1 00:00:01,130 --> 00:00:01,760 Hello everyone. 2 00:00:01,760 --> 00:00:03,020 Welcome to this recession. 3 00:00:03,020 --> 00:00:08,350 So in today's session what we will do we will try to solve one more problem with the help of the occasion. 4 00:00:08,360 --> 00:00:10,720 So the name of the problem is sum of digits. 5 00:00:10,730 --> 00:00:15,230 Okay then maybe the problem is some of the digits. 6 00:00:15,230 --> 00:00:16,160 So what is the problem. 7 00:00:16,160 --> 00:00:21,050 So the problem is very simple given the value often let's say it is one two three four and five. 8 00:00:21,080 --> 00:00:25,490 What we have to do we have to add all these numbers so the addition will be 15. 9 00:00:25,520 --> 00:00:26,870 So this is our answer. 10 00:00:26,900 --> 00:00:27,430 Okay. 11 00:00:27,470 --> 00:00:30,790 So we have to add all the digits of the number. 12 00:00:30,980 --> 00:00:31,240 Okay. 13 00:00:31,270 --> 00:00:35,180 Similarly the number and is 13 and I said will be three plus 1 food. 14 00:00:35,570 --> 00:00:40,190 If the value of an is doing now there will be two plus one which is three. 15 00:00:40,220 --> 00:00:40,480 Okay. 16 00:00:40,490 --> 00:00:43,160 So I hope you got done said of the value of this five. 17 00:00:43,180 --> 00:00:44,360 And the answer will be five. 18 00:00:44,660 --> 00:00:47,630 If the value of and is zeros then the answer will be zero. 19 00:00:47,840 --> 00:00:48,340 Okay. 20 00:00:48,410 --> 00:00:52,980 So what we have to do we have to add all the digits of the number. 21 00:00:53,290 --> 00:00:53,890 Okay. 22 00:00:53,960 --> 00:00:56,240 And then we have to return the sum. 23 00:00:56,240 --> 00:00:56,730 Okay. 24 00:00:56,780 --> 00:01:00,710 So we have already solved this problem might actively using Before we divide loop. 25 00:01:00,710 --> 00:01:06,230 But now in today's session since we are learning regression we will try to solve this same problem with 26 00:01:06,230 --> 00:01:07,250 the help of the occasion. 27 00:01:07,280 --> 00:01:13,370 Okay so what triggers Genesis occasions is I will if I really can get down some with a similar problem 28 00:01:13,400 --> 00:01:15,260 and you do the calculation. 29 00:01:15,260 --> 00:01:17,190 So what it goes it will do. 30 00:01:17,810 --> 00:01:24,440 So we have to find some of digits of any number some digit of the anything number. 31 00:01:24,800 --> 00:01:25,280 Okay. 32 00:01:25,340 --> 00:01:28,920 So what recursion were ludicrous you will see. 33 00:01:29,060 --> 00:01:32,440 So what they will do I will break the problem into smaller part. 34 00:01:32,840 --> 00:01:38,350 Okay I will qualification on this part and occasion will give me the answer. 35 00:01:38,950 --> 00:01:39,940 So what do the answer. 36 00:01:40,000 --> 00:01:43,520 Because it will give me that dance have all the smaller problems then. 37 00:01:43,810 --> 00:01:47,060 So you know the smaller answer how you will conclude the bigger answer. 38 00:01:47,080 --> 00:01:49,050 What I will do smaller answer. 39 00:01:49,120 --> 00:01:50,930 Plus the last digit. 40 00:01:51,020 --> 00:01:53,090 Okay so this is last digit. 41 00:01:53,260 --> 00:01:56,500 So smaller surplus last digit will be our answer. 42 00:01:56,500 --> 00:02:00,280 So 10 plus 5 which will be 15. 43 00:02:00,310 --> 00:02:00,680 Okay. 44 00:02:01,030 --> 00:02:04,740 Similarly now how it will work internally. 