WEBVTT 00:00:07.192 --> 00:00:08.566 SRINI DEVADAS: Morning, everyone. 00:00:08.566 --> 00:00:12.830 Welcome to 6.S095. 00:00:12.830 --> 00:00:14.520 Thanks for registering for this class. 00:00:14.520 --> 00:00:15.760 I hope you like it. 00:00:15.760 --> 00:00:17.180 My name is Srini Devadas. 00:00:17.180 --> 00:00:22.900 I'm a professor of computer science at MIT, obviously, 00:00:22.900 --> 00:00:26.275 and I've been teaching at MIT for 30 years. 00:00:26.275 --> 00:00:28.810 So I've been at it for a while. 00:00:28.810 --> 00:00:30.730 The reason I'm teaching this IAP class 00:00:30.730 --> 00:00:36.550 is because I want to try out this way of teaching 00:00:36.550 --> 00:00:40.750 programming that starts with the recreational world 00:00:40.750 --> 00:00:44.080 of mathematical puzzles, algorithmic puzzles, 00:00:44.080 --> 00:00:48.760 and I want to connect it up to writing programs. 00:00:48.760 --> 00:00:54.090 And I have taught this material before in 6.009 00:00:54.090 --> 00:00:57.620 that I think some of you are registered for, 00:00:57.620 --> 00:01:01.510 but I wanted to teach it in a more interactive, 00:01:01.510 --> 00:01:02.860 informal setting. 00:01:02.860 --> 00:01:06.250 And I should mention that I wrote a book 00:01:06.250 --> 00:01:09.970 on this, which is a book that's recommended, though not 00:01:09.970 --> 00:01:11.680 required, for 6.009. 00:01:11.680 --> 00:01:15.460 And so you might see this in the MIT Press 00:01:15.460 --> 00:01:17.440 Bookstore and other places. 00:01:17.440 --> 00:01:21.120 And most of the material I'm going to cover here 00:01:21.120 --> 00:01:22.510 is from the book. 00:01:22.510 --> 00:01:24.700 But I don't want you to read the book 00:01:24.700 --> 00:01:29.710 because I want you to listen to my explanations for the puzzles 00:01:29.710 --> 00:01:32.470 and try and think of the solutions 00:01:32.470 --> 00:01:37.810 yourself and then obviously do some amount of coding 00:01:37.810 --> 00:01:40.600 not during lecture but offline. 00:01:40.600 --> 00:01:43.120 And I'll show you some solutions to the puzzles, 00:01:43.120 --> 00:01:45.430 and there will be some exercises. 00:01:45.430 --> 00:01:48.970 So I don't want to spend a whole lot of time on logistics. 00:01:48.970 --> 00:01:52.690 This is an IAP class, as I mentioned. 00:01:52.690 --> 00:01:55.810 I'd like this to be informal and relaxed. 00:01:55.810 --> 00:01:59.920 So we meet every day for two weeks. 00:01:59.920 --> 00:02:01.630 We have the holiday coming up on Monday, 00:02:01.630 --> 00:02:06.930 so we'll have nine total lectures roughly for an hour. 00:02:06.930 --> 00:02:10.509 It might spill over, but hopefully, you'll be OK with it 00:02:10.509 --> 00:02:14.110 because you don't have another class to go to at noon. 00:02:14.110 --> 00:02:16.870 And if you do, well, let me know, 00:02:16.870 --> 00:02:20.920 and I'll give you that five minutes of overflow 00:02:20.920 --> 00:02:25.720 personally at a time of your choosing. 00:02:25.720 --> 00:02:29.780 But hopefully, I'll keep on time. 00:02:29.780 --> 00:02:32.930 And in terms of work, this is a pass/fail. 00:02:32.930 --> 00:02:34.900 It's a for-credit class. 00:02:34.900 --> 00:02:37.540 I know some of you may be listeners, but some of you 00:02:37.540 --> 00:02:38.710 are registered for it. 00:02:38.710 --> 00:02:40.660 So I'll have to assign you a grade, 00:02:40.660 --> 00:02:42.149 so there will be some exercises. 00:02:42.149 --> 00:02:43.690 And I'm going to make it very simple. 00:02:46.230 --> 00:02:48.320 There'll be exercises up on the website. 00:02:48.320 --> 00:02:51.550 They'll be due two days from when I put them up. 00:02:51.550 --> 00:02:54.070 And you'll have options in terms of whether to do 00:02:54.070 --> 00:02:56.590 a really simple exercise that's probably 00:02:56.590 --> 00:03:00.570 going to take about five minutes or do something harder. 00:03:00.570 --> 00:03:02.050 And for each of the puzzles, there 00:03:02.050 --> 00:03:05.650 are two or three exercises, and you get to do all of them 00:03:05.650 --> 00:03:06.560 if you want. 00:03:06.560 --> 00:03:11.010 You can choose to do one or the other. 00:03:11.010 --> 00:03:15.340 I'm going to have office hours every day from 1:00 to 2:00. 00:03:15.340 --> 00:03:18.400 I don't plan on putting solutions up to the exercises. 00:03:18.400 --> 00:03:21.390 The solutions to the puzzles themselves, 00:03:21.390 --> 00:03:23.350 they'll be shown mostly in lecture 00:03:23.350 --> 00:03:26.410 and put up on the Stellar website, 00:03:26.410 --> 00:03:28.920 but the solutions to the exercises, 00:03:28.920 --> 00:03:30.070 I'm not going to put up. 00:03:30.070 --> 00:03:32.290 But if you ever get stuck, well, that's 00:03:32.290 --> 00:03:33.880 what office hours are for. 00:03:33.880 --> 00:03:36.960 And if you can't solve the exercises, 00:03:36.960 --> 00:03:39.410 I'll help to solve them. 00:03:39.410 --> 00:03:42.070 So with that, without further ado, 00:03:42.070 --> 00:03:45.280 let's dive in and talk about puzzles 00:03:45.280 --> 00:03:50.050 and solving puzzles using algorithms and then programs. 00:03:50.050 --> 00:03:52.030 I'd really like this to be interactive, 00:03:52.030 --> 00:03:58.420 so please ask questions and suggest solutions 00:03:58.420 --> 00:03:59.510 that I haven't thought of. 00:03:59.510 --> 00:04:00.250 That'd be great. 00:04:00.250 --> 00:04:02.300 In my second edition, whenever that is, 00:04:02.300 --> 00:04:04.810 you'll get credit for that. 00:04:04.810 --> 00:04:14.490 So the first puzzle, I tried to have, I don't know, 00:04:14.490 --> 00:04:18.250 funny titles for all of these puzzles-- 00:04:18.250 --> 00:04:19.370 intriguing. 00:04:19.370 --> 00:04:22.900 And so the first puzzle is called "You Will All Conform." 00:04:22.900 --> 00:04:25.240 This is really a warm-up puzzle. 00:04:25.240 --> 00:04:27.867 As you'll see-- this is true for any class-- 00:04:27.867 --> 00:04:30.200 things are going to get more complicated as we go along. 00:04:30.200 --> 00:04:33.370 So we'll probably do 10 or 12 puzzles in the next two weeks. 00:04:33.370 --> 00:04:39.860 And by the end, you're going to see things like memoization 00:04:39.860 --> 00:04:41.620 and dynamic programming and things 00:04:41.620 --> 00:04:44.390 like that towards the end of next week. 00:04:44.390 --> 00:04:46.990 And if you don't know what those mean, well, 00:04:46.990 --> 00:04:50.320 that's great because hopefully, you 00:04:50.320 --> 00:04:52.630 will know by the end of the two weeks. 