[User] Please transcribe this text

[Assistant] We are unable to view around 20 to 30 degrees. Hence, we are not able to see the table when our one eye was closed.


[User] Please transcribe this text

[Assistant] Hey, did you know that our eyes see the same object from a slightly different angle? You don't believe me? Alright, look at this object.


[User] Please transcribe this text

[Assistant] Both your eyes see the object like this. Now, when you see only with your left eye, the object will look like this, while when you see only with your right eye, the object will look like this.


[User] Please transcribe this text

[Assistant] This means having two eyes enables us to judge the distance of the object or the depth at which the object is placed from us.


[User] Please transcribe this text

[Assistant] Or I'll recite the tight headband spell.


[User] Please transcribe this text

[Assistant] Please carry the boy, and don't be mean to him.


[User] Please transcribe this text

[Assistant] Who cooked the spring onion pancake and pork? How's me? Larissa, an absolutely delicious dish, worthy of one of those white Asians.


[User] Please transcribe this text

[Assistant] You never really know what's going to happen next in The MasterChef Kitchen.


[User] Please transcribe this text

[Assistant] So this year, not two, but three of you will get the chance to become.


[User] Please transcribe this text

[Assistant] Our MasterChef for 2019.


[User] Please transcribe this text

[Assistant] Normally, in the semi-final, we get you to cook for a restaurant full of diners in a service challenge. Not this year. This year, the semi-final is a pressure test.


[User] Please transcribe this text

[Assistant] Sensational, not lots of different components.


[User] Please transcribe this text

[Assistant] But, there's 40 steps, and within 15 minutes you need to be at step 10.


[User] Please transcribe this text

[Assistant] You've had 15 minutes, that means in 5 minutes time, you need to have your moose in the blast chiller. Guys, 1 hour and 45 minutes to go! Come on!


[User] Please transcribe this text

[Assistant] Now it's that last little bit where they get 15 minutes to work some magic to get it on the plate.


[User] Please transcribe this text

[Assistant] You know what, we're just, we're seriously proud of you, okay?


[User] Please transcribe this text

[Assistant] So who's going home today? I don't know, what do you think?


[User] Please transcribe this text

[Assistant] The coral is the centrepiece of the dish.


[User] Please transcribe this text

[Assistant] And today, one of your corals wasn't good enough. And that's why it's time to say goodbye.


[User] Please transcribe this text

[Assistant] Oh mate. You don't understand how much love there is in all of our hearts for you.


[User] Please transcribe this text

[Assistant] It's just a pleasure to have around the boy from Ballarat.


[User] Please transcribe this text

[Assistant] And mark our words. You are gonna be a superstar.


[User] Please transcribe this text

[Assistant] The other important thing is that this coral is shaped really beautifully. It's gotta look organic, it's gotta look like a piece of coral. That it needs to be served at the last moment. So if you tap it with a spoon...


[User] Please transcribe this text

[Assistant] It's good. Well, that's good. So you have some prune jam and chocolate ganache and also cream, then the prune ice cream.


[User] Please transcribe this text

[Assistant] The ice cream is ridiculous. The liquid white chocolate mousse, and then you put the coral on.


[User] Please transcribe this text

[Assistant] Oh, that coral just melts in your mouth. It's gorgeous. Beautiful. There is quite a few steps there.


[User] Please transcribe this text

[Assistant] What happened was that it was not cold enough when you started whisking it?


[User] Please transcribe this text

[Assistant] Right, you know that it's got eggs in it and cream.


[User] Please transcribe this text

[Assistant] Yeah, yeah. You know, I'll be really interested to see if this actually works for you.


[User] Please transcribe this text

[Assistant] So did you redo the caramel? Yeah, this is my, this is my new one. Okay. Was it really cold when you started whisking? Um, yeah, I've got it in the ice bath. Is the mix cold?


[User] Please transcribe this text

[Assistant] We good, we got everything done. Hey guys, guys, come around. Well done. I'm super impressed. Look, I hope the actual constructing goes well for you. You should be very proud of yourself. I'll see you in the tasting room, okay?


[User] Please transcribe this text

[Assistant] You know, in their preparation, they all did very well. They all got it done. But it's just the little nuances of how well did they make the mousse? Did they make the ice cream right? Did they get that caramel bang on? Yes. You know, and they're the things that are going to separate them out.


[User] Please transcribe this text

[Assistant] Absolutely. I think if they take the lids off and the corals don't fall, they're halfway there.


[User] Please transcribe this text

[Assistant] And how are they going to shape it? Is it going to look like there's a coral or is it going to be a square block on top?


[User] Please transcribe this text

[Assistant] It's that little bit of theater, a little bit of wow factor. It's great.


[User] Please transcribe this text

[Assistant] No, it was really impressive, like, you know, from the moment, the concentration on your face, you could see it. You did really well. Thanks, Peter. That means a lot.


[User] Please transcribe this text

[Assistant] I mean, there's a couple little technical things, but overall, it's not bad.


[User] Please transcribe this text

[Assistant] Look, generally I think the corals look quite good. I mean, they're really nicely shaped. Quite organic looking. Maybe a little dense to get through. Yeah. But, gee, a good effort. Yeah.


[User] Please transcribe this text

[Assistant] Yeah, the ice cream is very good. Overall, it's delicious. I think they will follow the recipe really, really well.


[User] Please transcribe this text

[Assistant] The flavour is fantastic. It's so funny, she looked like she was the least in control today, but she is absolutely nailed it.


[User] Please transcribe this text

[Assistant] Every year I get blown away by the standard, it seems to keep going up and up. Well done.


[User] Please transcribe this text

[Assistant] It's going to be tough, but they're gonna have to cook for their lives.


[User] Please transcribe this text

[Assistant] Let's travel back in time, way back to the 1830s when even Abraham Lincoln was still a young chap.


[User] Please transcribe this text

[Assistant] So it was in 1833 that that phenomenon of phenomenons, Karl Friedrich Gauss, first demonstrated the electrical telegraph for communicating electrically over long distances.


[User] Please transcribe this text

[Assistant] And around that same time, Samuel Morse and his collaborator Alfred Vale were also working on Telegraph, so they hadn't


[User] Please transcribe this text

[Assistant] They didn't quite beat Gauss to the punch, but Morse had been interested in developing


[User] Please transcribe this text

[Assistant] Developing telegraph technology since 1825. Actually, Morris, it's maybe a little known fact that he was actually an accomplished painter up until that time. That was his main profession. And in 1825, he was in Washington and he was doing a painting, but his home was in Connecticut.


[User] Please transcribe this text

[Assistant] And he got a letter in the mail, it was a tragic event, he got a letter in the mail stating that his wife was deathly ill.


[User] Please transcribe this text

[Assistant] He rushed home, but the letter had come, you know, by horseback. So it took several days to get there. But by the time he got home, tragically, his wife had died and he was, he was just devastated by this and he decided to spend the rest of his life developing electrical telegraph technology so they could have fast communications.


[User] Please transcribe this text

[Assistant] So Morse was very interested in this, and so they eventually, along with the help of some others, Morse and Vale, eventually got their Telegraph machine working, and Morse gets largely the credit for it in the United States.


[User] Please transcribe this text

[Assistant] But their real lasting legacy is the Morse code. So Vale and Morse both work together on developing the Morse code, the famous Morse code, which is still in use today, actually, in certain applications.


[User] Please transcribe this text

[Assistant] And so you're familiar with the Morse code, I'm sure. And they, they developed Morse code in order to be able to transmit text messages over the telegraph.


[User] Please transcribe this text

[Assistant] And so you can see here, as I'm sure you are well aware, in Morse code, each letter or numeral has, it corresponds to a sequence of these dots and dashes. So we call this sequence of dots and dashes the code word corresponding to that letter.


[User] Please transcribe this text

[Assistant] And this, so this Morse code is actually an example of a symbol code. That's what we're going to talk about. Symbol codes, or sometimes they're called variable length codes, because each of these words


[User] Please transcribe this text

[Assistant] Sample you can see in this example. Each of these code words has a different length.


[User] Please transcribe this text

[Assistant] Now you could think of these each as, you know, you could think of them in a couple different ways. You could think of these as being a sequence of dots and dashes, or you could alternatively think of them as being sequences of zeros and ones. Like this would be like one zero one one one.


[User] Please transcribe this text

[Assistant] One, one, one, zero, one, zero, one, zero, one and so on. So each dash has three ones, length of three ones.


[User] Please transcribe this text

[Assistant] And in Morse code, there's a space between each letter of, of three, uh, the, the, the length of three dots. So it would be like 000 before you start the next letter.


[User] Please transcribe this text

[Assistant] And between words, it's like seven, uh, spaces, seven zeros.


[User] Please transcribe this text

[Assistant] So you can think of Morse code as actually a binary, as a, as a symbol code where each letter goes to or numeral goes to a binary code word.


[User] Please transcribe this text

[Assistant] Now, note, and by the way, this picture here, this is the key, they call it the key, to key in the sequence of dots and dashes or dits and dots as they say. And this of course is Morse code in Morse code. Very nice.


[User] Please transcribe this text

[Assistant] Okay, so now you will notice, as I mentioned, I called it a variable length code, and you will notice, as we, as we noticed earlier, that each of these code words has a different length.


