00:01
Soon. I was looking for my phone, you know that more notes are worth. It can produce something federal job. You cannot so looking forward to participating in actually having incredible people

00:45
Looks good.

01:03
Don't have a way really tried, you know, like they might want to hurt you every year. Facebook careers. I have a feeling very back and forth, because there,

01:36
See a video. Have you called and the new top more on the top of the Just faculty that might have done when I think. How old is a couple years old?

02:13
I believe this is like more I want themselves, but it was was first to see

02:32
More, the people who ask for and then I could run with

02:51
One of them.

03:32
Notice we got to think shirt on again, you have another announcement that's fancy.

03:44
All right. So today we're going to do something.

03:59
So, good reason, why?

04:11
So today's workshop, we're going to have faculty completely. Okay, so that's a paper, you know, computer whatever I want to use, use your head to present and that results going to make them four teams. So one two, that's your kingdoms. Three. Four one, two, three, four. One two in.

04:44
The more people coming So D1 into.

04:58
Here, I'll move to the other side here. Do of this one. I don't know if that's what we have.

05:25
The to here to move over here. Should be curious. Yeah, you know.

05:52
Notes, where teachers?

06:02
Number one, voice.

06:08
And try to use my brain can be very high. So this before they start let's talk about personable brain systems. Kind of the difference equations. You know, different colors specifications have. In this particular, there's So break is on the right hand side, quite a control and the secret is on the left hand side.

06:53
Now, the simple and basically doing is just a checking sensor and making decisions because some rules So you can you are afraid to choose any rules you wanted and should be drones. But essentially we have the one sensing, we press the button below and it makes sense. The break is fully engaged automatically.

07:30
That would be different than other than what other people would talk. But it makes sense. There would be reasonable In most cases. Basically, we have the situation where if the button is, and the speed you're in in a moving gear for the rivers and the speed is low high or medium, whatever.

07:51
Then just think you tell what the break should be. And so you're free to choose anything as long as you grab the throat form, or as it makes sense so much, you know, after customer iterations. Everybody, I've got the right and, you know, really the, you know, I kind of gave to the pattern of

08:18
So there was not, it was not a difficult. Now on the homework of the elevator, basically remember that a couple of parts, the first part to do is so in other people have provided us with fresh classical help and they got help. And so based on that, other nations, Marty.

08:41
That when you, when you're doing the definitions of this, you standard rotation, you know, a little bullion number one, number two, use names that are easy.

09:01
You specifications going to be half a patient. It's not half a page, okay? Maybe but specific real specification that hundreds of papers. So if I have to go back to figure out that when we say I'm flawed not to mean the door on the floor, I mean it's just cumbersome.

09:24
And when you have a boolean, it's easier to use a boolean neurological expression. They destroy false because he's a true or not or not. Then to say, you know this equal that in the text for that, I wanted to offers So use Boolean when it's okay, make sure you use proper eyes.

09:44
You should use names. Like, for instance, you a lot of state motivates start cabin, location, cabin movement, cabin direction. So when you go into the text on a spec, you can see here a little about the camera. I don't have to think so and go back on the top of the page to see.

10:05
Well what do they mean by this particular form, so choose proper good names, you stand on notation for the decorations. Some of you have really used a lot of text for this state getting a more compact, okay. Just you know explain one line what it means. You know, rather than being often deadlines and you're using space and it is in the bandages of So on the outside states.

10:38
And by large basically everybody understands the state. We have the alarm which is a brilliant. Fire alarm College file, a lot. So we know and if you want to be even more explicit, it's far along on and it's obvious that if that's true, the true value and more is a negative one, we have them, they have to have that one afford the for the floors, we have to have the door open on the floors again it's a boolean so you know floor door open.

11:12
It's easier to and for the cabinet, and movement direction direction, location location. And then the cutting or not, the cabinet just moves, doesn't this? I Now the first specification basically is really Sleep service requirements, you have absolute service and upcoming your bank accounts service the downgold. You have requests on elevators and request an electoral three and then you have to remove that safety that you don't want the door to open and people to fall down or get their hands get.

12:15
And so that can be, if you use an economy, if that's a very strong constraint, so you don't have to write five different rules. You can write one and you can be very strong. The other thing is that, you know, there are those two in diagnosis, don't conference our button.

12:35
And that's all that is for the specification. And now however and we have to be very careful and believe how. So I think everybody make progress but I've seen mistakes that really should be very careful about. So for instance, you know, up invading app called implies blah blah, blah, carven as a door etc.

13:04
Then what that says. So remember cannot, I mean, alcohol implies cabinet. There was a door open at the floor. That's what it's what an example when you're not that basically says that as soon as I press the button, the companies to finish the materializers at this door. That's what it says.

13:34
And if that too means a test would be instantaneously appeared in all three places. And since you are not resetting, the life, the light may stay there forever. So we see how he creates specifications that are not, you know, are not reasonable. So that was one one problem with used and imply and be realized.

14:00
That means that has been happening. The same is the days, the other situation is using leads to, I mean, most people most of their leads to, but it is least true. And the problem is that if you say the hard call leads to eventually the carbon coming and servicing the alcohol.

14:24
Well it could come with century lake and I've called maybe disappearing in the meantime. Then why would the cabins too calm there? That deal says I have called and I've got is going to stay there. Cannot change because unless part cannot change cannot be turned off on this, you know, until we actually, I mean, the Canada cabinet rise and open the door and all of that.

14:57
So that those are two problems. I got another problem I found it was the people tried to control the up and down movement of the world of the of the elevator. It's as well at the disco conditions, move up, and that's for specific. That's what you put promises in place on how you will here and you put the surface requirements.

15:21
I have an alcohol eventually has to be ser. And this is what it means to be service. It means that, you know, our call is never turned off until the capital arrives with the open door on that floor. And he stopped When other operations. He sometimes, if you if you use once one specification, just, you know, so the inverse element of in general, which orderly writer, but for the reader does that?

15:57
Because if you have something where the door opens, keep the capitalism there. La. Okay. And you don't mention the fact that it's stop or something like, oh, yeah. And say, are you now opening the door? What the elevator is moving through this floor, then I go down on the next line and says if the elevator is moving not also open.

16:27
So if I take that two together people's perfectly but you shouldn't give me the first one first. So then I know that story because of the invariant that implication I can add without writing it down. I can assume that you can move because of the previous. So the order map okay now fire.

16:52
It is the same as alcohol down corner request. That is just another service. Requirement is just a service is different was not that difficult, but you're going to have to to deal with the fact that, you know, when you have a fire, you know, I've called down calls requests, a little cancel, so you have to capture them.

17:12
So that's why you can't. It's not as simple. You find them, they finally means. If you had some additional properties and constrained, the, the way things are happening, It is an opportunity In another refund of factory change in this bank. So that's why statewide no files. They it's a complete respite.

17:35
Some properties are copied over safety properties. Mostly. Okay? But the service requirements are now changed because of the fire. So you're not allowed to happen here complications. So, it's not because there's a fire, there's no fire saying, same old, same old, but if there's a fire, then you have to do something.

17:54
And then, for the third, the last specification, you have to look at the service requirements and start cut up with additional. It was so basically can just take take the service requirements and then come up with a new simple properties which control the elevator decide basically expressive rules by which the other veterans kill their most simple.

18:24
Okay. Give them very simple. I mean, the simplest is always that you go all the way to the top and go all the way to the bottom, on the way to the top, always in the bottom forever, that's not the post the best thing to do, but that's still okay because you are really basically describing the policy and I should be able now to take this policy and showed that if I had this set of rules that you're adding a specification three, I can prove that they imply the service requirements.