00:04:52.630 --> 00:04:56.570 And a lot of these things are algorithmic insights, 00:04:56.570 --> 00:05:02.390 are insights that will help you in Course 6 classes, for sure, 00:05:02.390 --> 00:05:10.080 and perhaps even if you follow a career outside of Course 6. 00:05:10.080 --> 00:05:16.820 So this particular puzzle is, as I said, a fairly simple puzzle, 00:05:16.820 --> 00:05:18.470 at least to describe. 00:05:18.470 --> 00:05:22.170 And the setting is as follows. 00:05:22.170 --> 00:05:25.004 So you're a gatekeeper at a baseball game. 00:05:25.004 --> 00:05:26.420 We'll just call it a baseball game 00:05:26.420 --> 00:05:28.100 because baseball players wear caps, 00:05:28.100 --> 00:05:33.019 and most people are watching games with caps on. 00:05:33.019 --> 00:05:35.060 And so you're a gatekeeper, and there are a bunch 00:05:35.060 --> 00:05:37.820 of people standing in line. 00:05:37.820 --> 00:05:41.390 Let's just say each of them knows their number. 00:05:41.390 --> 00:05:43.520 And this is Python, so the number 00:05:43.520 --> 00:05:46.790 starts at 0 as opposed to 1. 00:05:46.790 --> 00:05:48.410 And there are a whole bunch of people 00:05:48.410 --> 00:05:54.050 standing in line waiting to get in, and they all have caps. 00:05:54.050 --> 00:05:57.430 And some of them are wearing their caps forward, 00:05:57.430 --> 00:06:00.305 so with the-- 00:06:00.305 --> 00:06:02.090 I guess, what do you call it? 00:06:02.090 --> 00:06:05.150 What's the front of the cap called? 00:06:05.150 --> 00:06:09.940 The shade-- the thing that gives you shade up front. 00:06:09.940 --> 00:06:13.350 And so we just say-- 00:06:13.350 --> 00:06:14.870 let me try and draw this out. 00:06:14.870 --> 00:06:18.920 So this person is wearing his cap like that, 00:06:18.920 --> 00:06:23.820 and this lady here is wearing her cap like this. 00:06:23.820 --> 00:06:27.200 So that's forwards, and that's backwards. 00:06:29.990 --> 00:06:37.740 So your job here is straightforward. 00:06:37.740 --> 00:06:42.500 You can only let all of these people into line-- 00:06:42.500 --> 00:06:49.930 sorry-- into the stadium who are in line if they all conform. 00:06:49.930 --> 00:06:52.490 So they all have to wear their caps 00:06:52.490 --> 00:06:55.640 in a particular orientation, and you don't particularly 00:06:55.640 --> 00:06:57.980 care which one. 00:06:57.980 --> 00:07:00.200 And so they all have to be forwards, 00:07:00.200 --> 00:07:03.920 all, let's say, 13 of them. 00:07:03.920 --> 00:07:06.590 Or they all have to be backwards. 00:07:06.590 --> 00:07:11.330 Now, all of them know their position on the line. 00:07:11.330 --> 00:07:14.630 So this person knows that his position is 0, 00:07:14.630 --> 00:07:16.670 this lady here knows that her position 00:07:16.670 --> 00:07:19.640 is 1, et cetera, et cetera. 00:07:19.640 --> 00:07:24.830 And so obviously, you'd like to minimize the amount of work 00:07:24.830 --> 00:07:30.560 that you do, and you could certainly choose-- 00:07:30.560 --> 00:07:32.720 let's say you want everyone to be forwards. 00:07:32.720 --> 00:07:36.740 You could say, hey, lady in position 1, flip your cap. 00:07:36.740 --> 00:07:39.350 Oh, I should mention something that is important. 00:07:39.350 --> 00:07:41.240 So people have a different definition 00:07:41.240 --> 00:07:42.860 of forwards and backwards. 00:07:42.860 --> 00:07:47.060 It's sort of what's natural and what's unnatural to them. 00:07:47.060 --> 00:07:53.090 So we think that this person has his cap on forwards. 00:07:53.090 --> 00:07:55.160 But for all you know, he thinks he's got his cap 00:07:55.160 --> 00:07:57.050 on backwards or vice versa. 00:07:57.050 --> 00:08:00.830 So you can't assume that the definition 00:08:00.830 --> 00:08:04.880 of "forwards" and "backwards" is identical for all of the people 00:08:04.880 --> 00:08:09.170 in line and really is the same as your definition. 00:08:09.170 --> 00:08:11.090 It seems kind of unreasonable. 00:08:11.090 --> 00:08:17.677 Hey, this is a puzzle, so let's not argue about that. 00:08:17.677 --> 00:08:19.760 We can argue about other things, like how to write 00:08:19.760 --> 00:08:22.790 Python programs properly. 00:08:22.790 --> 00:08:24.860 So what you have to do now is you 00:08:24.860 --> 00:08:30.020 have to call out commands that correspond to saying, 00:08:30.020 --> 00:08:34.549 person in position 0, flip your cap. 00:08:34.549 --> 00:08:35.900 That's all you can say. 00:08:35.900 --> 00:08:38.690 You can just say, flip your cap. 00:08:38.690 --> 00:08:41.780 You can obviously see how these caps are oriented, 00:08:41.780 --> 00:08:43.850 and you can ask-- 00:08:43.850 --> 00:08:45.870 let's say that you had something like that. 00:08:45.870 --> 00:08:49.640 I'm just making this up as I go along, in terms of I'm 00:08:49.640 --> 00:08:52.160 not going to draw all the caps here. 00:08:52.160 --> 00:08:55.950 But this is what it looks like. 00:08:55.950 --> 00:09:01.010 And so according to you, you see F, B, B, in terms 00:09:01.010 --> 00:09:02.540 of Forwards and Backwards. 00:09:02.540 --> 00:09:06.230 And let's say you decide that you want everyone 00:09:06.230 --> 00:09:10.290 to have their cap on forwards. 00:09:10.290 --> 00:09:14.870 Then you could say, person in position 1, flip your cap. 00:09:14.870 --> 00:09:17.240 Person in position 2, flip your cap. 00:09:17.240 --> 00:09:21.230 And then person in position 4, 7, et cetera. 00:09:21.230 --> 00:09:23.900 And you want to make it easier on yourself 00:09:23.900 --> 00:09:30.260 because people do know their indices, their positions 00:09:30.260 --> 00:09:31.310 in line. 00:09:31.310 --> 00:09:33.560 And so to save yourself some trouble, 00:09:33.560 --> 00:09:37.160 you could say, people in positions 1 through 2-- 00:09:37.160 --> 00:09:40.910 and the implication is that it's inclusive-- flip your caps. 00:09:40.910 --> 00:09:44.540 And so that takes care of these two. 00:09:44.540 --> 00:09:53.930 And perhaps 8 here and 9 had their caps on backwards, 00:09:53.930 --> 00:09:57.950 and you could say, people in positions 7 through 9, 00:09:57.950 --> 00:09:59.540 flip your caps. 00:09:59.540 --> 00:10:01.220 So in this particular example, assuming 00:10:01.220 --> 00:10:05.630 that things ended with 10 people in line, 0 through 9, 00:10:05.630 --> 00:10:10.610 you could get away with three commands. 