1 00:00:01,580 --> 00:00:02,210 Hello everyone. 2 00:00:02,210 --> 00:00:06,140 So in this video we will try to solve one more equation problem. 3 00:00:06,140 --> 00:00:09,150 So I want to calculate power. 4 00:00:09,440 --> 00:00:11,990 OK so I want to calculate extra the power. 5 00:00:12,590 --> 00:00:19,040 OK so x is any number and and is a whole number that is 0 1 2 and so on. 6 00:00:19,040 --> 00:00:22,500 Okay so suppose I want to calculate 5 to the power tree. 7 00:00:22,520 --> 00:00:26,860 So this will be 5 to 5 and 2 5 which is 125. 8 00:00:26,870 --> 00:00:27,410 Okay. 9 00:00:27,410 --> 00:00:28,940 So I want to calculate power. 10 00:00:29,000 --> 00:00:29,230 Okay. 11 00:00:29,240 --> 00:00:35,030 So what I want to do I want to I want to write the power function and I want to find extra the power. 12 00:00:35,540 --> 00:00:39,890 Okay so X is a any number and n is a whole number. 13 00:00:40,450 --> 00:00:40,660 Okay. 14 00:00:40,670 --> 00:00:42,810 So how we can solve this problem. 15 00:00:42,890 --> 00:00:45,800 So first we have to think of the recursive case. 16 00:00:45,830 --> 00:00:53,470 Okay so what is extra the power and so can we write it like this X Multiply extra the power N minus 17 00:00:53,470 --> 00:00:54,550 one. 18 00:00:54,550 --> 00:00:54,960 Okay. 19 00:00:55,090 --> 00:01:02,440 So we can write it like this extra the power and is calculate excited about N minus one and then multiply 20 00:01:02,620 --> 00:01:03,380 x. 21 00:01:03,430 --> 00:01:03,870 Okay. 22 00:01:03,940 --> 00:01:05,790 So we have two. 23 00:01:05,860 --> 00:01:10,030 So I've learned to convert bigger problem than I have to calculate the smaller problem so this will 24 00:01:10,030 --> 00:01:11,170 be our recursive case. 25 00:01:11,950 --> 00:01:12,580 Okay. 26 00:01:12,580 --> 00:01:22,240 So if I want to find x to the power n what I will do first of all I will find X to the power end minus 27 00:01:22,240 --> 00:01:26,110 one and then I will multiply x. 28 00:01:26,260 --> 00:01:26,720 Okay. 29 00:01:26,830 --> 00:01:31,490 So this is our recursive case this will be our recursive case. 30 00:01:31,570 --> 00:01:31,870 Okay. 31 00:01:32,260 --> 00:01:34,240 So what will we our base case. 32 00:01:34,240 --> 00:01:37,310 So base case is the smallest problem whose solution we already know. 33 00:01:37,630 --> 00:01:40,050 So suppose if the value of minus zero. 34 00:01:40,900 --> 00:01:45,660 If the value of any is it also that if the power is zero then the output will be 1. 35 00:01:45,670 --> 00:01:46,860 So this will be the smallest. 36 00:01:46,870 --> 00:01:48,160 This is the base case. 37 00:01:48,220 --> 00:01:54,290 You can also take one as one also base case if X did about 1 will be X only. 38 00:01:54,320 --> 00:01:59,130 Okay so it is our choice you can pick this one and you can also take this one. 39 00:01:59,260 --> 00:01:59,540 Okay. 40 00:01:59,640 --> 00:02:01,930 You can take both our choice. 41 00:02:01,930 --> 00:02:07,920 Okay so let's write the code for it. 42 00:02:07,950 --> 00:02:10,570 So what I want to do I want to calculate. 43 00:02:10,650 --> 00:02:16,630 So there that I will be in danger the name of the function is powered it will take 2 in digit. 44 00:02:17,060 --> 00:02:21,990 I want to find extra the power in now what is the base case. 45 00:02:21,990 --> 00:02:25,850 So first of all base case. 46 00:02:25,850 --> 00:02:30,990 So base case will be the smallest problem whose solution we already know. 47 00:02:31,630 --> 00:02:36,490 So the smallest problem will be if the value of any 0 because and is a whole number. 48 00:02:36,490 --> 00:02:40,090 Okay so the smallest really often will be zero only. 49 00:02:40,090 --> 00:02:41,510 So if the value of any 0. 50 00:02:41,530 --> 00:02:45,590 What I have to do I have to return 1. 51 00:02:45,670 --> 00:02:46,530 Okay. 52 00:02:46,570 --> 00:02:54,590 And now our recursive case so recursive case we already decided what we will do. 53 00:02:54,700 --> 00:02:56,720 I will call on and minus 1. 