsonage, they were brought back to the Parsonage after eventually it was realized the school certainly wasn't working. The surviving...


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[Assistant] Bronte's Charlotte, Emily, Anne and Bramble wrote their fantastic sagas of Angria and Gondor. The house was a literary playground.


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[Assistant] These twin sagas, gondola and angria, are spiraling narratives chronicling the heeds, the deeds of superheroes based


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[Assistant] On the great military figures of the day, Wellington, Nelson, Napoleon, and Byron of course. Self-martyred, fighting for the cause of Greek independence. The glorious poet.


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[Assistant] The main literary influence was Sir Walter Scott. Marmion, Scott's great poem, is Jane Eyre's favourite reading.


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[Assistant] Charlotte, age 16, spent a year at school where, like Jane Eyre at Loward, she taught for a while. Better school than the one at which, uh, she suffered.


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[Assistant] She was already writing but nothing as yet was deemed publishable. She served.


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[Assistant] Uhm, as a governess in various households, but, but nothing, uh, as exciting or emotionally fulfilling as her heroine's experiences would be at Thornfield with Mr. Rochester, where of course she's also a governess. Jane is a governess.


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[Assistant] In the mid-19th century, the governess was regarded in most households as no more than an upper servant.


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[Assistant] And the image of the governess is, is idealized in, in much fiction. Jane Austen's Miss Taylor in Emma, for example, but upper.


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[Assistant] As in upper servant, didn't in fact mean very much. Often the governess would eat with the children, payment was miserly, bed and board was the main attraction.


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[Assistant] And of course, once the children reached a certain age, the governess would be redundant and would be obliged to move on. She was wanted no longer.


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[Assistant] The big, and in many ways, the transforming experience of Charlotte's life occurred in 1842, when, aged 26, she and Emily went to Brussels to work in a boarding house, or pensioner, run by the charismatic Constantin Eger and his wife, uh, Claire.


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[Assistant] Uh, it was a boarding house but also a boarding school. In return for living arrangements and tuition in French.


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[Assistant] The two young Bronte girls taught English, and Emily also taught music.


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[Assistant] Emily didn't stay on. She was always more the Yorkshire woman than Charlotte. Charlotte remained two years in Belgium at the Pensionneur. And the Belgian experience is directly recalled in two of her subsequent novels, The Professor and Villette.


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[Assistant] And the Belgian experience is indirectly reflected in the romance plot of Jane Eyre. Specifically, the heroines falling in love with her employer Rochester.


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[Assistant] In Belgium, Charlotte fell hopelessly in love with Monsieur Eger. Madame Eger was very, very nasty about this insignificant little anglaise upsetting her household with her absurd infatuations.


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[Assistant] Acutely painful as it was for Charlotte, and as far as we can make out, unreciprocated, although possibly encouraged by Egea.


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[Assistant] We can be grateful for the embarrassment of Charlotte's unhappy love. It inspired the longing relationships at the center of many of her narratives.


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[Assistant] Not least, the suffering governess's Amor Fou, her mad love for her masterful and for most of the novel apparently indifferent employer Rochester in Jane Eyre, that seems to have been inspired, the energy there seems to have come from Charlotte's unhappy love in Belgium.


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[Assistant] Now in fiction, such yearnings of the heart could have happy endings, but not, alas, in the real world.


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[Assistant] When she returned to England in the mid-1840s, Charlotte and her sisters made determined attempts to get into print with their poems, under the gender-neutral pseudonyms, Kara, Ellis, and Acton Bell. Their volume of verse, Vanity Published, sold only two copies, and a letter from the poet laureate, Robert Saithee,


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[Assistant] To whom they sent the volume, suggested they should stick to cooking and darning. Who now remembers Robert Southey? Time has its pleasing ironies. Everyone of course remembers the Brontes.


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[Assistant] Public indifference was hurtful. Even more was the, even more hurtful was the fatal illness sweeping through Howard Parsonage.


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[Assistant] Bramwell, the only son of the family, died of chronic bronchitis, heavy drinking and general moral dissolution in September 1848. Emily and Anne both died of pulmonary tuberculosis in December 1848 and May 1849 respectively. All wrote


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[Assistant] All were talented. None lived to see the name Bronte Famous. None that is but Charlotte.