00:10:10.610 --> 00:10:14.180 You could say, 1 through 2-- 00:10:14.180 --> 00:10:18.180 and the implication, as I said, is this is inclusive-- 00:10:18.180 --> 00:10:19.910 flip. 00:10:19.910 --> 00:10:25.040 And then you could say, 4, flip. 00:10:25.040 --> 00:10:32.870 And then you could say, 7 through 9, flip. 00:10:32.870 --> 00:10:36.620 And if you did it the other way, you 00:10:36.620 --> 00:10:39.290 could also say, person at 0, flip, 00:10:39.290 --> 00:10:41.050 and so this would go backwards. 00:10:41.050 --> 00:10:43.190 Person at 3, flip. 00:10:43.190 --> 00:10:45.020 Obviously, you can't say, 0 through 3 00:10:45.020 --> 00:10:46.760 because that would be wrong. 00:10:46.760 --> 00:10:51.540 And then you could say 5 through 6 here. 00:10:51.540 --> 00:10:57.980 So you would get three commands in that case, as well. 00:10:57.980 --> 00:11:03.170 But if in fact, for argument's sake, let's 00:11:03.170 --> 00:11:08.950 just say that I'm going to just turn this into 10 00:11:08.950 --> 00:11:12.630 and put an F down here. 00:11:12.630 --> 00:11:17.190 Then these three commands would still 00:11:17.190 --> 00:11:24.300 work if you wanted to focus on the B's, on the Backwards 00:11:24.300 --> 00:11:27.300 people, and make them make them go forwards. 00:11:27.300 --> 00:11:29.580 But if you wanted to make all of the forward people 00:11:29.580 --> 00:11:38.300 go backwards, you would need 1, 2, 3, 4, four commands. 00:11:38.300 --> 00:11:39.960 So in this particular case, you're 00:11:39.960 --> 00:11:43.950 better off doing that as opposed to doing four commands. 00:11:43.950 --> 00:11:51.000 So first straightforward question is-- 00:11:51.000 --> 00:11:53.150 and I'm not talking about code yet-- 00:11:53.150 --> 00:11:56.610 algorithmically, just in terms of pseudocode-- 00:11:56.610 --> 00:12:00.060 and I'm happy with English-- 00:12:00.060 --> 00:12:05.340 how would you determine the minimum set of commands given 00:12:05.340 --> 00:12:07.520 a particular set of people? 00:12:07.520 --> 00:12:09.960 There's an arbitrary set of people. 00:12:09.960 --> 00:12:14.010 You want to make sure that you have the absolute minimum set 00:12:14.010 --> 00:12:18.007 of commands, and you're going to have to use these intervals. 00:12:18.007 --> 00:12:19.590 So you definitely want to look for all 00:12:19.590 --> 00:12:21.381 the contiguous intervals because obviously, 00:12:21.381 --> 00:12:24.540 if you say 1 followed and then that's a separate command, then 00:12:24.540 --> 00:12:28.170 you say 2 and that's a separate command, 00:12:28.170 --> 00:12:32.670 you end up having more commands than necessary. 00:12:32.670 --> 00:12:35.830 So anyone want to tell me I guess roughly, 00:12:35.830 --> 00:12:41.280 in terms of pseudocode, how this would work? 00:12:41.280 --> 00:12:42.462 Yeah, go ahead. 00:12:42.462 --> 00:12:45.062 AUDIENCE: Well, you could go down the line 00:12:45.062 --> 00:12:48.205 and look at the groups. 00:12:48.205 --> 00:12:51.187 So start with the 0. 00:12:51.187 --> 00:12:52.675 You've got to write 0. 00:12:52.675 --> 00:12:53.175 Group them. 00:12:53.175 --> 00:12:55.570 And then whatever the second one is-- 00:12:55.570 --> 00:13:00.990 so whatever the second group is, if it's F or B, 00:13:00.990 --> 00:13:03.066 those are the ones that need to be flipped 00:13:03.066 --> 00:13:06.210 because that's going to be the minimum number of commands. 00:13:06.210 --> 00:13:10.300 And then so from what you pass through, 00:13:10.300 --> 00:13:13.765 whenever you get to those, you just tell them to flip. 00:13:13.765 --> 00:13:14.890 SRINI DEVADAS: Sounds good. 00:13:14.890 --> 00:13:16.150 Do you have anything to add to that? 00:13:16.150 --> 00:13:16.691 AUDIENCE: No. 00:13:16.691 --> 00:13:19.391 I was going to say, you find the backwards interval 00:13:19.391 --> 00:13:20.510 or forward interval. 00:13:20.510 --> 00:13:23.615 And whichever is the lower, then-- 00:13:23.615 --> 00:13:24.490 SRINI DEVADAS: Lower. 00:13:24.490 --> 00:13:25.000 That's good. 00:13:25.000 --> 00:13:25.240 Good. 00:13:25.240 --> 00:13:25.740 Excellent. 00:13:25.740 --> 00:13:27.280 And so both of you had it right. 00:13:27.280 --> 00:13:31.140 So let me explain what these two gentlemen-- what was your name? 00:13:31.140 --> 00:13:31.890 AUDIENCE: Ganatra. 00:13:31.890 --> 00:13:32.960 SRINI DEVADAS: Ganatra? 00:13:32.960 --> 00:13:33.643 Yours? 00:13:33.643 --> 00:13:34.510 AUDIENCE: Fadi. 00:13:34.510 --> 00:13:35.664 SRINI DEVADAS: Fadi? 00:13:35.664 --> 00:13:36.490 AUDIENCE: Yeah. 00:13:36.490 --> 00:13:39.650 SRINI DEVADAS: So Ganatra and Fadi said-- 00:13:39.650 --> 00:13:43.390 so basically, this is, as I said, 00:13:43.390 --> 00:13:47.470 the natural algorithm that you would use. 00:13:47.470 --> 00:13:49.600 The natural algorithm would be that you 00:13:49.600 --> 00:13:53.500 walk through this list, and you start 00:13:53.500 --> 00:13:55.420 computing what I would call-- you called it 00:13:55.420 --> 00:13:56.200 "groups," Ganatra. 00:13:56.200 --> 00:13:59.470 But I'd call them "intervals," and an interval 00:13:59.470 --> 00:14:01.750 is something that is unbroken. 00:14:01.750 --> 00:14:02.860 It's contiguous. 00:14:02.860 --> 00:14:05.380 It's a contiguous set of people who 00:14:05.380 --> 00:14:08.650 all have their caps in the same orientation, 00:14:08.650 --> 00:14:10.530 be it forward or backwards. 00:14:10.530 --> 00:14:16.720 And what you would do in this case is you would compute the-- 00:14:16.720 --> 00:14:19.810 you would say, I want to look at the forward intervals. 00:14:19.810 --> 00:14:21.390 And the forward intervals would be 0, 00:14:21.390 --> 00:14:24.340 0 because that's essentially what you have in here. 00:14:24.340 --> 00:14:27.730 And going through that list, you would also say, 00:14:27.730 --> 00:14:30.010 I'm going to be computing the backward intervals. 00:14:30.010 --> 00:14:35.110 And in this case, you discover 1, 2 as the backwards interval. 00:14:35.110 --> 00:14:37.150 So I'm going to write them out like that. 00:14:37.150 --> 00:14:39.850 And in general, in the mathematical notation, 00:14:39.850 --> 00:14:44.640 when you put square brackets, these are closed intervals. 00:14:44.640 --> 00:14:46.630 So 0 is included. 