title

3 Sum | Brute - Better - Optimal with Codes

description

Problem Link: https://bit.ly/3X34JSI
Notes/C++/Java/Python codes:
We have solved the problem, and we have gone from brute force and ended with the most optimal solution. Every approach's code has been written in the video itself. Also, we have covered the algorithm with intuition.
Full Course: https://bit.ly/tufA2ZYt
You can follow me across social media, all my handles are below:
Linkedin/Instagram/Telegram: https://linktr.ee/takeUforward
0:00 Introduction of Course
00:41 Problem Statement
02:56 Brute force approach (Using 3-pointer)
04:55 Pseudocode
07:36 Code
09:27 Complexity
10:26 Better approach (Using Hashing)
12:23 Dry run
18:09 Code
20:15 Complexity
22:20 Optimal approach (Using 2-pointer)
23:20 2-Pointer Technique
31:50 Code
36:41 Complexity

detail

{'title': '3 Sum | Brute - Better - Optimal with Codes', 'heatmap': [{'end': 625.671, 'start': 576.036, 'weight': 0.781}, {'end': 902.005, 'start': 850.076, 'weight': 0.928}, {'end': 1249.774, 'start': 1170.803, 'weight': 0.713}, {'end': 1365.787, 'start': 1311.215, 'weight': 0.744}, {'end': 1613.707, 'start': 1586.258, 'weight': 0.814}, {'end': 1962.403, 'start': 1933.113, 'weight': 0.829}, {'end': 2287.887, 'start': 2235.354, 'weight': 0.897}], 'summary': 'The stribus a2z dsa course comprises 455 modules and 400+ problems to ensure proficiency in ds algo and global employability. the 3sum problem is covered with its brute force solution, optimization to o(n^2) using hashing, and finding unique triplets in arrays. the chapters also delve into time and space complexity analysis, algorithmic logic, and optimal solutions for programming problems.', 'chapters': [{'end': 34.705, 'segs': [{'end': 34.705, 'src': 'embed', 'start': 3.137, 'weight': 0, 'content': [{'end': 4.299, 'text': 'Hey everyone, welcome back to the channel.', 'start': 3.137, 'duration': 1.162}, {'end': 5.861, 'text': 'I hope you guys are doing extremely well.', 'start': 4.319, 'duration': 1.542}, {'end': 9.106, 'text': 'So this is another lecture from the Stribus A2Z DSA course.', 'start': 6.262, 'duration': 2.844}, {'end': 13.252, 'text': "Just in case you're for the first time here, this is the world's most in-depth course when we talk about DS Algo.", 'start': 9.126, 'duration': 4.126}, {'end': 16.998, 'text': 'Why do I say that? Because this course has 455 modules.', 'start': 13.653, 'duration': 3.345}, {'end': 18.42, 'text': "By the end of the course, you'd have solved more than.", 'start': 17.018, 'duration': 1.402}, {'end': 20.181, 'text': '400 plus problems already.', 'start': 19, 'duration': 1.181}, {'end': 22.881, 'text': 'When it comes to DS Algo, you can go over the entire internet.', 'start': 20.441, 'duration': 2.44}, {'end': 24.442, 'text': 'you can buy any of the paid courses.', 'start': 22.881, 'duration': 1.561}, {'end': 26.663, 'text': 'none of them will be teaching you DS Algo in such depth.', 'start': 24.442, 'duration': 2.221}, {'end': 30.504, 'text': 'Something that I can give you as assurance is, once you complete this entire course,', 'start': 26.923, 'duration': 3.581}, {'end': 34.705, 'text': "you'll be able to clear any of the DS Algo routes in any of the companies in any part of the world.", 'start': 30.504, 'duration': 4.201}], 'summary': 'Stribus a2z dsa course offers 455 modules, with 400+ problems, guaranteeing expertise in ds algo for job placement worldwide.', 'duration': 31.568, 'max_score': 3.137, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk3137.jpg'}], 'start': 3.137, 'title': 'Stribus a2z dsa course', 'summary': 'Introduces the stribus a2z dsa course, with 455 modules and over 400 problems, guaranteeing proficiency in ds algo and employability worldwide.', 'chapters': [{'end': 34.705, 'start': 3.137, 'title': 'Stribus a2z dsa: in-depth course', 'summary': 'Introduces the stribus a2z dsa course, comprising 455 modules and over 400 problems, guaranteeing proficiency in ds algo and employability worldwide.', 'duration': 31.568, 'highlights': ["By the end of the course, you'd have solved more than 400 plus problems.", 'This course has 455 modules.', "Once you complete this entire course, you'll be able to clear any of the DS Algo routes in any of the companies in any part of the world.", 'None of the paid courses will be teaching you DS Algo in such depth.']}], 'duration': 31.568, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk3137.jpg', 'highlights': ['This course has 455 modules.', "By the end of the course, you'd have solved more than 400 plus problems.", "Once you complete this entire course, you'll be able to clear any of the DS Algo routes in any of the companies in any part of the world.", 'None of the paid courses will be teaching you DS Algo in such depth.']}, {'end': 566.43, 'segs': [{'end': 62.874, 'src': 'embed', 'start': 35.146, 'weight': 4, 'content': [{'end': 40.667, 'text': "So till now we have covered up till this particular problem and this video I'll be covering up the problem 3SUM.", 'start': 35.146, 'duration': 5.521}, {'end': 42.408, 'text': 'So what does the problem actually state?', 'start': 40.887, 'duration': 1.521}, {'end': 51.011, 'text': "It states that you'll be given an array of integers and your task is to find out all the triplets that sum up to give you a value of zero.", 'start': 42.568, 'duration': 8.443}, {'end': 53.872, 'text': 'So basically, in a triplet, there are three elements.', 'start': 51.271, 'duration': 2.601}, {'end': 57.853, 'text': 'So if you sum up those three elements, the summation should be zero.', 'start': 54.252, 'duration': 3.601}, {'end': 59.573, 'text': 'And there is a critical point over here.', 'start': 58.073, 'duration': 1.5}, {'end': 62.874, 'text': 'You cannot take same elements more than once.', 'start': 59.953, 'duration': 2.921}], 'summary': 'Covering problem 3sum, finding triplets that sum to zero in given array of integers.', 'duration': 27.728, 'max_score': 35.146, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk35146.jpg'}, {'end': 204.133, 'src': 'embed', 'start': 176.161, 'weight': 0, 'content': [{'end': 179.623, 'text': "So, if this question comes up in the interview, what is the first solution that you'll give to the interviewer?", 'start': 176.161, 'duration': 3.462}, {'end': 181.663, 'text': 'That is definitely the brute force solution.', 