[User] Please transcribe this text

[Assistant] And in fact, Vail, Alfred Vail, this dude here, looking very dapper, he


[User] Please transcribe this text

[Assistant] Chose the, the lengths of the code words so that


[User] Please transcribe this text

[Assistant] More frequent letters would have shorter code words.


[User] Please transcribe this text

[Assistant] Right, because, you know, if you have a very frequently occurring letter, like E for example, this shows up very frequently in the English language, then you want to have a short code word for that letter because you're going to use it a whole lot and you want your, your messages to be rather short on average.


[User] Please transcribe this text

[Assistant] So he actually looked at the frequency at which different letters occur in English. He tried to estimate their frequencies.


[User] Please transcribe this text

[Assistant] And then he chose these, these code words. Maybe, you know, he and Morris together, it's disputed who exactly chose them, but, but they chose these code words so that roughly that the shorter code words would be for more frequent letters. Now, of course you can't have


[User] Please transcribe this text

[Assistant] You know, not every letter can have a short code word. That's fairly obvious, right? Because there's only so many short code words to go around. So inevitably, some of the letters are going to have to have longer code words.


[User] Please transcribe this text

[Assistant] And like, for example, Q, you know, Q has a long one here. Q is a very infrequently occurring letter in the English language. So you may as well stick it with a long code.


[User] Please transcribe this text

[Assistant] So another way to describe what Bale was aiming for by, by, by doing that was that he was trying to compress those messages. He was trying to take English and, and represent it in these sequences of dots and dashes in a way that was efficient as possible, that was as compressed as possible.


[User] Please transcribe this text

[Assistant] So he was doing compression when he did this. And so these symbol codes, these variable length codes are one way to do lossless compression.


[User] Please transcribe this text

[Assistant] And whether Vail knew it or not, he was actually implicitly modeling the English language using a very simple probabilistic model. And the model he was using was that each letter


[User] Please transcribe this text

[Assistant] is chosen identically, is chosen independently and identically distributed according to its probability.


[User] Please transcribe this text

[Assistant] And this is what we refer to as a discrete memoryless source. So we now have some terminology that we need to


[User] Please transcribe this text

[Assistant] We need to say what that all means, so we have some terminology to define here.


[User] Please transcribe this text

[Assistant] So a source, I'll put it here maybe. Ah, we'll go down here. Source. What is a source?


[User] Please transcribe this text

[Assistant] That's all we mean by a source. You know, uh, it's just a terminology that we use in this context when we're thinking of these random variables as sort of emitting a sequence of symbols.


[User] Please transcribe this text

[Assistant] So I said this is a discrete memoryless source. What is memoryless? Memoryless in this context just means IID. In other words, these, these sequence of symbols, these sequence of random variables are independent and identically distributed. That's what we mean by IID.


[User] Please transcribe this text

[Assistant] And so what is a discrete memoryless source? Discrete memoryless source. Discrete memoryless source. What is that?


[User] Please transcribe this text

[Assistant] That is just, of course, we might write DMS to abbreviate. That's a sequence of random variables, x1 to xn, that are all taking values in some common set, which I'll denote by this script x with a line through it. And their iid,


[User] Please transcribe this text

[Assistant] So this is, this is the source part, and then the iid, that's the memoryless part. Maybe I'll put iid here. iid. And...


[User] Please transcribe this text

[Assistant] The discrete part is that this set, is that each of them is a discrete random variable. Or in other words, this set is countable.


[User] Please transcribe this text

[Assistant] A finite set, or it's countably infinite, so it can be put into bijection with the natural numbers.


[User] Please transcribe this text

[Assistant] So that is a discrete memory list source. That's all we mean when we say that. So another


[User] Please transcribe this text

[Assistant] Sort of a way that I may use the word source is that I might occasionally just write x.


[User] Please transcribe this text

[Assistant] You know, x in some taking values in some set here, where x is some random variable. I may refer to this as a source.


[User] Please transcribe this text

[Assistant] And if I do that, I just mean take a sequence of random variables that all have the same distribution as that guy and make them IID.


[User] Please transcribe this text

[Assistant] So that would be, if I refer to this x as being a discrete memoryless source just on its own. So that's a little remark.


[User] Please transcribe this text

[Assistant] Now, another piece of terminology that we will need. That's sort of the basics. An alphabet. What is an alphabet?


[User] Please transcribe this text

[Assistant] Well of course you know the usual alphabet, but this is going to be a slightly different definition of alphabet. We're going to generalize our notion, our usual notion of the alphabet, to just be some set of items, some set of elements, and then we're going to think about stringing those together into sequences of symbols or elements.


[User] Please transcribe this text

[Assistant] So, so this is just some set of elements. It's really just some arbitrary set of elements. Typically it's going to be a finite set. Almost always it's going to be, well either countable or a finite set. And we're going to be using


[User] Please transcribe this text

[Assistant] Two particular, we're gonna be using, usually we're gonna have two different alphabets flying around. We're gonna have a source alphabet.


[User] Please transcribe this text

[Assistant] Source alphabet, and I will often denote this


[User] Please transcribe this text

[Assistant] By this capital script x, and that's gonna be the same x as up here. This is going to be the alphabet, this is going to be the set of elements that the random variables are taking values in. Each of these, these, these random variables in our sequence here, that's our source. And then we're also going to have a code alphabet.


[User] Please transcribe this text

[Assistant] And I'll probably, fairly consistently, denote this by this script A.


[User] Please transcribe this text

[Assistant] So for example, the source alphabet, like you think about in Morse code here, the source alphabet would be all the letters, or rather, yeaah, so all the letters a through z, and all the numerals 0, 1, 2, 3, up to 9. So that would be the source alphabet, the set of all those, and the code alphabet,


[User] Please transcribe this text

[Assistant] Well, depending on your perspective, I think, I think that a good way to think about Morse code is as a sequence of zeros and ones. So there'd be like one, zero, one, one, one, zero, zero, zero, and so on. And so in that case, if you think about it that way, the source, rather the code alphabet would be zero and one.


[User] Please transcribe this text

[Assistant] So it's going to be, we're going to have sequences. We're going to string together these, these, these elements of this alphabet to get our code words.


[User] Please transcribe this text

[Assistant] But you can really have any, I mean this could be, you know, 0, 1, and 2, or 0, 1, 2, 3, and 4, or it could be, you know, these letters, these alphanumeric symbols, it could be, you know, just some, some, some set here.


[User] Please transcribe this text

[Assistant] And another piece of notation that we're going to find useful is


[User] Please transcribe this text

[Assistant] We take an alphabet and we write that to the asterisk, that to the star. So A star, what is that? That we're going to use to denote all the sequences, all the finite length sequences of elements of A.


[User] Please transcribe this text

[Assistant] So for example here, these, that would be like all the, all the possible code words that you could get. So this would be, how should I write this? This would be like a one, a two, a N.


[User] Please transcribe this text

[Assistant] Where, maybe I'll use k and using n for something else above. Where k is some


[User] Please transcribe this text

[Assistant] Some integer greater or equal to zero and all of the a's are in this alphabet a. So that's for all i.


[User] Please transcribe this text

[Assistant] And now, note I'm using concatenation here. I could, I could equally have, equally well have written, you know, this as a, as a little tuple here, a sequence. But I'm gonna use concatenation because that's sort of the, that's the, the standard thing that people do when they're talking about


[User] Please transcribe this text

[Assistant] Alphabets and code words and, and strings and things like that. So this is a, this is a string of letters, so to speak, from this alphabet. They're not always letters, but, you know, we could think about them as, as sort of letters in some sense.


[User] Please transcribe this text

[Assistant] Uh, by the way, if you are a computer scientist, this star is called the Clean Star, after Stephen Clean. Clean Star.


[User] Please transcribe this text

[Assistant] Sounds like a laundry service. So uhm, anyway, so this is some basic, some basic terminology and notation that we'll use and next we will define a symbol code or a variable length code and we'll look at some examples of symbol codes.


[User] Please transcribe this text

[Assistant] I did really well in the Miss Special Advantage Challenge. Any advantage at this stage is so important.


[User] Please transcribe this text

[Assistant] Thought I'm doing like a slice sort of idea, but adding sort of Greek flavours in there, like adding ouzo. As a kid, I used to always have this popsicle that used to have lemon sorbet and vanilla ice cream. It's gonna be creme fraiche sorbet.


[User] Please transcribe this text

[Assistant] Yeah. Yeah. I've got an added bit of pressure. There's no excuse to fail today.


[User] Please transcribe this text

[Assistant] I'm going to make a beautiful creme fraiche sorbet. I start off by making a sugar syrup.


[User] Please transcribe this text

[Assistant] I whisk together some crème fraîche and some lemon zest. Larissa, keep clean, yeah? Yep. And you need to hurry up. Yeah, mate. George is in the kitchen with us today. Keep wiping down! Yeah, mate. That is absolutely amazing and terrifying at the same time.


[User] Please transcribe this text

[Assistant] I've got my crème fraîche sorbet chilling in the fridge, and now it's time to get onto my lemon granita. My dish is all about that lemon. God, it's hurting my hand. Come on. I've gotta make sure I've got a lot of this granita.


[User] Please transcribe this text

[Assistant] I'm juicing so many lemons. I'm just going through boxes of lemons and it's just killing my arm right now.