45 00:02:04,780 --> 00:02:05,290 So. 46 00:02:05,710 --> 00:02:09,100 So this is our number okay. 47 00:02:09,230 --> 00:02:10,790 Let's make the whole code red. 48 00:02:10,800 --> 00:02:12,270 So what will happen. 49 00:02:12,350 --> 00:02:20,290 I will break the number the smaller part I will call the equation on this part then this is our number 50 00:02:20,430 --> 00:02:30,290 1 2 3 4 I will call that equation on a smaller product again I will call the equation on the smaller 51 00:02:30,290 --> 00:02:39,910 part again I will call the equation on smaller part and again I will call the equation on the smaller 52 00:02:39,910 --> 00:02:40,270 part. 53 00:02:41,020 --> 00:02:46,120 So this is 0 so I am calling records on this my love part. 54 00:02:46,250 --> 00:02:50,300 Okay so I am calling guys on a similar path so it will be zero. 55 00:02:50,300 --> 00:02:50,870 Okay. 56 00:02:50,870 --> 00:02:58,540 And the value of and is zero this is the smallest problem so this will become our base case so it will 57 00:02:58,540 --> 00:03:01,110 return 0 okay. 58 00:03:01,270 --> 00:03:03,390 So Don some of the smaller problem is 0. 59 00:03:03,460 --> 00:03:07,030 And then we have to add the last digit so 0 plus 1. 60 00:03:07,030 --> 00:03:08,390 It will be 1. 61 00:03:08,440 --> 00:03:11,340 Now the answer with the smaller part is 1. 62 00:03:11,440 --> 00:03:13,330 We have to add the last vision which is 2. 63 00:03:13,330 --> 00:03:16,380 So one plus two is three. 64 00:03:16,400 --> 00:03:19,810 Now the answer for the smaller part is 3. 65 00:03:19,820 --> 00:03:21,570 Now we have to where the last digit. 66 00:03:21,590 --> 00:03:24,670 So two plus three is six. 67 00:03:24,700 --> 00:03:28,360 Now the answer for the smaller parties came out to be six. 68 00:03:28,360 --> 00:03:30,200 Now we have to add the last digit. 69 00:03:30,220 --> 00:03:32,990 So six plus four which is 10. 70 00:03:33,080 --> 00:03:36,530 Now the answer for the smaller part came out to be 10. 71 00:03:36,530 --> 00:03:40,730 Now we have to add the lassitude to calculate the bigger problem. 72 00:03:40,730 --> 00:03:41,900 So 10 plus 5. 73 00:03:41,960 --> 00:03:43,210 It will be 15. 74 00:03:43,430 --> 00:03:43,910 Okay. 75 00:03:43,970 --> 00:03:46,800 So I hope by it now do we know the formula. 76 00:03:46,880 --> 00:03:51,680 So if you want to calculate some off and what we have to do. 77 00:03:51,770 --> 00:03:54,230 So some will be a function. 78 00:03:54,230 --> 00:03:59,330 It will take an M but n as input and it will give me the sum of the digits. 79 00:03:59,360 --> 00:03:59,680 Okay. 80 00:03:59,720 --> 00:04:02,100 What I will do I will give the sum function. 81 00:04:02,120 --> 00:04:03,120 The smaller problem. 82 00:04:03,140 --> 00:04:06,460 So this value is and by 10. 83 00:04:06,560 --> 00:04:07,190 Okay. 84 00:04:07,190 --> 00:04:09,790 So this will be what I will do. 85 00:04:09,790 --> 00:04:10,840 I will call. 86 00:04:10,910 --> 00:04:14,900 I will call the same function sum and I will give smaller problem. 87 00:04:14,900 --> 00:04:17,360 I will give it number by 10. 88 00:04:17,390 --> 00:04:18,570 Small problem. 89 00:04:18,590 --> 00:04:20,180 So I am giving this as input. 90 00:04:20,930 --> 00:04:24,410 So some will give me the output for the small problem. 91 00:04:24,410 --> 00:04:27,930 And now what we have to do we have to add the last digit. 