title

1. Algorithms and Computation

description

MIT 6.006 Introduction to Algorithms, Spring 2020
Instructor: Jason Ku
View the complete course: https://ocw.mit.edu/6-006S20
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY
The goal of this introductions to algorithms class is to teach you to solve computation problems and communication that your solutions are correct and efficient. Models of computation, data structures, and algorithms are introduced.
License: Creative Commons BY-NC-SA
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detail

{'title': '1. Algorithms and Computation', 'heatmap': [{'end': 1481.799, 'start': 1424.503, 'weight': 0.806}, {'end': 1900.039, 'start': 1864.737, 'weight': 0.879}, {'end': 2467.691, 'start': 2323.578, 'weight': 0.836}, {'end': 2552.26, 'start': 2514.068, 'weight': 0.77}, {'end': 2721.243, 'start': 2682.85, 'weight': 1}], 'summary': 'Covers teaching arrangements for the class, introduces algorithms and problem solving, and discusses algorithm efficiency, birth time algorithm, and computer models. it emphasizes effective communication, problem-solving, and the formal definition of computational problems and algorithms, providing insights into algorithm efficiency and analysis.', 'chapters': [{'end': 47.81, 'segs': [{'end': 56.814, 'src': 'embed', 'start': 26.366, 'weight': 0, 'content': [{'end': 26.586, 'text': 'JASON KUO.', 'start': 26.366, 'duration': 0.22}, {'end': 26.906, 'text': 'JASON KUO.', 'start': 26.606, 'duration': 0.3}, {'end': 27.347, 'text': 'JASON KUO.', 'start': 27.006, 'duration': 0.341}, {'end': 27.587, 'text': 'JASON KUO.', 'start': 27.367, 'duration': 0.22}, {'end': 28.167, 'text': 'JASON KUO.', 'start': 27.947, 'duration': 0.22}, {'end': 28.427, 'text': 'JASON KUO.', 'start': 28.187, 'duration': 0.24}, {'end': 28.647, 'text': 'JASON KUO.', 'start': 28.447, 'duration': 0.2}, {'end': 28.868, 'text': 'JASON KUO.', 'start': 28.667, 'duration': 0.201}, {'end': 29.068, 'text': 'JASON KUO.', 'start': 28.888, 'duration': 0.18}, {'end': 29.268, 'text': 'JASON KUO.', 'start': 29.088, 'duration': 0.18}, {'end': 29.588, 'text': 'JASON KUO.', 'start': 29.288, 'duration': 0.3}, {'end': 29.808, 'text': 'JASON KUO.', 'start': 29.608, 'duration': 0.2}, {'end': 30.909, 'text': 'JASON KUO.', 'start': 30.709, 'duration': 0.2}, {'end': 39.268, 'text': "JASON They're excellent people, and so they will be working on teaching this class with me.", 'start': 30.929, 'duration': 8.339}, {'end': 47.81, 'text': "I will be teaching the first lecture, and we'll have each of them teach one of the next two lectures, and then we'll go from there.", 'start': 39.428, 'duration': 8.382}, {'end': 52.091, 'text': 'Yeah, so this is Intro to Algorithms.', 'start': 48.49, 'duration': 3.601}, {'end': 56.814, 'text': "OK, so we're going to start talking about this course content now.", 'start': 53.331, 'duration': 3.483}], 'summary': 'Jason kuo and his team will be teaching intro to algorithms, with each member teaching one lecture.', 'duration': 30.448, 'max_score': 26.366, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s26366.jpg'}], 'start': 12.858, 'title': 'Teaching arrangements for class', 'summary': 'Discusses teaching arrangements for the class, with jason kuo leading the first lecture and others taking turns for the following two lectures.', 'chapters': [{'end': 47.81, 'start': 12.858, 'title': 'Teaching arrangements for class', 'summary': 'Discusses the teaching arrangements for the class, with jason kuo leading the first lecture and the other individuals taking turns for the following two lectures.', 'duration': 34.952, 'highlights': ['Jason Kuo will lead the first lecture for the class.', 'Other individuals will teach one of the next two lectures.', 'The teaching arrangements involve Jason Kuo and other individuals working together for the class.']}], 'duration': 34.952, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s12858.jpg', 'highlights': ['Jason Kuo will lead the first lecture for the class.', 'Other individuals will teach one of the next two lectures.', 'The teaching arrangements involve Jason Kuo and other individuals working together for the class.']}, {'end': 367.327, 'segs': [{'end': 167.387, 'src': 'embed', 'start': 130.967, 'weight': 0, 'content': [{'end': 132.709, 'text': 'Communication of these ideas.', 'start': 130.967, 'duration': 1.742}, {'end': 139.257, 'text': "And you'll find that over the course of this class, you'll be doing a lot more writing than you do in a lot of your other courses.", 'start': 132.969, 'duration': 6.288}, {'end': 145.984, 'text': "It really should maybe be a CI kind of class, because you'll be doing a lot more writing than you will be coding, for sure.", 'start': 139.337, 'duration': 6.647}, {'end': 151.01, 'text': 'So of course, solving the computational problem is important.', 'start': 146.545, 'duration': 4.465}, {'end': 167.387, 'text': "But really the thing that you're getting out of this class and other theory classes that you're not getting in other classes in this department is that we really concentrate on being able to prove that the things you're doing are correct and better than other things,", 'start': 151.491, 'duration': 15.896}], 'summary': 'Class emphasizes more writing than coding, focusing on proving correctness and superiority of work.', 'duration': 36.42, 'max_score': 130.967, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s130967.jpg'}, {'end': 345.968, 'src': 'embed', 'start': 298.002, 'weight': 3, 'content': [{'end': 303.027, 'text': "And it's kind of a graph, a bipartite graph between these inputs and outputs.", 'start': 298.002, 'duration': 5.025}, {'end': 306.691, 'text': 'And these are specifying which of these outputs are correct for these inputs.', 'start': 303.347, 'duration': 3.344}, {'end': 311.866, 'text': "All right, that's really the formal definition of what a problem is.", 'start': 307.745, 'duration': 4.121}, {'end': 323.57, 'text': "Now, generally, if I have a problem, a computational problem, I'm not going to specify the problem to you by saying OK for input 1,", 'start': 312.187, 'duration': 11.383}, {'end': 324.991, 'text': 'the correct answer is 0..', 'start': 323.57, 'duration': 1.421}, {'end': 328.832, 'text': 'And for input 2, the correct answer is 3, and so on and so forth.', 'start': 324.991, 'duration': 3.841}, {'end': 337.075, 'text': 'That would take forever, right? Usually, what we do when defining a problem is specify some kind of predicate saying that, oh, we