[User] Please transcribe this text

[Assistant] The amount of body strength you need is just ridiculous.


[User] Please transcribe this text

[Assistant] Behind you guys. My dish is a lemon granita with a creme fraiche sorbet, a cucumber and ouzo tea, deep bracket tapie pastry.


[User] Please transcribe this text

[Assistant] I'm using cucumbers because I want to add a savoury element to my dish. Right now I'm just making my cucumber and my ouzo tea.


[User] Please transcribe this text

[Assistant] I'm loving this flavour combination. This dish could mean that I could either go straight through to semi-finals or straight through to elimination and I definitely want to make it to semi-finals.


[User] Please transcribe this text

[Assistant] How long, Larry? So this is just around the corner.


[User] Please transcribe this text

[Assistant] The dish is coming together really nicely. The katafi pastry I'm gonna, uhm, deep fry just to add a bit of crunch. So I'm gonna submerge that first into the clarified butter. Start melting some butter for my katafi pastry. And while I do that, I need to churn my sorbet.


[User] Please transcribe this text

[Assistant] Today we're top 5. Gotta really amp it up. And so now I'm using liquid nitrogen. It just means the ice cream will be a lot smoother because there's less ice crystals.


[User] Please transcribe this text

[Assistant] I want to add some fresh cucumber to my dish, so I dice up those cucumbers and submerge that into some of that cucumber and ouzo tea that I've made earlier. And now it's time to plate up.


[User] Please transcribe this text

[Assistant] I'm putting the cucumbers at the base of the dish, a quenelle of that beautiful crème fraîche sorbet on top of that.


[User] Please transcribe this text

[Assistant] I feel so proud of myself because George is happy with my dish.


[User] Please transcribe this text

[Assistant] You know, to do a dish that is worthy enough to be served at the press club is amazing. Service please. I didn't think I'd be capable of doing that.


[User] Please transcribe this text

[Assistant] I've made to semi-final! I didn't think in a million years that I would make it this far in this competition. And it's just weird saying the words out loud, but I'm really, really proud.


[User] Please transcribe this text

[Assistant] Now we'll look at a problem that's related to sorting called selection that's also well solved by quicksort partitioning.


[User] Please transcribe this text

[Assistant] This is a simpler problem. We're given an array of n items that are ordered, and our task is to find the kth largest. Uh, there's lots of important applications for this. So, like if we wanted to find the minimum item, that's k equals 0, or the maximum item, that's k equals n minus 1, or the median, that's k equals n over 2.


[User] Please transcribe this text

[Assistant] Uh, and there's many kinds of applications when people processing data want to find the top K or the medium or other order statistics. So that's what selection is all about.


[User] Please transcribe this text

[Assistant] Now, here's an example where we want to use theory as a guide. What kind of efficiency might we expect in a selection algorithm?


[User] Please transcribe this text

[Assistant] Well first of all it's easy to see that we can solve selection in n log n time. How would we do that? Well we just sort the array and then if we want to find the smallest you look in the first position or the largest you look in the last position or the median you look in the middle.


[User] Please transcribe this text

[Assistant] Uh, because if you're looking for the smallest, you can just go through the array and find the smallest in one pass through. Or for two, you find it in two passes through. Uh, so you can imagine trying to look for a selection algorithm that takes time proportional to n.


[User] Please transcribe this text

[Assistant] Uh, and also the lower bound is N because you have to look at everything. If you don't look at everything, you might miss, uh, the one item that you're looking for.


[User] Please transcribe this text

[Assistant] Uh, but at this point, uh, the question is, uh, is there a linear time algorithm that works for every k? Or possibly selection is as hard as sorting.


[User] Please transcribe this text

[Assistant] This kind of question, uh, plagued a lot of people, uh, in the late 60s, early 70s as these types of problems, uh, emerged for computing applications. So it's an interesting question to think about for sure.


[User] Please transcribe this text

[Assistant] Well, uh, in his original paper in, uh, 1961, uh, Hoare gave a solution to the selection problem based on partitioning.


[User] Please transcribe this text

[Assistant] We're going to do our partitioning so that we get entry A of J in place in the array. Nobody to the left is larger, nobody to the right is bigger.


[User] Please transcribe this text

[Assistant] But then when we're doing selection, what we'll do is just go in one sub-array or the other depending on where j is. If j is equal to k, we're done. We found the kth largest.


[User] Please transcribe this text

[Assistant] If k is, uh, to the left of j, then we just do the left sub file. We just set high to j minus one.


[User] Please transcribe this text

[Assistant] Uh, and if k is to the right of j, we just do the right subfile, set low to j plus 1, and that's all this code does, is that you could do it with a recursive call, but this just does it by resetting the values of the parameters.


[User] Please transcribe this text

[Assistant] Do one partition, then check whether your kth element is going to be in the left part or the right part. Uh, reset lower high accordingly. If it's equal, then you found it, uh, and you return it, and you keep going, uh, until, uh, you get to a point where you have only one element.


[User] Please transcribe this text

[Assistant] That's the, uh, a quick sort, uh, like implementation, uh, solving the selection problem. Notice again that it depends on the random shuffle at the beginning. That's going to be important for performance.


[User] Please transcribe this text

[Assistant] We won't give the full proof. It's actually quite a bit more complicated than the one just done for quicksort. But intuitively, we can see kind of what happens. Each partitioning step maybe splits the array approximately in half.


[User] Please transcribe this text

[Assistant] So that, that means you'd have, if it did exactly in half, you'd have n plus n over 2 plus n over 4, uh, and so forth, which adds up to about 2n compares, so linear cost.


[User] Please transcribe this text

[Assistant] If you do the, it actually doesn't cut it in half exactly each time, only on average. So you need a fuller analysis like the one we did for quicksort.


[User] Please transcribe this text

[Assistant] And the bottom line of that analysis gives the number of comparisons required as a function of n and of k in terms of this formula here.


[User] Please transcribe this text

[Assistant] K equals n over 2, you get the result that the number of compares required to find the median, and that's the highest value this formula can take, is 2 plus 2 natural log of 2. So linear time to find the kth largest for any value of k.


[User] Please transcribe this text

[Assistant] Uh, now again, it's gonna use, this is a method that's linear time on the average. It's actually gonna be quadratic in the worst case. But again, the chance that that'll happen with a random shuffle is less than the chance that we'll be struck by lightning. Uh, it's a probabilistic guaranteed fast algorithm.


[User] Please transcribe this text

[Assistant] Now from a theoretical standpoint, that's a little unsatisfied, and in 1973 there's a famous paper that found a compare based selection algorithm that guarantees to solve the problem in linear time.


[User] Please transcribe this text

[Assistant] This was a real landmark in the theory of algorithms, uh, because, uh, for a long time it was not known. We knew we could have the average case be linear time, but could we find a worse case? And this paper found such a construction.


[User] Please transcribe this text

[Assistant] Now in practice, uh, this construction is, uh, is rather high. Uh, so the, the method's not really used in practice. And so there is still the goal of a, uh, a fast guaranteed linear time selection algorithm that maybe somebody in this class, uh, uh, will invent someday.


[User] Please transcribe this text

[Assistant] This is another example where we use theory as a guide. It's still worthwhile to look for a practical linear time worst case algorithm. Maybe somebody in this class will invent that.


[User] Please transcribe this text

[Assistant] But until something like that is discovered, use the quick select based on quick sort partitioning and you can get linear time selection when you don't need a full sort.


[User] Please transcribe this text

[Assistant] That's selection, a simple problem like sorting that is well solved with quick sort partitioning.


[User] Please transcribe this text

[Assistant] That is spectacular. I'm speechless.


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[Assistant] As they fight to stay in the competition. Who will impress the judges enough to stay?


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[Assistant] I'm doing a flash-fried prawn in vermicelli noodles. It's delicious. Could take all of my willpower not to eat it before I plate it.


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[Assistant] Oven baked fish with a tahini sauce and tabbouleh.


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[Assistant] Wow! Wow wow wow, isn't it? Welcome to the Melbourne Cricket Ground, the MCG. And just pointing out MasterChef on the big screens. And all we were missing there was the roar of 97, 98,000 people.


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[Assistant] There's no better location for your very first team challenge.


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[Assistant] Today, you're going to be cooking dinner for the players, coaches and staff of the Melbourne Football Club.


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[Assistant] Each team is going to prepare two canapes, a main course and a dessert for a hundred guests. You've got three hours to prep before service starts.


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[Assistant] And remember who you are cooking for. Athletes at the top of their game. Everything's gotta be delicious and nutritious in sure-footed MasterChef style. And remember...


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[Assistant] What's at stake? The losing team, the whole team goes into tomorrow's elimination. You know what happens from there. One person goes home.


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[Assistant] Out of the craziness of the kitchen, into the calm of the dining room. Puts it in perspective, doesn't it? Little bit, little bit. Right? Get back in there and get these canapes ready. Go.


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[Assistant] Right, listen up, blue team, red team, we're going out to the table. Panoply's have gotta go now. Good luck. Good luck.


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[Assistant] They are so good. Look how fine they are. They're absolutely perfect. Beautifully.


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[Assistant] Desserts, you're starting to run out of time. Let's move it.


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[Assistant] What happened? Does the other one look really beautiful and imbalanced? But this one's really messy.