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[Assistant] Her first novel, sent to the eminent London publisher George Smith, was politely turned down, but with the suggestion that she should write perhaps something rather longer and more exciting and something more...


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[Assistant] How shall we say womanly than her first effort? The professor had a male Belgian teacher as its hero narrator enough said.


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[Assistant] Kara Bell duly produced Jane Eyre in six weeks. Six weeks.


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[Assistant] Victorian readers at once apprehended that Cura must be a woman, and when she dedicated the second edition of Jane Eyre to Thackeray, William Thackeray, they assumed that she was Thackeray's mistress. People love to gossip about writers, mysterious writers.


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[Assistant] The novel was a huge success, The Talk of London. Thackeray, who in fact didn't know the author at this point, stayed up all night reading it, as did many others.


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[Assistant] Charlotte Currer was suddenly famous. And she was famous for the rest of her short life.


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[Assistant] She never entered London, the London literary world, although she did present herself at least once to prove that she was in fact herself.


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[Assistant] She wasn't, in fact, her novels weren't written by somebody else. She continued to live on at Harworth, writing a string of successful works, Billette and Shirley, notably.


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[Assistant] She also gallantly got Wuthering Heights, her dead sister's masterpiece, out under a respectable imprint at last. George Smith's, her own publisher.


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[Assistant] In June 1854, Charlotte married Arthur Bell Nicholls, her father's curate. A few months later, at the age of 38, she became pregnant.


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[Assistant] Her health declined rapidly during this time, uh, and she and her unborn child died on March the 31st, 1855. Um, posterity will never know her, will never identify her as Charlotte Nicholls, but that's what she was when she died. Let's now turn to Jane Eyre.


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[Assistant] As has been said, the narrative presents itself as a recollection of her early life from childhood to marriage by the heroine.


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[Assistant] The narrative opens with a powerfully uncompromising straightforwardness. It grips the reader by the throat, I think. This is the opening of Jane Eyre.


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[Assistant] I was glad of it. I never liked long walks, especially on chilly afternoons. Dreadful to me was the coming home in the raw twilight with nipped fingers and toes.


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[Assistant] And it's already, she's a wilful little body. This as we apprehend as a woman who does not, as they say, mince her words. Don't you, don't you love that downright? I was glad of it.


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[Assistant] Little Jane, she's around 10 years old at this point, misbehaves as her unlovable guardians, her unfeeling reed relatives and their pampered offspring think.


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[Assistant] In fact, throughout life, in this opening scene it's very clear, little Jane is merely standing up for her rights. She fights back against her bullying cousin John Reed, an odious creature. And retribution from the Reed family, who, as I say, pamper little John,


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[Assistant] And they're not really very happy looking after this orphan, Jane. Their retribution is ruthless and immediate.


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[Assistant] Four hands were immediately laid upon me and I was born upstairs.


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[Assistant] Uhm, now the red room is where corpses are laid out when someone dies in the, in the Reed family. Uh, the bed is a cold one. Cold with death.


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[Assistant] The little girl does not take her medicine quietly. She's a rebel, a little mad woman. Remember that word mad, it's going to recur meaningfully in the novel.


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[Assistant] For shame, for shame, cried the lady's maid. What shocking conduct.


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[Assistant] And finally locked in the red room, Jane sees what she thinks is a ghost, screams and wakes the house. Now, all this prefigures what is to be the central theme of Jane Eyre, what's been memorably called the mad woman in the attic theme, the rebel woman theme, the let me out of here I'm going crazy theme. It's not just the read home which imprisons women,


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[Assistant] It considers to be out of line. It's a condition of womanhood in the 19th century.


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[Assistant] Needless to say, perhaps, to be so confined. And what this novel says is they must protest, they must fight back. And indeed the novel shows, shows us Jane doing just that.


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[Assistant] Well Jane, uhm, in the story, as were the Bronte sisters, is sent to a truly hellish boarding school. This is, this it's thought will tame the wildcat.


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[Assistant] One doesn't know whether that's what, uh, the Reverend Patrick Bronte had in mind when he sent his daughters to Lowood.


