1 00:00:01,500 --> 00:00:03,500 Hello, everyone, welcome to this new session. 2 00:00:03,510 --> 00:00:08,900 So what we will do today, so we will try to solve one more problem with the help of the council so 3 00:00:08,910 --> 00:00:11,520 that our understanding of religion can become better. 4 00:00:11,550 --> 00:00:16,020 OK, so the name of the problem that we are going to solve today is multiplication. 5 00:00:16,410 --> 00:00:22,320 OK, so what we will do so given two numbers, we have to multiply them. 6 00:00:22,350 --> 00:00:27,570 OK, so there are two numbers, M and N and we have to multiply these two numbers. 7 00:00:27,600 --> 00:00:29,840 So that is M and doing OK. 8 00:00:30,000 --> 00:00:35,220 So the one way to solve this problem is to simply use the multiply operator, but we don't have to use 9 00:00:35,220 --> 00:00:36,170 multiply operator. 10 00:00:36,180 --> 00:00:38,100 We can only use an operator. 11 00:00:38,140 --> 00:00:41,490 OK, we can only use plus operator or minus operator. 12 00:00:41,690 --> 00:00:43,860 OK, we cannot use the multiply operator. 13 00:00:44,550 --> 00:00:47,650 Now I think we have to solve this problem but I'm not sure. 14 00:00:48,120 --> 00:00:52,200 So if you are multiplying two numbers and the end, can I write it like this. 15 00:00:52,210 --> 00:01:00,540 Basically I am adding the same number and times, ok, I am adding the same number and times. 16 00:01:00,750 --> 00:01:05,790 So we are using one lipless operator here so that the solution to the one solution for this problem 17 00:01:05,790 --> 00:01:14,010 is to just use a loop and that loop will run and times and inside the loop we will add Eminem. 18 00:01:14,190 --> 00:01:14,620 OK. 19 00:01:14,640 --> 00:01:19,160 So I think you can solve it very easily with the help of for a loop of a loop. 20 00:01:19,440 --> 00:01:22,320 But now we have to solve it using recursion. 21 00:01:22,400 --> 00:01:27,600 OK, so with the help of a loop, how you will solve you will keep a variable sum equals zero, you 22 00:01:27,600 --> 00:01:32,520 will run a loop and that group will run and times inside the loop. 23 00:01:32,520 --> 00:01:38,610 What we will do, you will write something like this simplistic to M and when the loop will be already 24 00:01:38,610 --> 00:01:39,600 you will return some. 25 00:01:39,890 --> 00:01:43,820 OK, so with the help of recursion, how we can solve this problem. 26 00:01:44,310 --> 00:01:44,760 So. 27 00:01:45,910 --> 00:01:47,680 We have to calculate Eman Duine. 28 00:01:48,780 --> 00:01:56,580 OK, let's say the value of M is five and let's say the value of industry, so our output will be 15 29 00:01:57,000 --> 00:01:58,860 to a. 15. 30 00:01:59,220 --> 00:02:00,600 OK, so. 31 00:02:01,490 --> 00:02:04,850 And in doing so, can I write Aminta in like. 32 00:02:06,070 --> 00:02:08,139 Multiply and minus one. 33 00:02:09,220 --> 00:02:11,860 Plus M can I write it like this? 34 00:02:13,620 --> 00:02:19,810 Yes, obviously, we can read it like this, this is nothing, but if you multiply inside this and then 35 00:02:19,830 --> 00:02:25,000 minus blessin and these two will cancel out, each others are totally Emman, OK. 36 00:02:25,230 --> 00:02:28,630 And so let's try it and how it will work. 37 00:02:28,670 --> 00:02:32,610 So in doing so, I want to calculate five into three. 38 00:02:32,910 --> 00:02:37,780 What I want to do here is multiply five with two and then add plus five. 39 00:02:37,950 --> 00:02:42,120 So the answer will be five into to that answer will be 15 only. 40 00:02:43,020 --> 00:02:47,140 OK, so basically what we're doing here is so five in total. 41 00:02:47,160 --> 00:02:51,570 This simply means five plus five plus five. 42 00:02:52,200 --> 00:02:53,130 So what we will do. 43 00:02:54,680 --> 00:03:01,640 I will tell recursion to solve this small problem and then I will add five, I will Erdem, OK, this 44 00:03:01,640 --> 00:03:07,130 is M, this is M and this is an OK, so I'm repeating myself. 45 00:03:09,750 --> 00:03:15,030 Let's take one more example, let's say the value of M is three and the value of and is five. 46 00:03:15,700 --> 00:03:19,170 OK, so I want to calculate them in doing so. 47 00:03:19,170 --> 00:03:23,400 Basically what we can do M plus M plus M, how many times. 