1 00:00:01,470 --> 00:00:02,070 Welcome back. 2 00:00:02,640 --> 00:00:06,870 We just learned our first notation of an. 3 00:00:08,110 --> 00:00:13,360 Or linear time, and we see here that we have a few others remaining. 4 00:00:14,200 --> 00:00:15,950 So let's talk about the next one. 5 00:00:16,600 --> 00:00:22,960 Another very common big notation that you're going to see what happens if we have a function like this. 6 00:00:24,580 --> 00:00:30,730 A function that says compressed 1st box that receives an array of boxes. 7 00:00:32,130 --> 00:00:43,860 And this function simply has console dialog boxes zero, so that is its logging out just the first item 8 00:00:43,860 --> 00:00:44,560 in the box. 9 00:00:45,480 --> 00:00:49,020 What would you say the big O of this function is? 10 00:00:50,350 --> 00:00:59,530 How many steps or operations does this function take if the boxes increase from zero to maybe 10 to 11 00:00:59,530 --> 00:01:01,660 maybe one hundred to one hundred thousand? 12 00:01:03,050 --> 00:01:05,590 What would happen here, ready for the answer? 13 00:01:06,580 --> 00:01:07,570 Well, this. 14 00:01:09,160 --> 00:01:13,720 Is what we call constant time, it's an O of one. 15 00:01:14,760 --> 00:01:21,120 That is, no matter how many times the boxes increase year or however many boxes we have, we're always 16 00:01:21,120 --> 00:01:24,260 just grabbing the first item in the array. 17 00:01:25,380 --> 00:01:33,120 If we look at this with an example, if we had an array of boxes here and we run it through the function, 18 00:01:33,120 --> 00:01:36,630 that just takes the first item in the array. 19 00:01:37,680 --> 00:01:43,390 Well, the number of operations is one, no matter how big this the number of boxes are. 20 00:01:43,440 --> 00:01:45,360 We're only doing one thing. 21 00:01:46,420 --> 00:01:48,310 So it's a constant time. 22 00:01:49,850 --> 00:01:52,940 If we look at this on a graph, if we have. 23 00:01:55,840 --> 00:02:03,040 Element or one box, we do one operation, if we have three again, we still do just one because we're 24 00:02:03,040 --> 00:02:04,900 just grabbing the first item in the array. 25 00:02:05,260 --> 00:02:07,850 If we have, let's say, five. 26 00:02:08,180 --> 00:02:08,860 Same thing. 27 00:02:09,520 --> 00:02:11,010 Seven, same thing. 28 00:02:11,470 --> 00:02:13,180 And what about nine? 29 00:02:13,360 --> 00:02:15,880 Again, same number of operation. 30 00:02:16,390 --> 00:02:20,500 And this is I don't know if you can see the line, but this is just constant time. 31 00:02:20,920 --> 00:02:26,740 It's not linear time like it was where it increases and increases with the number of operations, the 32 00:02:26,740 --> 00:02:29,620 number of operations just stays flat. 33 00:02:32,780 --> 00:02:34,320 But I have a question here. 34 00:02:34,370 --> 00:02:36,140 What if we do something different? 35 00:02:36,260 --> 00:02:37,730 What if we do something like this? 36 00:02:39,370 --> 00:02:42,160 What if we have a function that says function? 37 00:02:45,440 --> 00:02:47,720 Or log first. 38 00:02:51,080 --> 00:02:52,250 Two boxes. 39 00:02:53,300 --> 00:02:59,930 And this takes an array of boxes and is going to console the log. 40 00:03:01,300 --> 00:03:02,650 The first. 41 00:03:03,780 --> 00:03:04,710 Item in the array. 42 00:03:06,010 --> 00:03:11,890 And it's going to console dialogue, also the second item in the array. 43 00:03:15,290 --> 00:03:17,570 How do we measure the bigo of this function? 44 00:03:18,790 --> 00:03:25,810 Well, let me just comment this out for a second, because we don't need this right now and just create 45 00:03:25,810 --> 00:03:36,040 an array called boxes and this boxes has to say zero one, two, three, four and five. 46 00:03:36,050 --> 00:03:39,610 So five items or six in this case because we include zero. 47 00:03:41,720 --> 00:03:43,340 And if we run this function. 48 00:03:45,150 --> 00:03:48,870 Log first, two boxes and we give it the boxes of Ray. 49 00:03:49,920 --> 00:03:57,690 And we click run here, we have zero and one, so we've logged this one and then this one. 50 00:03:58,630 --> 00:04:00,280 What's the number of operations here? 51 00:04:01,430 --> 00:04:02,900 Well, we have. 52 00:04:04,770 --> 00:04:10,830 Oh, of one that is one operation here and then we have over here. 53 00:04:11,980 --> 00:04:14,110 Oh, of one again. 54 00:04:15,500 --> 00:04:19,250 Each time this function runs to operations. 55 00:04:20,860 --> 00:04:32,860 So this function in total is actually running O of two operations every time, so no matter how big 56 00:04:32,860 --> 00:04:40,120 the boxes get, the number of operations here is going to be, too, if we look at this on a graph. 57 00:04:41,460 --> 00:04:50,100 Instead of having all of one like we have before, we have O of two, and then if we had three operations, 58 00:04:50,100 --> 00:04:51,740 I'll just be out of three. 59 00:04:52,260 --> 00:04:55,410 But overall, it's still a flat line. 60 00:04:56,430 --> 00:04:58,800 And this is something we're going to get into later on. 61 00:04:59,590 --> 00:05:08,620 But when it comes to cost and time, we don't care about the nitty gritty of one or two or three of 62 00:05:08,620 --> 00:05:14,200 even a hundred, we round this down to just simply saying, oh, of one. 63 00:05:16,150 --> 00:05:23,440 That is, we have constant time, it's a flat line in terms of scalability, it doesn't matter how big 64 00:05:23,440 --> 00:05:28,540 our inputs are, we're always going to do the constant amount of time on a function. 65 00:05:30,790 --> 00:05:37,680 And if we look at this on a graph, we see that of one over here is the dark green area. 66 00:05:37,690 --> 00:05:38,940 It's excellent. 67 00:05:38,980 --> 00:05:42,250 We love of one because it's very scalable, right. 68 00:05:42,430 --> 00:05:45,670 It doesn't matter how many elements we have, it's always going to run. 69 00:05:45,670 --> 00:05:50,200 The same predictability when it comes to computing is very, very nice. 70 00:05:50,320 --> 00:05:54,190 And all of one is definitely excellent. 71 00:05:55,590 --> 00:06:03,420 OK, so we've learned about linear time, oh, of N and then Konstantine O of one. 72 00:06:04,920 --> 00:06:08,760 Let's do a bit of a fun exercise to really solidify our knowledge here.