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[Assistant] Or the original of Lowood, that is Karen Bridge. Lowood is a school for sadists. This is the school that, uh, Jane is sent to. Uhm, and not just for sadists, but masochists as well because


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[Assistant] Jane Befrends, a very self-punitive Christian girl, who's also a pupil at Lowood called Helen Burns, uh, and before Helen dies of maltreatment, she instructs Jane in the necessity of stoical suffering. Women must suffer if they are to endure.


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[Assistant] Now, the following is a typical example that Jane recalls of the discomfort and the, as it were, chronic, the dangerous unhealthiness of low wood.


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[Assistant] During January, February and part of March, the deep snows and after they're melting.


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[Assistant] The almost impassable roads prevented our stirring beyond the garden walls except to go to church. But within these limits we had to pass an hour every day in the open air. Our clothing was insufficient to protect us from the severe cold. We had no boots. The snow got into our shoes and melted there. Our ungloved hands became numbed and covered with chillblains as were our feet. Of course, there are worse things than chillblains.


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[Assistant] Uhm, and such brutal conditions, Charlotte believed, were responsible, had been responsible for...


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[Assistant] For the death of two of her more delicate sisters, more delicate than herself.


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[Assistant] James' particular persecutor at the school is the tyrannic evangelical minister, the Reverend Brocklehurst. And he believes that all children are the offspring of Satan and must be disciplined into Christian virtue by physical suffering. Not his, he doesn't have much suffering in his own life, of course. He, he, he hands it out, but he, he doesn't inflict it on himself.


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[Assistant] Jane Brocklehurst believes is possessed by a demon, which must be exorcised by pain.


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[Assistant] Brocklehurst, that later emerges, has been embezzling the school funds to support his family's luxurious lifestyle.


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[Assistant] Uhm, and as a result of these depredations, the girls are malnourished and freezing, as she described, and prone to these dangerous illnesses. A typhus epidemic strikes, killing many of them, and the Reverend Brocklehurst is finally disgraced and removed, but not in time to save poor Helen Burns, Jane's friend.


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[Assistant] Miss Temple's gentler regime takes over, and as she passes through adolescence, Jane herself becomes a teacher.


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[Assistant] Now 18, Jane decides there's more to life than school teaching, and she applies for a position as governess at Thornfield Hall. It's a large gothic pile, with many strange and mysterious crannies, some of which she's instructed never to enter.


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[Assistant] At Thornfield, she's charged with the tuition of a young French girl, Adele, the illegitimate child, we assume, of the absent but much feared master of the house, Mr. Edward Rochester. Now Jane meets her employer in typically melodramatic circumstances. It's a good example of the energy which Charlotte can inject into a scene.


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[Assistant] The young governess is out walking, she does a lot of work, she's a very active woman, Jane, in the wild countryside around the mansion. An ominous black dog, a hound to rival that of the Vescavilles, almost bounds into her vision, and behind it she hears the sound of a galloping horse.


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[Assistant] The horse followed a tall steed and on its back a rider. He passed and I went on a few steps and I turned a sliding sound and an exclamation. What the deuce is to do now? And a clattering tumble. I'll cut a long, a long story short, uh, is Rochester. He comes galloping in, he falls off his horse. Uhm, that's quite important this moment because


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[Assistant] What happens, he breaks out into swearing, at least as Jane thinks it's swearing, she's not quite sure. But what happens is, at this first meeting, he comes in a kind of figure of manly strength.


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[Assistant] He falls and what does he need? He needs the help of a woman. He sprained his ankle. And it is Jane who must help him get back to Thornfield. It's a symbolic moment in the novel. A very powerful moment. But it's also in fact prefiguring. This novel is full of little patterns which will recur.


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[Assistant] Now, Rochester, it emerges, uh, is going to stay at Thornfield for a while. He's looking for a wife apparently.


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[Assistant] Rochester proposes, Jane accepts. Her happiness is complete. But, we note, it is only halfway through the novel.


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[Assistant] There are strange phenomena at Thornfield, screams, mysterious fires, and Jane's bridal veil is torn apart the night before the ceremony.