18:56
Which so basically you take this service requirements alone and say we are going to define this and we replace it by more detailed requirements that actually control the elevated. So when we say that an outcall is eventually eventually service, it allows the elevator to go one sleep seven. Then eleven one two parts.

19:26
As always eventually service is fine, we've had it very, very free at the high level then we write controls on the on the elevator. So if you have to service three and four you'll get going up, you don't skip three, you stop it. You see that's straight and we had before and then you moved to four and you stop it forth because you have to serve as both.

19:57
So and then so these rules basically allow you to want to, you know really that's three or four. I say there's a fire for the rule and for service provisions. I should be able to look at this rules and actually show that given this policy of movement. Those service provisions is how to walk up to this.

20:26
When two person is are requesting and different floors When you want to follow somebody. So I'm on floor five, I press the button, one. Of course, six of us. What should be a prophecy there? The closer one? Well, I mean, if you are going up, the first one you encounter, you should serve that.

20:52
That should be a simple course. Now they're also requests from inside the cabin. So highly calling for four even calling for aid is somebody's accounting cost of selling so that elevator is going up stops at four. That starts at seven that stops it and eight. So if those the service environments are as one as two as three S4 a specifications three, you copy those and then it's user right below.

21:27
It, these are defined as follows and then you have a new cell and this specification that actually accomplishes the same thing at those three. But I controlling the elegant motive. So basically already finding those those rules, I'm looking at this, okay? What do we need to do today?

22:00
Their own.

22:09
Don't have a problem.

22:14
Can even have to develop a specter and actually depend on performance specifications for it. Then you're going to have to of, I can get you.

22:32
Then you have to develop a program.

22:39
And then you have to put because we learned that the fact that programs really have sensitive architecture and make sure different ways of loving the system based on the article. So what is the, what is a nature of the firm? I have series a, the same? Initially a little 8.

23:06
B2B cash. Sorted standing corner.

23:20
And narrow sizing. So if any three a maybe one, two seven, they may be page and see maybe three

23:38
That all the same size are inserted. And they have big man. Who because what? You want to get out. He's an array X. The size could be as much as sitting in if I want to play us in here and we need a holiday. And I'll see you in and it distorted no duplicates.

24:17
Time and has a same same values and as they begin. So basically, you have this three arrays and emergent together into a array x My also the X in one of the start business written part of the number of the elements in that could be necessary. So so it's so you need to have some mechanism to express, empty cells.

24:57
He has a question.

25:03
Okay, so first thing you're going to have to write a specification second architecture. You have to choose an architect, you like an architecture which is distributed so doesn't have a lot of global things and maybe they'd be synchronous if that in, that makes a problem. So sorry easier and so you're going to point out how to get that chair even picture and you want to show the you know how that architecture works.

25:39
What are the processors and what are the registers social contract? Then you're going to write the code and you have to make sure this code is going to map on that architecture. And when I was about in his bed and once you're all done with that, can you take the proof, you know, the architecture, you can program display looking over, I got two hours and minus something in this.

26:13
So, or having help raise your hand ask me questions whenever you compare the milestone in your hand and show them. Your remember specifications one thing that helps is having some good definitions.

26:37
The creations can be the same before complicated speakers.

26:45
Go. Thank you so you can access containing a lot. Yeah, I'm trying to figure out how to do it. Yeah.

27:37
In some way and also like things in general here here, I'm just going very general because for every value, any kids were here, don't get confused.

28:30
The following numbers between solutions middle.

28:56
Is and even if you go this way and then you walk these channels back here

29:15
Eating going to read back one exercise initially back exercise, three and five minutes and then do that. Okay. I mean, well, I think that makes sense. There goes, we're gonna have the value which you have for a simple life.

29:51
So we don't know what number is being so near, I guess it would be negative. So the orchestra is natural resources, maybe but I'll be going to. Okay. Let's okay, let's make up an assumption that arrays are straight depos, okay? Of course, we could use zero for no so that it could be one, they're not zero.

30:20
Okay, you know.

30:29
All right, so then so we're trying to clean up our services. So, yeah. So that's for merging these three listings. But let's just raise this one to, okay? It's really easy. Just so it is new to store you merge. Okay. Let's do a raise before. Yeah. Yeah. There have to be unique.

31:03
Yeah, so yeah. Finally answer the phone to three. Seven, three, seven, eight, what using and The x zero.

31:31
Post is and because it's hard. So, yeah. Okay. This is existing X standards. I mean, the way that it was separately,

32:11
Integer. So so this is really important. So so the point that you have very low social that we compare and heal it easy, I think particular too close to a program. I think we're just writing a speech. I don't think we're too worried about what they're going to do with it.

32:57
We're just we're just specifying it. Here's your input. This is what we need to be open. Yeah. Because they could do it starting from the back. If they it's still exactly the problem. We don't want to like fix species out. So what the outfits are trying. We read three answers.

33:23
So here we meet sorted, you know, you can write a formula which is a one line formula of every time you want to say. It's so that it's sorted or because they it's sorted W equals blah blah blah and then it's just use is short. That's a difference. So definitely so cheap birds.

34:23
So the beer is the red letter sent over here. That's good, it happens but but it's okay. Yeah, it's just perfect. It doesn't work. The daily feature. Yeah, already. So because we're given more because I don't think it's very good. Okay, okay. We're given them. So we marry to find us.

35:56
Eat eating through their friends that actually potions only. Maybe he was in there in it. He said, we're just saying it's just about that arrives, the size of him. So right now three things levels really early. Okay? That's right. We know. So we said so then problem, he's others.

36:34
So for X, which you can track color. So you can point the perfect thing before disordering the customers here so important because that's using this. That's because, yeah. Equal equals x x the interview. I mean for us like thinking of internet was like that's not really something new numbers.

37:08
Yeah. That's why. Yeah. What's the next feels like? Just that stuff concerned or passes. A greater than five definition in pennies. We'll just roll it, okay? Okay. Start with a. So having that right like that. Oh, let's do. I think we should do it is that? I think there's just be the stuff before.

38:10
If we didn't take one right here, we wanted this stuff four has to be soiler and it has to be items. Oh my goodness. Okay. They're not allowed know because, you know. Yeah, okay. So, for all the traffic and not even a bit about that those are just values.

39:18
Yeah, I'm just trying to get the building block out. Yeah. It's just here the KY and does that stand? Like that's fine. Both it works. It's just I like the map. You said yeah. It's almost.

40:08
So then we made our probably the last one. Yeah. So elements are or subset or It's ups and both that work. This is called an act, is sure that this is correct development a lot. And then just man that over the entire list. Yeah, that's what's completely just be like, yeah, we take the items coming, take away, we just check if that items in the right.

41:56
And then for all it, we feel like that for every item. Let's say that way. Yes, this makes it all right. How are you noticed that? You think Jordan? Yeah. So like a set would be like functioning, right? So that's what we're saying here. Okay, here is not equal to you so sorry just because we need this education now, what?

42:34
Oh yeah. Okay, you have here. Let's do. So here actually is criteria on, right? And I am not equal. In fact, No it's not there. Yes. But AI can't equal him. Yeah, we're slowly fine with sort of because it's great about people so you're here. So we ever miss you posters?

43:11
ABC where a b c or sorter and I'm sorry for sort of a versa. Okay. So the funny okay? Yeah, genetics, whatever. So we do because if not we have like us, that's weird. Thank you. Hey I'm not worried about community, that's my padding value. So you should say these are.

43:32
All right. So really that you survive, okay, Thursday. 8:30. Hello again because we're not worried about Jay. Z going through in that case we're just like that. There's a lot. If it's we just wanted to maybe not, we just want to make sure it's working. We're fine. As long as we can.