00:14:46.630 --> 00:14:48.252 And we're going to see a puzzle where 00:14:48.252 --> 00:14:50.210 you might see something a little bit different, 00:14:50.210 --> 00:14:51.650 so I wanted to point that out. 00:14:51.650 --> 00:14:54.610 So 1, 2 are both inside this interval. 00:14:54.610 --> 00:14:57.730 And these two you would generate as you 00:14:57.730 --> 00:14:59.380 would go through the list, and then you 00:14:59.380 --> 00:15:03.010 would generate 3, 3 over here. 00:15:03.010 --> 00:15:05.224 And then you would generate 4-- 00:15:05.224 --> 00:15:06.390 yeah, that's right, just 4-- 00:15:06.390 --> 00:15:08.890 I'm sorry, 4, 4 over here, if you 00:15:08.890 --> 00:15:10.660 want to call it an interval. 00:15:10.660 --> 00:15:12.670 You could represent this differently. 00:15:12.670 --> 00:15:14.950 There's nothing that stopping you in Python 00:15:14.950 --> 00:15:20.590 to have these slightly more complicated representations 00:15:20.590 --> 00:15:23.434 where you just have 0 here as a number. 00:15:23.434 --> 00:15:24.850 And if it's just a number, then it 00:15:24.850 --> 00:15:28.360 represents an interval of length 1, 00:15:28.360 --> 00:15:31.090 but let's just be uniform about this. 00:15:31.090 --> 00:15:33.160 Usually, when you have special cases 00:15:33.160 --> 00:15:35.700 and if you do things heterogeneously, 00:15:35.700 --> 00:15:37.550 then you have more code to write. 00:15:37.550 --> 00:15:40.000 It might get more efficient, but there's usually 00:15:40.000 --> 00:15:41.200 more code to write. 00:15:41.200 --> 00:15:42.850 So you do 4, 4 here. 00:15:42.850 --> 00:15:47.680 And then you'd go up, and then you'd have 5 comma 6. 00:15:47.680 --> 00:15:50.500 And then you would do 7 comma-- 00:15:50.500 --> 00:15:52.890 I'm sorry, 7 comma 9. 00:15:52.890 --> 00:15:55.030 So this is the first time you actually 00:15:55.030 --> 00:15:59.590 have something interesting, in the sense that the interval has 00:15:59.590 --> 00:16:02.230 a representation that only has two numbers in it, 00:16:02.230 --> 00:16:05.620 whereas you actually have three people in that interval. 00:16:05.620 --> 00:16:07.840 And obviously, this could be arbitrarily 00:16:07.840 --> 00:16:13.470 large in the context of people getting into a baseball game-- 00:16:13.470 --> 00:16:18.640 and so 7 through 9 and then finally here 10 through 10. 00:16:18.640 --> 00:16:21.744 And so now you go ahead, and you count 00:16:21.744 --> 00:16:24.160 and you realize that there's four intervals here and three 00:16:24.160 --> 00:16:25.270 intervals here. 00:16:25.270 --> 00:16:27.820 And then you say, I'm going to go ahead and go 00:16:27.820 --> 00:16:33.640 with the backwards and asking the people who are-- well, 00:16:33.640 --> 00:16:36.460 according to you-- backwards to flip their caps so we're all 00:16:36.460 --> 00:16:36.960 good. 00:16:39.310 --> 00:16:44.710 So I'm going to show you code that implements 00:16:44.710 --> 00:16:46.910 exactly this algorithm. 00:16:46.910 --> 00:16:50.050 And while you see the code, I want 00:16:50.050 --> 00:16:52.540 you to think about this harder question. 00:16:52.540 --> 00:16:55.690 This code is going to do exactly what we describe. 00:16:55.690 --> 00:17:01.490 It's going to go compute all of these things, 00:17:01.490 --> 00:17:04.770 and as you can imagine, he's going 00:17:04.770 --> 00:17:07.200 to make a pass through this entire Python 00:17:07.200 --> 00:17:13.230 list, this group of people, this queue of people, 00:17:13.230 --> 00:17:15.210 and is going to do this computation. 00:17:15.210 --> 00:17:19.380 Then it's going to say, 4 is greater than 3. 00:17:19.380 --> 00:17:23.970 And then it's going to go through and start calling out 00:17:23.970 --> 00:17:26.400 commands for each of the backward intervals. 00:17:26.400 --> 00:17:32.160 So in some sense, it's going to make two passes over the list. 00:17:32.160 --> 00:17:35.340 So the first pass is to get all of the intervals together. 00:17:35.340 --> 00:17:36.540 Then there's a check. 00:17:36.540 --> 00:17:38.040 And then the second pass is to take 00:17:38.040 --> 00:17:41.880 those backward intervals, in this case, 00:17:41.880 --> 00:17:43.650 and call out those commands. 00:17:43.650 --> 00:17:45.810 So that's what I mean by two passes. 00:17:45.810 --> 00:17:47.379 Yeah, please. 00:17:47.379 --> 00:17:49.504 AUDIENCE: You don't necessarily need to count them, 00:17:49.504 --> 00:17:56.240 the 4 and 3 because whichever orientation interval comes 00:17:56.240 --> 00:17:57.450 second is always going-- 00:17:57.450 --> 00:17:58.491 SRINI DEVADAS: Brilliant. 00:17:58.491 --> 00:18:01.180 Brilliant. 00:18:01.180 --> 00:18:03.250 So I was going to say-- 00:18:03.250 --> 00:18:05.060 if you didn't understand what Ganatra 00:18:05.060 --> 00:18:10.930 said, wonderful because then you can think about the question 00:18:10.930 --> 00:18:15.250 I'm going to ask and ignore what he said. 00:18:15.250 --> 00:18:20.360 And then we'll get to, I guess, the more efficient code. 00:18:20.360 --> 00:18:24.610 But what I was going to ask was, is there a way that I'm looking 00:18:24.610 --> 00:18:27.580 at this, and I'm just going-- and I'm going to just start 00:18:27.580 --> 00:18:29.830 calling out by-- 00:18:29.830 --> 00:18:34.730 the moment I see that there's an interval, the moment I see-- 00:18:34.730 --> 00:18:36.100 this is an interval. 00:18:36.100 --> 00:18:40.000 And I'm going to make a call with respect 00:18:40.000 --> 00:18:45.040 to whether I'm going to call out a command or not. 00:18:45.040 --> 00:18:50.830 And I'm going to do this in one pass through this array. 00:18:50.830 --> 00:18:53.410 I want to do this in one pass through the array. 00:18:53.410 --> 00:18:58.750 I want to look at this, and I say, I see the interval 0, 0. 00:18:58.750 --> 00:19:01.810 Is that going to be something that I 00:19:01.810 --> 00:19:04.360 need to worry about in terms of that person 00:19:04.360 --> 00:19:08.350 having to flip his cap? 00:19:08.350 --> 00:19:13.189 And then I see B, B. And I say, oh, the interval is 1 comma 2. 00:19:13.189 --> 00:19:14.980 Is that something I'm going to have to deal 00:19:14.980 --> 00:19:17.140 with in terms of a command? 00:19:17.140 --> 00:19:21.580 And so someone else other than Ganatra, 00:19:21.580 --> 00:19:24.790 tell me if there's a one-pass algorithm. 00:19:24.790 --> 00:19:30.040 And explain to me why you can do this in one pass 00:19:30.040 --> 00:19:31.280 through the array. 