WEBVTT 00:00:09.234 --> 00:00:10.220 PATRICK WINSTON: Today we're going to be 00:00:10.220 --> 00:00:11.030 talking about Search. 00:00:11.030 --> 00:00:13.220 I know you're going to turn blue with yet 00:00:13.220 --> 00:00:15.350 another lecture on Search. 00:00:15.350 --> 00:00:18.270 Those of you who are taking computer science subjects, 00:00:18.270 --> 00:00:20.360 you've probably seen in 601. 00:00:20.360 --> 00:00:22.270 You'll see it again as theory course. 00:00:22.270 --> 00:00:25.570 But we're going to do it for a little different purpose. 00:00:25.570 --> 00:00:29.480 I want you to develop some intuition about various kinds 00:00:29.480 --> 00:00:31.080 of Search work. 00:00:31.080 --> 00:00:35.800 And I want to talk a little bit about Search as a model of 00:00:35.800 --> 00:00:38.080 what goes on in our heads. 00:00:38.080 --> 00:00:40.630 And toward the end, if there's time, I'd like to do a 00:00:40.630 --> 00:00:43.660 demonstration for you of something never before 00:00:43.660 --> 00:00:49.960 demonstrated to a 603.4 class, because it was only completed 00:00:49.960 --> 00:00:51.600 last spring. 00:00:51.600 --> 00:00:56.470 And some finishing touches were added by me this morning. 00:00:56.470 --> 00:00:58.450 Always dangerous, but we'll see what happens. 00:01:01.430 --> 00:01:03.870 There's Cambridge. 00:01:03.870 --> 00:01:05.150 You all recognize it, of course. 00:01:08.230 --> 00:01:11.550 You might want to get from some starting position s to 00:01:11.550 --> 00:01:14.280 some goal position g. 00:01:14.280 --> 00:01:18.490 So, you'll hire a cab and hope for the best. 00:01:18.490 --> 00:01:31.430 So, here's what might happen, not too hot. 00:01:31.430 --> 00:01:34.175 Let's move the starting position over here. 00:01:41.250 --> 00:01:43.245 I've had cab drivers like this New York. 00:01:47.039 --> 00:01:48.460 But it's not a very good path. 00:01:48.460 --> 00:01:50.400 It's the path of a thief. 00:01:50.400 --> 00:01:54.930 Let's change the way that the search is done to that of a 00:01:54.930 --> 00:01:56.975 beginner, an honest beginner. 00:02:01.690 --> 00:02:04.100 Not too bad. 00:02:04.100 --> 00:02:09.360 Now, let's have a look at how the Search would happen if the 00:02:09.360 --> 00:02:13.440 cab driver was a Ph.D. in physics 00:02:13.440 --> 00:02:14.690 after his third post-doc. 00:02:25.800 --> 00:02:26.750 These are not actually traverse. 00:02:26.750 --> 00:02:31.050 These are just things that the driver is thinking about, and 00:02:31.050 --> 00:02:34.840 that is the very best of all possible paths. 00:02:34.840 --> 00:02:36.480 So, the thief does a horrible job. 00:02:36.480 --> 00:02:38.110 The beginner does a pretty good job, but 00:02:38.110 --> 00:02:39.960 not an optimal job. 00:02:39.960 --> 00:02:44.790 This is the optimal job as produced by the Ph.D. in 00:02:44.790 --> 00:02:48.910 physics after his third post-doc. 00:02:48.910 --> 00:02:51.230 So, would you like to understand how those all work? 00:02:51.230 --> 00:02:52.480 The answer, of course, is yes. 00:02:56.660 --> 00:03:01.070 I'm going to talk to you about procedures that are different 00:03:01.070 --> 00:03:05.260 from the way that you just solved this problem. 00:03:05.260 --> 00:03:08.420 I imagine that if I said to you, please find a path for s 00:03:08.420 --> 00:03:12.020 to g, you would, within a few seconds, find 00:03:12.020 --> 00:03:13.070 a pretty good path-- 00:03:13.070 --> 00:03:15.710 not the optimal one, but a pretty good one-- 00:03:15.710 --> 00:03:18.050 using your eyes. 00:03:18.050 --> 00:03:19.940 And we're not going to tell you about how that works, 00:03:19.940 --> 00:03:22.540 because we don't know how that works. 00:03:22.540 --> 00:03:27.030 But we do know that problem solving with the eyes is an 00:03:27.030 --> 00:03:29.260 important part of our total intelligence. 00:03:29.260 --> 00:03:31.260 And we'll never have a complete theory of human 00:03:31.260 --> 00:03:34.640 intelligence until we can understand the contributions 00:03:34.640 --> 00:03:38.990 of the human visual system to solving everyday problems like 00:03:38.990 --> 00:03:43.470 finding a pretty good path in that map. 00:03:43.470 --> 00:03:45.870 But, alas, we can't talk about that, because we don't know 00:03:45.870 --> 00:03:47.100 how to do it. 00:03:47.100 --> 00:03:48.820 We're working on it. 00:03:48.820 --> 00:03:51.450 But we don't know how to do it. 00:03:51.450 --> 00:03:53.880 So, I'm not going to use Cambridge in my illustrations. 00:03:53.880 --> 00:03:56.860 There's too much there to work through in an hour. 00:03:56.860 --> 00:03:59.620 So, we're going to use this map over here which has been 00:03:59.620 --> 00:04:02.850 designed to illustrate a few important points. 00:04:02.850 --> 00:04:06.520 You, too, can find a path through that graph pretty 00:04:06.520 --> 00:04:08.570 easily with your eyes. 00:04:08.570 --> 00:04:11.320 Our programs don't have eyes, and they don't have visually 00:04:11.320 --> 00:04:13.280 grounded algorithms, so they're going to have to do 00:04:13.280 --> 00:04:14.720 something else. 00:04:14.720 --> 00:04:17.180 And the very first kind of search we want to talk about 00:04:17.180 --> 00:04:19.980 is called the British Museum approach. 00:04:19.980 --> 00:04:23.100 This is a slur against at least the British Museum, if 00:04:23.100 --> 00:04:26.400 not the entire nation, because the way you do a British 00:04:26.400 --> 00:04:30.230 Museum search is you find every possible path. 00:04:30.230 --> 00:04:33.310 So, it'll be helpful to have a diagram of all possible paths 00:04:33.310 --> 00:04:34.409 on the board. 00:04:34.409 --> 00:04:36.200 We're going to start with a British Museum search. 00:04:41.930 --> 00:04:45.130 From the starting position, it's clear, you can go from my 00:04:45.130 --> 00:04:47.405 s to either a or b. 00:04:52.400 --> 00:04:54.600 And already there's an important quiz point. 00:04:54.600 --> 00:04:58.260 Whenever we have these kinds of problems on a quiz, we ask 00:04:58.260 --> 00:05:02.720 you to develop the tree associated with a search in 00:05:02.720 --> 00:05:04.470 lexical order. 00:05:04.470 --> 00:05:11.600 So, the nodes there under s are listed alphabetically, 00:05:11.600 --> 00:05:14.710 just to have an orderly way of doing it. 00:05:14.710 --> 00:05:18.830 So, from a we can go either b or d. 00:05:22.020 --> 00:05:24.940 And another convention of the subject, another thing you 00:05:24.940 --> 00:05:27.530 have to keep in mind in quizzes, is it we don't have 00:05:27.530 --> 00:05:30.180 these searches bite their own tail. 00:05:30.180 --> 00:05:33.400 So, I could have said that if I'm at a, I can 00:05:33.400 --> 00:05:35.570 also go back to s. 00:05:35.570 --> 00:05:40.730 But no path is ever allowed them to bite itself, to go 00:05:40.730 --> 00:05:45.190 around and enter and get back to a place that's 00:05:45.190 --> 00:05:47.580 already on the path. 00:05:47.580 --> 00:05:52.750 Now if I go on to b first, that means that from b I can 00:05:52.750 --> 00:05:55.600 go to either a or c. 00:05:55.600 --> 00:05:57.020 This is getting fat pretty fast. 00:05:57.020 --> 00:05:59.570 But let's see, s, a, b. 00:05:59.570 --> 00:06:03.930 The only place I can go is c and then to e. 00:06:03.930 --> 00:06:07.360 s, a, d, without biting my own tail and going back to a, the 00:06:07.360 --> 00:06:10.290 only place I can go is g. 00:06:10.290 --> 00:06:16.820 s b, a, I can only go to d and then to g. 00:06:16.820 --> 00:06:21.040 And finally, s, b, c, I can only go to e. 00:06:21.040 --> 00:06:26.190 So, that is a complete set of paths as produced by any 00:06:26.190 --> 00:06:31.720 program that you will feel you'd like to write that finds 00:06:31.720 --> 00:06:33.470 all possible paths. 