1 00:00:00,790 --> 00:00:01,690 Hi everyone. 2 00:00:01,690 --> 00:00:05,890 Let's now take a test case and walk through the code that we have written. 3 00:00:05,890 --> 00:00:06,550 For this. 4 00:00:06,550 --> 00:00:13,030 Let me take the array as two, minus one, five and three and let's take the target value as four. 5 00:00:13,540 --> 00:00:14,020 All right. 6 00:00:14,020 --> 00:00:16,090 Now we are inside the function. 7 00:00:16,090 --> 00:00:20,890 Let's say we have called the function and the this array and the target value is passed to it. 8 00:00:20,890 --> 00:00:27,520 Now we are over here for let I is equal to zero I less than array dot length minus one I plus plus. 9 00:00:27,580 --> 00:00:30,730 Now before that let me just write the indices of the given array. 10 00:00:30,730 --> 00:00:32,800 So that's 012 and three. 11 00:00:32,800 --> 00:00:33,400 All right. 12 00:00:33,430 --> 00:00:34,960 Now we are in this for loop. 13 00:00:34,960 --> 00:00:37,690 Now initially the value of I is equal to zero. 14 00:00:37,690 --> 00:00:38,020 All right. 15 00:00:38,020 --> 00:00:40,450 So let's write that over here I is equal to zero. 16 00:00:40,450 --> 00:00:43,900 And now we come into the next for loop. 17 00:00:43,900 --> 00:00:47,260 So over here we have initialized j as I plus one. 18 00:00:47,260 --> 00:00:52,060 Now because I is equal to zero j will be equal to zero plus one which is equal to one. 19 00:00:52,450 --> 00:00:53,080 All right. 20 00:00:53,080 --> 00:00:56,920 Now the values at these two indices is two and minus one. 21 00:00:56,920 --> 00:00:58,690 Right at index zero we have two. 22 00:00:58,690 --> 00:01:00,850 And at index one we have minus one. 23 00:01:00,850 --> 00:01:02,830 So the values are two and minus one. 24 00:01:02,830 --> 00:01:07,240 And over here we are checking whether these two add up to the target value. 25 00:01:07,240 --> 00:01:09,520 Now two plus minus one is equal to one. 26 00:01:09,520 --> 00:01:10,870 That's not equal to four. 27 00:01:10,870 --> 00:01:12,640 So this is not true right. 28 00:01:12,640 --> 00:01:16,210 So we are not returning I j now again j is incremented. 29 00:01:16,210 --> 00:01:17,770 So j becomes two. 30 00:01:17,800 --> 00:01:21,130 Now the values are two and five right. 31 00:01:21,130 --> 00:01:24,040 So the value at the second index is five. 32 00:01:24,040 --> 00:01:25,150 So two and five. 33 00:01:25,150 --> 00:01:27,040 When we add these we get seven. 34 00:01:27,040 --> 00:01:28,030 We don't get four. 35 00:01:28,030 --> 00:01:30,340 So again this does not become true. 36 00:01:30,340 --> 00:01:33,370 Again j is incremented and j becomes three. 37 00:01:33,370 --> 00:01:36,730 And at this point at this point the values are two and three. 38 00:01:36,730 --> 00:01:39,100 Right at index three the value is three. 39 00:01:39,100 --> 00:01:42,550 Now two plus three is equal to five, which is again not equal to four. 40 00:01:42,550 --> 00:01:45,250 Now we have reached the limit. 41 00:01:45,280 --> 00:01:47,410 Now our j is less than array dot length. 42 00:01:47,410 --> 00:01:49,390 That's uh three is less than four. 43 00:01:49,390 --> 00:01:50,890 Array dot length in this case is four. 44 00:01:50,890 --> 00:01:55,240 Right now when j is incremented and j becomes four this loop breaks. 45 00:01:55,240 --> 00:01:59,680 So we come out and we increment the value of I from 0 to 1. 46 00:02:00,010 --> 00:02:00,430 All right. 47 00:02:00,430 --> 00:02:01,780 Now I is equal to one. 48 00:02:01,780 --> 00:02:05,830 Now j again we come to the second for loop j is equal to I plus one. 49 00:02:05,830 --> 00:02:07,960 So j is equal to two at this point. 50 00:02:07,960 --> 00:02:13,030 And the values at these two indices are one minus one and five right. 51 00:02:13,030 --> 00:02:14,470 So minus one and five. 52 00:02:14,470 --> 00:02:17,980 When we add them we get the required value which is equal to four. 53 00:02:17,980 --> 00:02:19,840 So we have found our answer. 54 00:02:19,840 --> 00:02:24,640 And because the question asks us to return the indices we will return these two. 55 00:02:24,670 --> 00:02:25,780 That is one comma two. 56 00:02:25,780 --> 00:02:27,100 And that's our answer. 57 00:02:27,100 --> 00:02:32,170 Now again we have seen the time complexity of this solution is equal to o of n square. 58 00:02:32,170 --> 00:02:35,950 Why is that so over here we can see we have a nested for loop right? 59 00:02:35,950 --> 00:02:41,920 For every element in I we are again traversing the array to the second for loop over here. 60 00:02:41,920 --> 00:02:42,370 Right. 61 00:02:42,370 --> 00:02:44,170 So we have a nested for loop. 62 00:02:44,170 --> 00:02:46,930 So in the first for loop we have n operations. 63 00:02:46,930 --> 00:02:51,730 And for each operation in the first for loop we are doing n operations again. 64 00:02:51,730 --> 00:02:55,990 So that's why the time complexity of this solution is O of n square. 65 00:02:55,990 --> 00:02:58,450 And the space complexity is O of one. 66 00:02:58,450 --> 00:03:02,170 Because we are not taking any additional space, we are not storing anything. 67 00:03:02,170 --> 00:03:05,920 So again, we have seen that this is not the best way. 68 00:03:05,920 --> 00:03:07,300 This is the brute force solution. 69 00:03:07,300 --> 00:03:10,690 Now let's see in the next video how to optimize this.