1 00:00:01,590 --> 00:00:02,250 Hello everyone. 2 00:00:02,250 --> 00:00:03,540 Welcome to this new recession. 3 00:00:03,540 --> 00:00:05,010 So what do we do today. 4 00:00:05,010 --> 00:00:10,140 So we will try to solve one more problem with the help of the occasion so so that our understanding 5 00:00:10,140 --> 00:00:11,520 of religion can become better. 6 00:00:11,610 --> 00:00:12,310 OK. 7 00:00:12,450 --> 00:00:16,350 So the name of the problem that we are going to solve today is multiplication. 8 00:00:16,460 --> 00:00:17,950 Okay. 9 00:00:18,480 --> 00:00:19,880 So what do we do. 10 00:00:19,890 --> 00:00:22,440 So given two numbers we have to merge to play them. 11 00:00:22,440 --> 00:00:22,700 OK. 12 00:00:22,740 --> 00:00:27,600 So there are two numbers m and n and we have to multiply these two numbers. 13 00:00:27,630 --> 00:00:33,780 So that is M and doing OK so the one way to solve this problem is to simply use the multiply operator. 14 00:00:34,110 --> 00:00:36,180 But we don't have to use multiply or break that. 15 00:00:36,180 --> 00:00:38,090 We can only use additional played that. 16 00:00:38,100 --> 00:00:38,360 OK. 17 00:00:38,370 --> 00:00:42,060 We can only use plus operator or minus OPERATOR OK. 18 00:00:42,090 --> 00:00:44,680 We cannot use the money to play operator. 19 00:00:44,720 --> 00:00:48,150 Now I think we have hour to solve this problem but I'm not sure. 20 00:00:48,180 --> 00:00:52,200 So if you are more dipping into numbers I mean when can I write it like this. 21 00:00:52,200 --> 00:00:56,320 Basically I'm adding the same number and times. 22 00:00:56,420 --> 00:00:58,310 OK. 23 00:00:58,360 --> 00:01:00,810 I'm adding the same number and times. 24 00:01:00,810 --> 00:01:03,240 So we're using one live plus operator here. 25 00:01:03,270 --> 00:01:10,150 So the solution to the one solution for this problem is to just use a loop and that loop will run end 26 00:01:10,200 --> 00:01:13,990 times and inside the loop we will add Eminem. 27 00:01:14,310 --> 00:01:14,610 OK. 28 00:01:14,640 --> 00:01:19,500 So I think you can solve it very easily with the help of for loop part of a loop. 29 00:01:19,500 --> 00:01:22,320 But now we have to solve it using recursion. 30 00:01:22,440 --> 00:01:22,920 OK. 31 00:01:23,040 --> 00:01:27,480 So with that before loop how you will solve you will keep a variable sum equals zero. 32 00:01:27,480 --> 00:01:30,360 You will run a loop and that group will run. 33 00:01:30,370 --> 00:01:33,630 And times inside the loop what you will do. 34 00:01:33,630 --> 00:01:38,940 You will write something like this simplistic was to him and then the loop will be all whether you will 35 00:01:38,940 --> 00:01:39,930 have done some. 36 00:01:39,960 --> 00:01:41,130 OK. 37 00:01:41,340 --> 00:01:44,220 So with the help of recursion how we can solve this problem. 38 00:01:44,370 --> 00:01:49,190 So we have to calculate M in doing okay. 39 00:01:49,200 --> 00:01:54,840 Let's say the value of M is five and led to the value of minus three. 40 00:01:54,870 --> 00:01:59,310 So our output will be 15 m in the end is 15. 41 00:01:59,340 --> 00:02:00,000 Okay. 42 00:02:00,000 --> 00:02:10,660 So m in doing so can I write M into N like M multiply and minus one bless em. 43 00:02:10,660 --> 00:02:16,470 Can I add I did like this yes obviously we can write it like this. 44 00:02:16,650 --> 00:02:22,500 This isn't a thing but if you multiply inside this is I mean minus M lesson and these two will cancel 45 00:02:22,500 --> 00:02:23,070 out each other. 46 00:02:23,070 --> 00:02:25,210 So it totally M N okay. 47 00:02:25,320 --> 00:02:28,620 And so let's dry it and how we look. 48 00:02:28,650 --> 00:02:36,240 So m in doing so I want to calculate five into three what I want to do here is multiply five with two 49 00:02:36,330 --> 00:02:38,010 and then add plus five. 50 00:02:38,010 --> 00:02:40,670 So the answer will be five into two. 51 00:02:40,710 --> 00:02:42,980 That answer will be fifteen only. 52 00:02:43,020 --> 00:02:47,130 Okay so basically what we're doing here is so five in total. 53 00:02:47,160 --> 00:02:52,200 This simply means five plus five plus five. 54 00:02:52,230 --> 00:02:59,510 So what we will do I will tell the equation to solve this smaller problem and then I will add five. 55 00:03:00,080 --> 00:03:01,110 I will add m. 56 00:03:01,190 --> 00:03:01,460 Okay. 57 00:03:01,490 --> 00:03:07,100 This is m this is M and this is an okay so I'm building myself 58 00:03:09,810 --> 00:03:15,120 let's take one more example let's say the value of M is three and the value of n is five. 59 00:03:15,720 --> 00:03:18,830 Okay so I want to convert them into n. 60 00:03:18,990 --> 00:03:25,420 So basically what we can do M Plus M Plus M How many times and times. 