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[Assistant] The ceremony itself is interrupted at that moment in the service when it is asked if any member of the congregation knows any reason that these two should not be joined in holy matrimony. Yes, said a voice from the back of the church, Mr Rochester is already married. He's about to commit bigamy. The great secret is out.


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[Assistant] Rochester takes Jane back to the hall and up the stairs to the attic.


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[Assistant] There it emerges, he has confined the first Mrs. Rochester. She is mad. And it's, it's another red room.


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[Assistant] In the deep shade at the farther end of the room, a figure ran backwards and forwards. What it was, whether beast or human being, one could not at first sight tell. It groveled seemingly on all fours, it snatched and growled like some strange wild animal.


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[Assistant] And it is she in fact who came down the night before and tore up the bridal veil. She's been, as it were, running through this, this, this strange gothic mansion in which, in which Jane has found herself.


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[Assistant] Rochester then addresses the appalled watchers, including of course Jane, whom he's brought back with him from the church. I think that means the marriage was never consummated.


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[Assistant] Rochester then asked Jane to be his unmarried paramour, his mistress, and as was said earlier, her virtue would never permit such an arrangement. She runs away in a state of near breakdown, out of the house, away forever from Thornfield and happiness as she thinks. Well we of course know better. Jane Eyre was initially published


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[Assistant] It was initially published as a three volume novel and it's generally agreed that the last third of the narrative is slightly weaker than the other two.


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[Assistant] Not a let down, but not as gripping. By incredible coincidence, Jane collapses on the doorstep of an unknown relative, St. John Rivers, a clergyman and his sisters. They take her in, and she discovers that she's not after all an orphan, but an heiress, kept in ignorance by the villainous reeds.


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[Assistant] Sinjan Rivers falls in love with her and asks her to join him in his missionary work in India. She's tempted. She's a good man. But late one night, she hears an eerie voice calling to her. Jane! Jane! Jane!


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[Assistant] It was the voice of a human being, a known, loved, well-remembered voice, that of Edward Fairfax Rochester, and it spoke in pain and woe, wildly, eerily, urgently. I am coming, I cried, wait for me, oh, I will come.


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[Assistant] And come or go she does. Thorn fuel she discovers has burned down, arsonised by the mad birther.


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[Assistant] Whom I always tend to think he's killed has fallen to her death from the burning roof of the house. I think he pushes her off, but that's a speculation.


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[Assistant] Now widowed and tamed, Jane can accept his offer. Hence those immortal words. Reader, I married him. He's been to some extent made eligible by his mutilations. It's an archetypically romantic tale.


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[Assistant] But what remains in the mind, stirring our reflections after the excitement has died down.


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[Assistant] Uh, two images it seems to me. Little Jane locked and maddened in the red room. Mad birther locked and mad in the attic at Thornfield. What is Charlotte Bronte doing?


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[Assistant] More importantly, does she know she was doing it? Well, women readers particularly, and I think women respond to this novel better than men sometimes, women readers particularly have been astute in discerning that the real heroine of Jane Eyre is not just the narrator-governors, but that other woman.


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[Assistant] Jean Reiss, uhm, a 20th century novelist wrote a wonderful inverted novel on the subject called Wide Sargasso Theatre. Came out in 1966. Telling Jane Eyre from Bertha's point of view, in, in, in,


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[Assistant] In that novel, to some extent, we change perspective and it's nice to think that Charlotte Bronte would have approved of that.


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[Assistant] Jane Eyre has survived, the novel Jane Eyre has survived and triumphed for a century.


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[Assistant] And a half, 150 years, not merely because it's a rattling good melodrama, but because it is


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[Assistant] The great novel of womanhood, I would suggest. One that is both sympathetic to and critical of the age and society which gave at birth, and one would like to think, as novels could do at this time, actually made that society a better place for the women of the time.


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[Assistant] Shinra knows we're here now. Might be more of them outside.


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[Assistant] Right. Let's get back to tailing the guys in robes. They're our best chance of finding Sephiroth.


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[Assistant] Hate to break it to you, but pretty sure that guy's better off than he looks.


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[Assistant] Who's in there with you? Oh.


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[Assistant] Not really. But I'm happy to listen, so go ahead.