00:06:33.470 --> 00:06:36.780 I haven't been very precise about how to do that, because 00:06:36.780 --> 00:06:38.350 you don't have to be. 00:06:38.350 --> 00:06:40.780 You can't save much work by being clever, because you have 00:06:40.780 --> 00:06:43.570 to find everything. 00:06:43.570 --> 00:06:46.440 So, that's the British Museum expansion of the tree. 00:06:57.230 --> 00:06:58.409 So, what have I done? 00:06:58.409 --> 00:06:59.820 I've been playing around with a map. 00:06:59.820 --> 00:07:01.550 I showed you an example of a map. 00:07:01.550 --> 00:07:05.310 And pretty soon you're going to think that 00:07:05.310 --> 00:07:08.616 Search is about maps. 00:07:08.616 --> 00:07:14.820 So, before going even another tiny step, I want to emphasize 00:07:14.820 --> 00:07:18.030 that Search is not equal to maps. 00:07:18.030 --> 00:07:19.600 Search is about choice. 00:07:19.600 --> 00:07:22.690 And I happen to illustrate these searches with maps, 00:07:22.690 --> 00:07:25.390 because they are particularly cogent. 00:07:25.390 --> 00:07:26.790 But Search is not about maps. 00:07:26.790 --> 00:07:28.800 It's about the choices you make when you're trying to 00:07:28.800 --> 00:07:30.800 make decisions. 00:07:30.800 --> 00:07:34.470 These things I'm going to be talking to you about today are 00:07:34.470 --> 00:07:37.172 choices you make when you explore the map. 00:07:37.172 --> 00:07:39.630 You can make other kinds of choices when you're exploring 00:07:39.630 --> 00:07:40.630 other kinds of things. 00:07:40.630 --> 00:07:44.500 And, in fact, at the end, if there's time, I'll show you 00:07:44.500 --> 00:07:47.130 how you do searches when you're solving problems in a 00:07:47.130 --> 00:07:48.380 humanities class. 00:07:51.000 --> 00:07:52.409 That's the British Museum algorithm. 00:07:52.409 --> 00:07:53.950 Search is not about maps. 00:07:53.950 --> 00:07:58.240 Our first gold star idea, Search is about choice. 00:07:58.240 --> 00:08:00.660 But for our illustration, Search is about maps. 00:08:00.660 --> 00:08:03.530 So, the first kind of Search we want to talk about that's 00:08:03.530 --> 00:08:07.460 real is Depth-first Search. 00:08:10.412 --> 00:08:15.500 And the idea of Depth-first Search is that you barrel 00:08:15.500 --> 00:08:17.070 ahead in a single-minded way. 00:08:20.160 --> 00:08:27.832 So, from s, your choices are a or b. 00:08:27.832 --> 00:08:31.730 And you always go down the left branch by convention. 00:08:31.730 --> 00:08:35.350 So, from s, we go to a. 00:08:35.350 --> 00:08:36.919 From a we have two choices. 00:08:36.919 --> 00:08:46.990 We can go to either b or d following our lexical 00:08:46.990 --> 00:08:49.630 convention. 00:08:49.630 --> 00:08:52.660 After that, we can go to c. 00:08:52.660 --> 00:08:54.660 And after that we can go to e. 00:08:54.660 --> 00:08:58.871 And too bad for us, we're stuck. 00:08:58.871 --> 00:09:00.520 What are we going to do. 00:09:00.520 --> 00:09:04.790 We've got into a dead end, all is lost. 00:09:04.790 --> 00:09:06.640 But of course, all isn't lost. 00:09:06.640 --> 00:09:11.180 Because we have the choice of backing up to the place where 00:09:11.180 --> 00:09:16.280 we last made a decision and choosing another branch. 00:09:16.280 --> 00:09:20.350 So, that process is called variously back-up or 00:09:20.350 --> 00:09:21.600 backtracking. 00:09:23.330 --> 00:09:26.670 At this point, we would say, ah, dead end. 00:09:26.670 --> 00:09:30.110 The first place we find when we back up the tree where we 00:09:30.110 --> 00:09:34.070 made a choice is when we chose b instead of d. 00:09:34.070 --> 00:09:36.420 So, we go back up there and take the other route. 00:09:39.060 --> 00:09:42.730 s, a, d now goes to g. 00:09:42.730 --> 00:09:45.220 And we're done. 00:09:45.220 --> 00:09:47.220 We're going to make up a little table here of things 00:09:47.220 --> 00:09:50.880 that we can embellish our basic searches with. 00:09:50.880 --> 00:09:53.420 And one of the things we can embellish our basic searches 00:09:53.420 --> 00:09:55.680 with is this backtracking idea. 00:10:01.700 --> 00:10:04.410 Now, backtrack is not relevant to the British Museum 00:10:04.410 --> 00:10:07.120 algorithm, because you've got to find everything. 00:10:07.120 --> 00:10:10.000 You can't quit when you've found one path. 00:10:10.000 --> 00:10:12.940 But you'd always want to use backtracking with Depth-first 00:10:12.940 --> 00:10:16.140 Search, because you may plunge on down and miss the path that 00:10:16.140 --> 00:10:18.050 gets to the goal. 00:10:18.050 --> 00:10:22.480 Now, you might ask me, is backtracking, therefore, 00:10:22.480 --> 00:10:25.330 always part of Depth-first Search? 00:10:25.330 --> 00:10:28.350 And you can read textbooks that do it either way. 00:10:28.350 --> 00:10:29.190 Count on it. 00:10:29.190 --> 00:10:32.500 If we give you a Search problem on a quiz, we'll tell 00:10:32.500 --> 00:10:34.400 you whether or not your Search is supposed to use 00:10:34.400 --> 00:10:34.990 backtracking. 00:10:34.990 --> 00:10:38.200 We consider it to be an optional thing. 00:10:38.200 --> 00:10:40.320 You'd be pretty stupid not to use this optional thing when 00:10:40.320 --> 00:10:41.925 you're doing Depth-first Search. 00:10:41.925 --> 00:10:44.800 But we'll separate these ideas out and call 00:10:44.800 --> 00:10:47.300 it an optional add-on. 00:10:47.300 --> 00:10:51.600 so, that's Depth-first Search, very simple. 00:10:51.600 --> 00:10:55.670 Now, the natural companion to Depth-first Search will be 00:10:55.670 --> 00:11:02.454 Breadth-first Search, Breadth-first. 00:11:07.640 --> 00:11:11.620 And the way it works is you build up this tree level by 00:11:11.620 --> 00:11:16.160 level, and at some point, when you scan across a level, 00:11:16.160 --> 00:11:17.790 you'll find that you've completed a path 00:11:17.790 --> 00:11:20.100 that goes to the goal. 00:11:20.100 --> 00:11:27.310 So, level by level, s can go to either a or b. 00:11:27.310 --> 00:11:30.670 a can go either to b or d. 00:11:30.670 --> 00:11:34.620 And b can go to either a or c. 00:11:34.620 --> 00:11:35.480 So, you see what we're doing. 00:11:35.480 --> 00:11:38.030 We're going level by level. 00:11:38.030 --> 00:11:40.360 And we haven't hit a level with a goal in it yet, so 00:11:40.360 --> 00:11:42.510 we've got to keep going. 00:11:42.510 --> 00:11:44.800 Note that we're building up quite a bit of stuff here, 00:11:44.800 --> 00:11:49.360 quite a lot of growth in the size of the path set that 00:11:49.360 --> 00:11:51.540 we're keeping in mind. 00:11:51.540 --> 00:11:56.850 At the next level, we have b going to c, d going to g, a 00:11:56.850 --> 00:12:01.030 going to d, and c going to e. 00:12:01.030 --> 00:12:05.460 And now, when we scan across, we do hit g. 00:12:05.460 --> 00:12:08.530 So, we found a path with Breadth-first Search, just as 00:12:08.530 --> 00:12:09.985 we found a path with Depth-first Search. 00:12:12.650 --> 00:12:14.360 Now, you might say, well, why didn't you just quit 00:12:14.360 --> 00:12:15.420 when you hit g? 00:12:15.420 --> 00:12:18.340 Implementation detail. 