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[Assistant] Right, let's get into it. Red team, we love the sopes, those little tostadas. Lots of texture, lots of flavour.


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[Assistant] And the lamb rack was absolutely beautifully cooked. And that salad was full of flavour and texture. Couldn't have done any better.


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[Assistant] And your dessert, the presentation was clumsy and that quinoa was chewy and got stuck in our teeth.


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[Assistant] It's clock is ticking and I'm watching the red team already. The production line has already started.


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[Assistant] Guys, we need to make decisions or else we're gonna be in trouble.


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[Assistant] Yeah, thank you. You have to trust the Loki.


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[Assistant] Uh, pretty ready. Pretty ready. I want to deliver the best food that I've cooked so far.


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[Assistant] So, that's where my mind's at. You gonna deliver it? Oh god, yes. Absolutely. So excited.


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[Assistant] Simon. Yeah, I got my mother Therese, my dad Justin. Yeah.


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[Assistant] I'm feeling really good right now, but I know I'm very much under the pump. Come on, Sy! Soooo! To win the title of MasterChef today, I have to cook the best I have ever cooked.


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[Assistant] I have to be at the top of my game the whole way through. I absolutely adore eating vegetables. I have vegetables in my entree, my main, and my dessert. And I'm hoping to get all my vegetables prepped, chopped, and done in the first hour.


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[Assistant] My entree dish is called beets with beet tops. They're gonna be roasted and sitting on top of a beet top puree.


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[Assistant] I've got three types of beetroots. I've got basically a golden beetroot, your classic blood red, and then a pink and white target style beetroot. With my menu, I wanted to start with something that I love, showing that I can use the whole ingredient, leaving the root attached to the beetroot, and then for my main, flip it completely on its head and do something a little bit more rich and decadent.


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[Assistant] My main dish is lobster with a caviar champagne sauce, romanesco and dutch carrots.


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[Assistant] Main course is a bit of a nod to sort of my past, using a lot of champagne, a lot of bar and cocktails in my, like, history. Also my partner's a pescatarian. Classic decadent dish.


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[Assistant] My three course menu is a beetroot and beetroot top entree. The moment my beetroots are out, they're all tender and cooked through.


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[Assistant] I've got to blanch my lobsters. And a pumpkin seed oil and roasted pumpkin ice cream dessert.


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[Assistant] I wanna do this dessert because it represents something I believe in. It's making a cake at the moment for the dessert.


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[Assistant] Using a vegetable in my dessert could be a risk, absolutely, but I'm in the finale of MasterChef. With my menu, I want it to be a little bit adventurous, get the diners questioning everything they're eating. The pumpkin is a very sweet vegetable. I'm hoping it works as sort of a slightly savoury style dessert. Come on, size.


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[Assistant] 90 minutes till service, I take my cake out of the oven for my dessert. My dessert today is called different parts of pumpkin.


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[Assistant] It's a pumpkin seed oil cake with a roast Japanese pumpkin ice cream. Alright, question that's been better, but I think I owe you an apology.


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[Assistant] Okay, it's looking amazing, it's nice and set. It's got like a very trickily smell to it too. It really does, and that, oh yeah, that's done, that one's done. I'm happy with the flavor of the pumpkin and neon glaze. I think it's delicious, super pumpkin-y, nice and roasting flavor.


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[Assistant] Yeah. I taste the nutmeg in there. Yeah. Yep. So I'm putting all my anglaise in the ice cream machines to churn. You are feeling good?


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[Assistant] Yeah, that's gonna go in the churners now. I'm just going to sous vide my lobsters. Just doing a test one now.


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[Assistant] My main dish is lobster with a caviar champagne sauce. And you're going to be getting guests coming through. Yep. That's gonna fluster you. That's gonna throw you.


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[Assistant] There's so much pressure to have this lobster cook perfectly. If it is not then that could ultimately lead to a very bad score and definitely not a winning dish.


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[Assistant] Yum. This test of lobster's perfect. Soft.


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[Assistant] What I've gotta do is I've gotta make my puree for my beetroots. For my entree, my beetroots have been cooked in the oven, they're ready to go, but I really need to get onto that beet leaf puree.


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[Assistant] Using the beetroot tops, the puree has to be really smooth. This is a vegetarian dish. It can be quite risky. It needs to be full of flavour. I'm also gonna add a honey and vinegar mixture.


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[Assistant] I've got my honey and vinegar mixture. I'm thinking rather than just drizzle over the top, I'm gonna make a spray. And this is gonna be atomised on top. What do you mean atomised? The mixture's going to go into an atomiser and sprayed on at the end.


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[Assistant] I've gone for this entree dish because I think it's amazingly funky and fun.


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[Assistant] It's meant to be quite confronting and make people feel like they've picked a beetroot out of the ground.


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[Assistant] There's so much on the line, and I really wanna get good scores for my first dish put out.


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[Assistant] You know, it just means I have to work harder for my main and my dessert to claw back those points that I'm missing out.


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[Assistant] I was hoping to go into the main course feeling more confident. I don't Simon, come on! Bye.


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[Assistant] I got into this finale because I've worked really hard and I've fought through the whole competition.


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[Assistant] I've had dutch carrots poaching in macabre wine stock. It's time to strain it off because I want them slightly crunchy to counterbalance the fact that the lobster is soft.


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[Assistant] I'm also gonna butterpoach some leeks. Colour on one side. Yeah, it wants to be quite clean, and I love that sort of, sort of like, rosy flavour. Don't get too fine. Yep, okay. You've got such beautiful flavours with this sauce. Yep, okay. Gary's famous words to me as well.


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[Assistant] There is so much pressure cooking for these amazing cooks and chefs. There could be a few elements they're going to love or hate. It makes me extremely anxious. With the scores now, I've got a lot of catching up to do, so I've got to make sure I remain expectant.


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[Assistant] The champagne sauce looks amazing with the caviar through it. I love the decadence of the lobster.


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[Assistant] My veins are out, it's time to try and crawl back those points I lost in the entry. Oh.


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[Assistant] What I really want to do now is to serve an absolutely delicious dessert and be really proud with what I've done throughout this cook and finish off with a bang.


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[Assistant] My ice cream's looking really good, it's nice and tasty, it tastes like pumpkin. The elements that I've completed for my dessert are my ice cream on my cake. Ice cream scoop's a circle square, ice cream scoop instead of quenelle.


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[Assistant] I'm just gonna enjoy cooking my final dish. I'm putting everything on the line and showing what I can do. And one of these little things that I can do now is making a bergamot twill.


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[Assistant] By making bergamot tea and putting sugar with that and making that into a very dark caramel.


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[Assistant] A little bit of finesse is starting to pour out, and uh, I just don't want anyone to know, so I'm gonna keep it quite secret.


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[Assistant] What's the dessert, son? Pumpkin seed oil cake, with roast pumpkin ice cream, and a bergamot twirl.


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[Assistant] Look, I tell you what, I'd rather be, uh, down by a lot.


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[Assistant] Whoever's the first to harness fear and anxiety and turn it from your enemy to your ally, you're gonna be in the box seat.


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[Assistant] Okay, are you pumped? Yes. Alright, your time starts now.


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[Assistant] Yeah, okay. Me, I would be struggling to say that that could be a main course.


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[Assistant] There's not much else on your plate. You've got fennel. That's it. Fennel puree. And some diced fennel. That's it. It is another entree. Turn that into a main course.


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[Assistant] So that's the batter? Yep. Looks very runny. Yeah, it is. They're really wet cakes.


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[Assistant] You're gonna need to give yourself about one minute per marron. One minute.


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[Assistant] It's showtime! Ninety minutes to go!


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[Assistant] You need to scrape these sides, because that's sitting on the plate. This needs to be beautiful and white.


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[Assistant] In 30 minutes, I wanna see your entree, Simon, your entree, Larissa, your entree.


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[Assistant] You're starting to look a lot more, a bit more flustered. Oh yeah, pressure's only about to just start because once those guests start walking through and we've got to do some plate ups, I mean, they really don't know how they're plating these dishes.


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[Assistant] Roasting now at a beautiful temperature and then plenty of time to rest.


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[Assistant] This sous-vise, I really don't see how that goes with bone marrow.


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[Assistant] Right, I just really think that you've got to taste this dish.


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[Assistant] So this is sous vise. I really don't see how that goes with bone marrow. This is about tasting right now.


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[Assistant] Good girl, Riza. Alright. Service! Stick up! Service!


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[Assistant] One more time now, I want lights up. Let's go. Everyone, lights up.


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[Assistant] Okay, Chester, we've got a bit of a problem, huh? We've gotta start sending.


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[Assistant] Come on mate, come on. You need this dish to sing, okay? It's gotta go out super hot. Yep. I'm really proud of what I've done.


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[Assistant] I quite like the idea of you just, uhm, you break it, you break a piece of sponge. Shut up, that's a good idea.


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[Assistant] At the same time, I must also be wary of my other contestants. What they're gonna cook with the ingredients I've chosen.


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[Assistant] Since I've got the advantage, I will love that pin.


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[Assistant] I'm making a roast chicken with sage, orange and cinnamon. It looks delicious.


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[Assistant] But I have the extra pressure on me because I got to choose the eight ingredients since I have the golden amp under my mystery box.