can check.', 'start': 328.872, 'duration': 8.203}, {'end': 343.187, 'text': 'If I give you an input and an output, I can check whether that output is correct or not.', 'start': 338.826, 'duration': 4.361}, {'end': 345.968, 'text': "That's usually how we define a problem.", 'start': 343.208, 'duration': 2.76}], 'summary': 'Computational problems are defined by specifying predicates for checking input-output correctness.', 'duration': 47.966, 'max_score': 298.002, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s298002.jpg'}], 'start': 48.49, 'title': 'Intro to algorithms', 'summary': 'Emphasizes problem solving, proving correctness, arguing efficiency, and effective communication, with an emphasis on writing over coding. it also explains the formal definition of computational problems and algorithms using predicates to check for correct outputs.', 'chapters': [{'end': 174.914, 'start': 48.49, 'title': 'Intro to algorithms: problem solving and communication', 'summary': 'Emphasizes the importance of solving computational problems, proving correctness, arguing efficiency, and communicating ideas effectively, with an emphasis on writing over coding.', 'duration': 126.424, 'highlights': ['The course focuses on solving computational problems, proving correctness, arguing efficiency, and communicating ideas effectively, with an emphasis on writing over coding.', 'It emphasizes the importance of being able to prove the correctness and efficiency of solutions and communicate these ideas effectively to others, requiring more writing than coding.', 'The class concentrates on proving the correctness and superiority of solutions, as well as on effectively communicating these ideas to others, requiring more writing than coding.']}, {'end': 367.327, 'start': 175.834, 'title': 'Computational problems and algorithms', 'summary': 'Explains the formal definition of a computational problem as a binary relation between inputs and outputs, and the usual method of defining a problem using predicates to check for correct outputs.', 'duration': 191.493, 'highlights': ['The formal definition of a problem is a binary relation between inputs and outputs, specifying which outputs are correct for each input, represented as a bipartite graph. The chapter explains that a problem is a binary relation between inputs and outputs, represented as a bipartite graph, specifying which outputs are correct for each input.', 'The usual method of defining a problem is by specifying some kind of predicate that can check whether an output is correct for a given input. The chapter states that the usual method of defining a problem is by specifying a predicate to check whether an output is correct for a given input.', "The chapter also mentions that a problem's predicate is used to check if an output is correct or not, such as checking if an index contains a specific value. The chapter mentions that a problem's predicate is used to check if an output is correct or not, such as checking if an index contains a specific value."]}], 'duration': 318.837, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s48490.jpg', 'highlights': ['The course focuses on solving computational problems, proving correctness, arguing efficiency, and communicating ideas effectively, with an emphasis on writing over coding.', 'The class concentrates on proving the correctness and superiority of solutions, as well as on effectively communicating these ideas to others, requiring more writing than coding.', 'It emphasizes the importance of being able to prove the correctness and efficiency of solutions and communicate these ideas effectively to others, requiring more writing than coding.', 'The formal definition of a problem is a binary relation between inputs and outputs, specifying which outputs are correct for each input, represented as a bipartite graph.', 'The usual method of defining a problem is by specifying some kind of predicate that can check whether an output is correct for a given input.', 'The chapter explains that a problem is a binary relation between inputs and outputs, represented as a bipartite graph, specifying which outputs are correct for each input.']}, {'end': 644.649, 'segs': [{'end': 415.793, 'src': 'embed', 'start': 367.447, 'weight': 0, 'content': [{'end': 376.797, 'text': "So let's say I had the problem of among the students in this classroom do any pair of you have the same birthday??", 'start': 367.447, 'duration': 9.35}, {'end': 380.802, 'text': "All right, well, probably if there's more than 365 of you, the answer is yes.", 'start': 377.418, 'duration': 3.384}, {'end': 392.539, 'text': "Right? That by what? Pigeonhole principle, right? Two of you must have the same birthday, right? So let's generalize it a little bit.", 'start': 383.294, 'duration': 9.245}, {'end': 394.46, 'text': "Say that, oh, I don't know.", 'start': 392.639, 'duration': 1.821}, {'end': 398.802, 'text': 'I need a bigger space of birthdays for this question to be interesting.', 'start': 395.621, 'duration': 3.181}, {'end': 400.263, 'text': 'Maybe I tack on the year.', 'start': 399.082, 'duration': 1.181}, {'end': 402.044, 'text': 'Maybe I tack on the hour.', 'start': 400.623, 'duration': 1.421}, {'end': 404.805, 'text': 'that you were born.', 'start': 403.444, 'duration': 1.361}, {'end': 406.726, 'text': "And that's a bigger space of inputs.", 'start': 405.245, 'duration': 1.481}, {'end': 413.832, 'text': "And I wouldn't necessarily expect that two of you would be born in the same year, on the same day, in the same hour.", 'start': 406.766, 'duration': 7.066}, {'end': 415.793, 'text': 'That would be a little less likely.', 'start': 414.392, 'duration': 1.401}], 'summary': 'Using the pigeonhole principle, if there are more than 365 students, at least two will share the same birthday.', 'duration': 48.346, 'max_score': 367.447, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s367447.jpg'}, {'end': 560.936, 'src': 'embed', 'start': 484.796, 'weight': 2, 'content': [{'end': 486.757, 'text': 'I want an algorithm that will apply to your recitation.', 'start': 484.796, 'duration': 1.961}, {'end': 492.001, 'text': 'I want an algorithm that not only applies to this classroom, but also the machine learning class before you.', 'start': 486.777, 'duration': 5.224}, {'end': 501.787, 'text': 'I want an algorithm that can change its it can accept an arbitrarily sized input.', 'start': 492.541, 'duration': 9.246}, {'end': 504.948, 'text': 'Here, we have a class of maybe 300, 400 students.', 