00:12:18.340 --> 00:12:20.830 We'll talk about a sample implementation. 00:12:20.830 --> 00:12:22.990 You can write it in any way you want. 00:12:22.990 --> 00:12:26.080 But now that we know what these searches are, let's 00:12:26.080 --> 00:12:31.560 speed things up a little bit here and do a couple searches 00:12:31.560 --> 00:12:34.530 that now have names. 00:12:34.530 --> 00:12:38.590 The first type will be Depth-first, boom. 00:12:38.590 --> 00:12:43.870 That's the one that produces the thief path. 00:12:43.870 --> 00:12:46.070 And then we can also do a Breadth-first Search, which we 00:12:46.070 --> 00:12:47.310 haven't tried yet. 00:12:47.310 --> 00:12:49.350 What do you suppose is going to happen? 00:12:49.350 --> 00:12:53.030 Is it going to be fast, slow, produce a good path, 00:12:53.030 --> 00:12:53.840 produce a bad path? 00:12:53.840 --> 00:12:56.095 I don't know, let's try it. 00:12:56.095 --> 00:12:58.410 I had to speed it up, you see, because it's doing an awful 00:12:58.410 --> 00:12:59.670 lot of Search. 00:12:59.670 --> 00:13:01.410 It's generating an awful lot of paths. 00:13:08.420 --> 00:13:10.280 Finally, you got a path. 00:13:10.280 --> 00:13:11.030 Is it the best path? 00:13:11.030 --> 00:13:11.680 I don't think so. 00:13:11.680 --> 00:13:13.700 But we're not going to talk about optimal paths today. 00:13:13.700 --> 00:13:15.730 We're just going to talk about pretty good 00:13:15.730 --> 00:13:18.330 paths, heuristic paths. 00:13:18.330 --> 00:13:21.545 Let's move the starting position here in the middle. 00:13:21.545 --> 00:13:25.050 Do you think Breadth-first Search is going to be stupid? 00:13:25.050 --> 00:13:26.310 I think it's going to be pretty stupid. 00:13:26.310 --> 00:13:28.730 Let's see what happens. 00:13:28.730 --> 00:13:30.840 This Search is a lot to the left, which you would never do 00:13:30.840 --> 00:13:31.795 with you eye. 00:13:31.795 --> 00:13:35.050 Let me slow that down just to demonstrate it. 00:13:35.050 --> 00:13:37.190 It finds a shorter path, because it's right there in 00:13:37.190 --> 00:13:38.470 the middle. 00:13:38.470 --> 00:13:41.810 But it spends a lot of its time looking off to the left. 00:13:41.810 --> 00:13:44.740 It's pretty stupid. 00:13:44.740 --> 00:13:46.810 But that's how it works. 00:13:46.810 --> 00:13:49.760 So, now that we've got two examples of searches on the 00:13:49.760 --> 00:13:52.460 table, I'd like to just write a little flow chart for how 00:13:52.460 --> 00:13:54.800 the search might work. 00:13:54.800 --> 00:13:58.710 Because if I do that, then it'll be easier for us to see 00:13:58.710 --> 00:14:00.600 what kind of small differences there are between the 00:14:00.600 --> 00:14:04.550 implementations of these various searches. 00:14:04.550 --> 00:14:07.500 So, what we're going to do is we're going to develop a 00:14:07.500 --> 00:14:11.020 waiting list, a queue, a line, whatever you'd 00:14:11.020 --> 00:14:11.180 like to call it. 00:14:11.180 --> 00:14:12.380 Let's call if a queue. 00:14:12.380 --> 00:14:14.590 We're going to develop a queue of paths that are under 00:14:14.590 --> 00:14:16.960 consideration. 00:14:16.960 --> 00:14:20.120 So, the first step in our algorithm will be to 00:14:20.120 --> 00:14:26.242 initialize our queue. 00:14:29.410 --> 00:14:33.550 And I think what I'll do is I'll simulate Depth-first 00:14:33.550 --> 00:14:37.780 Search on this problem up there on the 00:14:37.780 --> 00:14:40.500 left using this algorithm. 00:14:40.500 --> 00:14:43.890 I need to have some way of representing my paths. 00:14:43.890 --> 00:14:46.960 And what I want to do is I'm going to betray my heritage as 00:14:46.960 --> 00:14:49.720 a list programmer, because I'm just going to put these up as 00:14:49.720 --> 00:14:52.320 if there were lisp s-expressions. 00:14:52.320 --> 00:14:55.140 To begin with, I just have one path. 00:14:55.140 --> 00:14:58.710 And it has only one node in it, s. 00:14:58.710 --> 00:15:01.400 That's the whole path. 00:15:01.400 --> 00:15:06.890 The next thing I do after I initialize the queue is I 00:15:06.890 --> 00:15:18.415 extend first path on the queue. 00:15:24.750 --> 00:15:27.785 OK, when I extend s, I get two paths. 00:15:30.300 --> 00:15:38.670 I get s goes to a, and I get s goes to b. 00:15:38.670 --> 00:15:41.460 I take the first one off the front of the queue. 00:15:41.460 --> 00:15:44.320 And I put back the two that are produced by 00:15:44.320 --> 00:15:47.070 extending that path. 00:15:47.070 --> 00:15:50.130 Now, after I've extended the first path on the queue, I 00:15:50.130 --> 00:15:56.820 have to but those extended paths on to the queue. 00:15:56.820 --> 00:15:59.200 In here there's an explicit step where I've checked to see 00:15:59.200 --> 00:16:01.620 if that first path is a winner. 00:16:01.620 --> 00:16:03.710 If it's not, I extend it. 00:16:03.710 --> 00:16:07.950 And I have to put those paths onto the queue. 00:16:07.950 --> 00:16:10.180 So, I'll say that what I do is I end queue. 00:16:18.390 --> 00:16:19.950 Now, I've done one step. 00:16:19.950 --> 00:16:21.160 And let's let me do another step. 00:16:21.160 --> 00:16:24.190 I'm going to take this first path off. 00:16:24.190 --> 00:16:27.580 I'm going to extend that path. 00:16:27.580 --> 00:16:30.760 And where do I put these new paths on the queue if I'm 00:16:30.760 --> 00:16:34.320 doing Depth-first Search? 00:16:34.320 --> 00:16:38.390 Well, I want to work with the path that I've just generated. 00:16:38.390 --> 00:16:43.800 I'm taking this plunge down deep into the search tree. 00:16:43.800 --> 00:16:47.290 So, since I want to keep going down into the stuff that I 00:16:47.290 --> 00:16:51.440 just generated, where then do I want to put these two paths? 00:16:51.440 --> 00:16:52.360 At the end of the queue? 00:16:52.360 --> 00:16:54.430 I don't think so, because it'll be a long 00:16:54.430 --> 00:16:55.370 time getting there. 00:16:55.370 --> 00:16:56.620 I want to put them on the front of the queue. 00:17:00.920 --> 00:17:12.858 For Depth-first Search, I want to put them on the 00:17:12.858 --> 00:17:15.220 front of the queue. 00:17:15.220 --> 00:17:24.510 And that's why s, a, b goes here, and s, a, d, and then 00:17:24.510 --> 00:17:25.800 that's s, b. 00:17:29.770 --> 00:17:31.100 So, s, b is still there. 00:17:31.100 --> 00:17:33.550 That's still a valid possibility. 00:17:33.550 --> 00:17:35.830 But now I've stuck two paths in front of it, both of the 00:17:35.830 --> 00:17:39.060 ones I generated by taking a path off the front of the 00:17:39.060 --> 00:17:42.310 queue, discovering that it doesn't go to the goal, 00:17:42.310 --> 00:17:46.130 extending it and putting those back on the queue. 00:17:46.130 --> 00:17:49.210 I might as well complete this illustration here. 00:17:49.210 --> 00:17:57.070 While I'm at it, I take the s, a, b off, s, a, b, and I can 00:17:57.070 --> 00:17:59.840 go only there to c. 00:17:59.840 --> 00:18:06.332 But, of course, I keep s, a, d and s, b on the queue. 00:18:09.170 --> 00:18:12.860 Now, I take the front off the queue again, and I get s, a, 00:18:12.860 --> 00:18:20.501 b, c, e, and not to forget s, a, d and s, b. 00:18:23.330 --> 00:18:25.340 I take the first one off the queue. 00:18:25.340 --> 00:18:27.900 It doesn't go to the goal. 00:18:27.900 --> 00:18:30.000 I try to extend it, but there's nothing there. 