'start': 179.923, 'duration': 1.74}, {'end': 184.725, 'text': 'And what is the most extreme, naive solution that comes to your brain?', 'start': 182.004, 'duration': 2.721}, {'end': 187.826, 'text': "It's like why not try out all the triplets?", 'start': 185.225, 'duration': 2.601}, {'end': 191.147, 'text': 'And the triplets that gives us the sum zero.', 'start': 188.306, 'duration': 2.841}, {'end': 192.208, 'text': 'that is what we will return.', 'start': 191.147, 'duration': 1.061}, {'end': 194.349, 'text': "And probably we'll just return the unique ones.", 'start': 192.508, 'duration': 1.841}, {'end': 201.752, 'text': 'So how do I try out all the triplets? So the triplets have three positions in them that you have to fill.', 'start': 194.909, 'duration': 6.843}, {'end': 204.133, 'text': 'The first element, the second element, and the third element.', 'start': 201.792, 'duration': 2.341}], 'summary': 'In an interview, the initial solution for finding triplets with a sum of zero is the brute force method, trying out all possible triplets and returning the unique ones.', 'duration': 27.972, 'max_score': 176.161, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk176161.jpg'}, {'end': 466.096, 'src': 'embed', 'start': 424.243, 'weight': 1, 'content': [{'end': 433.601, 'text': 'or even if i get like two, minus one, minus one, i can sort them And after sorting they will always be equivalent to this one which I have taken.', 'start': 424.243, 'duration': 9.358}, {'end': 437.062, 'text': "So what I'll do is I'll sort this particular triplet.", 'start': 434.121, 'duration': 2.941}, {'end': 443.004, 'text': 'And I know if I have to store unique, the data structure that we will use is set.', 'start': 437.482, 'duration': 5.522}, {'end': 444.964, 'text': 'I put that thing into the set.', 'start': 443.384, 'duration': 1.58}, {'end': 448.485, 'text': "And anytime a triplet comes, I'll always check.", 'start': 445.464, 'duration': 3.021}, {'end': 450.946, 'text': "Are you in the set? If you are, no, I'm not.", 'start': 448.905, 'duration': 2.041}, {'end': 454.647, 'text': 'So this is how we can easily store all the unique triplets.', 'start': 451.326, 'duration': 3.321}, {'end': 455.587, 'text': "I'll show you the code now.", 'start': 454.787, 'duration': 0.8}, {'end': 459.35, 'text': "So let's quickly go into the code editor and show you the brute force code.", 'start': 456.147, 'duration': 3.203}, {'end': 464.454, 'text': 'So we know that we have to run three loops and all the triplets that give you the sum as zero.', 'start': 459.71, 'duration': 4.744}, {'end': 466.096, 'text': 'That is what you have to store.', 'start': 464.615, 'duration': 1.481}], 'summary': 'Algorithm to store unique triplets with sum 0 using sorting and set data structure.', 'duration': 41.853, 'max_score': 424.243, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk424243.jpg'}], 'start': 35.146, 'title': '3sum problem', 'summary': 'Covers the 3sum problem, finding unique triplets in an array of integers that sum up to zero, and discusses the brute force solution. it also explains the process of generating unique triplets with a sum of zero using three nested loops, sorting, and storing them in a set data structure, resulting in a list of lists as the final output.', 'chapters': [{'end': 194.349, 'start': 35.146, 'title': '3sum problem: finding triplets that sum to zero', 'summary': 'Covers the 3sum problem, which involves finding unique triplets in an array of integers that sum up to zero, and discusses the brute force solution for this problem.', 'duration': 159.203, 'highlights': ['The 3SUM problem involves finding all the unique triplets in an array of integers that sum up to give a value of zero, with the constraint that the same element cannot be taken more than once.', 'The critical point of the 3SUM problem is the requirement to return all the unique triplets that sum up to zero, without any repetition, and in any order.', 'The brute force solution for the 3SUM problem involves trying out all the triplets in the array to find the ones that sum up to zero, and returning the unique solutions.']}, {'end': 566.43, 'start': 194.909, 'title': 'Generating unique triplets', 'summary': 'Explains the process of generating unique triplets with a sum of zero using three nested loops, sorting to avoid duplicates, and storing them in a set data structure to ensure uniqueness, resulting in a list of lists as the final output.', 'duration': 371.521, 'highlights': ['The process involves using three nested loops to try out all possible triplets, resulting in a total of n*(n-1)*(n-2) iterations.', 'Sorting the triplets in ascending order ensures that any duplicate triplets can be easily identified and stored uniquely using a set data structure.', 'The set data structure is used to store the unique triplets, ensuring that there are no duplicate entries, and the final output is a list of lists containing the unique triplets.']}], 'duration': 531.284, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk35146.jpg', 'highlights': ['The brute force solution for the 3SUM problem involves trying out all the triplets in the array to find the ones that sum up to zero, and returning the unique solutions.', 'The process involves using three nested loops to try out all possible triplets, resulting in a total of n*(n-1)*(n-2) iterations.', 'Sorting the triplets in ascending order ensures that any duplicate triplets can be easily identified and stored uniquely using a set data structure.', 'The set data structure is used to store the unique triplets, ensuring that there are no duplicate entries, and the final output is a list of lists containing the unique triplets.', 'The 3SUM problem involves finding all the unique triplets in an array of integers that sum up to give a value of zero, with the constraint that the same element cannot be taken more than once.']