92 00:04:28,070 --> 00:04:28,430 Okay. 93 00:04:28,460 --> 00:04:32,550 So I will add the last digit okay. 94 00:04:32,570 --> 00:04:34,280 So I am adding the last digit 95 00:04:37,580 --> 00:04:37,930 okay. 96 00:04:37,940 --> 00:04:39,260 I am writing the last digit. 97 00:04:39,530 --> 00:04:41,910 Now let us write the code and then we will do. 98 00:04:42,020 --> 00:04:44,720 Then they will write in again and we will again make the diagram. 99 00:04:44,780 --> 00:04:45,080 Okay. 100 00:04:46,680 --> 00:04:49,410 So first of all the return day will be in digit. 101 00:04:49,410 --> 00:04:50,960 We have to return the sum. 102 00:04:50,970 --> 00:04:54,070 Let's say the name of the function is someone Lee and what it does. 103 00:04:54,150 --> 00:04:58,420 It will take a number as input and now the base case. 104 00:04:58,440 --> 00:05:00,370 So base case is very simple. 105 00:05:00,540 --> 00:05:02,520 The smallest problem whose solution we know. 106 00:05:02,570 --> 00:05:02,930 Okay. 107 00:05:03,360 --> 00:05:06,630 So the value of any zero obviously the sum will be zero. 108 00:05:07,650 --> 00:05:14,250 Okay so this is our base case Okay so this is base case. 109 00:05:14,310 --> 00:05:16,050 Now it's time for the recursive case. 110 00:05:16,120 --> 00:05:27,730 OK so let's write a recursive case so for the recursive case what will be our small answer so our small 111 00:05:27,730 --> 00:05:29,770 answer will be very simple. 112 00:05:29,770 --> 00:05:35,940 So small answer will be calculate the answer for end by then. 113 00:05:36,030 --> 00:05:36,800 Okay. 114 00:05:36,810 --> 00:05:38,630 And now I want a conclusion. 115 00:05:38,630 --> 00:05:44,430 But so far the calculation but what we have to do we have to find out the last digit first 116 00:05:50,130 --> 00:05:50,640 okay. 117 00:05:50,740 --> 00:05:54,660 So for calculation what we have to do what is our last digit 118 00:05:57,920 --> 00:06:02,440 so calculating the last digit I can do something like this and more tonight. 119 00:06:02,640 --> 00:06:05,400 So with the help of this court I will get the last digit. 120 00:06:05,700 --> 00:06:13,390 And then what I have to do I have to return small answer plus last digit okay. 121 00:06:13,510 --> 00:06:22,910 Now let us call this function let us call the sum function and let us give the value 1 2 3 4 5 as input. 122 00:06:23,120 --> 00:06:28,340 Okay so what we write and set our answer will be 15 okay. 123 00:06:28,350 --> 00:06:36,070 So let's that this file so our answer is coming out 215 our code is working fine. 124 00:06:36,070 --> 00:06:41,660 Now let's try to make the diagram again and see what's happening okay. 125 00:06:41,660 --> 00:06:44,480 So the value of and is one two three four five. 126 00:06:44,480 --> 00:06:50,770 And so this is our value one two three four and five okay. 127 00:06:50,800 --> 00:06:52,810 So this is not close to zero. 128 00:06:52,810 --> 00:06:56,790 So I will come at this line and I will call four and by 10. 129 00:06:56,950 --> 00:07:04,200 So I I will call it 1 2 3 and 4 and this function is working a line number eleven. 130 00:07:04,340 --> 00:07:10,760 This function will go somewhere that line number eleven because it will call 1 2 3 it will wait at line 131 00:07:10,760 --> 00:07:11,540 number eleven. 132 00:07:11,570 --> 00:07:15,140 It will call well it will wait at line number eleven. 133 00:07:15,140 --> 00:07:19,910 It will call 1 and it will wait at line number eleven. 134 00:07:19,910 --> 00:07:21,410 It will call 0. 