00:18:30.000 --> 00:18:32.080 I've reached a dead end. 00:18:32.080 --> 00:18:34.670 So, in this operation, all I'm doing is taking the front one 00:18:34.670 --> 00:18:36.620 off the queue and shortening the queue. 00:18:42.030 --> 00:18:43.860 We're almost home. 00:18:43.860 --> 00:18:45.870 I take s, a,d off of queue. 00:18:45.870 --> 00:18:50.160 And I get s, a, d, c. 00:18:50.160 --> 00:18:54.300 And, of course, I still have s, b. 00:18:54.300 --> 00:19:00.650 Now, the next time I visit the situation, buried in that 00:19:00.650 --> 00:19:04.150 first step, I discover a path that actually does get to 00:19:04.150 --> 00:19:06.920 goal, and I'm done. 00:19:06.920 --> 00:19:10.810 So, each time around I visualize the queue. 00:19:10.810 --> 00:19:12.320 I check to see if I'm done. 00:19:12.320 --> 00:19:15.840 If not, I take the extensions and put them 00:19:15.840 --> 00:19:17.606 somewhere on the queue. 00:19:17.606 --> 00:19:25.000 And then I go back in. 00:19:25.000 --> 00:19:29.900 And then here there's a varied test which checks to see if 00:19:29.900 --> 00:19:32.280 we're done. 00:19:32.280 --> 00:19:36.650 That's how the Depth-first Search algorithm works. 00:19:36.650 --> 00:19:39.070 And now, would we have to start all over again if we did 00:19:39.070 --> 00:19:41.780 Breadth-first Search? 00:19:41.780 --> 00:19:42.310 Nope. 00:19:42.310 --> 00:19:44.220 Same algorithm. 00:19:44.220 --> 00:19:46.110 All the code we've got needs one line 00:19:46.110 --> 00:19:49.060 replaced, one line changed. 00:19:49.060 --> 00:19:51.080 What do I have to do different in order to get a 00:19:51.080 --> 00:19:52.800 Breadth-first Search out of this instead of 00:19:52.800 --> 00:19:54.580 a Depth-first Search? 00:19:54.580 --> 00:19:55.440 Tanya? 00:19:55.440 --> 00:19:56.930 TANYA: Change [INAUDIBLE] on the queue. 00:19:56.930 --> 00:19:57.940 PATRICK WINSTON: And where do I put it on the queue? 00:19:57.940 --> 00:19:58.840 She says to change it. 00:19:58.840 --> 00:19:59.720 TANYA: On the back? 00:19:59.720 --> 00:20:02.030 PATRICK WINSTON: Put it on the back. 00:20:02.030 --> 00:20:14.810 So, with Breadth-first Search all I have to do 00:20:14.810 --> 00:20:16.060 is put on the back. 00:20:21.290 --> 00:20:28.990 Now, if we were content with a inefficient search, and didn't 00:20:28.990 --> 00:20:31.350 care much about how good our path was, we'd be done. 00:20:31.350 --> 00:20:33.330 And we could go home. 00:20:33.330 --> 00:20:35.690 But we are a little concerned about the 00:20:35.690 --> 00:20:37.740 efficiency of our search. 00:20:37.740 --> 00:20:39.820 And we would like a pretty good path. 00:20:39.820 --> 00:20:41.630 So, we're going to have to stick around 00:20:41.630 --> 00:20:42.880 for a little while. 00:20:45.290 --> 00:20:49.770 Now, you may have noticed, up there in that the development 00:20:49.770 --> 00:20:57.180 of the Breadth-first Search, that the algorithm is 00:20:57.180 --> 00:20:58.430 incredibly stupid. 00:21:01.300 --> 00:21:03.115 Why is the algorithm incredibly stupid? 00:21:06.000 --> 00:21:07.200 Ty, what do you think? 00:21:07.200 --> 00:21:09.189 TY: It can't tell whether it's getting closer or further away 00:21:09.189 --> 00:21:09.540 from the goal. 00:21:09.540 --> 00:21:11.090 PATRICK WINSTON: It certainly can't tell whether it's 00:21:11.090 --> 00:21:13.330 getting closer or further away from the goal. 00:21:13.330 --> 00:21:16.090 And we're going to deal with that in a minute. 00:21:16.090 --> 00:21:17.640 But it's even stupider than that. 00:21:20.880 --> 00:21:21.540 Why is it stupid? 00:21:21.540 --> 00:21:22.474 What's your name? 00:21:22.474 --> 00:21:24.342 DYLAN: Dylan. 00:21:24.342 --> 00:21:26.677 It [? hits ?] the same nodes twice. 00:21:26.677 --> 00:21:30.340 PATRICK WINSTON: Dylan said it's extending paths that go 00:21:30.340 --> 00:21:33.660 to the same node more than once. 00:21:33.660 --> 00:21:34.970 Let's see what Dylan's talking about. 00:21:39.410 --> 00:21:42.522 Down here, it extends a. 00:21:42.522 --> 00:21:46.810 But it's already extended a up there. 00:21:46.810 --> 00:21:51.440 Down here, it extends a path that goes to b. 00:21:51.440 --> 00:21:54.900 And it's already extended a path that goes to d. 00:21:54.900 --> 00:22:02.170 Over here, it could extend a path that went through c, but 00:22:02.170 --> 00:22:05.800 it's already got a path that goes through c. 00:22:05.800 --> 00:22:09.450 So, all of these paths are duplicated. 00:22:09.450 --> 00:22:12.040 And we're still going through them. 00:22:12.040 --> 00:22:15.450 That's incredibly stupid. 00:22:15.450 --> 00:22:17.460 What we're going to do is we're going to amend our 00:22:17.460 --> 00:22:18.750 algorithm just a little bit. 00:22:23.940 --> 00:22:31.210 And we're not going to extend the first path on the queue 00:22:31.210 --> 00:22:49.440 unless final node never before extended. 00:22:56.550 --> 00:22:58.380 What we're going to do is we're going to look to see if 00:22:58.380 --> 00:22:59.780 there-- we've got this path. 00:22:59.780 --> 00:23:00.930 And we're going to extend it. 00:23:00.930 --> 00:23:02.190 And it's got a final note. 00:23:02.190 --> 00:23:05.700 If we've ever extended a path that goes to that final node, 00:23:05.700 --> 00:23:07.580 and it was a final node on that path, then we're not 00:23:07.580 --> 00:23:09.630 going to do it again. 00:23:09.630 --> 00:23:16.520 We got to keep a list of places that have already been 00:23:16.520 --> 00:23:19.506 the last piece of a path that was extended. 00:23:19.506 --> 00:23:20.830 Everybody got that? 00:23:20.830 --> 00:23:24.130 It's a little awkward to say it, because it's the last node 00:23:24.130 --> 00:23:24.870 we care about. 00:23:24.870 --> 00:23:30.640 If a path terminates in a node, and if some other path 00:23:30.640 --> 00:23:33.480 previously terminated in that node and got extended-- 00:23:33.480 --> 00:23:34.570 we're not going to do it again. 00:23:34.570 --> 00:23:35.820 Because it's a waste of time. 00:23:39.690 --> 00:23:41.260 Now, let's see if this actually helps. 00:23:51.470 --> 00:23:53.200 Now, use the extended list. 00:23:53.200 --> 00:24:00.305 Let's see, well, gee, we got that place 00:24:00.305 --> 00:24:01.050 in the center there. 00:24:01.050 --> 00:24:02.790 Let's just repeat the previous search. 00:24:15.200 --> 00:24:17.200 Wow, it's taking a long time. 00:24:17.200 --> 00:24:22.610 But notice it put 103 paths back on the queue. 00:24:22.610 --> 00:24:26.200 Now, let's add a filter and try again. 00:24:39.540 --> 00:24:41.640 A lot less. 00:24:41.640 --> 00:24:46.950 So, let's speed this up, and we'll start way over here. 00:24:46.950 --> 00:24:49.390 You remember how tedious that search was. 00:24:49.390 --> 00:24:55.240 And now we'll repeat it with this list, boom, there it is. 00:24:55.240 --> 00:24:58.050 That's all because we didn't do that silly thing of going 00:24:58.050 --> 00:25:01.610 back through the final node that's 00:25:01.610 --> 00:25:04.170 already been gone through. 00:25:04.170 --> 00:25:07.380 So, you would never not want to do this. 00:25:07.380 --> 00:25:09.220 We better list this as another option. 00:25:19.846 --> 00:25:22.420 It doesn't help with a British Museum algorithm, because 00:25:22.420 --> 00:25:24.670 nothing helps with the British Museum algorithm. 00:25:24.670 --> 00:25:25.950 Does it help with Depth-first? 00:25:25.950 --> 00:25:26.800 Yes. 00:25:26.800 --> 00:25:28.350 Does it help with Breadth-first? 