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[Assistant] The biggest concern is making sure the chicken is cooked perfectly.


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[Assistant] Usually a chicken breast will take you 10 to 15 minutes in the oven, but I'm leaving the breast on the crown.


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[Assistant] Because I want the flavors from the bones to be infused in the breast.


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[Assistant] This process will take me at least 30 minutes. I just hope that this chicken works out.


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[Assistant] I'm making a roast chicken with sage, orange and cinnamon.


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[Assistant] Time is a bit of a worry. I left the chicken for 25 minutes. Hopefully it comes to perfection.


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[Assistant] The worst thing what can happen is the chicken is underdone and the judges will not be able to taste my dish. I start to cut the chicken breast and prepare it for plating.


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[Assistant] I quickly ran to the pantry, grabbed a saucepan, and I want to sear the breast side down. I just hope that this chicken works out.


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[Assistant] Hopefully the chicken is cooked inside. Hopefully while waiting it cooked.


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[Assistant] The chicken breast was slightly under when I cut it out. Uh, then I had to pan sear, make sure that it cooked well in.


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[Assistant] So what have you cooked? We shall cut the chicken. I'm feeling very nervous. Because I didn't have the time to check the chicken.


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[Assistant] So it's a braised Maryland chicken in an orange sage and cinnamon sauce sitting on a parsnip puree.


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[Assistant] I'd be delighted if I'd made that. Looks extraordinary. Is truly amazing.


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[Assistant] I haven't eaten something quite so dreamily perfect.


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[Assistant] I was so much and I enjoyed the kind of brio and enthusiasm of everyone cooking and the real desire not just to cook but to learn. But what I also liked, and this is down to you guys, I feel that just as much you will want to teach and for me that was really inspiring.


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[Assistant] Passion fruit, what I love about it is that it's got this wonderful, heady perfume, and it's great, you know, in sweet cooking, but actually I use it as well when I make a dressing.


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[Assistant] Now, I don't know how everyone will feel about this, but I love them. Chicken livers. Yum. Squid. Condensed milk. Ginger. I couldn't resist the cherries. Chillies. I like fire in my food. Anchovies. I adore anchovies. The bacon of the sea.


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[Assistant] I really would. So, the winner of my mystery box challenge...


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[Assistant] Good luck everyone. Your time starts now.


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[Assistant] Now wait, there's no room for you to make a mistake with any of the components. And you haven't.


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[Assistant] It's very interesting because when you talk about your dish, it sounds like there are too many components. When you eat it, everything feels, funnily enough, quite restrained. And I think the reason for that is because you've balanced everything. Okay.


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[Assistant] Well, thank you to all of you and especially, you know, you five for producing really glorious food. How wonderful to come here and be given so much delight on the first day. So, thank you.


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[Assistant] I love chicken skin and I often make chicken crackling. Because even in a salad, you know a salad, probably enough, they're so full of crispness and crunch.


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[Assistant] This makes me smile eating it. So next up, it's Jo.


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[Assistant] Those parsnip chips are just fantastic.


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[Assistant] It was sensational. Dark, divine, and it's just pure pleasure.


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[Assistant] In a way the elements are there and you just were slightly disconnected from the food. Yeah.


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[Assistant] Well if I think of Snap, Crack and Pop, this is exactly what I think of.


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[Assistant] I love the look of that.


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[Assistant] It's in the nature of experiments that some experiments fail and that is part of cooking and it's what you do afterwards that makes the difference so onwards and upwards.


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[Assistant] There were so many good dishes, so much fantastic cooking that it was...


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[Assistant] Agony, frankly, to choose the top three. If I call your name, please step forward.


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[Assistant] So, you have 75 minutes to bring us a delicious dish. Obviously, you can use one or as many of those ingredients under that mystery box as you would like. You've got your staples underneath your bench, and what you need to know is we're only going to be tasting the five most appealing looking dishes. And remember what you're cooking for. The winner


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[Assistant] We'll go straight into this week's immunity challenge. For a shot at an immunity pin. But, it's also a season full of surprises, remember? And this week, the winner will get something else. Something very, very special. There's not quite enough varies in that. Nojela, would you like to tell them?


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[Assistant] If all of those elements were not in a bad spot with 10 minutes to go.


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[Assistant] Final little touches. Ten seconds. Nine. Eight. Seven.


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[Assistant] So 75 minutes to cook a beautiful dish out of the 10 ingredients that Nigella chose in the mystery box. And a grape.


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[Assistant] Couple of prizes on offer. First of all, the opportunity to compete for that immunity pin. But maybe best of all, the chance to have afternoon tea with Nigella in London. Oh my goodness.


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[Assistant] Not a bad start, is it? Feel weak? Pretty happy.


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[Assistant] I think what's very clever is the little dome, so with that crunchy praline on the top, the soft meringue and the cherries, it's a delicious and kind of heady combination which I love.


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[Assistant] It looks beautiful. Yeah. Looks really sophisticated, looks really well balanced, and the kind of dish we were looking for out of that mystery box.


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[Assistant] You know what the good news is? Not only are you going to go to London and have afternoon tea with Nigella, but you also go straight through to immunity. And that immunity could be yours. Head up to the gantry, the rest of you, back to your benches. Well done.


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[Assistant] Join Kristen in the immunity challenge later on this week. However, the contestants that deliver the three least impressive dishes will find themselves in tomorrow's pressure test. Are you ready? Yes. Your time starts now.


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[Assistant] It had 75 minutes to give us a dish that snapped, crackled or popped. Best three dishes. Send their makers along with Kristen.


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[Assistant] To cook for the chance at winning that immunity pin. But the bottom three.


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[Assistant] Unfortunately find themselves in tomorrow's pressure test.


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[Assistant] So, let's get this tasting underway. First dish up is... Ben.


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[Assistant] The spices that sing through the coffee and the chai.


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[Assistant] The last dish we'd like to taste today belongs to Buddha.


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[Assistant] What a great dessert. Eat the whole thing together is nothing but snap, crackle and pop.


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[Assistant] We have to say, and we all agree, we saw some absolutely amazing cooking today.


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[Assistant] The contestants that cook the best three dishes join Krista in this week's immunity challenge. However...


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[Assistant] The three contestants that cooked the least impressive dishes will find themselves in tomorrow's pressure test.


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[Assistant] The first episode of MasterChef I've ever watched in my life was Peter Gilmore's Challenge.


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[Assistant] It made me more driven to make beautiful food like Peter Gilmore.


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[Assistant] The dish is a poached meringue and then inside you've got a brulee with the masala. Oh, keep it clean, keep it clean. Cherry granita and on top of it is a caramel twill. Beautiful. I badly want to be in the top five.


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[Assistant] I'm hoping the caramel will set enough to have that crack on the top. I was hoping it melts through.


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[Assistant] I'm thinking about the crack on the egg. I'm scared that she's gonna be a slop on top.


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[Assistant] Snap crackle pop. So I'm thinking a black sesame panna cotta. And then for that snap I'm gonna use a squid inked wheel.


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[Assistant] I'm making double fried Korean chicken and serve it with a sweet chilli sauce. The beauty in the double fry method is that you're gonna get this nice crackling crunch in the batter and the skin of the chicken.


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[Assistant] I want that chicken to be so loud when they bite into it that the people in the back row can hear it.


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[Assistant] Mmm, this is so good. I'm just so happy you're eating my food, Nigella.


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[Assistant] You got everything on the line? I'm ready. Bring it on. Bring it on? I'm here for a reason, right? Yea? Gotta win that trophy, so let's start it. And Jenny? What about you?


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[Assistant] Today, you'll be cooking my Apple and Rosemary Tat-tat-tat.


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[Assistant] Your ice cream is so good, your custard will be great. Fantastic. Thank you.


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[Assistant] Sameera, that is so lovely for me to hear because if ever there was one thing I wanted to do is make people feel comfortable about food. I cook by feel and I saw you cooking by feel. Yes. And uhm, so, we have a connection.


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[Assistant] That first bite, I took it right from the edge because that lovely wavy part of the pastry where you could see all the layers.


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[Assistant] The caramel is just right because the apple is shining through. It's really good.


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[Assistant] Well, I think that the caramel is taken too far. It's not just the colour, it's that pooling of sort of globules of the caramel because what should just be nicely flowing is not.


[User] Please transcribe this text

[Assistant] The caramel too bitter, so it makes the apple too bitter. It's not balanced. And the apple doesn't have enough structure.


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[Assistant] Yeah. I'm so excited. It's the first immunity challenge of the year.


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[Assistant] I've got quite a bit going on today, all of which take a bit of time.


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[Assistant] I think I've probably bitten off a little bit more than I can chew, so I'm gonna need to, to run to get this done.


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[Assistant] There is this one point ahead after the mains, but her marangs have collapsed. Her sorbet is frozen rock solid.


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[Assistant] Welcome back, we're talking about symbol codes, and in the previous video we wrote down these three desirable properties of a symbol code. We said we'd like it to be efficient in terms of getting good compression.


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[Assistant] We'd also like it to be fast so that we can encode and decode very quickly. And we'd also like it to be simple so that we can understand it very easily and also implement it easily in an algorithm.