61 00:03:25,470 --> 00:03:25,770 Okay. 62 00:03:28,820 --> 00:03:35,320 So I want to multiply three into five so I will add three five times. 63 00:03:35,390 --> 00:03:40,250 So three plus three plus three plus three plus three. 64 00:03:40,700 --> 00:03:41,130 Okay. 65 00:03:41,210 --> 00:03:45,290 So now what we will do we will use the help of the equation. 66 00:03:45,380 --> 00:03:46,490 What we will use. 67 00:03:46,520 --> 00:03:49,360 So what we will do we will break the problem into smaller problem. 68 00:03:49,370 --> 00:03:53,030 I will tell recursion to solve this part for me. 69 00:03:54,330 --> 00:03:57,530 And that equation will give me the answer and the answer will be. 70 00:03:58,260 --> 00:04:01,030 And then I will add m. 71 00:04:01,080 --> 00:04:01,380 Okay. 72 00:04:01,380 --> 00:04:08,260 So this is M So the equation will give me the answer which is drill and then I will add M so if I have 73 00:04:08,260 --> 00:04:09,570 a function multiply. 74 00:04:10,710 --> 00:04:17,550 So how does multiplatform assembly look like it can take two input as outgoing M and then what I will 75 00:04:17,550 --> 00:04:22,700 call I will call the same function multiply a function for the smaller input. 76 00:04:23,100 --> 00:04:27,400 So I will tell occasion to give me down shut off. 77 00:04:27,420 --> 00:04:31,980 So what it will give me it will give me the onset of M multiply and minus 1. 78 00:04:32,070 --> 00:04:32,370 Okay. 79 00:04:32,370 --> 00:04:35,860 And this is M in two n. 80 00:04:35,970 --> 00:04:38,010 And finally what do we do. 81 00:04:38,100 --> 00:04:44,580 We will add after equation we give me the answer I will add this m okay so this will be our formula 82 00:04:44,610 --> 00:04:48,030 this will we this will be how that equation will look like. 83 00:04:48,150 --> 00:04:52,170 Okay now first let us write the code and then we will died in the code. 84 00:04:52,170 --> 00:04:54,780 Okay so what will be our base case. 85 00:04:54,780 --> 00:05:00,420 So the base case will be very simple you want to calculate M in doing so base case will be the value 86 00:05:00,420 --> 00:05:01,780 of any 0. 87 00:05:01,890 --> 00:05:06,750 Then if you multiply with zero then now good will be Z only okay if you multiply any number with zero 88 00:05:06,750 --> 00:05:08,010 that now it will be zero only. 89 00:05:08,010 --> 00:05:11,810 So this will be our base case if any 0 return 0. 90 00:05:11,910 --> 00:05:12,350 Okay. 91 00:05:12,420 --> 00:05:15,090 Now first let us write the code and then we will drive. 92 00:05:15,210 --> 00:05:15,470 Okay 93 00:05:19,150 --> 00:05:26,920 so that it I will be in digit and let's say the name of the function is multiply what it will take it 94 00:05:26,920 --> 00:05:30,740 will take two integer as argument M and then okay. 95 00:05:30,750 --> 00:05:40,500 And what we have to conclude we have to calculate M in doing we have to calculate M in doing but without 96 00:05:40,500 --> 00:05:43,560 using multiply or pretend without for loop or Y loop. 97 00:05:43,560 --> 00:05:46,430 Okay now it's time for the base case. 98 00:05:46,590 --> 00:05:51,590 So the base case is the smallest problem whose solution we already know save the value of any 0. 99 00:05:51,630 --> 00:05:55,320 So any number multiplied with zero will be zero only. 100 00:05:55,320 --> 00:05:57,560 So I will return 0. 101 00:05:57,650 --> 00:06:03,200 Now it's time for the recursive case what we have to do we have to solve the problem for the smaller 102 00:06:03,200 --> 00:06:04,460 input okay. 103 00:06:04,520 --> 00:06:11,020 And where did this Malone put similar input is led to the value of and this and minus one to small and. 104 00:06:12,830 --> 00:06:17,930 A small answer is you have to I'm calling the same function multiply 105 00:06:20,740 --> 00:06:24,390 and I wanted to conclude M and do n minus one. 106 00:06:24,730 --> 00:06:34,850 Okay so at this line I have done set off M and do and minus 1 and finally our calculation part of our 107 00:06:34,850 --> 00:06:36,980 calculation part is very simple. 108 00:06:37,980 --> 00:06:47,080 What we have to do I will return this small answer bless em and medicine. 