WEBVTT 00:00.060 --> 00:00.570 Hello again! 00:00.870 --> 00:03.690 In this video, we are going to look at two-dimensional arrays. 00:04.200 --> 00:07.050 We are going to use a two-dimensional array for the Game of Life. 00:07.380 --> 00:11.160 So I want to make sure that we are fully up to speed, before we get into the implementation. 00:12.850 --> 00:15.740 Let's imagine that we have some data, which is in tabular form. 00:16.120 --> 00:21.820 So this could be a table, in a word-processing document, or some cells in a spreadsheet. 00:22.420 --> 00:25.870 We have two rows and four columns. 00:26.890 --> 00:30.580 In C++ terms, we can represent this by a two-dimensional array. 00:31.030 --> 00:34.570 So this is an array, whose elements are themselves arrays. 00:35.900 --> 00:43.820 The outer array will represent the rows of this table, and the inner arrays will represent the columns 00:43.820 --> 00:44.480 of this table. 00:45.110 --> 00:47.870 So we have an array which has two elements. 00:48.200 --> 00:51.590 Each element is itself an array of four standard strings. 00:53.530 --> 00:58.400 In memory, a two-dimensional array is stored as a single memory block. 00:58.420 --> 01:02.260 So we have the first row followed by the second row. 01:02.680 --> 01:05.650 So it actually looks very much like a one-dimensional array 01:07.750 --> 01:12.490 We can in fact initialize it as though it were a one-dimensional array, so we can just write all the 01:12.790 --> 01:13.960 elements, one after the other. 01:14.560 --> 01:17.950 But it is better to initialize as nested arrays. 01:18.370 --> 01:21.250 So we have the first row and then the second row. 01:24.550 --> 01:30.490 We can use subscripting with two-dimensional arrays. If we just have a single subscript, that would 01:30.490 --> 01:31.930 apply to the outer array. 01:32.410 --> 01:34.030 So that will give us one of the rows. 01:34.600 --> 01:41.740 So if we put "names" subscript one, this will give us an array with Barney and his family as the elements. 01:43.060 --> 01:48.020 If we have a second subscript, then that will give us the element within the inner array. 01:48.550 --> 01:52.450 So we would get the element with index two, which is "Bamm-Bamm". 01:55.380 --> 02:01.230 If we're iterating over a two-dimensional array, we start off with the first row, then we go through 02:01.230 --> 02:02.400 all the columns in that row. 02:02.850 --> 02:07.180 Then we go on to the next row, we go through all the columns and so on, until we have gone through all 02:07.180 --> 02:07.590 the rows. 02:08.160 --> 02:14.970 So we iterate over all the rows, and then for each row we iterate over all the columns, and then 02:14.970 --> 02:18.420 we can get the element in that row, at that column. 02:21.590 --> 02:22.670 So let's try this out. 02:23.000 --> 02:25.010 Here is our two-dimensional array. 02:25.640 --> 02:31.460 We are going to print out the element in row one, column two, and then we are going to print out all the 02:31.460 --> 02:31.880 elements. 02:32.300 --> 02:37.760 I have put a new line after each row iteration, so all the elements for each row should be on a separate 02:37.760 --> 02:38.090 line. 02:40.040 --> 02:47.120 And there we are, the element in row one, column two is "Bamm-Bamm", and there we have the elements, with 02:47.120 --> 02:48.410 each row on a separate line. 02:50.000 --> 02:55.070 So a two-dimensional array looks very much like a one-dimensional array, as far as the program is concerned. 02:55.820 --> 03:02.140 And sometimes it is actually useful to store all this data in a one-dimensional array. So we could do this. 03:02.150 --> 03:06.050 So we have our one-dimensional array with all the characters in it. 03:06.500 --> 03:12.230 This will have eight elements, because there is four rows and two columns, and four times two is eight. 03:13.400 --> 03:16.040 Then this will work just like any other one-dimensional array. 03:16.040 --> 03:18.610 So if we subscript, we get the element. 03:18.620 --> 03:24.830 So subscript one is "Wilma". If we want to get the element at some row and some column, 03:25.250 --> 03:29.960 We need to calculate how far into the array we need to go, to get to that element. 03:31.790 --> 03:37.580 If we multiply the row by the total number of columns, and then add the column that will give us the 03:37.580 --> 03:38.350 right offset. 03:38.870 --> 03:45.530 So if we wants the element in row with index one and column index two, then one times four. 03:46.070 --> 03:50.000 So we go past the first row. That is four elements. And then another two. 03:50.510 --> 03:53.120 So "Bamm-Bamm" is the element we want. 03:54.110 --> 03:56.250 And what is the point of this? 03:56.270 --> 03:58.250 Why do we want to make life more complicated? 03:58.850 --> 04:03.920 The thing is, if you have a two-dimensional array, and you access an element in one of the inner arrays, 04:04.280 --> 04:06.380 then that requires a pointer dereference. 04:07.190 --> 04:13.430 Whereas, if you do it this way, you replace the pointer dereference by a multiplication, and on modern 04:13.430 --> 04:17.030 hardware, multiplying is much faster than dereferencing a pointer. 04:17.540 --> 04:23.210 So if you have an application which is performance critical, like games programming or scientific computing, 04:23.210 --> 04:26.480 for example, then this can be a useful trick. 04:27.050 --> 04:32.480 On the other hand, if you want nice, simple notation, then you can use a two-dimensional array instead. 04:34.890 --> 04:36.510 So let's quickly try this out. 04:36.990 --> 04:41.870 Here is our flattened-out, two-dimensional array. It is now a one-dimensional array. 04:42.900 --> 04:48.390 We are going to get the element in row one, column two, and then we are going to print out all the elements 04:48.390 --> 04:48.720 again. 04:49.170 --> 04:55.800 So, instead of having the extra pointer dereference, we calculate the position of the element within 04:55.800 --> 04:56.280 the array. 05:00.810 --> 05:01.320 And there we are. 05:01.560 --> 05:02.850 So we get the same results again. 05:03.690 --> 05:04.020 Okay. 05:04.020 --> 05:05.130 So that is it for this video. 05:05.490 --> 05:06.300 I will see you next time. 05:06.480 --> 05:08.390 Until then, keep coding!