43:58
Yeah. Okay. And I mean initially, initially are they sort? Yeah. Okay definitely we just use their resistance and what they began so they just correct. I mean and yes, yes, yes, yes, yes. I mean no, no not done yet. And so yeah because otherwise if that's if you are not required that they assorted I can have a real sort of and who knows what's gonna happen?

44:30
You can't get the right result. So yeah, thank you. So dirty, right? This early people, of course, were actually all elements of facts are element of the set that they could see have. Okay? And you say I'll say yeah x is also sorted x element of but that's dumb.

45:24
We actually I think we could just say it's equal to like A but let's just leave it like this this is more unity. Sure, both work if we change it we can so element dove says that there exists. Some I where a is equal to the thing we passed in and we're testing exist because it's equal to something in AI.

45:48
Very yeah, at that light. Yes. Then so the most other one, if you want them. If we wanted to do elements like compared to sequences, you can just do for all of us and for all a make sure that it's indeed. It's like the whole transit enclosure thing but he did was really something.

46:08
All in could take two arrays. Yep, size three. And we would say, oh, sorry. So we have an element of where we say that exist inside that array, we were going to do all one. What do you thought? We were making it easy here. Okay? Here, it's just that if you pass it a value and generate we get back that there exists, true and whether that is in that array or not.

46:37
So here we're gonna say draw elements of a, what I'm trying to do. So I think well working. We're trying to get to a final. So we have a net saying that everything's a sequel to infinity, we're trying to get to a post cleanly, but you need that says that we need basically says of x is initialized to something, but there's nothing about the variables.

46:58
A PNC. Okay? So and then I guess it'd be and a equals a, and it was be, but yeah, well, so close. So now I'm gonna give you a being sweet to one hour. Oh and there are sword and also to say that oh and we have a story.

47:29
So yeah, man, or and And sorted by. That's why we can all this time building up our pieces to try to make it. So it wouldn't be so hard to because I think our post will be pretty easier to write once we have all this stuff. Yeah, so and sort of see the infinity, sorry, man, reading so ugly, I really don't know.

47:55
Okay, so you're doing element of to check the same side. Well, we're gonna do a check of all in say, can you pass it a or a and x? And we say, like all of anything, sure that all of a b c are inside of text. Yes. So what would be a nice operation that I'll give you then, what is something?

48:29
We thought about this, we both were trying to use that we have Well because initially these contain duplicates, right? Yeah. So don't show the cardinality of this but should not have. I guess we wanted to post state that just because remember they can be difficult because between them too.

48:51
Yeah we just wanted some sort of check that says that yes, everything in here exists in x. So what is everything in here? That's also the same. I was thinking element of, but I guess we could use subset. Yeah, we wanted. But the problem of subsets isn't it doesn't, because my brain was like, okay, it could be an element of B, but if A is duplicates, both of those would have to be contained, indeed, right?

49:20
So like they would have to have two two.

49:28
That's what I have all in. Because I was thinking, like, Why don't you find a set? As that is right here, is it is an array that contains relative blankets and also, I can't equal up to, but okay, yeah, we are doing. We can't say that because that's the employee.

49:55
So yeah, thank you.

50:02
We to I thought it was okay. So maybe we or another way to do it. Our union elements in the rate, but extreme of reality for there are local concerns. Yeah. Because I mean you always say yeah because shortly like this and then you don't feel the brackets specifically so that gives you a set of all the elements in epidural thing to make it and then you can play with said you can do unions.

51:03
Intersections differences. Differences, and you say more. All right, so this next so that this this curly to make it move forming the yeah he didn't get really basically the stanchi again inside the class set and then a union and all the elements together. But if you union two sets that at the same thing, that's the original set.

51:31
Also union has some minions and he never that's kind of, that's what he's leveraging. Is the union of a set is also. So if you union duplicates to set you're still just the same size that's like he's working with oh union has this particular meaning? Yeah well obviously you could unions.

52:00
Oh, it does set a would be an set X because I've making seven move duplicates. So, like if you said set me right there, we'd have a set, containing two and eight. And we would have to confirm that set be exists in set x, which x in this case, should already say.

52:21
Then we couldn't use subset. Yeah. Okay. Oh, you know. So then So, then you're closed would be like post with, you know, there'd be a lot of conditions in a row, right? Or one option. Set a it says subset. It's this is the like mathematical. Okay, so actually no it's just it's just this the this is strips upset.

52:54
So if we want to be a strict subset which what's the definition of subset just says this episode just to and just do the the seat like this. Let's see. Looking thing. I don't remember what the difference. Oh it looking thing without subsidence. They're not the same which we could use if we want.

53:14
But we don't have to well then set a would be a subset of set X and blah be very problemable and only full noise false and let me think and then and to confirm that it's not. So that's set wide but we also want to confirm that our I think are things still stands is said, confirms that excess.

53:46
It's exit. Self is I said and right. Yeah, we should probably still do that maybe because that this doesn't confirm that. There are no duplicates in exit. Just confirms that these existence inside the soul, we wrote it. Let's use it. So, we'll find nice results. I think so, for our most visual, let's post.

54:07
Okay. Yeah. Yeah. This post is that. Yeah. And you need, it is this, it's just initially, all x values are equal to infinity and a little, a vehicle little soul. We care about. So we have milestones. Yeah, we technically have miles per month. We have ours back. We want to write that cleanly and oh yeah she wanted me.

54:39
You have cool big in right? Sure. You know what, with how much we've read? Maybe we should? Yeah. It's a lot. I mean we he saw it and he talked to us about it. We can just confirm do you want to think about architecture? We need to I don't know.

54:57
My question to me this what is this last week? We had left. Okay, on our detectors, let's see. Yeah, I was super zombie list class so I do we have to use this tribute. He said he wanted us to use a synchronous or to update something else. We think about which one we want.

55:18
We could use these synchronous here in memory so good all those things. Yeah, you handle it. Just I'm keeping my cards showing my hand. Okay, I'm pretty much our cat. The labs we do. Are you natural. I'm an internal graduate student. I work about 20 to 25 hours a week, so it's still feels weird.

55:55
I wasn't interned. And then I was tired as an R&D MTS. And so now we take one classes master after work, which is why like tired? I understandable you have to walk this morning. Yeah, from 6 to 3:30 and then I'm here. All six. Yeah, well I work from home though.

56:16
So I just like wake up and walk downstairs. Feel pretty bad and I work home soon. It's still pretty bad. Six, six in the morning. Yeah, so you'll still work for eight hours. I do four tens. And so all photos. Yeah. Usually I work from six to four without a lunch and Monday through Thursday and then after Friday's off.

56:40
Oh, luckily next mystery, are we taking algorithms from 11 to 12 and Dr. Vaughn said I gave you so I can just do it, college breaks and then I don't have to like rush away from work to come here. I don't know what the architecture. Okay, okay, I think people are kind of converging back.

57:13
Let's see, so and then we have a different sort of facility. I'm just going to wave my heavenly machine but we need. Okay. We have a equal a and b equals b and h to the greater than you see equals C 0. Then we have to make sure that that sort that.

57:40
So basically say sorted. Okay. So to the support, see person like that. And and then we have also internationalize x and the we know that, you know, we're going to have. We are starting them though, can be no gonna feel act. So we have to feel it. So the easiest way to put the feel of this to put infinity there which stands for there's nothing that is value.

58:21
So, basically, you can say thing, something like that, basically that takes care of all the of those, all they need then. Now.

58:38
Post.