54 00:02:56,740 --> 00:02:57,050 Okay. 55 00:02:57,070 --> 00:02:58,390 So our small output. 56 00:02:58,660 --> 00:03:09,450 Okay so the small output it will be I want to find extra the power in minus one. 57 00:03:09,630 --> 00:03:10,530 So add this line. 58 00:03:10,530 --> 00:03:12,850 We have extra about N minus one. 59 00:03:13,290 --> 00:03:20,180 Now after we have extra the power and minus one we have to do other conclusion part so what is our conclusion 60 00:03:20,190 --> 00:03:30,110 but basically I will return X Multiply small output Okay and let's call let's test our function. 61 00:03:30,150 --> 00:03:34,540 Suppose I want to find 5 to the power tree. 62 00:03:34,620 --> 00:03:39,600 Okay so five cube so five cube will be 125 okay. 63 00:03:39,830 --> 00:03:46,860 So let's say our file so our output is 125 solver code is working fine. 64 00:03:46,870 --> 00:03:50,460 Okay now we will write in our code after writing the code. 65 00:03:50,860 --> 00:03:51,950 So we think and learn. 66 00:03:52,000 --> 00:03:54,040 We think only in terms of PMI. 67 00:03:54,040 --> 00:03:56,500 And then after writing the code what do we do. 68 00:03:56,530 --> 00:03:57,600 We will dial in our code. 69 00:03:57,610 --> 00:03:58,590 We will make the diagram. 70 00:03:59,590 --> 00:04:00,050 Okay. 71 00:04:00,190 --> 00:04:02,720 So I want to find 5 2 about three. 72 00:04:02,740 --> 00:04:07,030 So what will happen this is 5 and this is 3 okay. 73 00:04:07,090 --> 00:04:12,150 So the value of x is not changing only the value of end is changing so I am writing only 3 here. 74 00:04:12,190 --> 00:04:18,050 Okay so this is 3 so 3 is not close to zero. 75 00:04:18,050 --> 00:04:22,840 So I will come at this line so and minus when we are calling 1 and minus 1. 76 00:04:22,850 --> 00:04:25,910 If you want you can also write 5 or so okay so 5. 77 00:04:25,910 --> 00:04:26,840 Commentary. 78 00:04:26,840 --> 00:04:29,010 Now this is 5 comma 2. 79 00:04:29,080 --> 00:04:32,030 Again we will call on 5 comma 1. 80 00:04:32,070 --> 00:04:35,280 Now we will call on 5 comma 0. 81 00:04:35,280 --> 00:04:36,270 Okay. 82 00:04:36,270 --> 00:04:40,950 If the value of end is it overtime returning I am returning 1 so this will return 1. 83 00:04:40,950 --> 00:04:47,520 Okay so our small output this is 1 then I am returning X Multiply small output so the value of x is 84 00:04:47,550 --> 00:04:50,220 5 so 5 multiply 1. 85 00:04:50,400 --> 00:04:51,910 So this will be 5. 86 00:04:51,990 --> 00:04:59,830 So our small output is 5 then I am returning X Multiply small output so 5 multiply 5. 87 00:05:00,060 --> 00:05:02,200 So I will return 25. 88 00:05:02,220 --> 00:05:09,670 So our small output is 25 then I am returning X Multiply small output so 5 multiplied 25. 89 00:05:09,930 --> 00:05:15,720 So it will return when 25 and 5 cube is 125 so I will our it is working fine. 90 00:05:15,760 --> 00:05:19,480 Okay so this will be their diagram okay. 91 00:05:19,680 --> 00:05:25,050 So I hope by this time we know the procedure first we have to write the code and after writing the code 92 00:05:25,710 --> 00:05:26,430 and when. 93 00:05:26,430 --> 00:05:29,730 And while we are writing the code will think only in terms of PMI. 94 00:05:29,730 --> 00:05:31,700 After writing the code we will draw this diagram. 95 00:05:31,710 --> 00:05:34,510 Okay too so that we can understand it better be. 96 00:05:34,590 --> 00:05:43,650 Okay so this is our code so base case our small output which is really recursive case and then our calculation 97 00:05:43,650 --> 00:05:44,220 part. 98 00:05:44,220 --> 00:05:48,990 So this is how this code is working this is how we calculate power function this is how we can read 99 00:05:48,990 --> 00:05:50,070 about using recursion. 100 00:05:50,460 --> 00:05:50,960 Okay. 101 00:05:51,120 --> 00:05:51,510 Thank you.