00:25:28.350 --> 00:25:29.680 Yes. 00:25:29.680 --> 00:25:32.000 Do we do backtracking with Breadth-first? 00:25:32.000 --> 00:25:38.870 No, because backtracking can't do us any good. 00:25:38.870 --> 00:25:43.990 OK, we're almost, except that search that's starting in the 00:25:43.990 --> 00:25:46.090 middle is still pretty stupid. 00:25:46.090 --> 00:25:52.200 Both the Breadth-first version and the Depth-first version 00:25:52.200 --> 00:25:53.940 are going off to the left. 00:25:53.940 --> 00:25:58.320 And we would never do that with our eyes in any case. 00:25:58.320 --> 00:26:01.720 The next thing we want to do is we want to have ourselves a 00:26:01.720 --> 00:26:07.020 slightly more informed search by taking into consideration 00:26:07.020 --> 00:26:08.525 whether we seem to be getting anywhere. 00:26:13.490 --> 00:26:17.550 So, in general, it's a good thing to get closer to where 00:26:17.550 --> 00:26:19.890 we want to go. 00:26:19.890 --> 00:26:24.200 In general, if we've got a choice of going to a node 00:26:24.200 --> 00:26:27.210 that's close to the goal or a node that's not so close to 00:26:27.210 --> 00:26:28.830 the goal, we'll always want to go to the one that's 00:26:28.830 --> 00:26:31.010 close to the goal. 00:26:31.010 --> 00:26:35.610 And as soon as we add that to what we're doing, we have 00:26:35.610 --> 00:26:47.290 another kind of Search, which goes by the 00:26:47.290 --> 00:26:48.540 name of Hill Climbing. 00:26:56.900 --> 00:26:59.830 And it's just like Depth-first Search, except instead of 00:26:59.830 --> 00:27:03.540 using lexical order to break ties, we're going to break 00:27:03.540 --> 00:27:06.290 ties according to which node is closer to the goal. 00:27:09.720 --> 00:27:11.260 I went to some trouble to talk to you about 00:27:11.260 --> 00:27:12.680 this enqueued list. 00:27:12.680 --> 00:27:14.020 And having gone to that trouble, I'm now 00:27:14.020 --> 00:27:15.860 going to ignore it. 00:27:15.860 --> 00:27:18.260 Not because it isn't a good idea, but because trying to 00:27:18.260 --> 00:27:20.490 keep track of everything in the example is 00:27:20.490 --> 00:27:21.310 confusing the example. 00:27:21.310 --> 00:27:24.350 It won't work out right in the small example and all that. 00:27:24.350 --> 00:27:28.270 Put the queueing thing aside, queued list aside, and think 00:27:28.270 --> 00:27:33.120 instead just about the value of going in the direction 00:27:33.120 --> 00:27:36.820 that's getting us closer to the goal. 00:27:36.820 --> 00:27:40.520 In Hill Climbing Search, just like a Depth-first Search, we 00:27:40.520 --> 00:27:42.790 have a and b. 00:27:42.790 --> 00:27:45.800 And we're still going to list them lexically on underneath 00:27:45.800 --> 00:27:47.636 the parent node. 00:27:47.636 --> 00:27:53.630 But now which one is so closer to the goal? 00:27:53.630 --> 00:27:56.620 Now, this time b is closer to the goal than a. 00:27:56.620 --> 00:27:59.340 So, instead of following the Depth-first course, which 00:27:59.340 --> 00:28:02.030 would take us down through a, we're going to go to the one 00:28:02.030 --> 00:28:04.890 that's closest which goes through b. 00:28:04.890 --> 00:28:08.140 And b can either go to a or c. 00:28:14.670 --> 00:28:19.040 b is six units away from the goal. a is about seven plus, 00:28:19.040 --> 00:28:20.620 not drawn exactly to scale. 00:28:20.620 --> 00:28:22.483 Use the numbers not your eyes. 00:28:25.420 --> 00:28:26.740 Now where are we? 00:28:26.740 --> 00:28:28.990 It's symmetric, so a and c are both equally 00:28:28.990 --> 00:28:30.920 far from the goal. 00:28:30.920 --> 00:28:32.220 Now we're going to use the lexical order 00:28:32.220 --> 00:28:34.160 to break the tie. 00:28:34.160 --> 00:28:41.510 Now from s, b, a, we'll go to d. 00:28:41.510 --> 00:28:44.190 And now, which is closest to the goal? 00:28:44.190 --> 00:28:45.340 That's the only choice we have. 00:28:45.340 --> 00:28:49.050 So, now we have no choice but to go down to the goal. 00:28:49.050 --> 00:28:53.250 That's the Hill Climbing way of doing the search. 00:28:53.250 --> 00:28:54.820 And notice that this time there's no backtracking. 00:28:57.740 --> 00:28:59.270 It's not the optimal path. 00:28:59.270 --> 00:28:59.940 It's not the best path. 00:28:59.940 --> 00:29:02.010 But at least there's no backtracking. 00:29:02.010 --> 00:29:02.830 That's not always true. 00:29:02.830 --> 00:29:07.180 That's just an artifact of this particular example. 00:29:07.180 --> 00:29:10.910 Do you think Hill Climbing would produce a faster search? 00:29:10.910 --> 00:29:13.030 I think so. 00:29:13.030 --> 00:29:15.040 Let's see what happens when we add these 00:29:15.040 --> 00:29:17.570 things at one at a time. 00:29:17.570 --> 00:29:22.790 First, let's turn off our extended list. 00:29:25.610 --> 00:29:27.010 We turned off our extended list. 00:29:27.010 --> 00:29:29.980 And we're going to do Depth-first again just for the 00:29:29.980 --> 00:29:33.040 sake of comparison. 00:29:33.040 --> 00:29:38.460 It produces a very roundabout path with 48 enqueueings. 00:29:38.460 --> 00:29:41.230 Now, let's switch over to Hill Climbing. 00:29:41.230 --> 00:29:41.780 And what do think? 00:29:41.780 --> 00:29:44.630 Do you think it will produce a straighter path, fewer 00:29:44.630 --> 00:29:46.720 enqueueings? 00:29:46.720 --> 00:29:47.970 Boom. 00:29:49.930 --> 00:29:52.180 You wouldn't not want to do that, would you? 00:29:52.180 --> 00:29:55.450 If you've got some kind of heuristic that tells you that 00:29:55.450 --> 00:29:58.360 you're getting close to the goal, you should use it. 00:29:58.360 --> 00:30:03.330 Now, it's easy to modify my example over there so that 00:30:03.330 --> 00:30:05.550 getting close to the goal gets you trapped in a 00:30:05.550 --> 00:30:06.690 blind alley on e. 00:30:06.690 --> 00:30:08.730 That's easy to do. 00:30:08.730 --> 00:30:10.280 But that's just an artifact of the example. 00:30:10.280 --> 00:30:13.130 In general, you want to go along a path that gets you 00:30:13.130 --> 00:30:15.060 closer to the goal. 00:30:15.060 --> 00:30:16.040 So, that's 23. 00:30:16.040 --> 00:30:18.400 I don't know, let's see if using the extended list filter 00:30:18.400 --> 00:30:19.650 does any good. 00:30:21.870 --> 00:30:23.360 Yeah, still 23. 00:30:23.360 --> 00:30:30.670 So, in that particular case the extension list didn't 00:30:30.670 --> 00:30:33.190 actually do us any good, because we're driving so 00:30:33.190 --> 00:30:34.440 directly toward the goal. 00:30:36.960 --> 00:30:38.740 OK, that's that. 00:30:38.740 --> 00:30:42.410 Now, let's see, is there any analog to-- 00:30:42.410 --> 00:30:47.580 well, we might say that this is yet another way of 00:30:47.580 --> 00:30:49.750 distinguishing the searches. 00:30:49.750 --> 00:30:57.990 And that is, is it an informed search? 00:31:00.620 --> 00:31:03.540 Is it making use of any kind of heuristic information? 00:31:03.540 --> 00:31:05.640 Certainly, a British Museum is not, Depth is 00:31:05.640 --> 00:31:07.530 not, Breadth is not. 00:31:07.530 --> 00:31:09.980 And now let's consider what we got for Hill Climbing. 00:31:09.980 --> 00:31:11.240 Do we want to use backtracking? 00:31:11.240 --> 00:31:12.410 Sure. 00:31:12.410 --> 00:31:14.010 Do we want to use an enqueued list? 00:31:14.010 --> 00:31:15.650 Sure. 00:31:15.650 --> 00:31:18.210 And it is informed, because it's taking advantage of this 00:31:18.210 --> 00:31:18.800 extra information. 