58:42
One, we want text to contain all the values that are in. The inner original. Not that original. A B and C could have been destroyed. I don't know what kind of program. You're right, right. Maybe that is true and they're not destroyed so we can't relate to capital, A, we have to look at lowercase a.

59:07
So basically, you know, one thing it's okay say it's lower case x so you find x and there's a set of all the non, you know, nonzeroes on infinity values. Several x equals equal to say nearly you need in, okay? The little overdose so that would be one. So that basically ensure that there holder is in Union infinity.

59:45
You also need infinity. And well, depends on if I said. So basically and I'm not I'm experiencing zeros and I'm including infinity process. It's part of the definition, I can come up with a little bit and this is not enough. We also have to have strictly starting.

1:00:13
And so basically it says that each other might be smaller strictly smaller than the element before, but I can play with the strictest sorted to ignore infinity. So even AI and a high price. One of those infinity, then AI has to be smaller than an opossum. And if it is infinity, you know,

1:00:44
Well, if you have to be careful how to be finding here, because you want the infinity, you want to compare against infinity at the end and you want the equal infinity to be fine. Carefully. And,

1:01:05
So AI is more than act plus one.

1:01:13
The eyes is different from infinity and loss of if AI and AI customer equal, both infinity. Also, can do we have to be strictly sorted since x is already a set? Well x is notice. That x is an array. So we're saying here, the eggs contain, all the values that are originally given to us.

1:01:37
That's what it says, but doesn't tell you that they're already. Anyway, this says that their order so it's like art is set. Those are the two lists are interfaces.

1:01:52
Okay. Difference between sorted. Yes. So that you can educate small smaller than, or equal to financial basically, in the strictly shortage. It's just these two, which is what we said here. Anyway, even though ADHD or he says they are gonna be, which is where we can't even send them I have.

1:02:19
So is set or no doses. It's this is they won't have to so no strictly. Sorted is a way to confirm the array X doesn't contain your kids. There's no way for us to the register, put the elements of ABC into I don't know. I guess we're always working with the raise but fair enough so I don't know.

1:02:48
I'll pick one because I don't even know this like all in or elements of handle it with you. So they're set eggs.

1:03:03
We didn't mean it's okay. We're very nice. That would not like that. Maybe. So we got all the problems lined up here. I was enabled back to right now. Just bother me that was late now, you're good. However, at all now I have to just think about this said, my new synchronous architecture.

1:03:29
Just do it. Thinkers share memories. Makes the most sense finish because I'm also distributed to us.

1:03:41
So anybody matter and that because there's something that's x context that they were. We also need those. It's fine. That's actually true serious. Obviously, instead of like many but then become a particularly distorted and that requires system, essentially forces to be modular there.

1:04:07
And I'm just having to care for this particular. So you know that infinity is at the end, you know, those adjectives that we don't count us into.

1:04:22
Do I need to write the definition? Let's write the definition of percent of mine. Like it's not that simple. So that's renamed. There's no. So we won't get confused now because it continues infinities. Yeah, so I think that's where you just called it over. Well, duplicates. You behind the.

1:04:56
Okay, so we can restrict our sorted to say AI, not equals zero, and a, I plus one equal infinity, or equal, and also here, and okay, what infinity equation here, right? That scenario so I don't so I don't include anything in the zero in the in a delicious that makes it easier and clean.

1:05:43
So see this in union of the elements accordingly. Other methods are not between 10.0.

1:05:57
Okay. All right. So now we have a specification. You notice that a B&C will not show up in the post, you don't care if you destroy them in, okay? If you keep them the way that don't care. If you use flags, like, minus 3 indicator, is what's used? So don't care.

1:06:17
Any seems like that can of course, we are only interested in the original arrays that I did now. And how many things? And that's why you can use true needs to fix point and things going is proposed because two implies whatever initialization you want by the extrude. Hold your side.

1:06:46
It's a 300 say I live under, but also I cannot even walk again. I was wondering if you can have the case for AI, cannot equal any. But yeah, plus one can and then also you can every case where AI and AI plus one, equip it. So you should cover all of your So combination is another way to do it.

1:07:11
It's a sorted. And then as soon as sorted and ignored infinity in that, in that part and then this is. All right, so everybody's on the same thing, okay? So the people come, Now we need to come up with an architecture. If it's going to to be amenable to solve this problem.

1:07:38
So, what you do in your mind is not on paper, please think about the current. And then you'll ask the question of what kind of machine would exactly? Do that go, but don't write the code down. It's just kind of informal in your mind to justify that effect, and that is just a drawing, okay?

1:08:00
Basically a boxes and that's all it is.

1:08:12
My wife is showing access to see if first, let me just give you money want to take it. So,

1:08:23
Is memory. The processor.

1:08:30
Okay, and here is a B.

1:08:38
And the processor runs the code and modifies ABS, okay? So that's a memory and a process. So I don't like that. Okay, that's that's complete. Shared memory. I want something. This one more distributed much more parallel. So push the level of problems into the think the closer to the other side level rather than you know desktop computer.

1:09:08
So don't do that. All right. No, he's way out. One down It goes. Remember each. We have one think message. Passing could be nice. That's one option. Just trying to see it. Yeah. Oh, you're good. So I'm trying to think if I had even more on our whole processors and so memories or processors.

1:10:06
Yeah, we could. That's why we could do key one for PACs this, former movies, but Question is on how do they communicate? Yeah, so there is a few options for how the stick would communicate. We could use. So, maybe since the element point is to so each processor and tens of pointer, and it sends a copy of the value pointed by two by the pointer to hex and x choose one, and replace a message to if, you know, I think that's what you're getting at.

1:11:20
Yeah. Okay, that works for me. And if so, X picks the smallest, one and sends a message back to, which he chose from, and then they sent a new one. Yeah, yes. Yeah. We can do that. Okay. That's a good idea. But I was going to say yes and I got here, so it'll be like this, we're going to have one processor per array following you, right?

1:11:56
And they're going to be using message passing to send towards P1 like their next element. If I'm following, what? Two large, still all right, not really. Yeah. Okay. Thank you. That's a little easier.

1:12:39
So, I had to be compared to use at the same.

1:13:06
So he said we could use synchronous architecture. If you mean these each processor would, that's tough. So that's tougher. Power than that here, that means you have to stop. You have to stop. He said, we could do it. Maybe don't worry explaining like when who is this is so we could have what if we had a certain chunk of each story on the process everywhere.

1:13:41
They're not. I don't give a architecture stuff, trying my best stuff so you're doing it. So keep going, speak helpful to you. Remember what he described as a friend? Is told up, the rain is too large which is just to say we have too much data and a single place.

1:14:11
Oh, I'd understand why he's saying that because this doesn't scale to do. If the array was too large to fit on a computer, like, in big data, we're just kind of out of luck. So when she see my last two, one processor, take one elements to something and put in x.

1:14:33
I just thinking like a tree just like flood up through the tree, right. But I don't know. That seems like a lot of pain. It was a since this. Yeah, I understand it although I did. So I understand why he gave us the. It's not very parallel because ours isn't parallel at all.

1:15:04
Since it's just called being flooded through here. One of them. How do we make this more parallel and sayings? Is this anything different? I don't know, my brain would want to just because so remove their duplicate. They're all the more in and they throw it. Yeah, the issue is he's talking about like, How do you do this on mobile?

1:16:06
Yeah, we're highly. So global these how this is also is distributed, but we want to run something. Highly handicapped. So the technology and fucking starting with Dean Martin is you know beer bottling company, okay. Basically the bottles are moving at high speed, you know, in kind of you know here they get, they get to be here, they get the cap here, they get, the label here, they get into the package ago, One of them nothing fast.

