WEBVTT 00:00.150 --> 00:06.860 Hello again! In this video, we are going to have a practical based upon the so-called "random walk". A 00:06.870 --> 00:08.910 random walk is in Mathematics or Physics. 00:09.270 --> 00:14.820 If we have something which is moving around, and it keeps changing its direction at random, we end up 00:14.820 --> 00:16.230 with this random walk pattern. 00:16.800 --> 00:21.510 It is also known as a "drunkard's walk", because it seems to stagger around and not really get anywhere. 00:23.040 --> 00:30.030 There is a more serious name for it as well, which is "Brownian motion". And there are many natural processes 00:30.480 --> 00:32.730 which resemble a random walk. 00:33.060 --> 00:37.980 For example, the way that insects move around when they are flying. The way that gas molecules bounce 00:37.980 --> 00:43.280 off each other. And for a long time, it was thought that financial markets follow a random walk. 00:43.290 --> 00:44.760 But in fact, that is not quite true. 00:45.270 --> 00:48.030 There are extreme movements which cannot be accounted for 00:48.030 --> 00:54.300 by randomness. In computer games, we can use the random walk to make characters move around in a more 00:54.300 --> 00:56.010 interesting and unpredictable way. 00:56.880 --> 00:57.810 So it looks like this. 00:57.810 --> 01:01.470 You can see there is a red dot bouncing around near the centre of the screen, which does not really 01:01.470 --> 01:02.520 manage to get away from it. 01:04.050 --> 01:08.520 I am not actually going to go through the code in this video. When we get to the project, 01:09.000 --> 01:13.470 I will show you how to set up a graphics library, and then we will go through this properly, along with other 01:13.470 --> 01:13.830 things. 01:15.060 --> 01:19.860 But I will give you the source code as a downloadable attachment for this video, so you can look through 01:19.860 --> 01:21.000 that, if you are interested. 01:21.720 --> 01:26.970 There are lots of comments, so if you have used a graphics library before, you can work out what is 01:26.970 --> 01:27.360 going on. 01:27.390 --> 01:30.900 I hope! This is using the SFML graphics Library. 01:32.190 --> 01:33.270 So how does this work? 01:33.600 --> 01:36.120 We have a character which is at some position on the screen. 01:36.570 --> 01:41.370 It will be "x" pixels from the left of the screen and "y" pixels from the top. 01:41.820 --> 01:47.340 So we are using the normal computer graphics convention, in which y equals 0 at the top of the screen 01:47.730 --> 01:52.620 and increases as you go downwards. As opposed to the bitmap format, which is the other way round. 01:54.210 --> 01:56.470 If we want the character to be at some other position. 01:56.490 --> 02:02.910 We need to find out how many pixels across, left or right, the character needs to move, and how many pixels 02:02.910 --> 02:05.010 up or down, to get to the new position. 02:07.350 --> 02:13.140 So we have something like this. We have the new position here. We need to move "vx" pixels, to the right 02:13.140 --> 02:16.650 in this case, and "vy" pixels down in this case. 02:17.250 --> 02:22.230 And then we can have a loop. And on each iteration, the character moves to a new position. 02:22.890 --> 02:24.150 We calculate this position. 02:24.720 --> 02:29.430 We clear the screen and then we draw the screen again, showing the character in the new position. 02:30.090 --> 02:33.750 And if we can do that quickly enough, the character will appear to move smoothly around the screen. 02:35.070 --> 02:40.440 These vx and vy have signs. If they are positive, then the character is going to move to the right, 02:40.440 --> 02:41.250 or downwards. 02:41.970 --> 02:45.240 If they are negative, the character is going to move to the left, or upwards. 02:48.140 --> 02:53.600 So to get the new position of the character, we just add vx to the x coordinate and vy to the 02:53.600 --> 02:54.350 y coordinate. 02:54.920 --> 02:59.990 If we use the same values of vx and vy all the time, with the same sign, then the character is 02:59.990 --> 03:04.370 just going to move in a straight line across the street, which is not going to be very interesting. 03:05.690 --> 03:08.490 We can make it more interesting by doing a random walk. 03:08.510 --> 03:10.070 So we need some randomness. 03:11.240 --> 03:13.310 We are going to use the Bernoulli distribution. 03:13.640 --> 03:17.060 This will convert the random numbers to either true or false. 03:17.660 --> 03:19.460 There will be a 50-50 chance of each one. 03:19.790 --> 03:23.690 And then if the random number is true, we are going to leave vx as it is. 03:23.750 --> 03:27.440 So if the character is going to the right, it is going to continue going to the right. 03:28.220 --> 03:29.960 If it is false, we invert the sign. 03:30.380 --> 03:34.940 So if it was going to the right before, it will now go to the left. And vice versa. And we do the same 03:34.940 --> 03:36.830 thing for the y velocity. 03:37.430 --> 03:43.380 So this vx and vy are just the velocity, the distance that the character moves in the horizontal 03:43.380 --> 03:45.260 or vertical direction between each update. 