}, {'end': 1210.353, 'segs': [{'end': 608.642, 'src': 'embed', 'start': 584.527, 'weight': 2, 'content': [{'end': 591.896, 'text': 'Will I consider this sorting? We should not because it is hardly three elements and the time will be as good as constant.', 'start': 584.527, 'duration': 7.369}, {'end': 597.458, 'text': 'So log, if the set is taking logarithmic, you can use unordered set as well.', 'start': 592.276, 'duration': 5.182}, {'end': 599.138, 'text': 'What about the space complexity?', 'start': 597.858, 'duration': 1.28}, {'end': 605.581, 'text': "We are using a set in order to store all the triplets and we're using an answer array to store all the triplets right?", 'start': 599.839, 'duration': 5.742}, {'end': 608.642, 'text': "It's like two into B go off number of triplets.", 'start': 606.021, 'duration': 2.621}], 'summary': 'Sorting is not recommended for three elements, use unordered set for logarithmic time, and consider space complexity.', 'duration': 24.115, 'max_score': 584.527, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk584527.jpg'}, {'end': 651.008, 'src': 'heatmap', 'start': 576.036, 'weight': 0, 'content': [{'end': 584.026, 'text': "a logarithmic of number of unique triplets because we're using a set data structure in order to store all the unique ones.", 'start': 576.036, 'duration': 7.99}, {'end': 591.896, 'text': 'Will I consider this sorting? We should not because it is hardly three elements and the time will be as good as constant.', 'start': 584.527, 'duration': 7.369}, {'end': 597.458, 'text': 'So log, if the set is taking logarithmic, you can use unordered set as well.', 'start': 592.276, 'duration': 5.182}, {'end': 599.138, 'text': 'What about the space complexity?', 'start': 597.858, 'duration': 1.28}, {'end': 605.581, 'text': "We are using a set in order to store all the triplets and we're using an answer array to store all the triplets right?", 'start': 599.839, 'duration': 5.742}, {'end': 608.642, 'text': "It's like two into B go off number of triplets.", 'start': 606.021, 'duration': 2.621}, {'end': 612.303, 'text': 'Again, number of triplets is something which will vary on inputs.', 'start': 609.002, 'duration': 3.301}, {'end': 614.204, 'text': 'And this is what you have to tell to the interviewer.', 'start': 612.583, 'duration': 1.621}, {'end': 614.584, 'text': 'Got it?', 'start': 614.324, 'duration': 0.26}, {'end': 615.805, 'text': 'So with the brute force,', 'start': 615.024, 'duration': 0.781}, {'end': 622.269, 'text': 'we are using something like an N cube and we are also using an extra space of the set data structure for which the interviewer will not be happy.', 'start': 615.805, 'duration': 6.464}, {'end': 625.671, 'text': 'This is where we will try to optimize the brute to a better solution.', 'start': 622.669, 'duration': 3.002}, {'end': 628.212, 'text': 'So N cube has to be optimized.', 'start': 626.011, 'duration': 2.201}, {'end': 632.895, 'text': 'And what can we optimize N cube? We can probably optimize that to N square.', 'start': 628.753, 'duration': 4.142}, {'end': 638.079, 'text': 'And if you remember, we were having three loops for I, J and K.', 'start': 633.656, 'duration': 4.423}, {'end': 640.3, 'text': 'That is why the complexity was N cube.', 'start': 638.079, 'duration': 2.221}, {'end': 644.563, 'text': 'So if I have to do it somewhere near about N square, somewhere near about n square.', 'start': 640.82, 'duration': 3.743}, {'end': 651.008, 'text': 'How can we do that? We have to get rid of this third loop and that is where the thought process starts for the better solution.', 'start': 644.823, 'duration': 6.185}], 'summary': 'Using set data structure, aim to optimize from n^3 to n^2 complexity.', 'duration': 74.972, 'max_score': 576.036, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk576036.jpg'}, {'end': 743.23, 'src': 'embed', 'start': 719.335, 'weight': 1, 'content': [{'end': 726.201, 'text': 'so i say, yes, we can form a triplet, but in order to look for this plus 2 in the array, What technique??', 'start': 719.335, 'duration': 6.866}, {'end': 730.444, 'text': 'Yes, the better solution will be using the technique hashing.', 'start': 726.522, 'duration': 3.922}, {'end': 736.867, 'text': 'So the best way to look up for this plus two in this array without traversing is definitely hashing,', 'start': 731.024, 'duration': 5.843}, {'end': 740.328, 'text': 'because it does it in logarithmic or constant time.', 'start': 736.867, 'duration': 3.461}, {'end': 743.23, 'text': 'So this is why the better solution will be using hashing.', 'start': 740.609, 'duration': 2.621}], 'summary': 'Using hashing technique for efficient lookup in array for plus 2.', 'duration': 23.895, 'max_score': 719.335, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk719335.jpg'}, {'end': 902.005, 'src': 'heatmap', 'start': 850.076, 'weight': 0.928, 'content': [{'end': 856.134, 'text': "If you remember the formula, For the third element, it's array of i plus array of j.", 'start': 850.076, 'duration': 6.058}, {'end': 858.156, 'text': 'This is what the third element was, if you remember.', 'start': 856.134, 'duration': 2.022}, {'end': 859.938, 'text': "So, I'm looking for the third element.", 'start': 858.817, 'duration': 1.121}, {'end': 865.043, 'text': 'So, what is array of i? Minus 1 plus 0 minus.', 'start': 860.238, 'duration': 4.805}, {'end': 867.966, 'text': 'So, this is minus 1 and this is plus 1.', 'start': 865.484, 'duration': 2.482}, {'end': 870.409, 'text': 'Is plus 1 in the set? No.', 'start': 867.966, 'duration': 2.443}, {'end': 873.372, 'text': "So, what you'll do is, you'll go ahead and you'll move this j.", 'start': 870.789, 'duration': 2.583}, {'end': 879.601, 'text': 'But before moving, just take this 0 and put it into your hash map.', 'start': 875.08, 'duration': 4.521}, {'end': 884.822, 'text': "Done This time when you try, you'll get minus 1 plus 1 and a minus of it.", 'start': 879.841, 'duration': 4.981}, {'end': 886.102, 'text': 'So minus 1 plus 1 is 0.', 'start': 884.882, 'duration': 1.22}, {'end': 887.762, 'text': "So we'll get 0.", 'start': 886.102, 'duration': 1.66}, {'end': 889.763, 'text': 'And the hash set, there is a 0.', 'start': 887.762, 'duration': 2.001}, {'end': 895.644, 'text': 'So apparently I got a triplet as minus 1, 1 and 0 from the hash set.', 'start': 889.763, 'duration': 5.881}, {'end': 898.144, 'text': 'I can sort it and then I can store it again.', 'start': 896.044, 'duration': 2.1}, {'end': 902.005, 'text': 'Something like minus 1, 0 and 1.', 'start': 898.524, 'duration': 3.481}], 'summary': 'The algorithm found a triplet of numbers: -1, 1, and 0.', 'duration': 51.929, 'max_score': 850.076, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk850076.jpg'}], 'start': 566.45, 'title': 'Optimizing