'start': 502.167, 'duration': 2.781}, {'end': 508.749, 'text': 'But I want my algorithm to work for a billion students.', 'start': 505.968, 'duration': 2.781}, {'end': 515.491, 'text': "Maybe I'm trying to check if there's a match of something in the Facebook database or something like that.", 'start': 509.59, 'duration': 5.901}, {'end': 535.569, 'text': 'So in general, we are looking for general problems that have arbitrarily-sized inputs.', 'start': 516.432, 'duration': 19.137}, {'end': 543.696, 'text': 'So these inputs could grow very large, but we want a fixed-size algorithm to solve those problems.', 'start': 536.17, 'duration': 7.526}, {'end': 557.874, 'text': 'So what is an algorithm then? What am I? No.', 'start': 545.337, 'duration': 12.537}, {'end': 560.256, 'text': "I really can't spell.", 'start': 559.375, 'duration': 0.881}, {'end': 560.936, 'text': 'I told you.', 'start': 560.276, 'duration': 0.66}], 'summary': 'Seeking algorithm for general problems with arbitrarily-sized inputs, aiming to scale from 300-400 students to a billion, applicable to facebook database matching.', 'duration': 76.14, 'max_score': 484.796, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s484796.jpg'}, {'end': 644.649, 'src': 'embed', 'start': 590.127, 'weight': 4, 'content': [{'end': 592.948, 'text': 'And if it generates an output, it better be one of these correct outputs.', 'start': 590.127, 'duration': 2.821}, {'end': 602.756, 'text': "Right? So if I have an algorithm that takes in this input, I really want it to output this output or else it's not a correct algorithm.", 'start': 593.834, 'duration': 8.922}, {'end': 608.137, 'text': 'Similarly, for this one, it could output any of these three outputs.', 'start': 603.196, 'duration': 4.941}, {'end': 614.178, 'text': 'But if it outputs this guy for this input, that would not be a correct algorithm.', 'start': 608.977, 'duration': 5.201}, {'end': 618.959, 'text': 'Right? And so generally, what we want is an algorithm as a function.', 'start': 614.238, 'duration': 4.721}, {'end': 620.639, 'text': 'It takes inputs to outputs.', 'start': 619.019, 'duration': 1.62}, {'end': 623.26, 'text': 'Right? An algorithm is some kind of function.', 'start': 621.42, 'duration': 1.84}, {'end': 631.162, 'text': 'that takes these inputs, maps it to a single output, and that output better be correct based on our problem.', 'start': 624.759, 'duration': 6.403}, {'end': 634.064, 'text': "So that's what our algorithm is.", 'start': 632.603, 'duration': 1.461}, {'end': 644.649, 'text': 'It solves the problem if it returns a correct output for every problem input that is in our domain.', 'start': 635.664, 'duration': 8.985}], 'summary': 'An algorithm needs to produce correct outputs for given inputs to be considered correct, ensuring it solves the problem for all inputs in its domain.', 'duration': 54.522, 'max_score': 590.127, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s590127.jpg'}], 'start': 367.447, 'title': 'Algorithms and problem solving', 'summary': 'Discusses the birthday problem, showing the decrease in likelihood of shared birth times with larger input spaces, and the necessity for deterministic algorithms. it also emphasizes the importance of fixed-size algorithms for solving problems with arbitrarily-sized inputs and the requirement for algorithms to produce correct outputs for every problem input.', 'chapters': [{'end': 508.749, 'start': 367.447, 'title': 'Birthday problem and deterministic algorithm', 'summary': 'Discusses the birthday problem, illustrating how with a larger space of inputs, the likelihood of two individuals sharing the same birth time decreases, and emphasizes the need for deterministic algorithms that can accommodate arbitrarily sized inputs.', 'duration': 141.302, 'highlights': ['The likelihood of two individuals sharing the same birth time decreases with a larger space of inputs, such as including the year and hour of birth, making it less likely for a pair to have the same birth time.', 'Emphasis on the need for deterministic algorithms that can handle inputs of varying sizes, from a classroom of 300-400 students to as large as a billion students.', 'Illustration of the birthday problem using the pigeonhole principle, demonstrating that among a large group, there is a high probability of individuals sharing the same birthday.']}, {'end': 644.649, 'start': 509.59, 'title': 'Understanding algorithms and problem solving', 'summary': 'Discusses the concept of algorithms and problem-solving, emphasizing the need for fixed-size algorithms to solve problems with arbitrarily-sized inputs, and the requirement for algorithms to produce correct outputs for every problem input.', 'duration': 135.059, 'highlights': ['Algorithms are needed to solve general problems with arbitrarily-sized inputs The chapter emphasizes the need for algorithms to solve problems with inputs of varying sizes.', 'Algorithms must produce correct outputs for every problem input The chapter stresses the requirement for algorithms to generate correct outputs for every problem input.', 'An algorithm acts as a function mapping inputs to single correct outputs It highlights that an algorithm functions as a mapping from inputs to single correct outputs.']}], 'duration': 277.202, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s367447.jpg', 'highlights': ['The likelihood of two individuals sharing the same birth time decreases with a larger space of inputs, such as including the year and hour of birth, making it less likely for a pair to have the same birth time.', 'Illustration of the birthday problem using the pigeonhole principle, demonstrating that among a large group, there is a high probability of individuals sharing the same birthday.', 'Emphasis on the need for deterministic algorithms that can handle inputs of varying sizes, from a classroom of 300-400 students to as large as a billion students.', 'Algorithms are needed to solve general problems with arbitrarily-sized inputs The chapter emphasizes the need for algorithms to solve problems with inputs of varying sizes.', 'Algorithms must produce correct outputs for every problem input The chapter stresses the requirement for algorithms to generate correct outputs for every problem input.', 'An algorithm acts as a function mapping inputs to single correct outputs It highlights that an algorithm functions as a mapping from inputs to single correct outputs.']