00:19:31.280 --> 00:19:34.930 And just in terms of code, I'll preview this. 00:19:34.930 --> 00:19:37.540 The first algorithm needs-- 00:19:37.540 --> 00:19:40.060 according to my coding, which, isn't great-- 00:19:40.060 --> 00:19:41.600 26 lines of code. 00:19:41.600 --> 00:19:43.810 The second one needs eight lines of code. 00:19:43.810 --> 00:19:45.520 So yeah, go ahead. 00:19:45.520 --> 00:19:48.732 AUDIENCE: So after you see the first interval, 00:19:48.732 --> 00:19:50.890 you know that the second interval at the very least 00:19:50.890 --> 00:19:54.620 is going to have the same number of commands as the first one. 00:19:54.620 --> 00:19:56.750 So you might as well always go with the second one. 00:19:56.750 --> 00:19:58.600 So once you've identified what type 00:19:58.600 --> 00:20:01.900 the first interval is, you iterate through the list 00:20:01.900 --> 00:20:03.020 seeing-- 00:20:03.020 --> 00:20:05.695 and once you identify the first and second intervals, 00:20:05.695 --> 00:20:08.750 you iterate through every type of the second interval 00:20:08.750 --> 00:20:10.298 and do a command for that. 00:20:10.298 --> 00:20:11.290 SRINI DEVADAS: That's absolutely right. 00:20:11.290 --> 00:20:11.890 What was your name? 00:20:11.890 --> 00:20:12.556 AUDIENCE: Kevin. 00:20:12.556 --> 00:20:13.470 SRINI DEVADAS: Kevin? 00:20:13.470 --> 00:20:15.130 So you had it right. 00:20:15.130 --> 00:20:17.500 And Kevin has it right, as well. 00:20:17.500 --> 00:20:21.220 So the observation here is actually-- 00:20:21.220 --> 00:20:23.740 it was said a little bit differently by Kevin, 00:20:23.740 --> 00:20:26.290 but I'm going to say it a little bit differently. 00:20:26.290 --> 00:20:31.030 The observation is simply that if you 00:20:31.030 --> 00:20:36.860 look at the very first orientation, 00:20:36.860 --> 00:20:41.500 the very first orientation is something which, 00:20:41.500 --> 00:20:47.390 at best, is going to be a tie. 00:20:47.390 --> 00:20:53.450 So if you had it ending with 10 people, 0 through 9, 00:20:53.450 --> 00:20:55.910 then the number of forward intervals 00:20:55.910 --> 00:21:00.350 is the same as the number of backwards intervals. 00:21:00.350 --> 00:21:03.020 And if you went here, obviously, the number of forward intervals 00:21:03.020 --> 00:21:05.570 is greater than the number of backwards intervals. 00:21:05.570 --> 00:21:10.956 So you really only have to look at the first person in line not 00:21:10.956 --> 00:21:12.580 to determine the intervals because when 00:21:12.580 --> 00:21:13.954 you see the first person in line, 00:21:13.954 --> 00:21:16.115 you have no idea what the intervals are 00:21:16.115 --> 00:21:18.129 that are coming after. 00:21:18.129 --> 00:21:19.670 You have to generate those intervals, 00:21:19.670 --> 00:21:22.160 so you have to make your pass through the array. 00:21:22.160 --> 00:21:25.040 But the first person in line gives it away 00:21:25.040 --> 00:21:28.490 in terms of what the final result is 00:21:28.490 --> 00:21:33.230 going to be with respect to your decision as to what 00:21:33.230 --> 00:21:37.070 set of commands you're going to call up. 00:21:37.070 --> 00:21:42.890 And so because this is an F, you basically say, I'm going to go, 00:21:42.890 --> 00:21:49.400 and I'm going to make the people with the B's flip their caps. 00:21:49.400 --> 00:21:59.090 And that's a small observation in terms of its insight. 00:21:59.090 --> 00:22:02.150 But obviously, it's potent, in the sense 00:22:02.150 --> 00:22:05.330 that it's going to give you a one-pass algorithm 00:22:05.330 --> 00:22:06.560 versus a two-pass algorithm. 00:22:06.560 --> 00:22:08.600 And as I mentioned, it's going to give you 00:22:08.600 --> 00:22:13.790 a substantial reduction in the amount of code that you write. 00:22:13.790 --> 00:22:17.219 So I'm going to show you a bunch of code now. 00:22:17.219 --> 00:22:19.010 So this is usually how this is going to go, 00:22:19.010 --> 00:22:22.880 by the way, this entire class. 00:22:22.880 --> 00:22:25.850 And this is kind of my way of teaching, 00:22:25.850 --> 00:22:28.340 at least this type of material that's algorithmic and has 00:22:28.340 --> 00:22:30.330 data structures and so on. 00:22:30.330 --> 00:22:33.080 I like explaining to people what they're 00:22:33.080 --> 00:22:36.500 going to see in the code without having to deal with Python 00:22:36.500 --> 00:22:39.770 syntax and worrying about whether it's while loops 00:22:39.770 --> 00:22:42.890 or for loops and things like that and tuples or arrays 00:22:42.890 --> 00:22:43.970 and things like that. 00:22:43.970 --> 00:22:47.330 So let's get into that. 00:22:50.400 --> 00:22:53.530 I don't need this. 00:22:53.530 --> 00:22:55.900 Ah, good. 00:22:55.900 --> 00:23:00.270 So the naive algorithm first-- 00:23:00.270 --> 00:23:04.560 so what you see here is an input. 00:23:04.560 --> 00:23:09.310 So "caps" is simply an input Python list that has, 00:23:09.310 --> 00:23:12.510 as you can see from our examples, the F's and the B's. 00:23:12.510 --> 00:23:14.640 And so F is Forwards, and B is Backwards. 00:23:14.640 --> 00:23:17.100 And there are a couple of different Python lists 00:23:17.100 --> 00:23:19.400 so you can run them with different things. 00:23:19.400 --> 00:23:22.200 And all of this hopefully is not at all surprising to you 00:23:22.200 --> 00:23:23.670 because we went through all of this 00:23:23.670 --> 00:23:25.860 in terms of the pseudocode. 00:23:25.860 --> 00:23:28.960 So the first initialization-- 00:23:28.960 --> 00:23:31.980 and I can just highlight that to make it easy. 00:23:31.980 --> 00:23:34.050 So that's initialization. 00:23:34.050 --> 00:23:35.910 And this part here-- 00:23:35.910 --> 00:23:37.800 the comment sort of gives it away-- 00:23:37.800 --> 00:23:41.610 is you're making a pass through the array, 00:23:41.610 --> 00:23:44.160 computing the intervals. 00:23:44.160 --> 00:23:47.620 And so how do you actually get the intervals? 00:23:47.620 --> 00:23:52.240 And there's one line of code that does that. 00:23:52.240 --> 00:23:54.750 And oh, by the way, if there are any questions about Python 00:23:54.750 --> 00:23:57.590 syntax, just don't feel shy. 00:23:57.590 --> 00:24:00.180 Just tell me. 00:24:00.180 --> 00:24:02.890 Ask me a question, and I'm happy to explain it. 00:24:02.890 --> 00:24:06.210 I don't want to explain things that you all know, obviously. 