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[Assistant] It's fine. We'll find time to talk. Just the two of us. Figure things out.


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[Assistant] Hanging out in the trees of Central and South America are some frogs with pretty unusual coloration. Which is to say, parts of them have no color at all. Their bellies are completely see-through, thanks to a combination of thin skin and a total lack of pigment-bearing cells. You can see everything, from their guts to their beating hearts. These frogs are known as glass frogs.


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[Assistant] And even though their bare-all bellies look like the perfect buffet preview for predators,


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[Assistant] Their translucency may actually be an interesting form of camouflage. There are about 150 species of glass frogs in the family Centrilenidae. All of them lack pigment on their bellies, and about a quarter of them are properly see-through. Their backs are a more familiar hue.


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[Assistant] They saw that the perceived brightness of a frog's green back changes depending on how much light bounces off the leaf the frog is sitting on. The leaf color essentially shines through the frog's translucent underside,


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[Assistant] And because some of the translucent parts are visible from above, it literally blends their edges into the background


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[Assistant] Making it tricky for a predator to see a nice, clear, froggy outline. It's like the frogs are using the blend and blur tools in Photoshop.


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[Assistant] The researchers dubbed this camouflage technique edge diffusion. And in their study, the froggy camouflage seemed to fool both people and wild animals. The researchers created a Where's Waldo-style experiment, where they randomly hid images of frogs with different patterns and degrees of see-throughness on a leafy background.


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[Assistant] They also made frogs out of gelatin that were either opaque or see-through. And they plonked them down on leaves in the frog's natural habitat to see which ones would be picked off by predators the quickest. And the opaque frogs became gummy snacks quicker and more often than the clear ones. Scientists have thought for a while that these bare bellies might help the frogs camouflage themselves.


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[Assistant] Even when it means putting everything on display. Thank you for watching this episode of SciShow, which, in the interests of transparency, we have to tell you, was supported by our patrons. Patrons get access to fun perks like bloopers and fancy facts as thanks for helping us make videos. If you'd like to get involved, check out patreon.com slash SciShow.


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[Assistant] Hey, if it isn't the Heroes of the Hour, I heard about what you did for that girl. Thank you so much.


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[Assistant] Your stay is on us. We insist. It's the least we can do for you, really. Now then, how many we got? Will four rooms be enough?


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[Assistant] Could you make it, Five? Five it is! Oh, everything is comped. So if you need anything at all, just ask.


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[Assistant] That's nice to have the place booked up again for once. Gosh, when was the last time that happened?


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[Assistant] And that story is filled with chapters that have made us who we are today.


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[Assistant] Those early chapters of that story sometimes are the ones that define us the most. The Center for Disease Control


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[Assistant] That adversity can have lasting effects.


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[Assistant] When I began to have opportunities to speak and advocate for students and for teachers,


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[Assistant] I found myself uniquely positioned to be able to speak about childhood trauma. But I had to make a decision first. I had to decide


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[Assistant] Did I want to just share the bright and shiny parts of my life? You know, those ones that we put out on social media that makes us all look perfect? Or ...


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[Assistant] Did I want to make myself vulnerable and become an open book? The choice became very clear.


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[Assistant] In order to make a difference in the life of a child, I had to become transparent.


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[Assistant] So I made the commitment to tell my personal story.


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[Assistant] And this story is filled with people that have loved me and taken care of me and grown me and have helped me overcome and heal. And now it's time for me to help others do the same.


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[Assistant] When I first started school, I was the picture of normalcy.


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[Assistant] I was from a good family. I was always dressed nicely, had a smile on my face. I was prepared for school. But my life was anything but normal.


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[Assistant] By this time, I had already become a victim of sexual abuse. And it was still happening. My parents didn't know, and I had not told anyone else.


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[Assistant] When I started school, I felt like this was going to be my safe place, so I was excited. Imagine my dismay when I met my teacher, Mr. Randolph. Now, Mr. Randolph was not my abuser, but Mr. Randolph


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[Assistant] I had already started these self-preservation techniques to where I took myself out of positions where I was going to be alone with a man.


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[Assistant] And here I was, as a student.


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[Assistant] I was going to be in a classroom with a man every day for a year of school. I was scared. I didn't trust him.