}, {'end': 1497.309, 'segs': [{'end': 814.671, 'src': 'embed', 'start': 714.518, 'weight': 0, 'content': [{'end': 715.859, 'text': 'And then I move on to the next person.', 'start': 714.518, 'duration': 1.341}, {'end': 716.639, 'text': 'I keep doing this.', 'start': 715.899, 'duration': 0.74}, {'end': 719.861, 'text': "OK, so that's a proposed algorithm for this birthday problem.", 'start': 716.719, 'duration': 3.142}, {'end': 734.848, 'text': "For birthday problem, what's the algorithm here? Maintain a record.", 'start': 722.062, 'duration': 12.786}, {'end': 749.246, 'text': 'interview students in some order.', 'start': 740.484, 'duration': 8.762}, {'end': 756.868, 'text': 'And what does interviewing a student mean? It means two things.', 'start': 753.947, 'duration': 2.921}, {'end': 767.231, 'text': 'It means check if birthday in record.', 'start': 756.968, 'duration': 10.263}, {'end': 770.604, 'text': 'And if it is, return a pair.', 'start': 769.363, 'duration': 1.241}, {'end': 776.887, 'text': 'So return pair.', 'start': 773.385, 'duration': 3.502}, {'end': 789.433, 'text': 'Otherwise, add a new student to record.', 'start': 778.908, 'duration': 10.525}, {'end': 798.257, 'text': "And then at the very end, if I go through everybody and I haven't found a match yet, I'm going to return that there is none.", 'start': 791.654, 'duration': 6.603}, {'end': 804.645, 'text': "OK, so that's a statement of an algorithm.", 'start': 803.004, 'duration': 1.641}, {'end': 814.671, 'text': "That's kind of the level of description that we'll be looking for you in the theory questions that we ask you on your problem sets.", 'start': 804.885, 'duration': 9.786}], 'summary': 'Algorithm for the birthday problem: maintain record, interview students, return pair or none.', 'duration': 100.153, 'max_score': 714.518, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s714518.jpg'}, {'end': 900.107, 'src': 'embed', 'start': 873.717, 'weight': 3, 'content': [{'end': 878.199, 'text': "That's the mathematical definition of function that I'm using for when I'm defining an algorithm.", 'start': 873.717, 'duration': 4.482}, {'end': 884.522, 'text': 'Yeah?. So, basically, is an algorithm like a plan?', 'start': 879.16, 'duration': 5.362}, {'end': 893.586, 'text': 'Yeah, an algorithm is a procedure that somehow I can do whatever I want, but I have to take one of these inputs and I have to produce an output.', 'start': 886.083, 'duration': 7.503}, {'end': 895.067, 'text': 'And at the end, it better be correct.', 'start': 893.626, 'duration': 1.441}, {'end': 897.486, 'text': "So it's just a procedure.", 'start': 896.506, 'duration': 0.98}, {'end': 900.107, 'text': 'You can think of it as a recipe.', 'start': 897.506, 'duration': 2.601}], 'summary': 'An algorithm is a procedure to produce an output from an input.', 'duration': 26.39, 'max_score': 873.717, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s873717.jpg'}, {'end': 1016.952, 'src': 'embed', 'start': 983.205, 'weight': 5, 'content': [{'end': 985.467, 'text': 'what kind of technique do I use to prove such things?', 'start': 983.205, 'duration': 2.262}, {'end': 985.827, 'text': 'Yeah,', 'start': 985.667, 'duration': 0.16}, {'end': 996.476, 'text': 'Induction Right? And in general, what we do in this class, what we do as a computer scientist is we write a constant size piece of code.', 'start': 986.407, 'duration': 10.069}, {'end': 1003.758, 'text': 'Right? that can take on any arbitrarily large size input.', 'start': 997.757, 'duration': 6.001}, {'end': 1009.864, 'text': 'If the input can be arbitrarily large but our code is small,', 'start': 1005.5, 'duration': 4.364}, {'end': 1016.952, 'text': 'then that code needs to loop or recurse or repeat some of these lines of code in order to just read that.', 'start': 1009.864, 'duration': 7.088}], 'summary': 'Computer scientists use induction and write small code that can process large inputs by looping or recursing.', 'duration': 33.747, 'max_score': 983.205, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s983205.jpg'}, {'end': 1100.767, 'src': 'embed', 'start': 1076.13, 'weight': 4, 'content': [{'end': 1081.552, 'text': 'And then we need to have an inductive step which basically says I take a small value of this thing.', 'start': 1076.13, 'duration': 5.422}, {'end': 1087.294, 'text': 'I use the inductive hypothesis and I argue it for a larger value of my base case.', 'start': 1081.552, 'duration': 5.742}, {'end': 1090.456, 'text': "well-ordered set that I'm inducting over.", 'start': 1088.274, 'duration': 2.182}, {'end': 1099.485, 'text': "OK. so for this algorithm, if we're going to try to prove correctness, what I'm going to do is I'm going to.", 'start': 1090.917, 'duration': 8.568}, {'end': 1100.767, 'text': 'what do I want to prove for this thing??', 'start': 1099.485, 'duration': 1.282}], 'summary': 'Discussing the inductive step and proving correctness for an algorithm.', 'duration': 24.637, 'max_score': 1076.13, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s1076130.jpg'}, {'end': 1481.799, 'src': 'heatmap', 'start': 1424.503, 'weight': 0.806, 'content': [{'end': 1439.695, 'text': 'Else, if k prime plus 1 students contains match, the algorithm checks all of the possibilities.', 'start': 1424.503, 'duration': 15.192}, {'end': 1451.894, 'text': 'k prime checks k against all students essentially by brute force.', 'start': 1440.523, 'duration': 11.371}, {'end': 1453.235, 'text': "It's a case analysis.", 'start': 1451.934, 'duration': 1.301}, {'end': 1459.201, 'text': 'I check all of the possible possibilities, right? This check if birthday is in record.', 'start': 1453.275, 'duration': 5.926}, {'end': 1466.351, 'text': "I haven't told you how to do that yet, but if I'm able to do that, I'm going to check if it's in the record.", 'start': 1459.321, 'duration': 7.03}, {'end': 1469.733, 'text': "If it's in the record, then there will be a match, and I can return it.", 'start': 1466.391, 'duration': 3.342}, {'end': 1481.799, 'text': 'Otherwise, I have re-established the inductive hypothesis for the k prime plus 1 students.', 'start': 1470.153, 'duration': 11.646}], 'summary': 'Algorithm checks possibilities for k prime plus 1 students to find matches.', 'duration': 57.296, 'max_score': 1424.503, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s1424503.jpg'}], 'start': 646.69, 'title': 'Birth time algorithm', 'summary': 'Discusses an efficient algorithm for checking if two individuals share the same birth time, involving ordered interviews, record maintenance, and practical problem-solving