00:24:06.210 --> 00:24:10.300 But if any one of you doesn't know any particular thing, 00:24:10.300 --> 00:24:12.810 please don't feel shy. 00:24:12.810 --> 00:24:15.870 Syntax is something that sometimes you even forget. 00:24:15.870 --> 00:24:17.460 I tend to forget things. 00:24:17.460 --> 00:24:21.210 So this thing here is essentially 00:24:21.210 --> 00:24:26.400 something that decides on what the intervals are. 00:24:26.400 --> 00:24:28.710 And the insight here is simple. 00:24:28.710 --> 00:24:32.370 You know that this interval ended when you see something 00:24:32.370 --> 00:24:36.440 here that is different from what the previous one is. 00:24:36.440 --> 00:24:37.440 So that's when you know. 00:24:37.440 --> 00:24:45.240 So you generate the interval when you go and find 00:24:45.240 --> 00:24:49.530 something that is different from the current location 00:24:49.530 --> 00:24:50.850 that you're pointing to. 00:24:50.850 --> 00:24:53.730 So that's really what's going on out here. 00:24:53.730 --> 00:24:59.950 In this line, you say, you're setting a "start" here. 00:24:59.950 --> 00:25:02.400 "Start" is your counter, and remember, "start" 00:25:02.400 --> 00:25:04.860 is getting set again here. 00:25:04.860 --> 00:25:06.519 Initially, it was set to 0. 00:25:06.519 --> 00:25:09.060 And if you ever get to the point where you're looking at "i," 00:25:09.060 --> 00:25:10.643 it's the next thing you're looking at, 00:25:10.643 --> 00:25:13.140 and if "caps start," which is the start of the interval, 00:25:13.140 --> 00:25:15.570 is different from "i," it meant that the interval that 00:25:15.570 --> 00:25:18.390 began with "start" ended. 00:25:18.390 --> 00:25:20.310 And so you essentially say, well, 00:25:20.310 --> 00:25:23.751 that needs to end at i minus 1 because obviously, "caps start" 00:25:23.751 --> 00:25:25.000 is different from "caps size." 00:25:25.000 --> 00:25:27.990 So this is the end of the interval right here. 00:25:27.990 --> 00:25:31.080 And this particular thing, our interval, 00:25:31.080 --> 00:25:35.240 is something that includes both these two numbers, 00:25:35.240 --> 00:25:36.510 so it's not exactly that. 00:25:36.510 --> 00:25:39.734 But it also includes-- 00:25:39.734 --> 00:25:43.300 where did my chalk go? 00:25:43.300 --> 00:25:46.930 It also includes whether this is an F or not. 00:25:46.930 --> 00:25:49.909 So each of these things has-- 00:25:49.909 --> 00:25:52.200 I'm not going to write it out for all of those things-- 00:25:52.200 --> 00:25:57.270 but has the orientation inside of it. 00:25:57.270 --> 00:25:59.370 So that's what you have out here. 00:25:59.370 --> 00:26:01.810 That's why we have three of these in this tuple. 00:26:01.810 --> 00:26:06.090 This is a tuple because it's got round brackets around it. 00:26:06.090 --> 00:26:09.980 I could have made it a list if I wanted. 00:26:09.980 --> 00:26:12.300 And so that's essentially what we have here. 00:26:12.300 --> 00:26:15.420 And now, here's what happens. 00:26:15.420 --> 00:26:19.020 In this particular piece of code, when you get to the end 00:26:19.020 --> 00:26:22.980 and you fall off the end-- 00:26:22.980 --> 00:26:28.500 so if you just end, then this code essentially 00:26:28.500 --> 00:26:32.940 skips over and doesn't actually put in the last interval 00:26:32.940 --> 00:26:34.800 because you don't see something. 00:26:34.800 --> 00:26:37.920 When you come up here and you're off the end of the array, 00:26:37.920 --> 00:26:40.320 you fall off the edge of the array, 00:26:40.320 --> 00:26:44.310 you don't see a B that is different from F. 00:26:44.310 --> 00:26:47.100 So if you just wrote that code-- 00:26:47.100 --> 00:26:54.810 so it's something that I'd say many people would 00:26:54.810 --> 00:26:56.830 have a quote, "bug," where they wouldn't 00:26:56.830 --> 00:27:01.500 add this part of the code here because they didn't realize 00:27:01.500 --> 00:27:03.750 this particular point that I made. 00:27:03.750 --> 00:27:07.830 And so that last interval doesn't get added in. 00:27:07.830 --> 00:27:09.990 And so you have a bit more code here 00:27:09.990 --> 00:27:13.470 that decides on the last interval. 00:27:13.470 --> 00:27:19.330 And then you count, and then you go ahead and call the commands. 00:27:19.330 --> 00:27:21.230 So this all looks good? 00:27:21.230 --> 00:27:23.220 Yeah, we're good with this? 00:27:23.220 --> 00:27:27.580 Is there a way that I could somehow 00:27:27.580 --> 00:27:29.515 eliminate these four lines of code which 00:27:29.515 --> 00:27:34.660 are a little bit annoying and just do things in the array? 00:27:34.660 --> 00:27:37.180 How could I, with a little trick, 00:27:37.180 --> 00:27:41.500 eliminate those four lines of code? 00:27:41.500 --> 00:27:45.610 I might need a little bit more in, quote, "pre-processing," 00:27:45.610 --> 00:27:46.920 but how would I eliminate that? 00:27:51.560 --> 00:27:52.364 Someone else? 00:27:52.364 --> 00:27:53.030 I'll get to you. 00:27:53.030 --> 00:27:53.530 Yeah. 00:27:53.530 --> 00:27:55.011 Go ahead. 00:27:55.011 --> 00:27:56.970 AUDIENCE: One way is you can check thoroughly 00:27:56.970 --> 00:27:59.260 you've reached the end of the-- 00:27:59.260 --> 00:28:00.856 the forward is equal to the backwards. 00:28:00.856 --> 00:28:02.070 SRINI DEVADAS: You could have an extra check. 00:28:02.070 --> 00:28:02.380 What's your name? 00:28:02.380 --> 00:28:03.250 AUDIENCE: Kanishka. 00:28:03.250 --> 00:28:04.249 SRINI DEVADAS: Kanishka? 00:28:04.249 --> 00:28:10.306 So Kanishka says that before you reach the end of the array 00:28:10.306 --> 00:28:11.930 or when you reach the end of the array, 00:28:11.930 --> 00:28:15.591 you go ahead and do a check that you've reached the end 00:28:15.591 --> 00:28:17.465 and generate the interval inside of it, which 00:28:17.465 --> 00:28:21.830 is kind of like moving this code inside of it. 00:28:21.830 --> 00:28:23.210 So that's reasonable. 00:28:23.210 --> 00:28:26.810 I'm not sure that's going to be as good as the way that I want 00:28:26.810 --> 00:28:29.000 and which I coded. 00:28:29.000 --> 00:28:31.970 Think about pre-processing. 00:28:31.970 --> 00:28:33.783 Think about taking the array-- yeah? 00:28:33.783 --> 00:28:37.010 AUDIENCE: I guess you could add a wrong interval at the end. 00:28:37.010 --> 00:28:38.090 SRINI DEVADAS: You could add on a wrong interval. 00:28:38.090 --> 00:28:38.881 What was your name? 00:28:38.881 --> 00:28:39.660 AUDIENCE: Kevin. 