WEBVTT 00:00.110 --> 00:03.590 So next up let's talk about the recursion. 00:03.590 --> 00:06.530 And for that we're gonna calculate the factorial. 00:06.560 --> 00:11.780 Now every function that's recursive needs to have a base case. 00:11.780 --> 00:15.440 That's a condition that basically stops the recursion. 00:15.440 --> 00:21.500 And that's the simplest instance of the problem that can be solved directly. 00:21.500 --> 00:24.440 This is how this can be technically described. 00:24.440 --> 00:32.690 And in the case of factorial, when you calculate factorial of zero or factorial of one, the result 00:32.690 --> 00:34.160 is always one. 00:34.160 --> 00:37.100 So this basically returns from the function. 00:37.100 --> 00:43.880 But then since the function is recursive, there needs to be a recursive case. 00:44.540 --> 00:48.260 That's the case when the function calls itself. 00:48.260 --> 00:57.290 And in case of factorial, everything above one is calling itself, but with an argument minus one. 00:57.290 --> 00:59.480 So this is how factorial works. 00:59.480 --> 01:02.900 Was this is a recursive function. 01:05.330 --> 01:11.100 So for example, if we call factorial with the argument five. 01:11.460 --> 01:16.290 Then you can see that clearly five is not zero or it isn't one. 01:17.400 --> 01:27.750 So it will multiply five by factorial of four, and so on and so on up until the factorial will receive 01:27.750 --> 01:30.330 either 1 or 0 as an argument. 01:30.360 --> 01:33.690 Then the final result will be returned. 01:34.860 --> 01:37.050 So in this case this is 120. 01:42.240 --> 01:44.880 So let's do an actual example. 01:44.880 --> 01:46.500 Let's run this code. 01:47.250 --> 01:50.070 Let me create a recursive PHP file. 01:50.130 --> 01:53.250 And let's type this code. 01:54.960 --> 01:56.280 So we need a starting tag. 01:56.280 --> 02:02.970 And we need the function called factorial which accepts n as a parameter. 02:03.000 --> 02:06.570 Let's also type that and it also returns an int. 02:06.570 --> 02:08.700 So we start with a base case. 02:09.660 --> 02:16.620 So base case is n is either zero or n is one. 02:18.090 --> 02:19.610 So that's our base case. 02:19.610 --> 02:23.990 That's the case that would let this function return. 02:23.990 --> 02:26.390 That will stop the recursion. 02:26.810 --> 02:36.170 Now there also needs to be a recursive case when we actually call factorial within factorial. 02:36.770 --> 02:40.880 So we're gonna multiply n by. 02:40.910 --> 02:43.430 Sorry that's not a variable by factorial. 02:43.460 --> 02:46.430 Passing n minus one. 02:47.750 --> 02:56.300 Let's reformat this now so we can actually see what argument was called and when. 02:56.840 --> 02:59.330 Let's echo. 03:01.520 --> 03:05.780 N and add a new line. 03:06.950 --> 03:14.600 Finally let's um let's run this function using var dump. 03:14.900 --> 03:18.530 Let's call factorial passing five. 03:18.530 --> 03:24.620 And what I expect is I expect to see every single time this function is being called. 03:24.620 --> 03:26.870 And with what argument. 03:28.680 --> 03:32.790 So we are running the recursive PHP file. 03:33.510 --> 03:36.510 So the first call is with the argument five. 03:36.510 --> 03:40.080 So we know that five is not 0 or 1. 03:40.230 --> 03:42.450 So this is causing the recursion. 03:42.450 --> 03:45.330 It's calling factorial again with four. 03:46.560 --> 03:48.900 So obviously four is also none of this. 03:48.900 --> 03:51.660 So it calls factorial with three. 03:51.660 --> 03:55.470 And then there is another nested call with two. 03:56.490 --> 04:03.600 And finally when factorial is called with one it returns one. 04:03.600 --> 04:06.390 So it doesn't call factorial again. 04:06.420 --> 04:13.590 It breaks the recursion so that all those nested factorial calls can also return the actual value, 04:13.590 --> 04:18.600 because now the actual value, the the row number is known. 04:18.600 --> 04:28.140 So then all of those nested factorial functions return up until the main factorial call, which can 04:28.140 --> 04:35.100 also return a value to the caller, which is this line, and this returns this value.