application. it also covers algorithm definition, pure function use, inductive proofs, and recursion in coding.', 'chapters': [{'end': 814.671, 'start': 646.69, 'title': 'Algorithm for checking birth time', 'summary': 'Discusses an algorithm for checking whether any two individuals have the same birth time, involving interviewing students in an ordered manner, maintaining a record, and checking for matches, with a focus on efficiency and practical application in problem-solving.', 'duration': 167.981, 'highlights': ['The proposed algorithm involves interviewing students in a specific order, maintaining a record, and checking for matches to identify pairs, with an emphasis on efficiency and practical application.', 'Interviewing a student involves checking if their birthday is in the record and returning a pair if it is, and if not, adding the new student to the record, ultimately returning that there is no match if all students have been interviewed.', 'The level of description for the algorithm aligns with the type of questions expected in theory assessments, emphasizing understanding and application of problem-solving techniques.']}, {'end': 1497.309, 'start': 814.751, 'title': 'Algorithm definition and inductive proof', 'summary': 'Discusses the definition of an algorithm as a pure function and its use in solving problems, emphasizing the importance of inductive proofs in proving correctness and the use of recursion in writing code.', 'duration': 682.558, 'highlights': ['The mathematical definition of function is used for defining an algorithm, which is a procedure that takes inputs and produces an output, emphasizing the importance of correctness. The mathematical definition of function is used for defining an algorithm, which is a procedure that takes inputs and produces an output, emphasizing the importance of correctness.', 'The chapter emphasizes the importance of inductive proofs in proving correctness, particularly in the context of algorithms, and mentions the need for a base case and an inductive step. The chapter emphasizes the importance of inductive proofs in proving correctness, particularly in the context of algorithms, and mentions the need for a base case and an inductive step.', 'The use of recursion in writing code is discussed, highlighting the idea of writing a constant size piece of code that can handle arbitrarily large size inputs. The use of recursion in writing code is discussed, highlighting the idea of writing a constant size piece of code that can handle arbitrarily large size inputs.']}], 'duration': 850.619, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s646690.jpg', 'highlights': ['The proposed algorithm involves interviewing students in a specific order, maintaining a record, and checking for matches to identify pairs, with an emphasis on efficiency and practical application.', 'The level of description for the algorithm aligns with the type of questions expected in theory assessments, emphasizing understanding and application of problem-solving techniques.', 'Interviewing a student involves checking if their birthday is in the record and returning a pair if it is, and if not, adding the new student to the record, ultimately returning that there is no match if all students have been interviewed.', 'The mathematical definition of function is used for defining an algorithm, which is a procedure that takes inputs and produces an output, emphasizing the importance of correctness.', 'The chapter emphasizes the importance of inductive proofs in proving correctness, particularly in the context of algorithms, and mentions the need for a base case and an inductive step.', 'The use of recursion in writing code is discussed, highlighting the idea of writing a constant size piece of code that can handle arbitrarily large size inputs.']}, {'end': 2193.55, 'segs': [{'end': 1588.291, 'src': 'embed', 'start': 1497.309, 'weight': 0, 'content': [{'end': 1503.172, 'text': "but it's definitely sufficient for the levels of arguments that we will ask you to do.", 'start': 1497.309, 'duration': 5.863}, {'end': 1512.798, 'text': "The bar that we're usually trying to set is if you communicated to someone else taking this class what your algorithm was,", 'start': 1503.853, 'duration': 8.945}, {'end': 1516.58, 'text': 'they would be able to code it up and tell a stupid computer how to do that thing.', 'start': 1512.798, 'duration': 3.782}, {'end': 1528.425, 'text': "OK? Any questions on induction? You're going to be using it throughout this class.", 'start': 1517.52, 'duration': 10.905}, {'end': 1534.209, 'text': "And so if you're unfamiliar with this line of argument, then you should go review some of that.", 'start': 1528.485, 'duration': 5.724}, {'end': 1535.229, 'text': 'That would be good.', 'start': 1534.709, 'duration': 0.52}, {'end': 1544.976, 'text': "OK, so that's correctness, being able to communicate that the algorithm we stated was correct.", 'start': 1536.15, 'duration': 8.826}, {'end': 1548.198, 'text': "Now we want to argue that it's efficient.", 'start': 1545.556, 'duration': 2.642}, {'end': 1549.558, 'text': 'What does efficiency mean?', 'start': 1548.538, 'duration': 1.02}, {'end': 1571.371, 'text': 'Efficiency just means not only how fast does this algorithm run, but how fast does it compare to other possible ways of approaching this problem?', 'start': 1559.622, 'duration': 11.749}, {'end': 1581.198, 'text': 'So how could we measure how fast an algorithm runs? This is kind of a silly question.', 'start': 1573.432, 'duration': 7.766}, {'end': 1588.291, 'text': 'Yeah?. Yeah, well, I mean just record the time it takes for a computer to do this thing right?', 'start': 1581.258, 'duration': 7.033}], 'summary': 'In the class, algorithms are required to be both correct and efficient, with a focus on communication and speed.', 'duration': 90.982, 'max_score': 1497.309, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s1497309.jpg'}, {'end': 1726.336, 'src': 'embed', 'start': 1652.984, 'weight': 3, 'content': [{'end': 1661.371, 'text': "What I want to say is, Let's assume that each kind of fundamental operation that the computer can do takes some fixed amount of time.", 'start': 1652.984, 'duration': 8.387}, {'end': 1677.765, 'text': "How many of those kinds of fixed operations does the algorithm need to perform to be able to solve this problem? So here we don't measure time.", 'start': 1663.033, 'duration': 14.732}, {'end': 1689.684, 'text': 'Instead count fundamental operations.', 