algorithms and finding unique triplets', 'summary': 'Discusses optimizing a brute force algorithm from o(n^3) to o(n^2) using hashing, emphasizing space complexity, and implementing efficient lookup. it also explains an algorithm to find unique triplets in an array using a hash set, running two loops, and sorting the result to return a list of unique triplets.', 'chapters': [{'end': 760.64, 'start': 566.45, 'title': 'Optimizing brute force algorithm', 'summary': 'Discusses the inefficiency of a brute force algorithm with a time complexity of o(n^3) and the use of hashing to optimize it to o(n^2), while also highlighting the importance of space complexity and the implementation of hashing for efficient lookups.', 'duration': 194.19, 'highlights': ['The time complexity of the brute force algorithm is O(n^3), due to the usage of three nested loops. The inefficient time complexity of O(n^3) is attributed to the use of three nested loops.', 'The importance of considering space complexity and the impact of using a set data structure for storing all unique triplets is emphasized. The space complexity consideration involves the use of a set data structure to store unique triplets.', 'Optimizing the brute force algorithm to O(n^2) is highlighted as a key improvement, achieved by eliminating the third nested loop and implementing hashing. The optimization to O(n^2) is achieved by eliminating the third nested loop and implementing hashing.', 'The significance of using hashing for efficient lookups in the array, with a time complexity of logarithmic or constant, is emphasized. The use of hashing for efficient lookups, with a time complexity of logarithmic or constant, is highlighted.']}, {'end': 1210.353, 'start': 760.78, 'title': 'Finding triplets algorithm', 'summary': 'Explains an algorithm to find unique triplets in an array, using a hash set to avoid duplication, running two loops for i and j, and sorting the result to return a list of unique triplets.', 'duration': 449.573, 'highlights': ['The chapter explains an algorithm to find unique triplets in an array, using a hash set to avoid duplication. ', 'Running two loops for i and j to iterate through the elements of the array. ', 'Sorting the result to return a list of unique triplets. ']}], 'duration': 643.903, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk566450.jpg', 'highlights': ['Optimizing the brute force algorithm to O(n^2) is highlighted as a key improvement, achieved by eliminating the third nested loop and implementing hashing.', 'The significance of using hashing for efficient lookups in the array, with a time complexity of logarithmic or constant, is emphasized.', 'The importance of considering space complexity and the impact of using a set data structure for storing all unique triplets is emphasized.', 'The chapter explains an algorithm to find unique triplets in an array, using a hash set to avoid duplication.']}, {'end': 1462.27, 'segs': [{'end': 1283.154, 'src': 'embed', 'start': 1234.447, 'weight': 0, 'content': [{'end': 1238.509, 'text': 'Can I see this? So the time complexity will be n-squared near about.', 'start': 1234.447, 'duration': 4.062}, {'end': 1242.01, 'text': 'and logarithmic of size of the set.', 'start': 1239.409, 'duration': 2.601}, {'end': 1249.774, 'text': 'Initially, the size of the set can be just 1, and then it becomes 2, then it has 3 elements, then it has 4.', 'start': 1242.571, 'duration': 7.203}, {'end': 1252.336, 'text': "So this log, I'll write it as m.", 'start': 1249.774, 'duration': 2.562}, {'end': 1253.856, 'text': "It's not exactly n.", 'start': 1252.336, 'duration': 1.52}, {'end': 1255.217, 'text': 'It is m, which is variable.', 'start': 1253.856, 'duration': 1.361}, {'end': 1257.438, 'text': 'For the first time, it just has 0.', 'start': 1255.737, 'duration': 1.701}, {'end': 1258.419, 'text': 'Then it will have 1.', 'start': 1257.438, 'duration': 0.981}, {'end': 1260.66, 'text': 'So the size of the set is varying.', 'start': 1258.419, 'duration': 2.241}, {'end': 1266.663, 'text': "Again, this logarithmic can be treated as constant if you're using something like an unordered set.", 'start': 1260.98, 'duration': 5.683}, {'end': 1269.185, 'text': 'so i can say near about n square.', 'start': 1267.043, 'duration': 2.142}, {'end': 1270.666, 'text': 'yes, what about the space complexity?', 'start': 1269.185, 'duration': 1.481}, {'end': 1275.089, 'text': "i'm using this particular hash set every time.", 'start': 1270.666, 'duration': 4.423}, {'end': 1281.173, 'text': 'for the first time it might end up showing one, two, three, four, four or five elements.', 'start': 1275.089, 'duration': 6.084}, {'end': 1283.154, 'text': 'next time it will store one, two, three, four.', 'start': 1281.173, 'duration': 1.981}], 'summary': 'Time complexity: n-squared, space complexity: variable', 'duration': 48.707, 'max_score': 1234.447, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1234447.jpg'}, {'end': 1365.787, 'src': 'heatmap', 'start': 1311.215, 'weight': 0.744, 'content': [{'end': 1316.757, 'text': "why? because we're also using a list of list which returns all the answer.", 'start': 1311.215, 'duration': 5.542}, {'end': 1325.001, 'text': "so, twice off this because we're using still our external data structure in order to get all the unique triplets.", 'start': 1316.757, 'duration': 8.244}, {'end': 1331.023, 'text': 'this external data structure is what the interviewer might not like, might be okay with the time complexity,', 'start': 1325.001, 'duration': 6.022}, {'end': 1334.744, 'text': 'because n square is somewhere what he might have expected.', 'start': 1331.023, 'duration': 3.721}, {'end': 1336.185, 'text': "so you've got it nearly.", 'start': 1334.744, 'duration': 1.441}, {'end': 1343.71, 'text': 'but if i still ask you to get rid of this external data structure and this is where the optimal solution comes in so in both the brute and better solution,', 'start': 1336.185, 'duration': 7.525}, {'end': 1349.295, 'text': 'we were using something like a set data structure which was helping us to get all the unique triplets,', 'start': 1343.71, 'duration': 5.585}, {'end': 1352.097, 'text': 'because it was filtering out all the duplicates.', 'start': 1349.295, 'duration': 2.802}, {'end': 1354.199, 'text': 'and how are we doing it?', 'start': 1352.097, 