1:16:42
So one way to think about this is you got the city race, they BC the whole fee internet and everything goes blue. So one bottle moves at a time. So this is your bottle here. It was in that direction and when they come through, they get sorted, you know, they merge together.

1:17:11
So for instance, we want to, you know, the beer situation. We have three counts of beer, and we're going to create a gift pack that contains one of each kind. So, what I do, when the one that beers come, you know, the bottle scan. We take one from here.

1:17:28
One from here, one from there. And then we send them together and they want to be in one there. See, so keeps the staff. Keep something fed and the output keeps on going out. So you get a lot of synchrony, a lot of parallelism but think of an architecture on those lines.

1:17:49
So but yeah, we want to ignore some fears for a while. So like say there's a seven and you know, what they do on those lines. What if there's a little beard that this doesn't have enough weight, the push of God because no, no. We know, we're waiting for the wait to be high enough.

1:18:11
Yeah. So like what he means is, like, saying exactly what you're thinking, okay? But you can do it. You. And basically if so if I wanted to have a Guinness here and this is how beginners, I just don't pick up this. I don't know. No, from there is a there's two golden goodnesses.

1:18:34
Yeah. Okay. On those ones but we're not applicable in Tennessee. We're at lights bronze. So then you pick up from that line. So how do you get from? You can take your three choose your max, pop it over and then you compare it against those again or these against this one.

1:18:50
Compare, those three pop over the max and then if this goes away, you compare these three and pop over the max. So eventually, you do still have, like, if you had an 11 down here, you would still eventually get that like that things that would fill in would be taken.

1:19:04
You just always have to say that. Basically you have to put some of these and that yeah controls so so like do we have to assume how the rice has tall is the this example each value is stored in one single component. Also, the So one other way is actually, this tribute One array is contains for every from every value, Every end index in.

1:19:42
The array contains itself In a cell is always exactly. In a cell is in different computers. Each one is a different accustomed tools. Oh, each cell is a different computer or cell and content. Oh, yes. You're trying to diagram and showed to me. So the next stage I was thinking like So don't draw your hand, I don't know.

1:20:18
So it's I'm sorry that you take over what to do. It's poison A and A1 is crazy voice here and A1 is here and okay and that's crazy. And not resolve would be extra somewhere. X1 is somewhere, very photography. Thus, this may have to be that way learning possibly.

1:21:10
So who are the message be like, is in Phoenix? The message was say, I have array A zero element and it's value. Each message will be. That means but how the message is exchange. Great question.

1:21:43
Well, I'm thinking that it is a largest machine.

1:21:50
It's feels like mobile computing. It does. So that the refrigerator level is this much better, you know, this would be when the clock says things, they won't go see.

1:22:13
To different way of thinking. Hmm. So then if each cell is the different processor, then they have to exchange messages, for example. Remember, you can have neighboring cells that can reach trust is memory. Oh, there's not because you don't have right confidence. Oh, also, see, I think from him.

1:22:42
He takes for me. You take from him. So it depends on which architecture we choose.

1:22:53
To each cell is it has its own process, but it doesn't have to be message passing. If we assume some kind of architecture doesn't really, we, we can know my neighbors he want to match just because they're sending order. So the largest any order. Oh, you are not a leading desert.

1:23:27
There is something right. He did a backwards problem. So, this is going to this is high. That means that you're taking something from the end of the product and pushing into the front. It's much more efficient to pick up something for the front of the bike and move it up.

1:23:46
Well, it's not like a link list. So target we have already a honorary, the an array like that HRA is made out of end process source within the memories and I can, I can do this. I'm gonna PGA very easily. Okay, and then I have, when I write x, you can see times larger.

1:24:17
And again, every cell, can I have a special flag to indicate the memory term? Introducing one of them. So what has to happen? Is that stuff from here has to be shifted into the. So there has to be some mechanism here, that allows us to emerge to much and some additional circulator here.

1:24:56
And you have to make sure that you do not get into a situation where two cells are trying to write at the same time.

1:25:25
From computer. This computer is not solution to a different material already, or they give them to this computer understand how the numbers important until what happens in between for what the merge does. Because you explain the internet Don't again. Yeah. But it's just so sorry. I was seven and it's three.

1:25:57
It hasn't much to do. It'll take the aid out of being put it into x. Okay. You get another and then not but they have to have room in there. What do they do for you? More for a point? Yeah. For each time you shift, you move shift it, right?

1:26:16
Yeah. Because like, that's what I'm writing here. Like this becomes exterior on first and then we get our second max value because x, this becomes, like zero that becomes x1 and so in your consciously shifting, all of them to the right but only one can shift at a time into a or into x.

1:26:36
I'm not necessary to find out these things so that you can shift all three of some time and sometimes when you want it. So, that's particularly they all have a seven, seven shift one, and two x node two away third, she want to shift it all over the problem.

1:26:59
If you shift them all at the same time is if you shift away all of these numbers and you're just assuming you can sort them into here. You're ignoring like numbers. No. I mean you're you'd be ignoring a number back here. That's like lower than that kind of order.

1:27:14
I'm just saying, if you process all three at the same time, you just counted equal seven, seven seven because oh, special purse, special case. Okay. So if there are seven one, we got a little rise. And then I'll have the merch. Yeah, you could. If there are all just natural numbers or national integers, you could also say if they're one apart shift, both of them into X know we're just part of the circuit he gets expensive.

1:27:46
Yeah, if they're equal. And then if they're not just got how many cases ways and research In case of one, max shift that one. This is maxi. You see that in that if this is my exercise you please send that and this is my accident you face and that.

1:28:11
Yeah. He posted this shift this and then yeah. Well he's more than I was just thinking of cases being yeah. There's three like you need. We can't there's there's one that's the most to that's the most three. That's how I think of anything in case when we're probably not taking a break because I go to the restroom took the coffee before class.

1:28:49
So stand. Remember, I hope you like staying here. Well, my life is now on travel. So I think how about I have to dogs from the problem then? So what did you remember about the tongue for the last semester? The children, if they were an example, this would get about your agency but only have eight and x.

1:29:28
And what we we want to take A and moving things and to forget about duplicates, we just copy it into it. How do we do that?

1:29:47
Think one element of a shift, right? One space everybody shit right? One space. Anybody shift one space anyway. Stop shifting. When this guy is here right Now, that will be the logic when you just have enough. Let's say that we have A which duplicates and we don't want to duplicate, we have to remember that the pattern that was put here for five.

1:30:22
And if we see another five here, we should this guy by noticing. Money. Can you to generalize ideas for your age? Do we write words? Do we write? No, just like the box developer thought the word version, okay? So now we explain to me, okay? It's a nice paint to do what you can inform them, you know, okay.

1:30:49
Because X is very empty because I can explain to you. What? The So we it's so exciting.

1:31:05
Some of research step You can do that. I guess we're just pulling from the Android. We're looking at the end of all three, same time. And greater than shorting circuit is easy and all the students. So it's informal just, you could also just write max of the three, I was trying to just do case bike.

1:31:41
Okay? Okay so it means greater than both of those. Well I think about you know you're right. You're correct. Did we need to care about pairs or duplicates? So if A and is the biggest workout, in fact I am also shift this and then also they shift. Yeah, right there, That's fine for now And I don't think we need to write the other symmetric cases.

1:32:09
Do they give those out? Yeah, for brevity. We should probably say x shift an Xi equals or X 1 equals. So, like in case X had stuff, we always want to shift out stuff first. I'll delete the first one open. So before this debtor is before it's assigned to something, we want to shift everything over to leave the first, what shift at the end?