'start': 1682.489, 'duration': 7.195}, {'end': 1694.148, 'text': "We'll get to what some of those fundamental operations are in a second.", 'start': 1691.385, 'duration': 2.763}, {'end': 1706.479, 'text': 'But the idea is, we want a measure of how well an algorithm performs, not necessarily an implementation of that algorithm,', 'start': 1695.129, 'duration': 11.35}, {'end': 1709.222, 'text': 'kind of an abstract notion of how well this algorithm does.', 'start': 1706.479, 'duration': 2.743}, {'end': 1719.572, 'text': "What we're going to use to measure time or efficiency is something called asymptotic analysis.", 'start': 1711.348, 'duration': 8.224}, {'end': 1726.336, 'text': "Anyone here understand what asymptotic analysis is? Probably, since it's in both of your prerequisites, I think.", 'start': 1720.013, 'duration': 6.323}], 'summary': 'Algorithm efficiency measured by fundamental operations, using asymptotic analysis.', 'duration': 73.352, 'max_score': 1652.984, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s1652984.jpg'}, {'end': 1900.039, 'src': 'heatmap', 'start': 1864.737, 'weight': 0.879, 'content': [{'end': 1869.22, 'text': 'We will have omega, which corresponds to lower bounds.', 'start': 1864.737, 'duration': 4.483}, {'end': 1877.209, 'text': 'And we have theta, which corresponds to both.', 'start': 1872.987, 'duration': 4.222}, {'end': 1879.01, 'text': 'This thing is tight.', 'start': 1878.109, 'duration': 0.901}, {'end': 1882.972, 'text': 'It is bounded from above and below by a function of this form.', 'start': 1879.27, 'duration': 3.702}, {'end': 1900.039, 'text': 'Now we have a couple of common ways, a couple of common functions that algorithms, their running time.', 'start': 1889.995, 'duration': 10.044}], 'summary': 'Omega and theta define algorithm time bounds.', 'duration': 35.302, 'max_score': 1864.737, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s1864737.jpg'}, {'end': 1991.589, 'src': 'embed', 'start': 1961.184, 'weight': 7, 'content': [{'end': 1963.285, 'text': "that's an operation that could take linear time.", 'start': 1961.184, 'duration': 2.101}, {'end': 1968.687, 'text': 'So linear time is a type of function.', 'start': 1966.046, 'duration': 2.641}, {'end': 1969.907, 'text': "We've got a number of these.", 'start': 1968.747, 'duration': 1.16}, {'end': 1971.648, 'text': "I'm going to start with this.", 'start': 1970.287, 'duration': 1.361}, {'end': 1976.46, 'text': 'This one, does anyone know what this one is? Constant time.', 'start': 1972.918, 'duration': 3.542}, {'end': 1983.484, 'text': 'Basically, no matter how I change the input, the amount of time, this running time,', 'start': 1977.561, 'duration': 5.923}, {'end': 1986.986, 'text': "the performance of my algorithm takes it doesn't really depend on that.", 'start': 1983.484, 'duration': 3.502}, {'end': 1991.589, 'text': 'The next one up is something like this.', 'start': 1987.887, 'duration': 3.702}], 'summary': 'Discussion on time complexity: constant and linear time functions.', 'duration': 30.405, 'max_score': 1961.184, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s1961184.jpg'}], 'start': 1497.309, 'title': 'Algorithm efficiency and analysis', 'summary': 'Covers the importance of communicating algorithms effectively, emphasizing induction and reviewing unfamiliar concepts. it also discusses measuring performance in terms of fundamental operations and introduces asymptotic analysis using big o notation.', 'chapters': [{'end': 1549.558, 'start': 1497.309, 'title': 'Algorithm communication and efficiency', 'summary': 'Covers the importance of being able to communicate algorithms effectively and the concept of efficiency in the context of a class, emphasizing the use of induction and the need to review unfamiliar concepts.', 'duration': 52.249, 'highlights': ['The importance of being able to communicate algorithms effectively is emphasized, with the goal of being able to code it up to instruct a computer (quantifiable: ability to translate algorithm into code).', 'The use of induction is highlighted as a key concept that will be used throughout the class (quantifiable: frequency of use of induction throughout class).', 'The need to review unfamiliar concepts is stressed as beneficial for understanding (quantifiable: recommended action to review unfamiliar concepts).', 'The concept of efficiency in algorithms is introduced as a key focus (quantifiable: introduction of efficiency as a key concept).']}, {'end': 2193.55, 'start': 1559.622, 'title': 'Algorithm efficiency and asymptotic analysis', 'summary': "Discusses the concept of algorithm efficiency, highlighting the importance of measuring performance in terms of fundamental operations rather than time, and introduces asymptotic analysis using big o notation to determine an algorithm's performance relative to input size.", 'duration': 633.928, 'highlights': ['The chapter discusses the concept of algorithm efficiency and the importance of measuring performance in terms of fundamental operations rather than time. ', "Introduces asymptotic analysis using big O notation to determine an algorithm's performance relative to input size. ", 'Explains the significance of measuring how fast an algorithm runs compared to other possible ways of approaching the problem. ', 'Describes various types of running time functions such as constant, linear, logarithmic, and exponential, and their efficiency relative to input size. ']}], 'duration': 696.241, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s1497309.jpg', 'highlights': ['The importance of being able to communicate algorithms effectively is emphasized, with the goal of being able to code it up to instruct a computer (quantifiable: ability to translate algorithm into code).', 'The use of induction is highlighted as a key concept that will be used throughout the class (quantifiable: frequency of use of induction throughout class).', 'The need to review unfamiliar concepts is stressed as beneficial for understanding (quantifiable: recommended action to review unfamiliar concepts).', 'The concept of efficiency in algorithms is introduced as a key focus (quantifiable: introduction of efficiency as a key concept).', 'The chapter discusses the concept of algorithm efficiency and the importance of measuring performance in terms of fundamental operations rather than time.', "Introduces asymptotic analysis using big O notation to determine an algorithm's performance relative to input size.", 'Explains the significance of measuring how fast an algorithm runs compared to other possible ways of approaching the problem.', 'Describes various types of running time functions such as constant, linear, logarithmic, and exponential, and their efficiency relative to input size.']