'duration': 2.102}, {'end': 1362.965, 'text': 'basically, if the triplet generated over something like zero, minus one one, we were trying to sort it And that gave us minus one, zero and one.', 'start': 1354.199, 'duration': 8.766}, {'end': 1365.787, 'text': 'And then we are putting that into a set data structure.', 'start': 1363.405, 'duration': 2.382}], 'summary': 'Using a set data structure to get unique triplets, sorting helped filter out duplicates.', 'duration': 54.572, 'max_score': 1311.215, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1311215.jpg'}, {'end': 1434.54, 'src': 'embed', 'start': 1406.223, 'weight': 2, 'content': [{'end': 1410.025, 'text': "Why do we require a sorted array? As I tell you about the algorithm, you'll understand it.", 'start': 1406.223, 'duration': 3.802}, {'end': 1413.407, 'text': 'So the algorithm will be a two pointer approach.', 'start': 1410.485, 'duration': 2.922}, {'end': 1416.149, 'text': 'A very, very straightforward two-pointer approach.', 'start': 1414.167, 'duration': 1.982}, {'end': 1425.259, 'text': "So what am I looking for? I'm looking for array of i plus array of j plus array of k.", 'start': 1416.61, 'duration': 8.649}, {'end': 1426.5, 'text': "Okay, this is what I'm looking for.", 'start': 1425.259, 'duration': 1.241}, {'end': 1429.263, 'text': "This time what I'll do is I'll say, hey, listen.", 'start': 1427.221, 'duration': 2.042}, {'end': 1432.178, 'text': "I'll probably fix the I.", 'start': 1430.356, 'duration': 1.822}, {'end': 1434.54, 'text': 'So what I do is I fix the I over here.', 'start': 1432.178, 'duration': 2.362}], 'summary': 'Discussion on the use of a sorted array and a two-pointer approach in finding the sum of three elements in an array.', 'duration': 28.317, 'max_score': 1406.223, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1406223.jpg'}], 'start': 1210.713, 'title': 'Time and space complexity analysis and algorithm for finding unique triplets', 'summary': 'Discusses the time complexity of the algorithm, approximately n-squared, and the space complexity, o(n). it also highlights the use of a set data structure and external data structure for calculating unique triplets, along with an algorithm for finding unique triplets in a sorted array using a two-pointer approach.', 'chapters': [{'end': 1343.71, 'start': 1210.713, 'title': 'Time and space complexity analysis', 'summary': 'Discusses the time complexity of the algorithm, which is approximately n-squared, and the space complexity, which is o(n), while also highlighting the use of a set data structure and external data structure for calculating unique triplets.', 'duration': 132.997, 'highlights': ['The time complexity of the algorithm is approximately n-squared due to multiple loops and the use of a set data structure to find every time, with the size of the set varying logarithmically.', 'The space complexity is O(n) as the algorithm repeatedly uses the same hash set and an external data structure to store all the unique triplets, resulting in a space complexity of O(n).', 'The use of an external data structure for storing unique triplets may not be optimal, and the interviewer might expect a solution without this external data structure.']}, {'end': 1462.27, 'start': 1343.71, 'title': 'Algorithm for finding unique triplets', 'summary': 'Discusses an algorithm for finding unique triplets in a sorted array using a two-pointer approach, aiming to eliminate the need for an external data structure to filter out duplicates.', 'duration': 118.56, 'highlights': ['The algorithm involves a two-pointer approach to find the sum of elements at indices i, j, and k in a sorted array, aiming to eliminate the need for an external data structure to filter out duplicates.', 'Sorting the array is the initial step in the algorithm, followed by fixing the index i and using two pointers, j and k, to find unique triplets in a sorted order.', 'The use of a set data structure for filtering out duplicates in the previous approach is being replaced by a more efficient algorithm that eliminates the need for an external data structure.']}], 'duration': 251.557, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1210713.jpg', 'highlights': ['The time complexity of the algorithm is approximately n-squared due to multiple loops and the use of a set data structure to find every time, with the size of the set varying logarithmically.', 'The space complexity is O(n) as the algorithm repeatedly uses the same hash set and an external data structure to store all the unique triplets, resulting in a space complexity of O(n).', 'The algorithm involves a two-pointer approach to find the sum of elements at indices i, j, and k in a sorted array, aiming to eliminate the need for an external data structure to filter out duplicates.', 'Sorting the array is the initial step in the algorithm, followed by fixing the index i and using two pointers, j and k, to find unique triplets in a sorted order.']}, {'end': 1923.609, 'segs': [{'end': 1586.218, 'src': 'embed', 'start': 1563.626, 'weight': 2, 'content': [{'end': 1572.07, 'text': 'so what i did was i just kept on moving and i tried to reach near zero and apparently at this moment i have one.', 'start': 1563.626, 'duration': 8.444}, {'end': 1577.472, 'text': 'sorry, i have one i, i have one j and i have one k, and that is one of my triplets.', 'start': 1572.07, 'duration': 5.402}, {'end': 1578.753, 'text': "i'll probably store it.", 'start': 1577.472, 'duration': 1.281}, {'end': 1580.493, 'text': 'i know the triplet is very simple.', 'start': 1578.753, 'duration': 1.74}, {'end': 1581.854, 'text': "it's minus two, zero two.", 'start': 1580.493, 'duration': 1.361}, {'end': 1586.218, 'text': "It's already in the sorted order.", 'start': 1584.938, 'duration': 1.28}], 'summary': 'Reached a triplet near zero, with one i, one j, and one k, in sorted order.', 'duration': 22.592, 'max_score': 1563.626, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1563626.jpg'}, {'end': 1613.707, 'src': 'heatmap', 'start': 1586.258, 'weight': 0.814, 'content': [{'end': 1590.639, 'text': "If you carefully see it's already in the sorted order because you took a sorted array.", 'start': 1586.258, 'duration': 4.381}, {'end': 1595.34, 'text': 'You had I at the left, you had J in the middle, you had K at the right.', 'start': 1591.019, 