1:32:34
Because if we shift at the start, we'll shift at the very beginning of, when we start merging all have an empty thing at the at the end. See I'm going on exactly Florida students thinking. Yeah, if we shift first, just the edge cases on the first time step we'll shift X, right?

1:32:55
And then we'll add something. So always have this empty it cell on the end, right? If you see what I'm saying. If we shift everything right, we have an empty cell at the front. Then we assign something to it here. You want to shift when you want to shift.

1:33:10
I think I might be we have something that we can assign to it. Yeah. Shift everything over then assign. Oh well I guess when you're initially you can just override the first value. That's why something we can just shift it. Afterwards is what I was thinking, life is second case.

1:33:26
Say that happens. Again, then you would just override what you have in there and you chip that oh, if we shifted the end. Yeah, then I guess we can. But then we always have an empty value at the front and that's true. Because if we shift at the end we have an empty value at the front.

1:33:43
I mean that's an empty value to be filled around. So I say this. She's got general idea but let's let's kind of refine. It doesn't. So what you want to do here is kind of architecture-wise. What are they going to have? Is basically we have this parallel arrays that can be shifted.

1:34:06
Now they don't always shift so we are going to have to have some signal which says shed lotion. So from this, whatever? Okay? You're going to be a single here.

1:34:36
That signal is going to go along the entire line, just one wire very cheap, which link to that. So what you do? If I pull the wire down the next clock, you five, if I leave the wire out on the next clock, you can go to because that's a basic circuit in it.

1:34:56
One, one another strategy. Another element of strategy is a fact of everybody's being ashamed. Sheep brothers. And now we want to add some fixed cells here to shifting zeros, but we see the whole thing is one line. Okay, that's not just constant values that shifted to make the circuit in more uniform.

1:35:22
Because it's easier to say you don't want the special case I have the last one in the array. Basically, the last one there, they act like anybody else in the array has exactly the same circuit task. It doesn't exactly the same work so we can. So we have two, two things shift, we have a shift signal and then we have the shift, okay?

1:35:46
Like I said, the sheep semen is cheap to implement this by doing this. We have after uniform secretary, all the cells of the set. Now what's alive? We look at this. This is much reads this device and so, let's call this alpha beta and that it reads and it computes a maximum

1:36:23
And also knows this value here. It's quite what either? Okay, So he's a maximum here. He's the same as eager. This room shift, we have no new valves. If the maximum here is different from either than because to shift, and then we have to see is a maximum belongs to A D or C.

1:36:56
If the maximum of A, a gets a signal to shift, either maximum belongs to B, it gets a signal and it's also possible that all three are the same and the ocean. Now, this is computer certainty. It doesn't require any register for us to store. It has computer values that is I'm not available to us computers.

1:37:26
And then when the clock from the clock hits, this cells, check the line and say, am I supposed to shift? Yes, I shift and that happens everywhere and it's all Now they to do the shift. We always we know how to do a shift to do the parallel bar AI.

1:37:50
Plus one quantico a survivor that the ship and to the founding bottom, of course all. So basically have a parallel bar here product by here, part of our hair product there. So we got another three shades. Now, we have to do this conditional, if the shift shift a is on, as you think just, it's just about it is computed in dollars.

1:38:19
And then let it say, it was the same thing for one of it.

1:38:27
So, what happens is that, we have an older section that impenets emerge and makes sense, because it uses no memory. It's all communicatorial circuits and all gates that just gets. It's all the district. And and and then for each one of the array, we have one big parallel bar.

1:38:50
It just does a shift, but the sheet is done, only if shift, a key define is true, If they find, it's true here in the first section. Or again it's an always section. So the only section contains max of AV of the AN and VMs CNN, right? And in parallel checks, the max with x 1 with A and B and N and CN.

1:39:29
So they're basically 40th. Four definitions of shift, one definition of max he always section. Okay, nice color. And then we improve. We just finished the architecture. We could also do one decision max and one definition issue, your first step, max returning things, the value and what array comes through here would say.

1:40:03
And I know how you think because I I want to see before, let's maybe max first, I think Max is just going to be one definition, right? Yeah. So stop to the declarance section different and I first met.

1:40:32
Yeah, you can give it the arrangements of this and for always wants max. It's also just comparing the max of three values, right? Yeah. Okay. Sounds good is to your first. Yes. How would we define that? And, by the way, the next assignment would say, leave my next day, it's gonna be exactly.

1:41:11
Kind of like this. Oh gosh. So that's why they're being trained and being prepared. Okay, let's take the fuller and so taking the values, okay, you can oh, just take an array. Like I know I'm saying, take all three. I mean, let me write out what I was thinking because he wants us to just pass in.

1:41:32
Check those last three values each time. So why did you do your declare? Did you already need to clear image almost? So, do the declaratively need first, then to the knowledge, and then when you have to always dance like to me,

1:41:54
So, if you, I'm not answer it's emerge and take three hours we can resist. You cool bar, one of those books like and then anywhere really want to shift. If for him, I am here. That works and Max. Hello, and

1:42:50
To beautiful shirts.

1:42:58
A little bit shape on you videos from one to end of integer will have I equals a material 0 and really because there we needed to clear a yet, but I'm using a X equals infinity and he got done through and we were repeating this for this. So we also needed in resorted probably in our eyes, we haven't established that.

1:43:47
He said, he wanted us to make sure that A B and C were shorted. John just copied our definition, from his face. We wrote it in, unity is code. I think it was basically quality energy. I'm trying to recommend it. Yeah.

1:44:10
The question. Yeah, there's going to be.

1:44:21
Plus one was on this thing. You say zero schools? Yeah, waste a time. What happened? I was thinking about returning the vowel. That was the max and then the raise that were equal to that so that you could know which ones you want to shift. So he's wanting us to always analyze and see.

1:44:46
So really, we could just return. If we call max, we can just call max this here. And that current max is of all the end, the blank end of them. That's what I was gonna think about. Because I'd like to know, is we have where that maximum always. He actually don't even have to pass max.

1:45:06
Anything technically, we could just have an expert turn. What the max is of the three at any given time. It's called what the max is, is. Yeah.

1:45:27
The bigger number. So you like everybody? He is here because Max X if you're taking a list from me from one mmm one told me how to do this. I forgot there's a way to write max and unity and it's basically just place of the thing you want. When you say anything, just do it.

1:46:19
Do we have to declare a pointer variable. That points will be easier. It might be easier if we shift the arrays instead. Oh sure. Yeah, he wants us to shift all the arrays so when they're supposed to shift so we can relax the same. Like he did the set here with union.

1:46:40
Yeah, he was too max and then just constantly compare the two values. Maximally it's always been the bigger one. Remember how you're supposed to like, say of multiple things? Oh, so we draw this down yet now. Yeah. Oh for shipping the whole list is oh that's my want that.

1:47:09
Think about how we look, and, yes, I think just use this or you're just saying, mathematical max of qualified. We can use it always but it's so and then, yeah. Okay. Set my homework feedback quarter Celtic man can go for some fish and chips anywhere. Two foods. That sounds good because we are only considering three opportunity.

1:48:00
Always first element next. A zero ship days just as returnable of if Asian share is what he says. So just get amazed. Yeah if there is an also to check if and equals max How do you go? How about we write everything? Assuming max exists and then we can go back and write max, Okay?

1:48:50
So we got in here. Is finished, What anybody else is there? Always say your brother. Okay guys, finishes your father and soon because I'm doing, you have the same last name. That's cool. So this author or young girl, or there by 22 minutes, earlier please, that's okay. I'm gonna just keep her head down.