03:48.100 --> 03:52.750 And then we add the velocities to the x andy y, and we can re-draw the screen. And that will cause 03:52.750 --> 03:54.580 the character to follow a random walk. 03:55.600 --> 03:58.270 I have some code to this, which does not use graphics. 03:58.270 --> 04:03.280 We are going to use the console and print a row of spaces with a dot. 04:04.060 --> 04:07.930 So depending on the number of spaces, the dot will appear in a different position. 04:09.490 --> 04:15.280 We are just using one dimension, so we only have x and vx to worry about. There is no y or vy. 04:16.450 --> 04:18.460 We need to know how long this row is going to be. 04:18.460 --> 04:21.040 I am going to make it 40 because that is a nice, safe number. 04:22.720 --> 04:24.400 We need to be able to clear the screen. 04:24.400 --> 04:29.260 That means printing a row which is completely blank, so nothing but spaces. 04:29.800 --> 04:32.770 So we need to have a string which has 40 spaces in it. 04:34.720 --> 04:37.390 Then we have our random number engine and distribution. 04:38.710 --> 04:39.610 And then we have our loop. 04:39.640 --> 04:43.390 So every time through this loop, the character is going to move to a new position. 04:45.540 --> 04:47.010 Then we get our random number. 04:48.930 --> 04:53.610 If it is true, then the character is going to move to the right and if it is false, the character is 04:53.610 --> 04:54.630 going to move to the left. 04:55.140 --> 04:57.590 So this this is actually slightly different from this slide, 04:57.810 --> 04:58.650 so apologies for that. 05:00.060 --> 05:04.170 We also need to make sure that the character stays within its rightful place. 05:04.710 --> 05:09.690 So if it gets to the left-hand edge of the screen, where x equals 0, then we are going to make 05:09.690 --> 05:10.770 the velocity positive. 05:11.190 --> 05:13.530 So it is going to move to the right, away from the edge of the screen. 05:14.040 --> 05:19.380 So that will make it look as though the dot is bouncing off the edge of the screen. And at the other side, 05:19.380 --> 05:21.690 if x is equal to width at the right hand side of the screen, 05:22.140 --> 05:25.920 we are going to make the particle go to the left. So it is going to bounce off the side of the screen. 05:27.510 --> 05:31.680 Then, once we have our x velocity, we add it to the x coordinate. 05:32.910 --> 05:34.920 Then we clear the screen, by printing the blank line. 05:35.670 --> 05:40.140 This is the carriage return character. So it means that anything that appears after that is going to 05:40.140 --> 05:42.810 be on the same line, but at the start of the line. 05:43.830 --> 05:46.230 So that is going to overwrite anything that was already there. 05:48.150 --> 05:53.610 And then we make up a string which has "x" number of spaces, and then print 05:53.610 --> 05:54.720 that, followed by a dot. 05:55.080 --> 05:59.070 So if x is 6, we are going to have 6 pieces, followed by a dot. 06:00.090 --> 06:03.960 And again, we use the carriage return, to make sure this appears at the start of the line. 06:05.490 --> 06:09.120 Then the last thing we are going to do is to slow the program down a bit, so we can see what is going on. 06:09.810 --> 06:12.990 There is now a standard way to make a C++ program 06:12.990 --> 06:17.970 pause or sleep. It is actually from the threads library, but you can use it with single-threaded programs 06:17.970 --> 06:18.390 as well. 06:20.010 --> 06:25.650 This underscore thread, double colon, sleep underscore four. And then the argument is the length 06:25.650 --> 06:28.200 of time that the program is going to stop for. 06:29.400 --> 06:31.280 And that will need the header. 06:33.960 --> 06:39.180 Right. I am not actually going to run this in Visual Studio, because it flickers rather badly, so I am 06:39.180 --> 06:40.260 going to run this in MinGW. 06:42.960 --> 06:43.860 And there we are. 06:43.860 --> 06:45.750 We can see it is performing this random walk. 06:48.000 --> 06:50.700 And again, it is not really getting very far away from the left side. 06:54.120 --> 06:58.380 By default, this Bernoulli distribution gives a 50-50 chance of getting true or false. 06:58.950 --> 07:03.150 So if we call it 10 times, we expect to get 5 "true" and 5 "false". 07:04.020 --> 07:06.380 We can provide an argument to this constructor. 07:06.900 --> 07:10.110 So this will introduce a bias to the distribution. 07:10.560 --> 07:16.710 So if we put 0.8, that means we get "true" 8 times out of 10 and "false" only twice. 07:17.430 --> 07:21.810 So this should mean that the character is going to move to the right eight times and to the left only 07:21.810 --> 07:22.230 twice. 07:23.370 --> 07:29.170 So let's run that in MinGW, and we should see the character start moving. 07:29.190 --> 07:29.900 Yes, there it goes. 07:30.210 --> 07:31.230 So it is now going to the right. 07:31.620 --> 07:35.430 So 8 out of 10 times it is going to go that way, and now it's stuck at the end. 07:36.600 --> 07:38.040 Okay, so that is it for this video. 07:38.520 --> 07:39.300 I will see you next time. 07:39.510 --> 07:41.190 Until then, keep coding!