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[Assistant] But you know what? Mr. Randolph would turn out to be my greatest advocate.


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[Assistant] But in the beginning, oh, I made sure he knew I did not like him. I was noncompliant. I was that kid that was disengaged.


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[Assistant] And I also made it really hard on my parents, too.


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[Assistant] I didn't want to go to school, so I fought them every morning getting on the bus.


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[Assistant] At night, I couldn't sleep because my anxiety was so high. So I was going into class exhausted.


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[Assistant] Which exhausted children are cranky children, and they're not easy to teach. You know that. Mr. Randolph could have


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[Assistant] Approach me with frustration, like so many teachers do with students like me, but not him.


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[Assistant] He approached me with empathy and with flexibility. I was so grateful for that.


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[Assistant] He saw the six-year-old was tired and weary.


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[Assistant] Instead of sitting at the teacher table, at lunch he would come and sit with the students at the student table.


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[Assistant] He would engage me and all of my classmates in conversation.


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[Assistant] And I now look back and I know he had a purpose for that. He was listening. He was asking questions. He needed to find out what was going on. He built a relationship with me. He earned my trust.


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[Assistant] And slowly but surely, those walls that I had built around myself, he started chipping away at. And I eventually realized he was one of the good guys.


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[Assistant] And got my mom's permission to let me start seeing the school guidance counselor. Miss McFadden.


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[Assistant] I started seeing Ms. McFadden once or twice a week for the next two years. It was a process.


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[Assistant] But she connected the dots, I know she did, because everything that she did with me,


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[Assistant] Was to empower me and help me find my voice.


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[Assistant] She taught me how to use mental images to push through my fears. She taught me breathing techniques to help me get through those anxiety attacks that I would have so often. And she role-played with me.


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[Assistant] And she made sure that I could stand up for myself in situations. And the day came,


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[Assistant] Where I was in a room with my abuser and one other adult, and I told my truth. I told about the abuse. Immediately, my abuser began to deny, and the person that is close to


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[Assistant] They just weren't equipped to handle the bombshell that I had just dropped on them. It was easier to believe the abuser rather than a child. So I was told never to speak of it again.


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[Assistant] I was made to feel like I had done something wrong. Again.


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[Assistant] But you know what, something good came out of that day. My abuser knew that I was no longer going to be silent.


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[Assistant] But you know what? There are so many kids that aren't as fortunate as me. And you have them in your classrooms.


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[Assistant] And you can start asking the questions that need to be asked and paying attention to these students.


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[Assistant] So you too can help them find their way. As a kindergarten teacher,


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[Assistant] I start my year off with my kids making box biographies. These are two of my students.


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[Assistant] And I encourage them to fill those boxes with things that tell me about them and about their life. What's important to you?


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[Assistant] And during that time, I'm an active listener.


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[Assistant] Because the things they say, the facial expressions that they give me, the things they don't say can become red flags for me.


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[Assistant] And can help me figure out what their needs are. What is driving them?


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[Assistant] How can I be a better teacher? By listening to their voices.


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[Assistant] I also make times to develop relationships with them, much like Mr. Randolph did with me. I sit with them at lunch. I have conversations with them at recess. I go to their games on the weekends. I go to their dance recitals. I become a part of their life.


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[Assistant] Because in order to really know a student, you gotta infuse yourself into their lives.


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[Assistant] Now, I know some of you are middle school teachers and high school teachers, and you might think that those kids have already kind of developed and, you know, they're on autopilot at that point.


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[Assistant] But don't be deceived. Especially the kids that you think have it all together, because those are the ones that might need you the most.


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[Assistant] If you were to look at my yearbook, you would see me on about every page, because I was involved in everything. I even drove a school bus.


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[Assistant] So I was that kid that teachers thought was the overachiever, the popular person, the one that had it together. But guys, I was lost.


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[Assistant] Was I running away from someone? Was I running away from something? Why did I not want to be


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[Assistant] Now don't get me wrong, all overachievers in your schools are not victims of abuse or trauma, but I just want you to take the time to be curious. Ask them why.


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[Assistant] You may find out that there is a reason behind it. You could be the reason that they