[User] Please transcribe this text

[Assistant] And to start getting a handle on B and C to understand what properties of a symbol code might give us good speed and simplicity, we started playing with these, these just very simple examples A and B of two little symbol codes where the source, the source alphabet was just this little set A, B, C, and D.


[User] Please transcribe this text

[Assistant] And we decoded these two, just these two special cases of possible strings that we might have to decode. And we found that A was significantly easier to decode than B. And I said that that was because A has this special property called the prefix property.


[User] Please transcribe this text

[Assistant] So what is the prefix property? Well, what we started, so let's think about what, what made, what made A easy to decode.


[User] Please transcribe this text

[Assistant] Well, when we started, maybe we'll start out here, think about when we were at this point in the decoding process. We had decoded up to ACAD, and then we were looking at 1 here. So we had a 1.


[User] Please transcribe this text

[Assistant] And then we said, okay, the next codeword has to start with 1, so therefore it can't be A.


[User] Please transcribe this text

[Assistant] And then we have a zero, so we have one zero. So let's see, it could be B, but it can't be C or D. So we can cross those off, and then we know that it must have been B.


[User] Please transcribe this text

[Assistant] So as soon as we got to the end of the code word B, we could just immediately, instantaneously write down what the correct code word was to decode to.


[User] Please transcribe this text

[Assistant] And so that, uh, that, that is, that is the property that is, that made this so nice to decode. Whereas, you know, for example, over here for this one, say when we were at this point in the decoding process, we had already decoded D and A.


[User] Please transcribe this text

[Assistant] And we wanted to see what was coming next. Well, we look at, we have a zero. Okay, so it could be B or C. We know it's, the next one's not A or D.


[User] Please transcribe this text

[Assistant] And then we have another zero. So it could be B or C. Those are still candidates. So we don't have the property that as soon as we got to this, the next code word, we know it's going to be B here. I mean, just from looking ahead.


[User] Please transcribe this text

[Assistant] But we don't have the property that we can instantaneously write down b. We have to keep on looking. We have to say, okay, zero, zero. We had to look all the way until we got to this one before we could even say whether this was, uhm, well, maybe we didn't have to go that far, but we had to at least go a couple more symbols before we could say that, definitively, that this was a b.


[User] Please transcribe this text

[Assistant] You know, what was it about this code that made it fail the condition that we were able to instantaneously decode? Well, it was because B...


[User] Please transcribe this text

[Assistant] There's another code word that starts with the same thing as the code word for B, right? Because C starts 0, 0, and that is exactly the code word B. So even though we have read through, you know, 0, 0, it might still be that there's, that we're just at the beginning of another code word. So in other words,


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[Assistant] We say that the code word for be here is a prefix of this code word.


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[Assistant] So let's make that, let's write down formally what I just said.


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[Assistant] Is, and this is a sequence, this is a string in A star, is a prefix.


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[Assistant] So in other words, b1 to bm, this string, starts out looking like a1 to an. It starts out with this string.


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[Assistant] Just like, just like here. So this would have been b1, b2, b3, b4, and this would have been a1, a2. So, so b1, b2,


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[Assistant] That would be this part, equaled A1A2. That would be this part. Okay, so that is what we mean when we say prefix. And a prefix code


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[Assistant] So now we have the definition, definition.


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[Assistant] C is a prefix, whoa, got a little wild there. Prefix code, or let me say,


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[Assistant] Put in parentheses. A-K-A. Prefix. There's all kinds of different ways to...


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[Assistant] Call these things prefix or sometimes when people say prefix free, sometimes people say instantaneous. Instantaneous. Instantaneous code. Those all mean the same thing. If no code word is a prefix of another.


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[Assistant] So C is a prefix code if, if no code word of C is a prefix of another code word of C.


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[Assistant] So here, let's check. So is A indeed a prefix code according to our definition?


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[Assistant] Well, we need to check that no codeword is a prefix of another, so let's see, is the codeword for A zero? That's certainly not a prefix because no other codeword starts with zero. Now how about one zero?


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[Assistant] Well, no other code word starts with one zero, so we're good there.


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[Assistant] 110, certainly these are shorter so they can't start with that. And this one doesn't start with that either. So, and likewise, 111, of course none of these start with 111. So therefore, this code, this code A is indeed a prefix code. Whereas B is certainly not because, like we were talking about,


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[Assistant] Well here, you know, zero zero is a prefix of zero zero zero one. And likewise, one is a prefix of one zero one. So it's doubly non-prefix, we could say.


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[Assistant] So A is prefix and B is not. This is our definition of a prefix code. And I claimed earlier in the previous video, I think I said that A is indeed uniquely decodable.


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[Assistant] And that follows from the fact that is, it is a prefix code because any prefix code is uniquely decodable. So this is a note we make. I'll say note.


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[Assistant] That is a fact and I will leave that to you as an exercise to prove.


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[Assistant] And you're, you have another exercise which is to prove that B is also uniquely decodable.


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[Assistant] Okay, so that's, so one way to think about this, that condition that, that, that we were, that made a desirable was this prefix condition. Another way to think about the same thing, the prefix condition,


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[Assistant] Is by thinking about this, these codes as, as trees. So maybe where can I draw a tree? Let me make a little space here. Let me make some space right here.


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[Assistant] Cut this out. Let's draw a tree for A here. So how could we represent this as a tree? Well, we could start out, let's say,


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[Assistant] You know, think about the decoding process, right? Maybe if we start out at the root of the tree, let me do that in a different color. So we start at the root, and then,


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[Assistant] We either get a zero or a one, so like say we were here and we got a one, but we could have gotten a zero, so we had two possibilities.


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[Assistant] And then if we got a zero, then we know we're at A, so we can just decode to A. Whereas if we got a one, well we have some more decoding to do. So if we get a one, then we have to draw another node here. Then we might get either another zero, or we might get a one. So we have


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[Assistant] We can split, we can branch the tree here. If we get zero, we know we're at B.


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[Assistant] And if we get a one, we have to look one more time, so we split once more.


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[Assistant] You might be able to see that any prefix code


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[Assistant] For any prefix code, each node will be, will have either, either two children?


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[Assistant] Or one child or zero children. If it has zero children, it's just, it's just a leaf.


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[Assistant] Uh, and if it has two, you know, you're splitting at that node. But it could also have one. And that, that would still be


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[Assistant] Still have that property of being prefix, and what was it about this tree that made it a prefix code?


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[Assistant] Well, it was because, I mean, if you think about just what, what it means for one of these code words to be a prefix of another, like, so B here was, was one zero, right? That was B, one zero.


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[Assistant] If B was a prefix of some other code word, maybe there was, you know, there happened to be some other code word, 101.


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[Assistant] Then, then b would be on the path from the root, this is the root of our tree, b would have been on the path from the root to that other node, maybe this is, I don't know, e, c of e is this. So e, we would have


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[Assistant] So the, so a, a, one codeword being a prefix of another directly corresponds to that, the, the node for that codeword


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[Assistant] Being on the path from the root to the other, to the node for the other code word.


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[Assistant] So another way to think about a prefix code is to think about its tree. And the tree for a prefix code has the property


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[Assistant] That, that the path from the root to any of the codeword nodes with any of the leaves of the tree does not pass through any of the other codeword nodes.


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[Assistant] Well, so yeaah, I should say that the path from the root to any code word node does not pass through the code word node for any other code word.


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[Assistant] Okay, hopefully that was clear. I think you, if you play around with this you'll, you'll see, you'll see what I mean if that wasn't completely clear.


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[Assistant] So this is another nice way to think about prefix codes.


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[Assistant] And so we claim that any prefix code is uniquely decodable, and you might ask yourself, well, is, you know, the natural thing when you have an implication like this is to say, does the converse hold? Is every uniquely decodable code a prefix code?


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[Assistant] And well, of course, you know, we already know the answer to that. I, because I, I told you here that B was a pre, was not, B was uniquely decodable, but obviously it's not prefix. So, so the converse does not hold.


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[Assistant] Okay, so, so we, so we defined prefix, we thought about the tree representation, and this is an important way to think about them later on when we talk about the Kraft-McMillan inequality. Thinking about these, these codes in terms of their trees is a very nice way to think about them. And one other thing I'd like to mention here is left prefix versus right prefix. So,


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[Assistant] Left prefix, what I've been talking about so far, you might call a left prefix, the left prefix condition. And you could compare this with right prefix.


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[Assistant] So left prefix, or I mean maybe it would be better to say postfix, I'm not sure, maybe postfix would be a better way than right prefix.


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[Assistant] But by write prefix, I just mean that, uhm, if you were like, uh, you know, if you were reading the, the, the encoded message in reverse, so what I mean by a write prefix code is that


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[Assistant] If you were to read the encoded message in reverse, that uhm,


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[Assistant] That, uh, from the right, that no code word is a prefix of another.


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[Assistant] So for example here, this would not be a right prefix code because zero would be a right prefix of one zero. Cause, cause this one and same thing here, zero would be a right prefix of this. B, the codeword for B, one zero would be a right prefix of this codeword cause it ends in one zero.


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[Assistant] And, uh, it's pretty easy to see, just by analogy with, you know, the proof is exactly the same as proving that a prefix code is unique, a left prefix code is unique.


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[Assistant] The exact same proof, but just sort of in reverse, you know, starting from the right instead of the left, shows that any right prefix code is also uniquely decodable.