00:31:18.800 --> 00:31:20.500 It may not be in your problem. 00:31:20.500 --> 00:31:24.570 It's not often the case you've got this information in a map. 00:31:24.570 --> 00:31:28.040 Your problem may not have any heuristic measurement of 00:31:28.040 --> 00:31:29.325 distance to the goal. 00:31:29.325 --> 00:31:31.090 In which case, you can't do it. 00:31:31.090 --> 00:31:33.980 But if you've got it, you should use it. 00:31:33.980 --> 00:31:35.550 Oh, yeah, there's one more. 00:31:35.550 --> 00:31:40.020 And I've already given it away by having it on my chart. 00:31:40.020 --> 00:31:41.110 It's called Beam Search. 00:31:41.110 --> 00:31:46.210 And just as Hill Climbing is an analog of Depth-first 00:31:46.210 --> 00:31:51.770 Search, Beam Search is a complement or addition of an 00:31:51.770 --> 00:31:55.140 informing heuristic to Breadth-first Search. 00:31:55.140 --> 00:31:56.880 What you do is you start off just like 00:31:56.880 --> 00:31:58.130 Breadth-first Search. 00:32:01.190 --> 00:32:05.230 But you say I'm going to limit the number of paths I'm going 00:32:05.230 --> 00:32:09.550 to consider at any level to some small, fixed number, 00:32:09.550 --> 00:32:12.530 like, in this case, how about two. 00:32:12.530 --> 00:32:15.970 So, I'm going to say that I have a Beam of 00:32:15.970 --> 00:32:18.080 two for my Beam Search. 00:32:25.530 --> 00:32:29.080 Otherwise, I proceed just like Breadth-first 00:32:29.080 --> 00:32:30.330 Search, b, d, a, g. 00:32:36.230 --> 00:32:38.880 And now I've got that stupid thing where I'm duplicating my 00:32:38.880 --> 00:32:42.110 nodes, because I'm forgetting about the enqueued list. 00:32:42.110 --> 00:32:44.760 But to illustrate Beam Search, what about I'm going to do now 00:32:44.760 --> 00:32:47.080 is I'm going to take all these paths I've got at the second 00:32:47.080 --> 00:32:49.190 level, and I'm only going to keep the best two. 00:32:49.190 --> 00:32:51.130 That's my beam width. 00:32:51.130 --> 00:32:54.220 And the best two are the two that get closest to the goal. 00:32:54.220 --> 00:32:58.430 So, those four, b, c, a, and d, which two get 00:32:58.430 --> 00:32:59.945 closest to the goal? 00:32:59.945 --> 00:33:02.160 Now, b and d. 00:33:02.160 --> 00:33:05.530 These guys are trimmed off. 00:33:05.530 --> 00:33:08.030 I'm only keeping two at every level. 00:33:08.030 --> 00:33:11.690 Now, going down from b and d, I have, at the next 00:33:11.690 --> 00:33:14.250 level, c and g. 00:33:14.250 --> 00:33:15.860 And now I've found the goal. 00:33:15.860 --> 00:33:17.790 So, I'm done. 00:33:17.790 --> 00:33:19.040 We could do that here, too. 00:33:22.750 --> 00:33:32.350 We could choose a Beam Search, not bad. 00:33:32.350 --> 00:33:34.940 Let's see, let's try this thing from the middle. 00:33:34.940 --> 00:33:37.530 Let's slow my speed down a little bit. 00:33:37.530 --> 00:33:39.853 Now, are we going to see anything going off to the left 00:33:39.853 --> 00:33:44.950 like we did with ordinary Breadth-first Search? 00:33:44.950 --> 00:33:47.640 No, because it's smart. 00:33:47.640 --> 00:33:49.780 It doesn't say, I want to go to a place that's further away 00:33:49.780 --> 00:33:51.030 from my goal. 00:33:53.870 --> 00:33:57.940 Now, let's see, maybe we can go back to our algorithm now 00:33:57.940 --> 00:34:07.620 and talk about that enqueueing mechanism and 00:34:07.620 --> 00:34:08.870 talk about Hill Climbing. 00:34:17.170 --> 00:34:21.060 Can I use the same basic search mechanism, just change 00:34:21.060 --> 00:34:22.199 that one line again? 00:34:22.199 --> 00:34:23.570 Yes. 00:34:23.570 --> 00:34:27.199 How do I add new paths to the queue this time? 00:34:27.199 --> 00:34:29.210 Well, it's very much like Hill Climbing, right? 00:34:29.210 --> 00:34:31.880 I want to add them to the front but 00:34:31.880 --> 00:34:32.960 with one little flourish. 00:34:32.960 --> 00:34:34.210 What's the flourish? 00:34:34.210 --> 00:34:36.460 [? Krishna, ?] what do you think? 00:34:36.460 --> 00:34:39.500 Remember, I want to use my heuristic information. 00:34:39.500 --> 00:34:41.900 So, I not only add them to the front, but amongst the ones 00:34:41.900 --> 00:34:43.705 I'm adding to the front, what do I do? 00:34:43.705 --> 00:34:44.980 AUDIENCE:Check the distance? 00:34:44.980 --> 00:34:45.850 PATRICK WINSTON: Check the distance. 00:34:45.850 --> 00:34:47.120 And how do you arrange them? 00:34:47.120 --> 00:34:47.958 AUDIENCE:[? You ?] 00:34:47.958 --> 00:34:49.219 [? keep the ?] minimum [? first. ?] 00:34:49.219 --> 00:34:51.570 PATRICK WINSTON: Yeah, you can put the minimum 00:34:51.570 --> 00:34:52.290 first if you like. 00:34:52.290 --> 00:34:53.739 But let's sort them. 00:34:53.739 --> 00:34:56.520 We'll sort them, that will keep everything straight. 00:34:56.520 --> 00:35:03.060 So Hill Climbing is front-sorted. 00:35:13.370 --> 00:35:14.580 And, finally, how about Beam? 00:35:14.580 --> 00:35:17.860 What do we do with Beam Search to add them to the queue? 00:35:17.860 --> 00:35:21.175 Well, it doesn't matter where we add them, because all we're 00:35:21.175 --> 00:35:25.840 going to do is we're going to keep the w best. 00:35:25.840 --> 00:35:30.270 So, with Beam, we'll just abbreviate that by 00:35:30.270 --> 00:35:35.070 saying keep w best. 00:35:41.330 --> 00:35:43.870 Now, you have some of the basic 00:35:43.870 --> 00:35:46.450 searches in you're toolkit. 00:35:46.450 --> 00:35:48.800 There's one more that's sometimes talked about. 00:35:48.800 --> 00:35:53.710 We've got Depth, Breadth, Best, and Beam, one more is 00:35:53.710 --> 00:35:57.720 Best, Best-first Search. 00:35:57.720 --> 00:36:04.250 It's a variant where you say, I've got this tree. 00:36:04.250 --> 00:36:08.270 It's got a bunch of paths that terminate in leaves. 00:36:08.270 --> 00:36:10.510 Let me just always work on the leaf node that's 00:36:10.510 --> 00:36:12.790 closest to the goal. 00:36:12.790 --> 00:36:15.510 It can skip around a little bit from one place to another. 00:36:15.510 --> 00:36:18.490 Because as it pursues one path, it may not do very well 00:36:18.490 --> 00:36:20.350 in some other path quite distant. 00:36:20.350 --> 00:36:21.870 And the tree will become the best one. 00:36:24.710 --> 00:36:28.930 We've actually seen an instance of that in then 00:36:28.930 --> 00:36:30.690 integration program. 00:36:30.690 --> 00:36:32.840 It's capable of skipping all over the place, because it's 00:36:32.840 --> 00:36:37.950 always taking the easiest problem in the search tree, in 00:36:37.950 --> 00:36:39.940 the and/or tree, working on that. 00:36:39.940 --> 00:36:43.300 That's Best-first Search. 00:36:43.300 --> 00:36:44.340 You can do these sorts of things in 00:36:44.340 --> 00:36:46.780 continuous spaces, too. 00:36:46.780 --> 00:36:47.830 And you've done the mathematics of 00:36:47.830 --> 00:36:52.580 that in 1802 or something. 00:36:52.580 --> 00:36:56.190 But in continuous spaces, the Hill Climbing sometimes leads 00:36:56.190 --> 00:36:59.470 to problems or doesn't do very well. 00:36:59.470 --> 00:37:04.140 What kind of a problem can you encounter in a continuous 00:37:04.140 --> 00:37:08.210 space with Hill Climbing? 00:37:08.210 --> 00:37:11.726 Well, how would you do Hill Climbing in 00:37:11.726 --> 00:37:12.840 a continuous space? 