1:49:24
Yeah. Focused shift a I mean, yeah. He's always happy. And he knows how much we returns if yeah, if so it should take

1:49:49
Thank you. Anyways, the functions is just supposed to clean up your color or something. Yeah. Just is anyone bless your day in my name?

1:50:31
Oh, so you are assuming that this is zero. This is you're going to write always section on the book on the board discuss it and if you don't need differently, explain why you're done a differently or maybe programmer. So we do have shit this 19 and including that in all reception, pay somebody zero

1:51:13
So that they scared of his. And but that also, because the dollars, Then we have some tips. We have the max. Okay, so we can give it a name so we cannot have the right max again, and again again. So it's a next equal, max of and okay, cool, we just did.

1:51:34
Yeah, military. And that is nice. Now, the only thing we do is find out one is shift, what shifting should be? You should say. So we'll say shoot. Hey, we didn't draw our false. So one of your should pay a m equals next. This should be about if you say n equals next, right, right?

1:52:13
And that left.

1:52:23
Next. Not. Oh, yeah. And next not equal to x one or x zero. Do we have to check that? No, no YouTube is just later. So connect message. So, yeah, that's probably how you need to shift day, right. One of those AM is zero. So he finished array. So and even greater than zero, you might want one zero even though it is 0 in our shifting we're not but that's makes it cleaner.

1:53:11
So, so it's now B. See. Okay, but you need to decide what to shift x.

1:53:29
So, what we want to, what do you understand next?

1:53:42
Taxes numbers different than when the head of the list is different than the next. So we want x 1 of responses different from next.

1:54:03
And X is not good Next different from 0. Okay. So that makes it very, very nice. Only everybody agrees. So if we go very and this is wondering, zero next one,

1:54:34
So, the value that we have the lowest value in x is different than what's in next. I'm not a zero. If there is zero, would want to close zero. Zero. Correct. Next is zero. That means A and is zero. B is zero. We are done. We don't want to yes.

1:54:58
Could it be enough to say that x1 is greater than? And which is the same thing because that order. So it's just different is good enough. This first, it actually happens again. Now there's only one. So this everything is nice because I can now write the code for this things and being basically AI and plus one colonical AI.

1:55:28
If patient only parallel bars in our back and I found this and that's that and that the only part that is not nice. Here is the fact that when I when I do this shit here x1 is to get the value next. So it's a special case. So that means my circuitry has to be different.

1:55:56
So I can play a trick here in basically, say x 0, which is not part of x to just create enrollment section equals to connect. So now the code or x looks exactly like the code for everybody else tested shared, right? With the

1:56:26
If you have puzzle, ask questions now. Hmm, doing so we need to write their code, you know, see what kind of what we were thinking about the whole way, this one. Yeah. Where does the ship show? Yeah, the wind do we shipped or not the key of where you, please put, Xmas building stations here.

1:56:57
So the code looks like I don't have to I don't understand. It's you don't have to handle that separately. It's like movies of code one which doesn't get and one that takes an x and putting the x 1 that basically. This less nicely. Exactly. Just the same way that 50 days deal because they play this as a variable so that we can in the code, we can just make it 24 questions.

1:57:46
All right. Well, now you have the proof, I'm doing the right. Statement which for branches in transport is a nuclear war here. In our zero, very high step seven. Also, in our programs, in our program, there is only one statement, right? Yeah. With all parallel bars. So I have there's one stick, you'll have statement saying, a shift between a, it's the same thing for all of them basically.

1:58:35
It's like, okay. So here's always right, yes, aside. Yeah there. Yeah. Stronger earlier elements and shifting it over if you did this turn, right? Oh,

1:59:07
Okay. Proof.

1:59:15
Feel like proofs.

1:59:28
Among this one. If you're assigning eyed, I'm sorry. I did. Well, my brain was like three to be. Okay, in guidance.

1:59:45
Know you need a message.

1:59:50
Okay, so we need by themselves, we're going to want some variance them that you know, here the next metric, you helpful excess, maybe ideas.

2:00:21
Because then we've just need to show that x continues to grow until it's matching the until it's at. It's kind of thing about we used that set notation. Yeah, we just have to make sure that we need the set. X is the same size as effectively set. A mutants you said see or has as many non-zeroes I guess.

2:00:44
Yeah, functionally the same. Yeah, So I guess the post the post is set x equals say. Yeah. And so he saying we have to pick a. Yeah. And the metric could be the number of non infinities and x squares until it's equal to the number of elements from those three.

2:01:21
So we are proving you seeing and it to post and in this table pose. Yeah. So we metaphors that were had to worry about post and statement post 20 years. So do we do stable posts first assume We can everyone assume post is true and then yes the stable basically means we have to just say, it's not going to grow.

2:02:01
That's right. The x isn't going to shift or grow. I guess is what post would be, which is somewhat cereal because the max of zero, because they're also all avians here, all going to be zeros. The max of zero is zero So shit. The shift flag will never trick it.

2:02:24
Yeah, So it's never going to shift. So stable host is totally easy money. So impulse is true. Yeah, and we look at the statement. Yeah, facility. It has to be initially true. And then stager is very or nothing. No statement could make it under. Yeah, nothing. So the master and the zeros.

2:02:53
Yeah it'll always be true, right? Because and all of will be a zero v0 and zero. So that point the shift, those will never trigger it. When everyone move to shift anything anymore, they'll be no assignments. We can't change. X will be fixed point at that point. Yeah, so we have that English.

2:03:20
So close. This is true. Yeah. That means and we kind of know that one. But how does this redirect to the shift? A shift base you shift? See? Yes, we're resumed. That it's true to start which means our program satisfies the spec right? One post history. Yeah. Supposed to true the program is finished.

2:03:52
We just showed not going to destroy its created. Yes. So you guys the metric idea that I had was a comparison between acts and X is not zeros the amount of too complicated, right? Yeah. Looking to be a lead singer because multiplication little, what's happening? Look at the arrays.

2:04:17
The importance. What's happening here? Yeah, to our initially as our messenger, our metric is there slowly empty. How many entries are in all three of them combined? You know it's just the easier way of saying but I was talking about this. That's what exits. So there was that metric.

2:04:45
Initially could be three in. Yeah so it'll always we know what? All is decrease so and you have to prove that it decreases. Yeah. And proven one of the shifts are true. Yeah. Probably. Now it will be and I had sweetness. That's right. It yeah. So no matrix now empty entries in ABC and D oh yeah.

2:05:10
Combined ABC, non empty and then we can yeah. So initially that I have a is one through n entries. B is one through an entries sees one through an entry. So that's why you can say initially that metric is equal to three and okay and then by post that entry should be equal to zero.

2:05:32
You should have all three of your arrays just empty all zeros, maybe you can write the right for one of these reasons having together for the to something. You're right right? That's so what is that one? If oh yeah she's not equal to zero so that I guess this should be what you need a summation time.

2:05:56
Yeah. Or plus? Yes. Okay. It was like, what do you mean? What. I'm just gonna use. What Roman did. I'm not gonna write it. Oh yeah. I'm just gonna thought at least on Roman. What do you come on? That's how he, well, that's what he want by your cooler than I mind class.

2:06:15
Real long. I can. Yeah, I can send him wrong. So then we did it. Then we just need to show that this was decrease over time. Yeah. And we can always point to the statement because I'm just trying to go through it anyway. More. Technically, they're always most exists that these aren't zeroes.

2:06:41
There must exist, maximal vehicles of zero. So they're going to exist and here and that moves, the max of those would be that I haven't seen enough, right? Okay.