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[Assistant] So often times you'll, you'll, maybe people will throw at you a code and say, is this uniquely decodable? And you look and you say, oh, it's not prefix. Oh my goodness. You know, this might be difficult to determine.


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[Assistant] But if you can see that it's right prefix, that's a frequent trick that people use. If it's right prefix, then you can just very easily say, aha, yes, I know that it is uniquely decodable.


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[Assistant] Okay, so that's, that's prefix codes, and next we're gonna start talking about, uh, the Kraft-McMillan inequality.


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[Assistant] So the Kraft and McMillan inequality will be our first theorem. It's quite a surprising little result and it'll be very useful for us. Okay, so see you soon.


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[Assistant] The hurdles have been pretty tough over the last couple of years. You know, I haven't always been the best person to be with. I used to be a pretty heavy drinker. I was pretty much a wreck in the gutter alcoholic. I lost my job, but pretty much lost my girlfriend and one of the things that helped pull me out of the gutter was food. Instead of hitting the bottle, it was, it was hit in the kitchen.


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[Assistant] You know, pretty lackluster at life and it's all about moving forward for me.


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[Assistant] I open up the box with the stuff from my pantry, and on top there's a letter from Lauren.


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[Assistant] Hey babe, I really hope that you're having fun. I just wanted to talk a little bit about how proud of you I am. When we met two and a half years ago, you were a completely different person. I know it hasn't been easy, but over time you developed and grown as a man in ways that bring tears to my eyes. Getting a letter from home is amazing.


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[Assistant] But 15 minutes has passed. I'm a little bit overwhelmed for choice.


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[Assistant] Because this is my fridge and my pantry, I thought it'd be easy to come up with a dish, but at this stage I'm drawing blanks.


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[Assistant] There's so many ingredients there, but not a lot of them are binding together to make this one whole dish.


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[Assistant] I've got such a weird spread of ingredients, like it's kinda hard to incorporate it all, so.


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[Assistant] Lauren loves salmon and it's something that we always cook together and then sit down together and enjoy. It's a huge relief to finally get started on a dish.


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[Assistant] So I'm doing the crispy skin salmon. I've just salted the skin just to dry out the moisture so I get a nice crispy skin. I know the crispy skin salmon will be the hero of my dish. Now I just need to find something to pair it with.


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[Assistant] What are you thinking Brent? I'm going to incorporate the tahini and the mint together.


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[Assistant] Finally my dish is coming together and I'm feeling in the zone.


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[Assistant] I spent the first half of this cook fluffing around looking for ideas, but I managed to refocus and use Lauren as inspiration.


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[Assistant] So I've got some really nice elements on my dish now and it's coming together, but it's still missing something.


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[Assistant] I think she'd be pretty excited. This is kind of all flavors that happen in our kitchen. Right. But, uh, I had a bit of trouble kind of coming together with the concept. Yeah, yeah.


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[Assistant] I look down and see the ingredients that I'm using and I realize this is quite a middle eastern dish.


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[Assistant] I've got the spicy carrot puree, pistachio pesto and the crispy skin salmon. But I need something crunchy to tie this dish together.


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[Assistant] I'm feeling pretty confident and can't wait to get my, uh, salmon on and just get that cooking and then everything should come together. The crispy skin salmon is the hero of this dish. It's really important that I get that crispy skin.


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[Assistant] I've cranked the heat up really high so I can get this salmon skin super crispy.


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[Assistant] I have to watch this summon like a hawk. There's absolutely no room for error.


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[Assistant] The chickpeas alright, right? It smells a bit like burning. Few minutes to go and I get my chickpeas out of the oven. I may have left the chickpeas in the oven for a touch too long.


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[Assistant] But Lauren and I like them super crispy and I hope the judges do too.


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[Assistant] And then the other elements scattered across, kind of like a beautiful, crispy skin comment.


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[Assistant] 100 ideas pop into my head. That's a, that was the problem.


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[Assistant] There's some things where I kind of went down a bit of a track and then I realized that I didn't have some of the ingredients to finalize it and I lost a bit of clarity. If this is a dish that sends me home today, I'd be devastating. What is the dish?


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[Assistant] It's a crispy skin salmon with cumin carrot puree, pesto, pistachio, mint, and oven roasted chickpeas.


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[Assistant] Yesterday you made a mistake. Is this dish a redemption? I'm really happy with this dish.


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[Assistant] Lauren and I like to roast the chickpeas up and eat them as snacks at home. So I had her in mind when I made it and something that I was really happy with.


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[Assistant] Meeting all these guys actually. It was unreal. Like him.


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[Assistant] Brett started pan frying his salmon. I'm a bit concerned that he's leaving it in that hot pan for just way too long.


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[Assistant] I know he wants his skin really crispy, but if it's overcooked, that could send him home.


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[Assistant] Four dishes to all come up at the same time is a very difficult thing to manage in a kitchen at home, let alone in a pressure test. It's gonna be crazy.


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[Assistant] When I bite into the brownie, there's a crunch of the walnuts, the fudginess of the chocolate, you get a little bit of crisp from the outside.


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[Assistant] I start to fold my chocolate with the cream mixture. This part is crucial because you need to incorporate all the chocolate with the cream mixture, but you don't want to overwork it because you'll change the texture of the cream cheese. Nijella's was really nice and smooth, so I've got to be careful.


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[Assistant] We're working with the rarest chocolate in the world. In every feast, there's always a centerpiece. And for me, I feel like the cheesecake is that, so I want to get it spot on for Nigella. Good job Jenny, that looks so nice.


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[Assistant] I grab my melted chocolate, pop it on the scale, and I start pouring olive oil into the chocolate. Okay, here we go.


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[Assistant] The slightest gram the wrong way could send you home. You go from a silky beautiful mousse to a loose oily chocolate mess.


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[Assistant] As a part of Nigella's Chocolate Feast, one of the dishes is a dark chocolate olive oil mousse. I'm working on it and I've over-whipped my egg whites.


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[Assistant] I want this so badly, to be in the competition, to keep going further, you know, to go on to win this. I know I can do it. You've got it Jen. I'm just gonna give it everything I've got.


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[Assistant] It looks like they underwipped me. But I know I'm on the clock and I haven't started my cookie pods. Egg whites.


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[Assistant] I know of now the ruby chocolate cheesecake, and the brownies look fantastic, but I'm really scared about the other two.


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[Assistant] 10 minutes ago I didn't think I'd get the fourth dish on, uhm, but I got it on. There's definitely things in each.


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[Assistant] So I think I might be a little bit under, uhm, I just, it doesn't have the body, it doesn't have enough air in it.


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[Assistant] If anything, I'd probably say I've done pretty bad since I got here.


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[Assistant] Episode 5. Mull. Overboard.


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[Assistant] Guess who was on the river today, said Otter. Who? asked Rat.


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[Assistant] Toad, he's in his new racing boat, said Otter. Toad is always trying new things, said Rat.


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[Assistant] Mole was putting the oars in the boat. We're going too, said Rat.


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[Assistant] Can't believe a few weeks ago I was trying to catch crabs and now I'm here and really excited about it.


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[Assistant] Today I'm making brulee pancakes with orange segments and orange juice. And I think I'll do a mascarpone and mousse. Just giving it a really simple color.


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[Assistant] A brulee pancake is when you put sugar on top of the pancake. When you flip it, you get that brulee nice caramelization on top. Brulee pancakes. Go Ben. The batter's gotta rest for at least 10 to 15 minutes and then I can work on the rest of the elements.


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[Assistant] Get a toffee glaze on it. Ah, look, I think if it's done right, it definitely could be up there, yeah. I've been trying it at home. Let's hope it all works. Thanks.


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[Assistant] Flipping it over, the pancakes should get a sweet caramelized top. So when I serve it, you've got a nice crust over the top of the pancake.


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[Assistant] I really need the nice brulee caramelised top on these pancakes. If I don't, I might as well serve nothing.


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[Assistant] Two minutes to go and I'm still trying to get that perfect caramelization.


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[Assistant] Orange segments and the juice of the citrus as well.


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[Assistant] Like he's really showing off at the moment. He's filleted and deboned that fish like a pro. He's killing it.


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[Assistant] A pancake recipe is a pancake recipe. It shouldn't be too difficult.


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[Assistant] Today I'm making Fluffy Buttermilk Pancakes with fresh berries, berry syrup, a yoghurt sorbet.


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[Assistant] Our long journey through English literature has brought us almost a thousand years now, from the Ale Hall and that distant epic Beowulf, to the neo-classical grandeur and coffeehouse elegance of Dr. Johnston, the great literary lawgiver. But during that,


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[Assistant] Long voyage. One important word has been largely missing from our discussions. It's been out of the frame. And that word of course is the novel.


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[Assistant] And that, in literary historical terms, is exactly what the novel is or what it was when it first happened.


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[Assistant] And we've now arrived at the moment at which that new thing, that literary novelty, the novel, came into being. Now,


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[Assistant] The novel is the one major literary form whose emergence we can date.


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[Assistant] More precisely, which we can see emerging in its modern form out of the traditional forms of narrative at the beginning of the 17th century.


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[Assistant] Now I think that literary evolution is as fascinating as the evolution of any other species. It's interesting, it's more than interesting. It's in fact a privilege to see, as it were, something of this importance coming into being.