00:28:39.660 --> 00:28:40.800 SRINI DEVADAS: Kevin, too? 00:28:40.800 --> 00:28:44.090 Just how many Kevins do we have here? 00:28:44.090 --> 00:28:47.650 So you could do this. 00:28:47.650 --> 00:28:51.960 So let me show you something that's a little bit more-- 00:28:51.960 --> 00:28:55.620 so that was 26 lines of code. 00:28:55.620 --> 00:28:57.330 And so this says-- 00:28:57.330 --> 00:28:59.100 this is the line that's interesting. 00:28:59.100 --> 00:29:03.780 So I had F and B, and so I don't want to add F or B there. 00:29:03.780 --> 00:29:06.750 But what is convenient to do, as it turns out, 00:29:06.750 --> 00:29:08.880 is to just have something that essentially says, 00:29:08.880 --> 00:29:09.910 there's an ending point. 00:29:09.910 --> 00:29:14.160 So you have an explicit end to the array that is actually 00:29:14.160 --> 00:29:17.640 not something that would crash if you tried to access it. 00:29:17.640 --> 00:29:20.340 You had n people in line, and now you have effectively 00:29:20.340 --> 00:29:21.720 n plus 1 people in line. 00:29:21.720 --> 00:29:25.300 But that n plus one person is a dummy, 00:29:25.300 --> 00:29:27.660 or you can call them "end." 00:29:27.660 --> 00:29:30.600 And then if you do that, then that's it. 00:29:30.600 --> 00:29:33.150 The previous code works. 00:29:33.150 --> 00:29:35.190 You can just remove those four lines, 00:29:35.190 --> 00:29:39.510 and it'll all just work because your F or your B 00:29:39.510 --> 00:29:41.430 is not equal to "end." 00:29:41.430 --> 00:29:45.240 So whatever you had at the end-- 00:29:45.240 --> 00:29:46.440 I'm sorry. 00:29:46.440 --> 00:29:48.510 I'm overloading terms here. 00:29:48.510 --> 00:29:53.400 Whatever you had at the last element-- 00:29:53.400 --> 00:29:57.530 whether it was a B because it ended here or F-- 00:29:57.530 --> 00:30:00.150 when you equate that to "end," you're 00:30:00.150 --> 00:30:02.440 going to get an inequality. 00:30:02.440 --> 00:30:05.340 And so that last interval gets generated-- 00:30:05.340 --> 00:30:06.810 so small optimization. 00:30:06.810 --> 00:30:10.380 Tony Hoare was a very famous computer scientist-- 00:30:10.380 --> 00:30:12.960 said that "inside every program, there's 00:30:12.960 --> 00:30:15.860 a smaller program waiting to get out." 00:30:15.860 --> 00:30:18.690 So this is kind of one of the themes 00:30:18.690 --> 00:30:23.670 that I'd like to harp on in this class, which is it's 00:30:23.670 --> 00:30:25.620 nice to write compact code. 00:30:25.620 --> 00:30:28.300 Usually, if you can write compact code, 00:30:28.300 --> 00:30:29.502 there are fewer bugs in it. 00:30:29.502 --> 00:30:30.960 And you don't want to go overboard. 00:30:30.960 --> 00:30:33.360 You don't want too many subtleties, 00:30:33.360 --> 00:30:36.280 but it's nice to write compact code. 00:30:36.280 --> 00:30:39.210 And so this is a little bit more compact. 00:30:39.210 --> 00:30:45.000 And then finally, here's the one-pass algorithm. 00:30:45.000 --> 00:30:49.240 So the whole thing, the "pleaseConformonepass," 00:30:49.240 --> 00:30:55.560 is the smarter algorithm that essentially says, 00:30:55.560 --> 00:30:59.010 look, if I just look at the very first thing, 00:30:59.010 --> 00:31:03.540 I'm going to be able to skip that and then move on. 00:31:03.540 --> 00:31:07.230 So this is fairly complicated. 00:31:07.230 --> 00:31:09.030 You know the algorithm. 00:31:09.030 --> 00:31:11.890 Trying to map that to this code is non-trivial, 00:31:11.890 --> 00:31:14.640 so we'll spend a minute or two on it. 00:31:14.640 --> 00:31:21.570 But here's how this works. 00:31:21.570 --> 00:31:23.700 And by the way, just to make sure-- 00:31:28.480 --> 00:31:30.280 so I've repeated things here. 00:31:30.280 --> 00:31:34.950 So the optimized algorithm for that particular example 00:31:34.950 --> 00:31:36.930 produced these first three commands. 00:31:36.930 --> 00:31:40.320 And then the one-pass algorithm produced 00:31:40.320 --> 00:31:42.090 exactly the same commands. 00:31:42.090 --> 00:31:44.765 So this is good to do. 00:31:44.765 --> 00:31:46.140 It's always nice to have a couple 00:31:46.140 --> 00:31:48.780 of different ways of solving a problem 00:31:48.780 --> 00:31:51.990 because then you can verify things. 00:31:51.990 --> 00:31:55.980 Anyway, so this piece of code is essentially 00:31:55.980 --> 00:32:01.020 something that does a similar trick to what we had before, 00:32:01.020 --> 00:32:07.800 in terms of adding to the original list, 00:32:07.800 --> 00:32:09.480 adding an element. 00:32:09.480 --> 00:32:11.700 But we're not using "end" here. 00:32:11.700 --> 00:32:14.719 We're actually saying, what we want 00:32:14.719 --> 00:32:17.260 to do because we're going to go ahead and skip this, anyway-- 00:32:17.260 --> 00:32:19.160 we know we're going to skip the F. 00:32:19.160 --> 00:32:25.020 So whatever that is, we could just sort of add up here. 00:32:25.020 --> 00:32:29.560 And so that makes it easy. 00:32:29.560 --> 00:32:33.810 You don't have to worry about what the actual characters are 00:32:33.810 --> 00:32:36.060 and cooking up this "end," which is different 00:32:36.060 --> 00:32:38.910 from the F or the B because hey, it's 00:32:38.910 --> 00:32:41.880 possible that people might use whatever 00:32:41.880 --> 00:32:45.150 they want to represent a forward cap or a backward cap. 00:32:45.150 --> 00:32:46.710 So this is very clean. 00:32:46.710 --> 00:32:48.840 You go ahead and put exactly that over here. 00:32:48.840 --> 00:32:51.810 You know you're going to skip that interval because you're 00:32:51.810 --> 00:32:56.880 going to skip the first interval, effectively, 00:32:56.880 --> 00:33:01.050 because that is what the algorithm allows you to do. 00:33:01.050 --> 00:33:06.690 And then this part here is doing what we had before. 00:33:06.690 --> 00:33:08.510 We're not even generating the intervals. 00:33:08.510 --> 00:33:11.340 We're just directly making the commands. 00:33:11.340 --> 00:33:15.390 So there are no tuples in terms of the tuples 00:33:15.390 --> 00:33:17.880 and the appending of the intervals data structure 00:33:17.880 --> 00:33:18.450 that we had. 00:33:18.450 --> 00:33:20.040 It's all gone. 00:33:20.040 --> 00:33:23.760 I'm just going to go ahead and fire off these commands. 