2:07:07
No, probably measure promise. Yeah, but the number of zeros, total all over your races the opposite because you want something that decreases, okay? So far metric is going to be I'm just writing that as well as, right? Yeah. Some perfume, some of the some see, and then we want our metric to continue to increase, decrease.

2:07:40
So we show that if we say, oh sir, how do we write that? I guess, how do we write that degree in English? Okay. Trying to remember you do that thing. We're like okay, this is a metric. And so you said metric initially equal decay and focus on the cameras.

2:08:06
So basically you can read some of my previous meals but there's a function of zero of Avenue and basically it's going to be the sun. I,

2:08:36
Oh yeah. If So this basically counts of the number of non-zeroes Then introduce a metric new which is long zero a plus zero zero. You know, I should have come up with a shorter name.

2:09:03
See that kind of now? Notice that the progress it depend on what the computation does. We could write a program. The basically takes everything sucks, everything and dumps. It doesn't give us the right result, but this is a good way to decide the parameters. So what we need to do now is we need, you need to be sure that you equal K greater than 0, please do.

2:09:35
But by the way, it needs to Some of you in the last homework, used this where you let us and idea. What that means, is it these two like in this for. So, this group or is an implication,

2:10:02
If I interpreted it as being the lead to you got 30 points on your home, you find different as an application. You can 90 points around so bad things are what symbols you are using because I was gracious, this time and I said I'm interested in this way. But next time, I will not only tempted, the worst possible way because in the requirements specifications, you always have to assume that.

2:10:30
If you are submitting application, we should choose a worse possible column situation. So don't do that. Please. It is spell outlets to or you know make a note that this I mean listen to or if it's implication has to be implication the standard logical operator that's implies. This is even only if you start a logic, sorry for the sidebar, okay?

2:11:03
So that leads to new smaller than cake and we also just to show that the new is equal to 0 that implies suppose. Those are the two obligations. Now to prove this, why do we need to do it to prove this?

2:11:42
3D to show that at least one of the chefs will occur. Yes, how they program? This partnership works to read to show that the issuing this initial is that this is not an idea that combinationally and this basically, we assume that at some point in the computation, we have so many non-zeroes

2:12:08
And he just picked something and then do one. Well once it's so how do you prove that? This is how to revenue. So like, I mean, we know that the only way to happen is only way to get more one more zero case for one of these scenarios to ship, but maybe none of them ships and then they come through.

2:12:29
That's so how do so then? So yes, the logic goes at least one of them shifts. How do we prove that there is modern shifts since the newest over here is much better. So, some images, so that's good. Good start thinking? Yes, it's holiday there. So, basically what he's saying is that since new is better than zero, it must be some loan zero elements in this case, and we, we know that there are this side by the way.

2:13:04
We know that the North heroes are on this side, not in the middle so that might find an embarrassing. Okay. So, you're saying that we know that at the front of the rain, there is something that is normally one of them must be the best therefore that shift is going to take place.

2:13:37
Right. So, but we use an invalid there, which said that the part of the non-zero part is all here So that we can prove it without this invariant your pointer stuff. Okay. And then you also need to ask yourself. Is it possible that we do this without relying on the fact that seems about it?

2:14:23
As imaginative order or not nursing son, if you have an array of items and there's non-zero and there in any order, there will always be

2:14:42
To progress and still take place as long as it's on the, we have the ability, which tells us that we are in

2:15:04
Okay, so even them. So that's a very important of their direction because you think of what the surface we are making because we don't want to single data execution, want to sign only about the piece of the code. So that means that we need to add this in variant which says all the zeros are in the lab.

2:15:25
And then we can prove that with a reason because you we know that there is one said there's to shift in any more than one but we only have to proceed at one and that's the ship that will shift. And No, when musical 0 implies post, when I'm really going to zero means means that all of these are here means, the next is zero.

2:15:55
Max, is you, okay?

2:16:06
So we don't have anything here. Everything isn't here. But what is our forest?

2:16:19
Super started. Yeah. Strictly people to the equal to all the values and the initial DC, we can prove just by the fact that there are zeros. But basically has to do with the fact that if we take the union set of a is union set of B union said of C union said of x.

2:17:04
So I'm not leaving all the elements in the system. Okay, this is equal to G. Where G was, I just was the union of low case, a low case be so that and basically says we're not losing anything So, all the elements are in the system. How to put this in variable before the initial is true or initially.

2:17:41
X is empty. So this is 0. I mean, that's not all the length and this are equal to 8 capability. Say, in our case, we log in C, which is the definition for G. So this Now let the flu that molecular program. The evaluate is preserved. So a solarist is true.

2:18:04
So, we have a couple of cases here, this will be possible that we shift, and we lose data.

2:18:14
Okay, so we need to show that, whatever is whatever we are. Shifting is going to be possible somewhere, I'll use somewhere else. So really going to have to do an analysis by cases. So, for instance, in if we want to shift a who that two cases? We shift a because there's a duplicate already.

2:18:40
So the element is already in x, so nothing doesn't sound. The union doesn't change, or we shift a because that element moves into words, therefore nothing changes and they have to do all this, all those cases. And probably you go into need an inquiry. That says that next is bigger than everybody else.

2:19:13
Because that's not the case and we could lose, we could lose data. And we also going to probably need the value and everything is sorted in those settings. So we face, we need sorted ABN to their all, disembodied and all that to improve.

2:19:51
Now, assume that they have obviously values proven if music or to zero, this is empty. This is an individuality. So this contains G, which is exactly the post condition, but we kind of just prove it from this. We are improving this because I need doesn't guidance then. We also need to prove that x is typically sticking order.

2:20:22
So we doesn't need guardians, which says that x is strictly harder. And the way we prove that is that we do not shift tax. Anytime a value is coming here. It's same. So therefore we only ship on the values and in doing in order to that prove we're going to need to rely on the fact that next is smaller particle to everybody in the array so I'm going to have to use that evaluate as well.

2:20:58
So you see it's not it's not just kind of listening guardians, you know, you have to think, what are you, what are they needed? If we find out that we have, any value that we don't need that. Something wrong with our pool. We felt it need to put it in clearly with public was important, but then we actually do the proof is not there.

2:21:18
Then something most likely would? We do not provide we made some handwave summer something. Okay so three people audience is this one plus KB and C are sorted x. Another ABC and X that are all sorted plus, Texas thick.

2:21:45
We can actually separate it and we have proven in the correct order. So I got sorted gives us actually that gives us this condition that could use here.

2:22:11
In that sort of the zero set to understand. So, we don't need a nice value here, which has used that educarient to show that this he was

2:22:26
Not easy, is it? But is every interaction will learn something questions, soul for the Uranus. So we need to cool that because we need to show that the cost is the result we want, okay? Okay. But it's not only that you cannot prove the progress without any something, guys.

2:22:52
See. We decided that this was only very beginning to put the products. We didn't need the fact that they were sorted in sending order. They thought that we need that but then we realized that we need to have see those is enough. Since then you're saying from the fact that there are sort of and up using them.

2:23:19
So, in improving this to, if I need some values, not all of them. Improving the post. You're going to need someone to sign values closer to continue for the more.

2:23:43
All right. Go. Nice working with you guys. Yes, I don't think we're gonna have to come there. We can also experience just went over here. I appreciate that. I'm not posting. Contracting.

2:24:12
Yeah, there's like eight.

2:24:43
Here. Yeah. Just not ever free. Oh from a swirl of their factory. Go from from buying on sale food and awesome there was like mailing for shipping was a dollar is whatever. Whatever a letter cost is shipped These happen, presumably and then they took it off that shelf. I get a free.

2:25:28
Problems is the last part.

2:25:46
Yeah.