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[Assistant] Now, it's not difficult to see where in the most primal sense the novel comes from. It's primal soup, so to speak.


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[Assistant] Narrative, storytelling, is as old as literature itself. It's probably as old as humanity itself. And along with the song, narrative is what the ancients called the primum materium, the basic substance.


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[Assistant] The DNA, we might say, is one of the big aspects, one of the big trends or traditions in literature.


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[Assistant] One has to be precise about this, the novel is not, is not the same thing as a story.


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[Assistant] Beowulf, for instance, tells a story. The Canterbury Tales tells many stories. Shakespeare tells stories. A bestseller of the 19th century was Charles Lamb's Tales from Shakespeare, taking Shakespeare and turning him into stories.


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[Assistant] But none of these storytellers are novelists writing novels.


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[Assistant] In this lecture, we look at the first great novelist in English literature. The maker, if you want to call him that. The creator of the literary form, if that's not too grand. I think he would have given us a wry smile, have we?


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[Assistant] Put that label around his neck. And I'm talking about Daniel Defoe. Not a very English name, but he was a very English writer.


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[Assistant] And we're also talking about the archetypal work of fiction, which came from his pen, Robinson Crusoe. Again, not a terrible English name.


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[Assistant] Which is quite important. I think Dafoe is on the edge of society. That's important, uh, given the kind of the views which she has of England.


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[Assistant] But first, the question, why did the novel happen at this particular point in historical time? And why did it arise in this particular place?


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[Assistant] Now, that place is, is England, London specifically, at the beginning of the 18th century.


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[Assistant] 1719, if we want to be pinpoint precise about it. Now to help answer those questions, why then and why there, we may note that something else simultaneously was happening.


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[Assistant] Very simply, was the birth of modern capitalism.


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[Assistant] Now Robinson, Robinson Crusoe is, as I'll try to show, homo economicus. He's a new kind of man for a new kind of economic system. It's not new to us, but it was new to the 18th century. One of the things that makes Robinson Crusoe so fascinating is that it talks to us very directly because he's to some extent describing our world.


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[Assistant] Even though in fact, of course, we're looking at something which is 300 years old.


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[Assistant] Now the critic Ian Watt, in his classic study, The Rise of the Novel, ties these two phenomena very stimulatingly together. Namely, the rise of the novel and the rise of capitalism.


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[Assistant] What, to simplify, sees the literary form, the novel, as inextricably connected with what was going on financially. Not in the publishing houses of the city of London, but the city of London.


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[Assistant] In the counting houses, the banks, the shops, the great Thameside warehouses, and the great markets, Covent Garden for vegetables, Smithfields for meat, Billingsgate for fish, everyone was a money changer. The money changers, in biblical terms, had come back into the temple, had taken it over. This was capitalism. Very simply, this was capitalism. Entrepreneurship.


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[Assistant] Now, entrepreneurship depends on a notion of society which is made up of individuals. Each with their own store of property and each keen to acquire more property. Each with their own wallet which they're trying to fill.


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[Assistant] By doing this, they're going to rise in the world. The class system becomes very fluid, because in fact the more money you have, the better chances you have of promotion. Social mobility is part of this, of this, of this very complicated system.


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[Assistant] Worth, at this point in history, is not something that's inherited like a title, blood, good breeding or an estate. Worth is something that can be made or earned. You can die a very different person from what you were born in a very different station of life. Now,


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[Assistant] Worth, at this period of history, has a pound sterling sign at the front, and lots of zeros at the end. Money.


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[Assistant] Uh, now, society at this point, one way of looking at it, and thinkers like Adam Smith did see it this way,


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[Assistant] The principal and most dynamic factor in capitalism is the accumulation of individual, not communal or collective wealth and property.


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[Assistant] Now, everyone knows the story of Robinson Crusoe, homo economicus as I called him.


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[Assistant] It's one of those works of literature that's familiar, even to those who've never read it and never will read it. It starts in 1651.


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[Assistant] It's a very interesting year, because the civil war is going on, though Robinson never mentions it.


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[Assistant] A merchant seaman, merchant here is the operative word, Robinson, goes to sea to trade. Indirectly the novel hints, and at some point makes it very clear, slaves are among the goods that he's going to deal in.


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[Assistant] Why don't I just read the title page, as Robinson Crusoe was published in, in 1719.


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[Assistant] And spend a couple of minutes just digging around in it for what first readers and first purchasers, this one must remember as a commodity. This is a world where nothing is for nothing. People bought and sold this novel.


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[Assistant] And listen to this title page and work out exactly what it's, what it's telling us.


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[Assistant] The life and strange, surprising adventures of Robinson Crusoe of York, Maryland.


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[Assistant] Who lived eight and twenty years, all alone, in an uninhabited island on the coast of America, near the mouth of the great river of Orunok.


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[Assistant] Having been cast on shore by shipwreck, wherein all the men perished but himself.


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[Assistant] With an account of how he was at last strangely delivered by pirates.


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[Assistant] Written by himself, printed for W. Taylor at the ship in Paternoster Row, 1719.


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[Assistant] Learn a lot from this pedantic signage which is hanging over the novel. Not least of course, there's no author's name.


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[Assistant] It's a hugely, bulgingly expansive subtitle, and it gives us the name of the publisher. We know who he is. Mr. Taylor. But one name is missing, that of Daniel Defoe.


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[Assistant] Why? Because this purports to be an authentic book of travel and adventure. And many first readers, and this is a well authenticated fact, many first readers assumed that there was a real Robinson Crusoe who spent 28 years in total isolation on an island off the mouth of the Oranuku River in South America. Now, with the novel,


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[Assistant] In short, we encounter for the first time


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[Assistant] A convention of literary representation which we know as realism. Is this a true story or is it a factual fiction?


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[Assistant] Now, this confusion, and it's a very creative confusion, is compounded by the fact that we're not told what kind or what variety of book this is.


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[Assistant] There had, as it happened, been a recent bestseller four years before Robinson Crusoe on exactly the same lines. An authentic account of a sailor who'd be marooned on a desert island, Alexander Selkirk.


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[Assistant] And Defoe's story was most likely influenced. It was a knockoff, if one wants to be blunt about it.


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[Assistant] It was a homage or a kind of an imitation of plagiarism.


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[Assistant] Of the real life experiences of Alexander Selkirk, a Scottish castaway who lived more than four years on the Pacific island that was called Masatiera. It's now, by a nice turn, a fate called Robinson Crusoe Island.


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[Assistant] Now, how would the gullible reader in 1719, looking at this title page, know that Robinson Crusoe wasn't exactly the same kind of book as Selkirk's book? As I say, many early readers were fooled. We are not fooled, because we've become, and this is very important, sophisticated readers.


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[Assistant] Let's say literature changes, and so do reading practices. Generally speaking, they become more skilled. And without the kind of sophistication that we have, uh, the novel Robinson Crusoe simply wouldn't work. And neither would any novel, to be honest.


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[Assistant] And of course, we're also helped by the fact that Robinson Crusoe, uh, in our bookstores and libraries is not placed in the travel section, but in the fiction section. That's to say, we have a sense of genre, which is, at that point,


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[Assistant] Only emerging, only, only, as it were, sort of becoming worked out.


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[Assistant] We, we, we could play the double think game, this is a real story, this is a fiction, simultaneously, and...


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[Assistant] And we can actually do that and it is necessary for us to get a kind of maximum.


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[Assistant] benefit from, from, from the novel. This in fact is the essence of literary realism and it's a trick which the reading public has learned in the eighteenth century and it's necessary to the rise of the novel.


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[Assistant] And not every reader, one suspects, when the novel was still a new arrival on the literary scene, was able to do this. This kind of, what I call the double think, which realism requires, is, as I say, not, not


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[Assistant] In our DNA, one has to learn it as a kind of, a skill, a trick, or as a technique.


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[Assistant] Now, with that in mind, realism, uh, let's look at the wonderfully prosaic opening paragraph and as, as you listen to it, try and work out whether is this true or is it false? What, what, what markers, what kind of clues are there, are there in this? And of course the, the fact is it, it teases us.


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[Assistant] This is how it goes. This is the opening paragraph. Wonderfully so direct.


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[Assistant] Defoe has this capacity of writing so simply and yet so powerfully.


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[Assistant] I was born in the year 1632 in the city of York of a good family, though not of that country, my father being a foreigner of Bremen who settled first at Hull.


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[Assistant] He got a good estate by merchandise, and leaving off his trade, lived afterwards at York, from whence he had married my mother, whose relations were named Robinson. A very good family in that country. And from whom I was called Robinson Kreutzner.


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[Assistant] But, by the usual corruption of words in England, we are now called, we call ourselves and write our name, Crusoe. And so, my companions always called me.


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[Assistant] Now, if you read that blind, so to speak, without knowing where it's coming from, how would you know that is not autobiography written in proper persona? That is to say, by a real person in the real world, really called Robinson Crusoe.


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[Assistant] So the novel, we may say, is a genre which characteristically looks like something else. It's a, a, a chameleon genre. Indeed, some theorists of literary aesthetics argue that it's not a genre at all, but an anti-genre.


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[Assistant] We have, as it were, to change the whole, the whole kind of framework if we're to understand how the novel works.