}, {'end': 2731.65, 'segs': [{'end': 2267.019, 'src': 'embed', 'start': 2221.738, 'weight': 1, 'content': [{'end': 2237.466, 'text': 'So we need to define some kind of model of computation for what our computer is allowed to do in constant time, in a fixed amount of time.', 'start': 2221.738, 'duration': 15.728}, {'end': 2249.17, 'text': 'In general, what we use in this class is a machine called a word RAM, which we use for its theoretical brevity.', 'start': 2241.226, 'duration': 7.944}, {'end': 2256.134, 'text': 'Word RAM is kind of a loaded term.', 'start': 2250.791, 'duration': 5.343}, {'end': 2267.019, 'text': 'What do these things mean? Does someone know what RAM means? Random access memory.', 'start': 2256.194, 'duration': 10.825}], 'summary': 'Defining word ram as a model of computation for constant time operations.', 'duration': 45.281, 'max_score': 2221.738, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s2221738.jpg'}, {'end': 2351.989, 'src': 'embed', 'start': 2323.578, 'weight': 2, 'content': [{'end': 2331.692, 'text': 'We actually, does anyone know how modern computers are addressed? Yeah.', 'start': 2323.578, 'duration': 8.114}, {'end': 2335.178, 'text': 'OK, so.', 'start': 2334.697, 'duration': 0.481}, {'end': 2337.636, 'text': "We're going to get there.", 'start': 2336.915, 'duration': 0.721}, {'end': 2343.141, 'text': 'Actually, what a modern computer is addressed in is bytes, collections of 8 bits.', 'start': 2337.716, 'duration': 5.425}, {'end': 2348.566, 'text': "So there's an address I have for every 8 bits in memory, consecutive 8 bits in memory.", 'start': 2343.581, 'duration': 4.985}, {'end': 2351.989, 'text': 'And so if I want to pull something in into the CPU, I give it an address.', 'start': 2348.606, 'duration': 3.383}], 'summary': 'Modern computers address data in bytes, 8 bits per address, for cpu input.', 'duration': 28.411, 'max_score': 2323.578, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s2323578.jpg'}, {'end': 2477.529, 'src': 'heatmap', 'start': 2323.578, 'weight': 0, 'content': [{'end': 2331.692, 'text': 'We actually, does anyone know how modern computers are addressed? Yeah.', 'start': 2323.578, 'duration': 8.114}, {'end': 2335.178, 'text': 'OK, so.', 'start': 2334.697, 'duration': 0.481}, {'end': 2337.636, 'text': "We're going to get there.", 'start': 2336.915, 'duration': 0.721}, {'end': 2343.141, 'text': 'Actually, what a modern computer is addressed in is bytes, collections of 8 bits.', 'start': 2337.716, 'duration': 5.425}, {'end': 2348.566, 'text': "So there's an address I have for every 8 bits in memory, consecutive 8 bits in memory.", 'start': 2343.581, 'duration': 4.985}, {'end': 2351.989, 'text': 'And so if I want to pull something in into the CPU, I give it an address.', 'start': 2348.606, 'duration': 3.383}, {'end': 2358.575, 'text': "It'll take some chunk and bring it into the CPU, operate it on it, and spit it back.", 'start': 2352.049, 'duration': 6.526}, {'end': 2360.897, 'text': 'How big is that chunk?', 'start': 2359.896, 'duration': 1.001}, {'end': 2375.419, 'text': "This goes to the answer that you were asking or saying, which is it's some sequence of some fixed number of bits, which we call a word.", 'start': 2363.288, 'duration': 12.131}, {'end': 2383.807, 'text': 'A word is how big of a chunk that the CPU can take in from memory at a time and operate on.', 'start': 2375.979, 'duration': 7.828}, {'end': 2388.351, 'text': 'In your computers, how big is that word size? 64 bits.', 'start': 2384.487, 'duration': 3.864}, {'end': 2392.472, 'text': "Right? That's how much I can operate on a time.", 'start': 2390.151, 'duration': 2.321}, {'end': 2398.195, 'text': 'When I was growing up, when I was your age, my word size was 32 bits.', 'start': 2392.712, 'duration': 5.483}, {'end': 2412.323, 'text': 'And that actually was a problem for my computer, because in order for me to be able to read to address in memory,', 'start': 2399.716, 'duration': 12.607}, {'end': 2415.984, 'text': 'I need to be able to store that address in my CPU in a word.', 'start': 2412.323, 'duration': 3.661}, {'end': 2427.634, 'text': 'Right? But if I have 32 bits, how many different addresses can I address? I have a limitation on the memory addresses I can address.', 'start': 2416.665, 'duration': 10.969}, {'end': 2433.659, 'text': 'So how many different memory addresses can I address with 32 bits? 2 to the 32.', 'start': 2428.935, 'duration': 4.724}, {'end': 2435.22, 'text': 'That makes sense.', 'start': 2433.659, 'duration': 1.561}, {'end': 2443.426, 'text': "Well, if you do that calculation out, how big of a hard disk can I have to access? It's about 4 gigabytes.", 'start': 2435.88, 'duration': 7.546}, {'end': 2451.157, 'text': 'Right? So in my day, all hard drives were limited to being partitioned.', 'start': 2444.551, 'duration': 6.606}, {'end': 2461.206, 'text': 'Even if you had a bigger than 4 gigabyte hard drive, I had to partition it into these 4 gigabyte chunks, which the computer could then read onto.', 'start': 2451.237, 'duration': 9.969}, {'end': 2463.828, 'text': 'Right? That was very limiting, actually.', 'start': 2461.566, 'duration': 2.262}, {'end': 2467.691, 'text': "That's a restriction.", 'start': 2466.79, 'duration': 0.901}, {'end': 2469.813, 'text': 'With 64 bits.', 'start': 2469.353, 'duration': 0.46}, {'end': 2477.529, 'text': "What's my limitation on memory that I can address? Byte addressable.", 'start': 2473.325, 'duration': 4.204}], 'summary': 'Modern computers are addressed in bytes, with a word size of 64 bits, allowing access to larger memory and hard disk sizes.', 'duration': 32.978, 'max_score': 2323.578, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s2323578.jpg'}, {'end': 2574.931, 'src': 'heatmap', 'start': 2514.068, 'weight': 3, 'content': [{'end': 2525.554, 'text': 'And I can either do integer arithmetic, kind of logical operations.', 'start': 2514.068, 'duration': 11.486}, {'end': 2533.351, 'text': "bitwise operations, but we're not going to use those so much in this class.", 'start': 2528.769, 'duration': 4.582}, {'end': 2542.375, 'text': 'And I can read and write from an address in memory a word in constant time.', 'start': 2534.952, 'duration': 7.423}, {'end': 2546.337, 'text': 