'duration': 4.321}, {'end': 1597.421, 'text': 'So it is already in the sorted order.', 'start': 1595.641, 'duration': 1.78}, {'end': 1600.582, 'text': 'Got it? Next you are at zero.', 'start': 1597.701, 'duration': 2.881}, {'end': 1604.003, 'text': 'What can you do? You know, this cannot be taken.', 'start': 1601.022, 'duration': 2.981}, {'end': 1606.343, 'text': 'This cannot be taken any further.', 'start': 1604.963, 'duration': 1.38}, {'end': 1609.764, 'text': 'So what you will do is you will simply move both of them.', 'start': 1606.943, 'duration': 2.821}, {'end': 1613.707, 'text': 'And the moment you move both of them, it will come over here.', 'start': 1610.524, 'duration': 3.183}], 'summary': 'Given a sorted array, no further action is needed to maintain order.', 'duration': 27.449, 'max_score': 1586.258, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1586258.jpg'}, {'end': 1903.736, 'src': 'embed', 'start': 1847.594, 'weight': 0, 'content': [{'end': 1848.494, 'text': "Because it's greater than zero.", 'start': 1847.594, 'duration': 0.9}, {'end': 1852.775, 'text': "Reduce So you'll move this because if you move left, the values will reduce.", 'start': 1848.514, 'duration': 4.261}, {'end': 1855.596, 'text': 'Two pointers usually work like this.', 'start': 1854.055, 'duration': 1.541}, {'end': 1860.357, 'text': 'Still Still.', 'start': 1857.836, 'duration': 2.521}, {'end': 1865.903, 'text': 'Stay greater than zero and you reach here.', 'start': 1862.481, 'duration': 3.422}, {'end': 1868.104, 'text': 'So you get another triplet.', 'start': 1866.563, 'duration': 1.541}, {'end': 1869.185, 'text': 'Very, very careful.', 'start': 1868.184, 'duration': 1.001}, {'end': 1871.206, 'text': 'Sorry, very, very important.', 'start': 1869.205, 'duration': 2.001}, {'end': 1875.289, 'text': 'You get another triplet.', 'start': 1874.228, 'duration': 1.061}, {'end': 1877.65, 'text': 'Will you consider this? You will.', 'start': 1875.929, 'duration': 1.721}, {'end': 1882.077, 'text': 'because their three zeros are from different.', 'start': 1878.973, 'duration': 3.104}, {'end': 1883.679, 'text': 'So you will take another triplet.', 'start': 1882.217, 'duration': 1.462}, {'end': 1887.723, 'text': 'Perfect Next, you know, this zero is there.', 'start': 1884.6, 'duration': 3.123}, {'end': 1890.286, 'text': "So you'll move K after this K moves, J moves.", 'start': 1887.763, 'duration': 2.523}, {'end': 1891.267, 'text': "So it's over.", 'start': 1890.667, 'duration': 0.6}, {'end': 1896.193, 'text': "So in this way, you can keep on doing and eventually you'll get all your triplets.", 'start': 1891.588, 'duration': 4.605}, {'end': 1902.375, 'text': 'But when I moves, when it moves here, same as previous, same as previous.', 'start': 1897.332, 'duration': 5.043}, {'end': 1903.736, 'text': 'So I will again start from here.', 'start': 1902.395, 'duration': 1.341}], 'summary': 'Using two pointers to identify triplets greater than zero, moving through the values to find all triplets.', 'duration': 56.142, 'max_score': 1847.594, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1847594.jpg'}], 'start': 1462.75, 'title': 'Finding triplets', 'summary': 'Discusses the process of finding triplets in a sorted array and a sequence by using pointers and logic, ultimately resulting in just three triplets for a given sequence.', 'chapters': [{'end': 1657.314, 'start': 1462.75, 'title': 'Finding triplets in sorted array', 'summary': 'Discusses the process of finding triplets in a sorted array, explaining how to manipulate the elements to reach zero and store the unique triplets.', 'duration': 194.564, 'highlights': ['The speaker demonstrates the process of manipulating the elements in a sorted array to reach zero and store unique triplets.', 'The approach involves adjusting the values of the elements to reach zero, ensuring the triplets are stored in sorted order.', 'The speaker emphasizes the need to avoid duplicates by moving the elements appropriately to store only unique triplets.']}, {'end': 1923.609, 'start': 1657.754, 'title': 'Finding triplets', 'summary': 'Explains the process of finding triplets in a sequence by using pointers and logic, ultimately resulting in just three triplets for a given sequence.', 'duration': 265.855, 'highlights': ['The chapter explains the process of finding triplets in a sequence using pointers and logic, ultimately resulting in just three triplets for a given sequence.', 'The speaker emphasizes the importance of not taking the same elements again to avoid generating the same triplets.', 'The logic and process of moving pointers to identify and form triplets in the sequence is detailed, resulting in the identification of triplets and the eventual completion of the process.']}], 'duration': 460.859, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1462750.jpg', 'highlights': ['The logic and process of moving pointers to identify and form triplets in the sequence is detailed, resulting in the identification of triplets and the eventual completion of the process.', 'The approach involves adjusting the values of the elements to reach zero, ensuring the triplets are stored in sorted order.', 'The speaker demonstrates the process of manipulating the elements in a sorted array to reach zero and store unique triplets.']}, {'end': 2296.534, 'segs': [{'end': 1962.403, 'src': 'heatmap', 'start': 1933.113, 'weight': 0.829, 'content': [{'end': 1938.675, 'text': 'if you remember, whenever i was imagine standing here, it is equivalent to the previous.', 'start': 1933.113, 'duration': 5.562}, {'end': 1940.115, 'text': "so you'll not do.", 'start': 1938.675, 'duration': 1.44}, {'end': 1941.456, 'text': 'this was also equal to the previous.', 'start': 1940.115, 'duration': 1.341}, {'end': 1943.677, 'text': "you'll not only for the first element.", 'start': 1941.456, 'duration': 2.221}, {'end': 1945.077, 'text': 'there is no previous.', 'start': 1943.677, 'duration': 1.4}, {'end': 1958.56, 'text': "so i'm like one thing for sure if it is not the first element, And that num of i is not equal to num of or you can say equal to num of i, minus one.", 'start': 1945.077, 'duration': 13.483}, {'end': 1960.081, 'text': "That means it's equivalent.", 'start': 1958.68, 'duration': 1.401}, {'end': 1962.403, 'text': "So you'll say, please go ahead and continue.", 'start': 