00:33:23.760 --> 00:33:30.540 And those commands are written in kind of a funny way 00:33:30.540 --> 00:33:35.070 because I'm going to go ahead and if I 00:33:35.070 --> 00:33:36.450 wanted to print these things out, 00:33:36.450 --> 00:33:38.520 you'd have to do this in this funny way. 00:33:38.520 --> 00:33:40.960 If you're willing to wait and collect up the intervals, 00:33:40.960 --> 00:33:42.390 you can certainly do that. 00:33:42.390 --> 00:33:45.270 But this is absolutely the most compact code 00:33:45.270 --> 00:33:49.350 that I could think of, and I'm printing a command 00:33:49.350 --> 00:33:51.510 in two different parts. 00:33:51.510 --> 00:33:54.270 I'm printing the first part of the command that says, 00:33:54.270 --> 00:33:56.970 people in positions. 00:33:56.970 --> 00:34:00.450 And that's the start of the interval "i," 00:34:00.450 --> 00:34:02.710 and I'm just using a Python construct. 00:34:02.710 --> 00:34:07.590 This "end" here is something that the print command 00:34:07.590 --> 00:34:08.429 can recognize. 00:34:08.429 --> 00:34:10.560 And this simply says, don't give me a new line. 00:34:10.560 --> 00:34:11.909 I want to print it exactly. 00:34:11.909 --> 00:34:14.130 As you saw from when I ran the code, 00:34:14.130 --> 00:34:18.810 the printing was exactly the same as the original algorithm. 00:34:18.810 --> 00:34:21.780 And so this "end" simply says, don't print a new line 00:34:21.780 --> 00:34:24.590 at the end of people in positions, 00:34:24.590 --> 00:34:25.650 whatever this number is. 00:34:25.650 --> 00:34:26.969 Call it 7. 00:34:26.969 --> 00:34:28.800 And you don't print the new line. 00:34:28.800 --> 00:34:32.520 And then you have a space here because you didn't 00:34:32.520 --> 00:34:34.770 print a new line or a space. 00:34:34.770 --> 00:34:37.770 And you go through i minus 1, which is exactly the same 00:34:37.770 --> 00:34:38.940 as we had before. 00:34:38.940 --> 00:34:42.449 You only discover that the end of an interval after you 00:34:42.449 --> 00:34:46.889 see the person that comes after the interval. 00:34:46.889 --> 00:34:48.909 So you have to go back to i minus 1. 00:34:48.909 --> 00:34:50.790 So this makes sense? 00:34:50.790 --> 00:34:53.250 Any questions about this code? 00:34:53.250 --> 00:34:54.296 Yeah, go ahead. 00:34:54.296 --> 00:34:55.670 AUDIENCE: So the first line, like 00:34:55.670 --> 00:34:57.980 you said, if we're going to move the first-- 00:34:57.980 --> 00:35:00.249 SRINI DEVADAS: Not move, duplicate-- 00:35:00.249 --> 00:35:01.540 AUDIENCE: Duplicate the first-- 00:35:01.540 --> 00:35:02.373 SRINI DEVADAS: Yeah. 00:35:02.373 --> 00:35:05.030 So the plus there is a concatenation, 00:35:05.030 --> 00:35:05.990 and you have two lists. 00:35:05.990 --> 00:35:07.310 "Caps" is a list. 00:35:07.310 --> 00:35:11.170 And when you use a plus operator in Python, 00:35:11.170 --> 00:35:14.420 you can only add things that are of the same type. 00:35:14.420 --> 00:35:17.990 And so "caps" is a list, and "cap 0" 00:35:17.990 --> 00:35:19.710 is an element of the list. 00:35:19.710 --> 00:35:21.500 And so you need to make it a list in order 00:35:21.500 --> 00:35:23.342 to use the plus operator. 00:35:23.342 --> 00:35:25.550 There are also other things you could do using a pen, 00:35:25.550 --> 00:35:26.574 for example. 00:35:26.574 --> 00:35:28.990 So you could take that line, and you could do "caps start" 00:35:28.990 --> 00:35:30.229 at "pen" "cap 0." 00:35:30.229 --> 00:35:32.270 And you wouldn't need all of the square brackets, 00:35:32.270 --> 00:35:34.330 but that's just neither here nor there. 00:35:34.330 --> 00:35:36.820 But I'm obviously not answering your question, so go ahead. 00:35:36.820 --> 00:35:37.320 Yeah. 00:35:37.320 --> 00:35:39.248 AUDIENCE: So I was going to say that we 00:35:39.248 --> 00:35:40.435 skip the first interval. 00:35:40.435 --> 00:35:43.134 And then we flip all the second-type orientation. 00:35:43.134 --> 00:35:44.300 SRINI DEVADAS: That's right. 00:35:44.300 --> 00:35:46.210 AUDIENCE: But here, we're focusing on the first element. 00:35:46.210 --> 00:35:46.710 Why-- 00:35:49.190 --> 00:35:52.640 SRINI DEVADAS: Ah, but that's OK because remember, 00:35:52.640 --> 00:35:57.830 the if statement is going to skip this one, too. 00:35:57.830 --> 00:35:59.690 So if I had two F's in the beginning-- 00:35:59.690 --> 00:36:01.220 I think your question is, what would 00:36:01.220 --> 00:36:04.905 happen if I had two F's or three F's in the beginning? 00:36:04.905 --> 00:36:07.280 So I'm going to go ahead, and first thing I'm going to do 00:36:07.280 --> 00:36:09.530 is I'm going to put an F at the end here, 00:36:09.530 --> 00:36:11.310 and then maybe there's a bunch of stuff. 00:36:11.310 --> 00:36:14.750 But then the nice thing is that I'll skip this F, too, 00:36:14.750 --> 00:36:20.780 because the not equal to is not going to fire. 00:36:20.780 --> 00:36:25.220 The next line, the "caps i not equal to i minus 1," 00:36:25.220 --> 00:36:27.512 this is going to be equal to. 00:36:27.512 --> 00:36:29.720 So I'm going to go ahead and go to the next iteration 00:36:29.720 --> 00:36:30.770 of the loop. 00:36:30.770 --> 00:36:31.910 That makes sense? 00:36:31.910 --> 00:36:34.770 Did people understand Fadi's question? 00:36:34.770 --> 00:36:36.740 It was a good question. 00:36:36.740 --> 00:36:41.630 So the question was, you skipped the first one. 00:36:41.630 --> 00:36:43.970 But what is making you skip this one because you want 00:36:43.970 --> 00:36:46.280 to skip the first interval? 00:36:46.280 --> 00:36:50.580 And so that if statement is making you do that. 00:36:50.580 --> 00:36:51.080 Good. 00:36:51.080 --> 00:36:53.587 So as you can see, even a fairly straightforward puzzle-- 00:36:53.587 --> 00:36:55.670 this is the simplest puzzle we're going to do here 00:36:55.670 --> 00:36:57.610 is the first one. 00:36:57.610 --> 00:37:01.830 And there are nuances associated with how you solve it 00:37:01.830 --> 00:37:03.980 but also how you code it. 00:37:03.980 --> 00:37:06.080 And this is kind of-- 00:37:06.080 --> 00:37:12.960 like I said, this was my eureka moment a few years ago, 00:37:12.960 --> 00:37:15.380 where I said, I think the way you 00:37:15.380 --> 00:37:17.790 want to teach programming, at least 00:37:17.790 --> 00:37:21.560 some aspects of programming, is in this fashion. 00:37:21.560 --> 00:37:22.550 Anyway, good. 00:37:22.550 --> 00:37:25.100 So we're done with this. 00:37:25.100 --> 00:37:27.540 Any questions about this puzzle? 00:37:27.540 --> 00:37:28.040 All right. 00:37:28.040 --> 00:37:29.590 Good.