135 00:07:21,500 --> 00:07:22,420 So what will happen. 136 00:07:22,460 --> 00:07:23,440 It will are done zero. 137 00:07:24,180 --> 00:07:26,150 So it is returning 0. 138 00:07:27,140 --> 00:07:27,400 Okay. 139 00:07:27,440 --> 00:07:34,610 So the small answer small answer is zero then I am calculating the last digit which is and more than 140 00:07:34,670 --> 00:07:35,680 the value of this one. 141 00:07:35,690 --> 00:07:38,540 So one by ten that will be when only. 142 00:07:38,540 --> 00:07:39,030 Okay. 143 00:07:39,170 --> 00:07:41,420 So small answer plus last digit. 144 00:07:41,450 --> 00:07:43,400 So 0 plus 1 which is 1. 145 00:07:43,400 --> 00:07:46,940 So I am returning 1 Okay. 146 00:07:47,100 --> 00:07:50,850 Now here the value of small answer is 1. 147 00:07:51,180 --> 00:07:56,750 Okay so last digit and more 10 so well more than that will be 2. 148 00:07:56,760 --> 00:07:59,410 Okay so the last digit is 2. 149 00:07:59,610 --> 00:08:06,240 And then I am returning the addition of these two so two plus 1 3 I'm returning 3 now the value of small 150 00:08:06,240 --> 00:08:10,580 answer is 3 and then I'm calculating the last digit. 151 00:08:10,590 --> 00:08:12,180 So lost digit is one the. 152 00:08:12,180 --> 00:08:18,270 MARTIN So last digit is came out to be three and then nanometer Dunning the addition of these two so 153 00:08:18,270 --> 00:08:24,670 three plus three which is six so I am returning six small answer is six. 154 00:08:25,000 --> 00:08:26,560 And last digit will we. 155 00:08:26,740 --> 00:08:30,850 So and more ten so that is it is this this will be our last digit. 156 00:08:30,850 --> 00:08:33,650 So last as it is four so six plus four. 157 00:08:33,680 --> 00:08:39,610 I'm returning the addition of these two so I am returning 10 and small answer is 10. 158 00:08:39,880 --> 00:08:43,870 And the last digit will be and more 10. 159 00:08:43,870 --> 00:08:49,060 So last digit will be five and then I am returning the addition of these two so 10 plus five which is 160 00:08:49,090 --> 00:08:49,600 15. 161 00:08:50,320 --> 00:08:50,630 Okay. 162 00:08:50,650 --> 00:08:54,280 So that's how my answer is give out to be 15. 163 00:08:54,310 --> 00:08:54,840 Okay. 164 00:08:54,940 --> 00:08:56,680 So I hope you have understood the code. 165 00:08:56,710 --> 00:08:58,670 So the code is very simple. 166 00:08:59,020 --> 00:09:03,310 We have to write the base case then the recursive case we have to calculate. 167 00:09:03,310 --> 00:09:06,550 We have to call the same function for a smaller input. 168 00:09:06,580 --> 00:09:07,120 Okay. 169 00:09:07,150 --> 00:09:08,910 And then the calculation part. 170 00:09:09,040 --> 00:09:09,540 Okay. 171 00:09:09,610 --> 00:09:12,160 So we are writing the code with the help of PMI only. 172 00:09:12,190 --> 00:09:12,520 Okay. 173 00:09:12,550 --> 00:09:18,280 We are thinking about this diagram late that first we are thinking about this diagram later. 174 00:09:18,280 --> 00:09:23,610 First we are thinking only in terms of PMI we have to think of three steps. 175 00:09:23,630 --> 00:09:30,040 Base case because if case and the calculation part okay if you will write these three steps perfectly 176 00:09:30,130 --> 00:09:32,270 then linear call will definitely work. 177 00:09:32,330 --> 00:09:33,270 Okay. 178 00:09:33,530 --> 00:09:35,310 So I hope you understood this problem. 179 00:09:35,330 --> 00:09:35,750 Thank you.