1960.542, 'duration': 1.861}], 'summary': 'Discussing the equivalence between elements and the condition for continuation.', 'duration': 29.29, 'max_score': 1933.113, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1933113.jpg'}, {'end': 2046.08, 'src': 'embed', 'start': 2023.886, 'weight': 0, 'content': [{'end': 2031.811, 'text': 'If sum is less than 0 is 1, Else if sum is greater than 0 is other and the else is less.', 'start': 2023.886, 'duration': 7.925}, {'end': 2035.974, 'text': 'So I know if it is less than 0, I need to increase.', 'start': 2032.452, 'duration': 3.522}, {'end': 2038.696, 'text': "In order to increase, it's a sorted element.", 'start': 2036.494, 'duration': 2.202}, {'end': 2039.776, 'text': "It's a sorted array.", 'start': 2038.956, 'duration': 0.82}, {'end': 2042.638, 'text': 'So please make sure you sort the entire array.', 'start': 2040.156, 'duration': 2.482}, {'end': 2044.179, 'text': 'Otherwise, it will be an issue.', 'start': 2043.118, 'duration': 1.061}, {'end': 2046.08, 'text': 'Please go ahead and sort the entire array.', 'start': 2044.699, 'duration': 1.381}], 'summary': 'Sort entire array to address issue with increasing when sum is less than 0.', 'duration': 22.194, 'max_score': 2023.886, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk2023886.jpg'}, {'end': 2287.887, 'src': 'heatmap', 'start': 2196.904, 'weight': 3, 'content': [{'end': 2199.465, 'text': 'And now we can go ahead and run this and see if it is running fine.', 'start': 2196.904, 'duration': 2.561}, {'end': 2204.166, 'text': 'So what about the time complexity? n log in to sort it.', 'start': 2200.885, 'duration': 3.281}, {'end': 2208.287, 'text': 'So I can say an n logarithmic of n to sort the array.', 'start': 2204.786, 'duration': 3.501}, {'end': 2211.007, 'text': "And then you're running an external n loop.", 'start': 2208.887, 'duration': 2.12}, {'end': 2214.008, 'text': "So that's a big O of n.", 'start': 2211.708, 'duration': 2.3}, {'end': 2221.973, 'text': 'And then the while, how many times will the while loop run at first? n minus one time.', 'start': 2214.008, 'duration': 7.965}, {'end': 2225.823, 'text': 'Next n minus two time.', 'start': 2222.354, 'duration': 3.469}, {'end': 2229.173, 'text': 'Next n minus three.', 'start': 2226.265, 'duration': 2.908}, {'end': 2233.214, 'text': "So it's kind of running every time for n, near about n.", 'start': 2229.493, 'duration': 3.721}, {'end': 2234.734, 'text': 'So n into n, near about.', 'start': 2233.214, 'duration': 1.52}, {'end': 2240.075, 'text': 'So n log n plus near about n square will be my time complexity.', 'start': 2235.354, 'duration': 4.721}, {'end': 2245.476, 'text': "What about the space complexity? We're not using anything to solve the array.", 'start': 2240.555, 'duration': 4.921}, {'end': 2247.296, 'text': "We're just using a big of three space.", 'start': 2245.616, 'duration': 1.68}, {'end': 2252.958, 'text': 'But yes, we are using a answer list in order to return the answer.', 'start': 2247.657, 'duration': 5.301}, {'end': 2255.158, 'text': 'So that is for returning, not in our algorithm.', 'start': 2253.118, 'duration': 2.04}, {'end': 2262.059, 'text': "So because of number of unique triplets, we will not be counting this temp because it's just three elements.", 'start': 2255.578, 'duration': 6.481}, {'end': 2267.02, 'text': 'This is the time complexity and space complexity for the most optimal solution.', 'start': 2262.519, 'duration': 4.501}, {'end': 2270.761, 'text': "Now I'll go back to the sheet and I'll mark this as done and completed.", 'start': 2267.42, 'duration': 3.341}, {'end': 2275.442, 'text': "I hope I've understood all the three approaches, all the three quotes, just in case you did.", 'start': 2271.081, 'duration': 4.361}, {'end': 2280.103, 'text': "Please, please do give us a like because it won't cost you anything, but that will do me a world of good.", 'start': 2275.802, 'duration': 4.301}, {'end': 2284.504, 'text': "And if you haven't followed me on Instagram, you're missing out on a lot of informative content.", 'start': 2280.483, 'duration': 4.021}, {'end': 2287.887, 'text': 'so striveoutdisco79 is what i go by on instagram.', 'start': 2284.844, 'duration': 3.043}], 'summary': 'Time complexity: o(n log n + n^2), space complexity: o(1)', 'duration': 58.254, 'max_score': 2196.904, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk2196904.jpg'}], 'start': 1924.409, 'title': 'Algorithmic logic and optimal solution', 'summary': 'Discusses the logic behind array sorting algorithms, emphasizing equivalence checking and handling three conditions for element sum, stressing the need for array sorting. it also analyzes optimal solutions for programming problems, highlighting time complexity as n log n plus near n square, and space complexity as big o of three space plus an answer list.', 'chapters': [{'end': 2046.08, 'start': 1924.409, 'title': 'Algorithmic logic and array sorting', 'summary': 'Discusses the logic behind an algorithm for array sorting, emphasizing the importance of checking for equivalence and handling three conditions to determine the sum of elements, while stressing the need to sort the entire array to avoid issues.', 'duration': 121.671, 'highlights': ['The chapter emphasizes the significance of checking for equivalence and handling three conditions to determine the sum of elements, highlighting the importance of sorting the entire array to avoid issues.', 'The algorithm involves checking for equivalence and handling three conditions to determine the sum of elements, stressing the need to sort the entire array to avoid issues.', 'The algorithmic logic involves checking for equivalence, handling three conditions to determine the sum of elements, and stressing the need to sort the entire array to avoid issues.']