48 00:03:24,240 --> 00:03:24,890 And Bems. 49 00:03:25,350 --> 00:03:25,770 OK. 50 00:03:28,760 --> 00:03:29,300 So. 51 00:03:30,450 --> 00:03:32,370 I want to multiply three to five. 52 00:03:33,410 --> 00:03:40,160 So I will add three, five times, so three plus three plus three plus three plus three. 53 00:03:40,640 --> 00:03:46,170 OK, so now what we will do, we will use the help of recursion, what we will use. 54 00:03:46,490 --> 00:03:49,310 So what we will do, we will break the problem into smaller problem. 55 00:03:49,340 --> 00:03:52,760 I will tell recursion to solve this part for me. 56 00:03:54,210 --> 00:04:00,860 And that equation will give me the answer and the answer will be 12 and then I will add em. 57 00:04:00,990 --> 00:04:06,690 OK, so this is M so the question will give me the answer, which is well, and then I will add. 58 00:04:06,690 --> 00:04:09,460 And so if I function multiply. 59 00:04:10,650 --> 00:04:11,770 So how does one multiply. 60 00:04:11,770 --> 00:04:16,050 A function will look like it will take to input as argument and then. 61 00:04:17,010 --> 00:04:25,020 What I will call I will call the same function multiply function for the smaller input, so I will tell 62 00:04:25,260 --> 00:04:26,640 you to give me the shut off. 63 00:04:27,360 --> 00:04:31,600 So what it will give me it will give me the answer off and multiply and minus one. 64 00:04:31,950 --> 00:04:35,610 OK, and this is in the end. 65 00:04:35,850 --> 00:04:40,440 And finally, what we will do, we will add after recursion will give me the answer. 66 00:04:40,440 --> 00:04:41,710 I will add this m. 67 00:04:42,780 --> 00:04:44,600 OK, so this will be our formula. 68 00:04:44,610 --> 00:04:47,670 This will be, this will be how that equation will look like. 69 00:04:48,040 --> 00:04:51,900 OK, now first let us write the code and then we will tighten the code. 70 00:04:52,050 --> 00:04:54,740 OK, so what will be our base case. 71 00:04:54,750 --> 00:04:56,580 So the base case will be very simple. 72 00:04:57,000 --> 00:04:58,410 You want to calculate Aminta. 73 00:04:58,410 --> 00:05:01,530 And so this case will be the value of Aniceto. 74 00:05:01,830 --> 00:05:04,770 Then if you multiply with zero then our good will be visit only. 75 00:05:04,800 --> 00:05:07,950 OK, if you multiply any number with zero, the output will be zero only. 76 00:05:08,010 --> 00:05:11,310 So this will be our base case if any zero return zero. 77 00:05:11,820 --> 00:05:15,100 OK, now first let us write the code and then we will try again. 78 00:05:15,160 --> 00:05:15,510 OK. 79 00:05:19,060 --> 00:05:26,650 So the return type will be integer and let's say the name of the function is multiply what it will take, 80 00:05:26,650 --> 00:05:29,530 it will take to integer as argumentum and then. 81 00:05:30,370 --> 00:05:34,570 OK, and what we have to calculate, we have to calculate and doing. 82 00:05:36,500 --> 00:05:37,640 We have to calculate. 83 00:05:38,710 --> 00:05:43,390 And in doing but without using multiply or pretend without for loop or loop. 84 00:05:43,440 --> 00:05:46,070 OK, now there is time for the base case. 85 00:05:46,530 --> 00:05:49,120 So the base case is the smallest problem or solution. 86 00:05:49,140 --> 00:05:49,720 We already know. 87 00:05:49,720 --> 00:05:54,570 So if the value of any zero so any number multiplied with zero will be zero only. 88 00:05:55,270 --> 00:05:56,370 So I will return zero. 89 00:05:57,590 --> 00:06:00,290 Now it's time for the recursive case, what we have to do. 90 00:06:01,400 --> 00:06:03,690 We have to solve the problem for the smaller input. 91 00:06:03,770 --> 00:06:08,840 OK, and what are the smaller and smaller and what is the value of and and minus one? 92 00:06:08,850 --> 00:06:09,230 So. 93 00:06:10,170 --> 00:06:11,070 Smiled and said. 94 00:06:12,780 --> 00:06:15,720 That's my answer is you have to I'm calling the same function. 95 00:06:17,270 --> 00:06:17,930 Multiply. 96 00:06:20,620 --> 00:06:24,400 And I want to calculate and do end minus one. 97 00:06:24,610 --> 00:06:29,320 OK, so at this lane, I have done set off Amerindo and minus one. 98 00:06:31,640 --> 00:06:36,860 And finally, our calculation part, so our calculation part is very simple. 99 00:06:37,890 --> 00:06:38,670 What we have to do. 100 00:06:39,910 --> 00:06:42,130 I will return this my answer. 