00:37:12.840 --> 00:37:16.550 Let's say we're in the mountains, and a big 00:37:16.550 --> 00:37:18.500 fog has come up. 00:37:18.500 --> 00:37:20.470 We're trying to get to the top of the hill before 00:37:20.470 --> 00:37:22.720 we freeze to death. 00:37:22.720 --> 00:37:28.006 And we take a few steps north, a few steps east, west, and 00:37:28.006 --> 00:37:30.380 south using our compass. 00:37:30.380 --> 00:37:33.510 And we check to see which direction seems to be doing 00:37:33.510 --> 00:37:37.220 the best job of getting us moving upward. 00:37:37.220 --> 00:37:39.140 And that's our Hill Climbing approach, right? 00:37:39.140 --> 00:37:43.700 We have explored four directions we can go and pick 00:37:43.700 --> 00:37:45.180 the best one. 00:37:45.180 --> 00:37:47.940 And from there, we pick four, try all those, pick the best 00:37:47.940 --> 00:37:48.800 one, and away we go. 00:37:48.800 --> 00:37:51.180 We've got ourselves a Hill Climbing algorithm. 00:37:51.180 --> 00:37:53.210 What's wrong with it? 00:37:53.210 --> 00:37:54.710 Or what can be wrong with it? 00:37:54.710 --> 00:37:56.840 Sometimes it works just fine. 00:37:56.840 --> 00:37:57.330 Yes. 00:37:57.330 --> 00:37:59.605 SPEAKER 1: You might get stuck in a local maximum. 00:37:59.605 --> 00:38:02.320 PATRICK WINSTON: We might get stuck in a local maximum. 00:38:02.320 --> 00:38:10.590 So, problem letter a is that if this is your space, it may 00:38:10.590 --> 00:38:11.450 look like that. 00:38:11.450 --> 00:38:16.640 And you may get stuck on a local maximum. 00:38:16.640 --> 00:38:18.330 Is there any other kind of problem that can come up? 00:38:26.215 --> 00:38:28.820 Well, it all depends on what the space is like. 00:38:28.820 --> 00:38:30.645 Here's a problem where the space has local maxima. 00:38:33.230 --> 00:38:35.010 Now, a lot of people have been killed on Mt. 00:38:35.010 --> 00:38:38.000 Washington when the fog comes up. 00:38:38.000 --> 00:38:40.270 And they do freeze to death, why? 00:38:43.270 --> 00:38:47.440 The reason they freeze to death is the Hill Climbing 00:38:47.440 --> 00:38:49.080 fails them, and they can't get to the top 00:38:49.080 --> 00:38:50.960 to the ranger station. 00:38:50.960 --> 00:38:53.660 And the reason is that there are large lawns on the 00:38:53.660 --> 00:38:54.230 shoulders of Mt. 00:38:54.230 --> 00:38:54.580 Washington. 00:38:54.580 --> 00:38:57.140 It's quite flat. 00:38:57.140 --> 00:38:58.555 So, it's the telephone pole problem. 00:39:02.090 --> 00:39:06.120 That space looks like this. 00:39:06.120 --> 00:39:07.040 Well, this isn't what Mt. 00:39:07.040 --> 00:39:07.910 Washington looks like. 00:39:07.910 --> 00:39:10.620 But it's the telephone pole problem. 00:39:10.620 --> 00:39:14.370 So, when you're wandering around here, the idea of 00:39:14.370 --> 00:39:17.720 trying a few directions and picking the one that's best 00:39:17.720 --> 00:39:20.210 doesn't help any, because it's flat. 00:39:20.210 --> 00:39:23.090 That can be a problem with Hill Climbing. 00:39:23.090 --> 00:39:26.160 Now, there's one more problem with Hill Climbing that most 00:39:26.160 --> 00:39:29.000 people don't know about. 00:39:29.000 --> 00:39:30.253 But it works like this. 00:39:34.600 --> 00:39:36.210 This is a particularly acute problem in 00:39:36.210 --> 00:39:37.280 high dimensional spaces. 00:39:37.280 --> 00:39:39.110 I'll illustrate it here just in two. 00:39:39.110 --> 00:39:44.370 And I'm going to switch from a regular kind of view to a 00:39:44.370 --> 00:39:46.570 contour map. 00:39:46.570 --> 00:39:54.950 So, my contour map is going to betray the presence of a sharp 00:39:54.950 --> 00:40:04.050 bridge along the 45 degree line. 00:40:04.050 --> 00:40:07.500 Now you see how you can get in trouble there. 00:40:07.500 --> 00:40:10.280 You get in trouble, because if you take a step in each 00:40:10.280 --> 00:40:13.350 direction, every direction takes you downhill. 00:40:13.350 --> 00:40:15.610 And you think you're at the top. 00:40:15.610 --> 00:40:19.826 So, suppose you're right here and you go north. 00:40:19.826 --> 00:40:24.180 That takes you down over a contour line. 00:40:24.180 --> 00:40:27.550 If you go south, that also takes you down 00:40:27.550 --> 00:40:29.000 over contour lines. 00:40:29.000 --> 00:40:33.870 Likewise, going west and east all appear to be taking you 00:40:33.870 --> 00:40:38.015 down, whereas, in fact, you're climbing a ridge. 00:40:38.015 --> 00:40:42.270 And that contour line is the highest that I've shown. 00:40:42.270 --> 00:40:43.900 So, sometimes you can get fooled-- 00:40:43.900 --> 00:40:46.000 not stuck, but fooled-- into thinking you're at the top 00:40:46.000 --> 00:40:47.250 when you're actually not. 00:40:49.830 --> 00:40:54.410 Now, this is a model something. 00:40:54.410 --> 00:40:58.130 This subject is about modeling intelligence. 00:40:58.130 --> 00:41:01.680 And this is a kind of algorithm you frequently need 00:41:01.680 --> 00:41:04.580 in order to build an intelligent system. 00:41:04.580 --> 00:41:07.360 But do we have any kind of Search happening in our heads? 00:41:11.650 --> 00:41:13.820 If we're going to model what goes on inside our heads, do 00:41:13.820 --> 00:41:19.850 we have to model any kind of searching in order to do the 00:41:19.850 --> 00:41:24.010 kinds of things that we humans do? 00:41:24.010 --> 00:41:24.720 I suppose so. 00:41:24.720 --> 00:41:28.250 Anytime we make a plan, we're actually evaluating a bunch of 00:41:28.250 --> 00:41:31.340 choices and seeing how they work. 00:41:31.340 --> 00:41:33.020 Let me see if I can illustrate it another way. 00:41:37.120 --> 00:41:42.260 This is a system that I showed you a little bit of last time. 00:41:42.260 --> 00:41:46.590 And, shoot, I might as well review one or two things here. 00:41:51.970 --> 00:41:53.640 I showed you a Macbeth story. 00:41:53.640 --> 00:41:56.220 This is the story I showed you. 00:41:56.220 --> 00:41:59.500 And if you had this in a humanities class, the simplest 00:41:59.500 --> 00:42:04.620 questions that might be asked is why did Macduff kill 00:42:04.620 --> 00:42:08.240 Macbeth down there at the bottom? 00:42:08.240 --> 00:42:10.960 Did I demonstrate the answering of questions last 00:42:10.960 --> 00:42:13.340 time, or just the development of the graph? 00:42:13.340 --> 00:42:14.000 I can't remember. 00:42:14.000 --> 00:42:16.210 But we'll do it again, anyway. 00:42:16.210 --> 00:42:19.895 This is somewhat stylized English. 00:42:19.895 --> 00:42:22.570 Just so you'll know, it doesn't have 00:42:22.570 --> 00:42:23.660 to be stylized English. 00:42:23.660 --> 00:42:27.330 This is English that's made available to the Genesis 00:42:27.330 --> 00:42:31.950 system by way of something called Story Workbench. 00:42:31.950 --> 00:42:32.800 There's no free lunch. 00:42:32.800 --> 00:42:35.740 Either you can use your human resources to rewrite the plot 00:42:35.740 --> 00:42:37.540 in third grade English. 00:42:37.540 --> 00:42:39.940 Or you can use your human resources to take a more 00:42:39.940 --> 00:42:43.240 natural, adult-type version of the story and decorate it with 00:42:43.240 --> 00:42:46.510 annotations that make it possible to absorb it. 00:42:46.510 --> 00:42:49.970 Just this summer, in a miracle of summer [? Europe, ?] 00:42:49.970 --> 00:42:50.313 [? Brit ?] 00:42:50.313 --> 00:42:50.656 [? van ?] 00:42:50.656 --> 00:42:51.280 [? Zijp-- ?] 00:42:51.280 --> 00:42:52.790 one of you-- 00:42:52.790 --> 00:42:54.630 connected these two systems together. 