}, {'end': 2296.534, 'start': 2047.401, 'title': 'Optimal solution time and space complexity', 'summary': 'Discusses an optimal solution for a programming problem, analyzing time complexity as n log n plus near about n square, and space complexity as big o of three space plus an answer list.', 'duration': 249.133, 'highlights': ['The time complexity of the optimal solution is n log n plus near about n square. The time complexity includes n log n to sort the array and running an external n loop, resulting in a time complexity of n log n plus near about n square.', 'The space complexity of the optimal solution is big O of three space plus an answer list. The space complexity considers the usage of a big of three space and an answer list for returning the answer, contributing to the space complexity of the solution.', 'The algorithm does not use anything additional to solve the array, resulting in a space complexity of big O of three space. The algorithm only uses a big of three space, with the answer list being used for returning the answer and not contributing to the space complexity of the algorithm.']}], 'duration': 372.125, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/DhFh8Kw7ymk/pics/DhFh8Kw7ymk1924409.jpg', 'highlights': ['The chapter emphasizes the significance of checking for equivalence and handling three conditions to determine the sum of elements, highlighting the importance of sorting the entire array to avoid issues.', 'The algorithm involves checking for equivalence and handling three conditions to determine the sum of elements, stressing the need to sort the entire array to avoid issues.', 'The algorithmic logic involves checking for equivalence, handling three conditions to determine the sum of elements, and stressing the need to sort the entire array to avoid issues.', 'The time complexity of the optimal solution is n log n plus near about n square. The time complexity includes n log n to sort the array and running an external n loop, resulting in a time complexity of n log n plus near about n square.', 'The space complexity of the optimal solution is big O of three space plus an answer list. The space complexity considers the usage of a big of three space and an answer list for returning the answer, contributing to the space complexity of the solution.', 'The algorithm does not use anything additional to solve the array, resulting in a space complexity of big O of three space. The algorithm only uses a big of three space, with the answer list being used for returning the answer and not contributing to the space complexity of the algorithm.']}], 'highlights': ["By the end of the course, you'd have solved more than 400 plus problems.", 'This course has 455 modules.', "Once you complete this entire course, you'll be able to clear any of the DS Algo routes in any of the companies in any part of the world.", 'None of the paid courses will be teaching you DS Algo in such depth.', 'The brute force solution for the 3SUM problem involves trying out all the triplets in the array to find the ones that sum up to zero, and returning the unique solutions.', 'The process involves using three nested loops to try out all possible triplets, resulting in a total of n*(n-1)*(n-2) iterations.', 'Sorting the triplets in ascending order ensures that any duplicate triplets can be easily identified and stored uniquely using a set data structure.', 'The set data structure is used to store the unique triplets, ensuring that there are no duplicate entries, and the final output is a list of lists containing the unique triplets.', 'The 3SUM problem involves finding all the unique triplets in an array of integers that sum up to give a value of zero, with the constraint that the same element cannot be taken more than once.', 'Optimizing the brute force algorithm to O(n^2) is highlighted as a key improvement, achieved by eliminating the third nested loop and implementing hashing.', 'The significance of using hashing for efficient lookups in the array, with a time complexity of logarithmic or constant, is emphasized.', 'The importance of considering space complexity and the impact of using a set data structure for storing all unique triplets is emphasized.', 'The chapter explains an algorithm to find unique triplets in an array, using a hash set to avoid duplication.', 'The time complexity of the algorithm is approximately n-squared due to multiple loops and the use of a set data structure to find every time, with the size of the set varying logarithmically.', 'The space complexity is O(n) as the algorithm repeatedly uses the same hash set and an external data structure to store all the unique triplets, resulting in a space complexity of O(n).', 'The algorithm involves a two-pointer approach to find the sum of elements at indices i, j, and k in a sorted array, aiming to eliminate the need for an external data structure to filter out duplicates.', 'Sorting the array is the initial step in the algorithm, followed by fixing the index i and using two pointers, j and k, to find unique triplets in a sorted order.', 'The logic and process of moving pointers to identify and form triplets in the sequence is detailed, resulting in the identification of triplets and the eventual completion of the process.', 'The approach involves adjusting the values of the elements to reach zero, ensuring the triplets are stored in sorted order.', 'The speaker demonstrates the process of manipulating the elements in a sorted array to reach zero and store unique triplets.', 'The chapter emphasizes the significance of checking for equivalence and handling three conditions to determine the sum of elements, highlighting the importance of sorting the entire array to avoid issues.', 'The algorithm involves checking for equivalence and handling three conditions to determine the sum of elements, stressing the need to sort the entire array to avoid issues.', 'The algorithmic logic involves checking for equivalence, handling three conditions to determine the sum of elements, and stressing the need to sort the entire array to avoid issues.', 'The time complexity of the optimal solution is n log n plus near about n square. The time complexity includes n log n to sort the array and running an external n loop, resulting in a time complexity of n log n plus near about n square.', 'The space complexity of the optimal solution is big O of three space plus an answer list. The space complexity considers the usage of a big of three space and an answer list for returning the answer, contributing to the space complexity of the solution.', 'The algorithm does not use anything additional to solve the array, resulting in a space complexity of big O of three space. The algorithm only uses a big of three space, with the answer list being used for returning the answer and not contributing to the space complexity of the algorithm.']}