WEBVTT 0 00:00.290 --> 00:08.450 Now, up to this point, we've only been using for loops in association with lists, so we've been looping 1 00:08.450 --> 00:13.790 through the list and getting hold of each of the items in the list and then doing something with it, 2 00:13.790 --> 00:14.390 right? 3 00:14.390 --> 00:19.040 But we're not always going to be working with lists and using for loops. 4 00:19.220 --> 00:24.230 Sometimes we might want to use a loop completely independent of a list. 5 00:24.230 --> 00:31.260 And a good example of this is when Carl Gauss, the German mathematician, was just a child. 6 00:31.260 --> 00:36.510 When he was ten years old, his math teacher gave him an exercise that she probably thought would tie 7 00:36.510 --> 00:43.950 him up for a little while, and the idea was to get him to add all of the numbers from 1 to 100. 8 00:43.950 --> 00:49.920 So 1 + 2 +3 + 4 + 5 et cetera, all the way until 100. 9 00:50.040 --> 00:54.810 And even though she thought this would keep him busy for an hour or so, getting this young child to 10 00:54.810 --> 00:59.180 add up these numbers and I can have some peace and quiet scrolling on Facebook, 11 00:59.180 --> 01:03.800 but unfortunately, he came back to her within two minutes and gave her the answer. 12 01:04.370 --> 01:06.230 So how did he work it out? 13 01:06.260 --> 01:11.930 Well, he is actually a really smart kid, and he figured out that if you flip the numbers around. 14 01:11.930 --> 01:20.360 So 100 plus 99 plus 98, and you look at both of these two lines, you can see that 1 + 100 = 101 15 01:20.360 --> 01:21.250 , 16 01:21.250 --> 01:23.380 2 + 99 = 101, 17 01:23.380 --> 01:25.570 3 + 98 = 101. 18 01:25.570 --> 01:31.720 Basically, if you tie all of these numbers together, there's actually 50 pairs of 101. 19 01:31.720 --> 01:37.750 So he could simply just do 50 multiplied by 101 which is 5050. 20 01:37.810 --> 01:40.030 And that's how he figured out the answer. 21 01:40.150 --> 01:47.040 But we can actually outshine Gauss because we can do this calculation in less than a minute just by 22 01:47.040 --> 01:48.510 writing a few lines of code. 23 01:48.870 --> 01:56.070 But in order to do this, we first have to learn about using for loops with the range function. 24 01:56.580 --> 02:02.820 Now the range function is something that is really, really helpful if you want to generate a range 25 02:02.820 --> 02:04.800 of numbers to loop through. 26 02:04.920 --> 02:08.220 And the syntax looks something like this. 27 02:08.220 --> 02:15.630 So we've still got our for and our in keywords highlighted in blue, but instead of looping through 28 02:15.630 --> 02:21.990 a list, we define how our loop is going to work by creating a range. 29 02:21.990 --> 02:26.700 So in this case I'm creating a range between a and b, 30 02:26.700 --> 02:32.550 and then I'm going to get hold of each number in that range and do something with that number. 31 02:33.330 --> 02:39.080 Now it's important to remember that the range() function doesn't actually do anything by itself. 32 02:39.080 --> 02:46.520 So if we create a range between 1 and 10 and we say, just try to print this and we run, you can see 33 02:46.520 --> 02:47.900 it doesn't actually do anything. 34 02:47.900 --> 02:51.170 It doesn't print out the numbers 1 through to 10 at all. 35 02:51.170 --> 02:55.880 This function has to be used in conjunction with another function, 36 02:55.880 --> 02:59.120 and in our case it's going to be with the for loop. 37 02:59.420 --> 03:08.270 So for example if I wrote, "for number in range..." and then my range is going to be (1, 10). 38 03:08.270 --> 03:12.620 So this is going to be the range that I'm going to create between 1 and 10, 39 03:12.620 --> 03:16.640 and then I want to get hold of each of the numbers inside that range. 40 03:16.640 --> 03:21.950 And this is going to be between 1 and 10 and not including ten. 41 03:21.950 --> 03:28.250 So if I go ahead and print out the number that I create from my for loop, then you'll see that what 42 03:28.250 --> 03:36.410 happens is it prints 123456789, but not the last digit, which I've included here. 43 03:36.410 --> 03:44.210 So if I wanted all of the numbers from 1 to 10, I actually have to set a range between 1 and 11. 44 03:44.210 --> 03:49.310 And now when you run the code, you can see that it goes from one all the way up to ten. 45 03:50.330 --> 03:59.020 Now by default the range() function will step through all the numbers from the start to the end, and 46 03:59.020 --> 04:00.640 it will increase by one. 47 04:00.670 --> 04:06.250 Now, if you wanted to increase by any other number, then you have to add another comma to the end 48 04:06.250 --> 04:11.860 of it and specify how large you want the step to be. 49 04:11.980 --> 04:15.070 So let's say we change the step size to 3. 50 04:15.100 --> 04:19.420 Now if I rerun the same code, you'll see that it goes from 1, 51 04:19.420 --> 04:25.420 and then it steps by 3 to 4, and then it steps by 3, and then it steps by 3, finally to 10. 52 04:26.770 --> 04:30.940 Now let's come back to the problem that I mentioned at the beginning of this lesson, 53 04:30.940 --> 04:36.430 How can we add up all of the numbers from 1 to 100 by using code? 54 04:36.670 --> 04:42.550 So I want you to pause the video and see if you can solve the Gauss challenge. 55 04:42.550 --> 04:43.600 Have a go now. 56 04:46.980 --> 04:47.520 All right. 57 04:47.520 --> 04:49.380 So how do we solve this? 58 04:49.410 --> 04:51.570 Well, it's going to involve the for loop, 59 04:51.570 --> 04:56.910 and it's going to involve the range() function because we're going to get hold of every number in the 60 04:56.910 --> 05:00.450 range between 1 and 100. 61 05:00.450 --> 05:02.340 So we need to write 101. 62 05:02.610 --> 05:08.790 Once we've got hold of all of these numbers it's as simple as using an accumulator. 63 05:08.790 --> 05:11.970 So let's say a total = 0. 64 05:11.970 --> 05:13.740 And then inside the for loop. 65 05:13.740 --> 05:15.150 So that means indented, 66 05:15.150 --> 05:21.210 we're going to say total += number. 67 05:21.810 --> 05:28.530 So now it's going to add every number in this range to the total starting from zero. 68 05:28.530 --> 05:33.870 And this is basically going to give us the sum of every number from 1 to 100. 69 05:33.870 --> 05:38.960 So let's go ahead and print it out and see if it matches Gauss's value. 70 05:40.340 --> 05:43.820 And there you have it, 5050. 71 05:44.180 --> 05:49.370 So now that we've beaten Gauss at his own game of math using programming, let's head over to the next 72 05:49.370 --> 05:55.100 lesson and try to complete a challenge using the range() function to see if you managed to internalize 73 05:55.100 --> 05:57.920 and understand everything we talked about in this lesson. 74 05:57.920 --> 06:00.740 So for all of that and more, I'll see you there.