00:42:54.630 --> 00:42:57.030 So, we can now work with stories that are expressed in 00:42:57.030 --> 00:42:59.140 pretty natural English. 00:42:59.140 --> 00:43:02.890 Everything in our system is expressed in English, 00:43:02.890 --> 00:43:04.230 including common sense knowledge-- 00:43:04.230 --> 00:43:06.810 like if somebody kills you, you're dead-- 00:43:06.810 --> 00:43:10.880 but more importantly, for today's illustration, that 00:43:10.880 --> 00:43:14.920 reflective level knowledge, that knowledge about what 00:43:14.920 --> 00:43:17.180 revenge is. 00:43:17.180 --> 00:43:17.790 Here you are. 00:43:17.790 --> 00:43:20.280 You're in the humanities class, and someone says, 00:43:20.280 --> 00:43:21.800 what's really going on in the story? 00:43:21.800 --> 00:43:24.420 Not the details of who kills whom, but is 00:43:24.420 --> 00:43:26.560 there a Pyrrhic victory? 00:43:26.560 --> 00:43:28.140 Does somebody have a success? 00:43:28.140 --> 00:43:30.120 Is there an act of revenge? 00:43:30.120 --> 00:43:33.380 These are all kinds of things you might be asked about in 00:43:33.380 --> 00:43:34.800 some kind of humanities class. 00:43:40.470 --> 00:43:42.810 So, let me fire up the genesis system. 00:43:52.150 --> 00:43:53.400 Pray for internet connectivity. 00:43:58.730 --> 00:44:02.850 Launch the system on a read of that Macbeth story that I 00:44:02.850 --> 00:44:05.110 showed you just a moment ago. 00:44:05.110 --> 00:44:08.220 At the moment, it's absorbing information about background 00:44:08.220 --> 00:44:09.960 knowledge, and about reflective level knowledge, 00:44:09.960 --> 00:44:11.210 and all that sort of thing. 00:44:15.780 --> 00:44:18.010 It's building itself this thing we call 00:44:18.010 --> 00:44:20.100 an elaboration graph. 00:44:20.100 --> 00:44:21.320 It's not quite there yet. 00:44:21.320 --> 00:44:22.570 It's still reading background knowledge. 00:44:30.750 --> 00:44:32.140 Now it's reading Macbeth. 00:44:32.140 --> 00:44:36.100 It's building it's elaboration graph, the same thing you saw 00:44:36.100 --> 00:44:39.060 last time, except not quite. 00:44:39.060 --> 00:44:41.570 Do you see that stuff down at the bottom? 00:44:41.570 --> 00:44:44.500 Those are higher level concepts that it's managed to 00:44:44.500 --> 00:44:46.930 find in the Macbeth story. 00:44:46.930 --> 00:44:48.180 So, its found a revenge. 00:44:51.010 --> 00:44:53.510 How did it do that? 00:44:53.510 --> 00:44:55.560 It searched. 00:44:55.560 --> 00:44:58.810 It had a description of what a revenge is, and it looked to 00:44:58.810 --> 00:45:01.270 see if that pattern was exhibited in 00:45:01.270 --> 00:45:03.420 the elaboration graph. 00:45:03.420 --> 00:45:05.940 So, in a combination of things that were said explicitly and 00:45:05.940 --> 00:45:08.650 things that were produced by knee-jerk if/then rules, the 00:45:08.650 --> 00:45:11.280 elaboration graph was sufficiently instantiated that 00:45:11.280 --> 00:45:15.580 the revenge pattern could be found. 00:45:15.580 --> 00:45:19.030 That's interesting, Pyrrhic victory is a little harder. 00:45:19.030 --> 00:45:21.070 You'd probably get an a if you said, oh, there's a Pyrrhic 00:45:21.070 --> 00:45:24.220 victory in here. 00:45:24.220 --> 00:45:26.320 There it is. 00:45:26.320 --> 00:45:27.750 So, I'll blow that up a little bit so you can 00:45:27.750 --> 00:45:29.870 see what that is. 00:45:29.870 --> 00:45:32.220 You know what a Pyrrhic victory is. 00:45:32.220 --> 00:45:36.190 It's a situation where everything seems to be going 00:45:36.190 --> 00:45:41.910 good at first, and then not so hot. 00:45:41.910 --> 00:45:46.580 So, Macbeth wants to be King down here. 00:45:46.580 --> 00:45:48.975 And eventually that leads to becoming King. 00:45:48.975 --> 00:45:51.610 But too bad for Macbeth, because eventually he gets 00:45:51.610 --> 00:45:52.540 killed in consequence. 00:45:52.540 --> 00:45:54.650 So, it's a Pyrrhic victory. 00:45:54.650 --> 00:45:56.580 All that produced by Search programs who are looking 00:45:56.580 --> 00:45:58.670 through this graph. 00:45:58.670 --> 00:46:01.030 Now once you've got the capability of doing that, of 00:46:01.030 --> 00:46:04.470 course, then you can find all sorts of things. 00:46:04.470 --> 00:46:05.820 And you can report them in English. 00:46:05.820 --> 00:46:09.510 But, more interestingly, you can answer questions. 00:46:09.510 --> 00:46:12.060 Why did Macbeth-- 00:46:12.060 --> 00:46:13.520 it cares not a hoot about capitalization. 00:46:19.920 --> 00:46:22.160 ARTIFICIAL INTELLIGENCE: On a common sense level, it looks 00:46:22.160 --> 00:46:24.690 like Dr. Jekyll thinks Macduff killed Macbeth because Macbeth 00:46:24.690 --> 00:46:26.520 angered Macduff on a reflective level. 00:46:26.520 --> 00:46:29.200 It looks like Dr. Jekyll thinks Macduff killed Macbeth 00:46:29.200 --> 00:46:32.720 as part of acts of mistake, Pyrrhic victory, and revenge. 00:46:32.720 --> 00:46:35.410 PATRICK WINSTON: Pretty corny speech output. 00:46:35.410 --> 00:46:36.620 But you see the point. 00:46:36.620 --> 00:46:40.726 How did it get the stuff on the common sense level? 00:46:40.726 --> 00:46:43.420 The same way all those programs that build goal trees 00:46:43.420 --> 00:46:46.600 report, answers the questions. 00:46:46.600 --> 00:46:48.687 It's just looking locally around in the connections in 00:46:48.687 --> 00:46:50.410 the goal tree. 00:46:50.410 --> 00:46:52.880 How did it get the stuff on the reflective level? 00:46:52.880 --> 00:46:59.240 By reporting on the searches that produced information-- 00:46:59.240 --> 00:47:03.670 it does that by looking for higher level thoughts about 00:47:03.670 --> 00:47:07.540 its own thoughts and reporting in which of those higher level 00:47:07.540 --> 00:47:12.995 thoughts the incident we asked about actually occurs. 00:47:12.995 --> 00:47:17.020 So, let's see, just for fun, we might be interested in why 00:47:17.020 --> 00:47:20.660 Macbeth murdered Duncan. 00:47:20.660 --> 00:47:22.600 Wouldn't this be handy if you hadn't actually read the play, 00:47:22.600 --> 00:47:25.276 and here it is, you've got to write that paper? 00:47:25.276 --> 00:47:26.400 ARTIFICIAL INTELLIGENCE: On a common sense 00:47:26.400 --> 00:47:27.790 level, it looks like-- 00:47:27.790 --> 00:47:29.150 PATRICK WINSTON: I'll pull the plug on that, because that's 00:47:29.150 --> 00:47:30.400 just annoying. 00:47:32.768 --> 00:47:36.340 Yeah, pretty good, Macbeth wants to be King, and Duncan 00:47:36.340 --> 00:47:37.620 is the King. 00:47:37.620 --> 00:47:39.740 Let's see, why did Macbeth become King? 00:47:51.820 --> 00:47:53.450 Oh, it won't answer the question 00:47:53.450 --> 00:47:54.700 unless I spell it right. 00:48:01.670 --> 00:48:03.990 I wouldn't be able to show that to you until last spring. 00:48:03.990 --> 00:48:07.480 In fact, I wouldn't have been able to show you this today 00:48:07.480 --> 00:48:10.760 until last week with a tweak this morning. 00:48:10.760 --> 00:48:15.090 Because we've just now connected the language output 00:48:15.090 --> 00:48:17.910 to, of course, [? Cass's ?] 00:48:17.910 --> 00:48:19.910 parser system, which is running in reverse, in order 00:48:19.910 --> 00:48:21.040 to generate that English. 00:48:21.040 --> 00:48:23.660 So, that's something that has never before been seen by any 00:48:23.660 --> 00:48:25.830 eyes but me. 00:48:25.830 --> 00:48:27.650 So, that will conclude what we have to do today.