101 00:06:43,280 --> 00:06:44,780 Plus M. 102 00:06:45,780 --> 00:06:49,530 And NetSol, OK, now let's call this function. 103 00:06:51,660 --> 00:06:57,390 So let's call this function and let us give the value of Immonen. 104 00:06:58,610 --> 00:06:59,780 So multiply. 105 00:07:01,580 --> 00:07:03,570 And have the values are three and five. 106 00:07:04,210 --> 00:07:04,610 OK. 107 00:07:06,590 --> 00:07:09,730 Now, if we learn this code, our output will be 15. 108 00:07:09,800 --> 00:07:10,190 OK? 109 00:07:11,710 --> 00:07:12,880 So let's send the file. 110 00:07:15,100 --> 00:07:18,540 So our output is coming out 15, basically, our goal is working fine. 111 00:07:18,600 --> 00:07:18,920 OK. 112 00:07:20,970 --> 00:07:23,010 So there is a big mistake here. 113 00:07:24,960 --> 00:07:28,460 OK, now let's try to understand how the output is coming out to 15. 114 00:07:28,500 --> 00:07:28,820 OK. 115 00:07:30,890 --> 00:07:32,510 So the values are three in five. 116 00:07:32,540 --> 00:07:35,240 OK, so we have three and we have five. 117 00:07:35,270 --> 00:07:36,840 So these are the values of Immonen. 118 00:07:37,180 --> 00:07:39,460 OK, so five is not close to zero. 119 00:07:40,550 --> 00:07:46,520 So basically, this function will wait at line number 10 and I call the function for Tecoma for. 120 00:07:48,030 --> 00:07:55,080 Again, this will be headline number 10 and I will call for three commentary, similarly, I will call 121 00:07:55,080 --> 00:07:56,100 for three two. 122 00:07:57,130 --> 00:08:02,800 Then I will call for triggermen and then I will call for Tecoma Zero. 123 00:08:04,010 --> 00:08:06,470 So the value of any zero return zero. 124 00:08:06,540 --> 00:08:13,310 OK, so basically this will return zero, so zero will be stored in this Moylan's so small answer becomes 125 00:08:13,310 --> 00:08:13,760 zero. 126 00:08:13,790 --> 00:08:15,360 I guess my answer becomes zero. 127 00:08:16,070 --> 00:08:18,260 Now I am returning small surplus. 128 00:08:18,260 --> 00:08:20,570 And what is the value of my value of a mystery. 129 00:08:21,050 --> 00:08:24,860 OK, so zero plus three that will be three. 130 00:08:26,770 --> 00:08:28,520 So my list of small answers. 131 00:08:28,600 --> 00:08:34,510 This is my answer, then I'm returning small surplus and the value of mystery only. 132 00:08:34,510 --> 00:08:36,370 So three plus three, which is six. 133 00:08:38,039 --> 00:08:42,690 So six is small and also six plus three, which is nine. 134 00:08:43,799 --> 00:08:47,910 OK, so small dancer becomes nine, then nine plus three. 135 00:08:48,950 --> 00:08:57,140 Basically, to so small answer is 12 and then 12 plus three, which is 15, OK, so 15 is our answer. 136 00:08:57,690 --> 00:09:00,080 OK, so that's how that equation is working. 137 00:09:00,760 --> 00:09:04,160 OK, so but you do not have to think all of this, OK. 138 00:09:04,490 --> 00:09:09,620 We will not think I love this, but I will think we will think like first. 139 00:09:09,620 --> 00:09:09,850 Right. 140 00:09:09,860 --> 00:09:11,150 The basic is very simple. 141 00:09:11,720 --> 00:09:14,330 Then write the recursive case. 142 00:09:14,570 --> 00:09:19,850 We will, we are calculating and with about minus one you have to assume, OK, you add line number 143 00:09:19,850 --> 00:09:20,170 10. 144 00:09:20,540 --> 00:09:26,360 What we are trying to do here is we are assuming that this multiplier function works, OK, this multiplier 145 00:09:26,360 --> 00:09:31,340 function, if if you will give to input as argument, it will give me Emmental and minus one. 146 00:09:31,550 --> 00:09:33,770 OK, you have to assume this, OK? 147 00:09:33,770 --> 00:09:35,600 You have to assume that this function will work. 148 00:09:36,700 --> 00:09:43,380 This dysfunction is working, at least give me the small answer I will add plus M to get to get our 149 00:09:43,380 --> 00:09:45,240 prop to get down to what the bigger problem. 150 00:09:45,480 --> 00:09:47,620 OK, and then we are turning our answer. 151 00:09:47,950 --> 00:09:51,640 OK, so first write the code, then think about the diagram. 152 00:09:51,660 --> 00:09:54,620 OK, first write the code and then go to the diagram. 153 00:09:54,630 --> 00:09:56,310 So I hope this problem is clear. 154 00:09:56,490 --> 00:09:58,010 If you have any doubt you can ask me. 155 00:09:58,050 --> 00:09:59,130 OK, thank you.