109 00:06:47,620 --> 00:06:57,360 Okay now let's call this function so let's call this function and let us give the value of a man an 110 00:06:58,670 --> 00:07:03,680 so multiply and led to the values that three and 5. 111 00:07:04,320 --> 00:07:06,510 Okay. 112 00:07:06,700 --> 00:07:09,830 Now if we learn this code our output will reach 15. 113 00:07:09,890 --> 00:07:10,380 Okay. 114 00:07:11,770 --> 00:07:18,680 So let's send the file salad out for this coming out 215 basic level code is working fine. 115 00:07:18,680 --> 00:07:22,970 Okay so this typing mistake here. 116 00:07:25,110 --> 00:07:27,810 Okay now let's try to understand how output is coming out. 117 00:07:27,810 --> 00:07:32,590 215 Okay so the values are 3 and 5. 118 00:07:32,600 --> 00:07:32,900 Okay. 119 00:07:32,930 --> 00:07:35,280 So we have three and we have five. 120 00:07:35,300 --> 00:07:37,210 So these are the values of him and then. 121 00:07:37,280 --> 00:07:37,820 Okay. 122 00:07:37,910 --> 00:07:40,570 So 5 not articles 2 0. 123 00:07:40,610 --> 00:07:44,040 So basically this function will wait at line number 10. 124 00:07:44,060 --> 00:07:49,110 And I call the function for three comma food again. 125 00:07:49,380 --> 00:07:53,560 This will wait at line number 10 and I will call for true commentary. 126 00:07:53,710 --> 00:08:01,930 Similarly I wouldn't call for a on my 2 then I will call for three call my 1 and then I will call for 127 00:08:01,930 --> 00:08:06,620 three comma zero so the value of any zero redundancy two. 128 00:08:06,650 --> 00:08:07,120 Okay. 129 00:08:07,220 --> 00:08:09,290 So basically this will be done zero. 130 00:08:09,620 --> 00:08:11,600 So zero will be stored in this small answer. 131 00:08:11,600 --> 00:08:13,820 So small answer becomes zero. 132 00:08:13,820 --> 00:08:14,160 Okay. 133 00:08:14,200 --> 00:08:17,900 My lines it become zero now I am returning a small answer. 134 00:08:17,900 --> 00:08:18,660 Bless em. 135 00:08:18,680 --> 00:08:20,570 What is the value of m m value of a mystery. 136 00:08:21,170 --> 00:08:28,450 Okay so zero plus 3 it will be three so that's my leave small answer. 137 00:08:28,450 --> 00:08:35,140 So this is small answer then I am returning small answer plus M and the value of a mystery only so three 138 00:08:35,140 --> 00:08:43,830 plus three which is six so six is small answer so six plus three which is nine. 139 00:08:43,990 --> 00:08:49,780 Okay so small answer becomes nine then nine plus three basically twelve. 140 00:08:49,820 --> 00:08:55,250 So small answer is Twin and then twelve plus three which is fifteen. 141 00:08:55,250 --> 00:08:55,540 Okay. 142 00:08:55,550 --> 00:08:57,130 So fifteen is our answer. 143 00:08:57,800 --> 00:08:58,250 Okay. 144 00:08:58,340 --> 00:09:00,760 So that's how that equation is working. 145 00:09:00,800 --> 00:09:01,250 Okay. 146 00:09:01,400 --> 00:09:03,780 So but you do not have to take all of this. 147 00:09:03,800 --> 00:09:04,390 Okay. 148 00:09:04,550 --> 00:09:06,470 We will not think all of this. 149 00:09:06,590 --> 00:09:11,670 What do we think we will think like first right the base case very simple. 150 00:09:11,960 --> 00:09:14,960 Then write the recursive case we will. 151 00:09:14,960 --> 00:09:18,000 We are calculating M2 the power in minus one you have to assume. 152 00:09:18,020 --> 00:09:18,580 Okay. 153 00:09:18,800 --> 00:09:20,480 You add line number 10. 154 00:09:20,630 --> 00:09:25,590 What we are trying to do here is we are assuming that this multiplier function looks okay. 155 00:09:25,700 --> 00:09:31,100 This multiplier function if it if you will give 2 input as argument it will give me m in 2 and minus 156 00:09:31,100 --> 00:09:31,380 1. 157 00:09:31,610 --> 00:09:31,850 Okay. 158 00:09:31,850 --> 00:09:33,760 You have to assume this okay. 159 00:09:33,770 --> 00:09:39,250 You have to assume that this function will work since this function is working it will give me the small 160 00:09:39,250 --> 00:09:45,310 lines so I will add plus M to get to get our prop to get down to what the bigger problem. 161 00:09:45,600 --> 00:09:45,900 Okay. 162 00:09:45,900 --> 00:09:47,610 And then we add turning our answer. 163 00:09:48,030 --> 00:09:52,270 Okay so first write the code then think about the diagram okay. 164 00:09:52,420 --> 00:09:56,480 First write the code then thing go to the diagram to I hope this problem is cleared. 165 00:09:56,580 --> 00:09:58,060 If you have any doubt you can ask me. 166 00:09:58,080 --> 00:09:59,290 Okay thank you.