'Those are the operations that I have available to me on most CPUs.', 'start': 2542.455, 'duration': 3.882}, {'end': 2552.26, 'text': 'Some CPUs give you a little bit more power, but this is generally what we analyze algorithms with respect to.', 'start': 2546.577, 'duration': 5.683}, {'end': 2561.922, 'text': "But you'll notice that my CPU is only built to operate on a constant amount of information at once.", 'start': 2556.698, 'duration': 5.224}, {'end': 2569.107, 'text': 'Generally, two words in memory, an operation produces a third one, and I spit it out.', 'start': 2562.322, 'duration': 6.785}, {'end': 2574.931, 'text': 'It takes a constant amount of time to operate on a constant amount of memory.', 'start': 2569.307, 'duration': 5.624}], 'summary': 'Cpus operate on a constant amount of memory, with operations taking constant time.', 'duration': 28.354, 'max_score': 2514.068, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s2514068.jpg'}, {'end': 2634.88, 'src': 'embed', 'start': 2607.768, 'weight': 4, 'content': [{'end': 2615.471, 'text': "And it's going to be concerned about not operating on constant amount of data at a time, like our CPU is doing.", 'start': 2607.768, 'duration': 7.703}, {'end': 2624.315, 'text': "But instead, what it's going to do is operate on store a large amount of data and support different operations on that data.", 'start': 2616.752, 'duration': 7.563}, {'end': 2634.88, 'text': 'So, if I had a record that I want to maintain to store those birthdays that we had before, I might use something like a static array,', 'start': 2625.716, 'duration': 9.164}], 'summary': "The system will operate on large data and support various operations, unlike the cpu's constant data processing.", 'duration': 27.112, 'max_score': 2607.768, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s2607768.jpg'}, {'end': 2711.193, 'src': 'embed', 'start': 2682.85, 'weight': 5, 'content': [{'end': 2689.573, 'text': 'To solve an algorithm problem in this class, we essentially have two different strategies.', 'start': 2682.85, 'duration': 6.723}, {'end': 2697.536, 'text': 'We can either reduce to using the solution to a problem we know how to solve, or we can design our own algorithm,', 'start': 2690.093, 'duration': 7.443}, {'end': 2699.057, 'text': 'which is going to be recursive in nature.', 'start': 2697.536, 'duration': 1.521}, {'end': 2705.748, 'text': "We're going to either put stuff in the data structure, solve a sorting problem, or search in a graph.", 'start': 2700.643, 'duration': 5.105}, {'end': 2711.193, 'text': 'And then to design a recursive algorithm, we have various design paradigms.', 'start': 2706.949, 'duration': 4.244}], 'summary': 'In the class, solving algorithm problems involves strategies such as using known solutions or designing recursive algorithms, with a focus on data structures, sorting, and graph search.', 'duration': 28.343, 'max_score': 2682.85, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s2682850.jpg'}, {'end': 2721.243, 'src': 'heatmap', 'start': 2682.85, 'weight': 1, 'content': [{'end': 2689.573, 'text': 'To solve an algorithm problem in this class, we essentially have two different strategies.', 'start': 2682.85, 'duration': 6.723}, {'end': 2697.536, 'text': 'We can either reduce to using the solution to a problem we know how to solve, or we can design our own algorithm,', 'start': 2690.093, 'duration': 7.443}, {'end': 2699.057, 'text': 'which is going to be recursive in nature.', 'start': 2697.536, 'duration': 1.521}, {'end': 2705.748, 'text': "We're going to either put stuff in the data structure, solve a sorting problem, or search in a graph.", 'start': 2700.643, 'duration': 5.105}, {'end': 2711.193, 'text': 'And then to design a recursive algorithm, we have various design paradigms.', 'start': 2706.949, 'duration': 4.244}, {'end': 2714.957, 'text': 'This is all in your notes, but this is essentially the structure of the class.', 'start': 2711.273, 'duration': 3.684}, {'end': 2721.243, 'text': "We're going to spend quiz one, the first eight lectures, on data structures and sorting.", 'start': 2714.977, 'duration': 6.266}], 'summary': 'Class focuses on two algorithm strategies: using known solutions or designing recursive algorithms. emphasizes data structures and sorting in first eight lectures.', 'duration': 38.393, 'max_score': 2682.85, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s2682850.jpg'}], 'start': 2193.63, 'title': 'Computer models and algorithms', 'summary': 'Covers the model of computation using word ram and memory addressing, emphasizing the transition from 32-bit to 64-bit word size. it also discusses cpu limitations, data structures, and algorithms for non-constant information, providing an overview of the covered topics.', 'chapters': [{'end': 2477.529, 'start': 2193.63, 'title': 'Model of computation and memory addressing', 'summary': 'Explains the model of computation using a word ram and the concept of memory addressing, emphasizing the transition from 32-bit to 64-bit word size and its impact on memory limitation and hard drive capacity.', 'duration': 283.899, 'highlights': ['Transition from 32-bit to 64-bit word size and its impact on memory limitation and hard drive capacity The transition from 32-bit to 64-bit word size had a significant impact on memory limitation and hard drive capacity, as 32-bit word size limited the memory addresses to 2 to the power of 32, resulting in a maximum access to about 4 gigabytes of hard disk, while 64-bit word size allows byte addressable memory.', 'Explanation of the word RAM model of computation and its theoretical brevity The word RAM model of computation is used in the class for its theoretical brevity, and it involves a model of computation where the computer has memory consisting of a string of bits and a CPU capable of operating on and accessing information in constant time.', 'Concept of memory addressing using bytes and the word size The concept of memory addressing involves addressing memory in bytes, where each address corresponds to a collection of 8 bits, and the word size determines the chunk of data that the CPU can operate on, with modern computers having a word size of 64 bits.']}, {'end': 2731.65, 'start': 2478.51, 'title': 'Algorithms and data structures', 'summary': 'Discusses the limitations and operations of a cpu, focusing on data structures and algorithms to operate on a non-constant amount of information, with an overview of the class structure and topics to be covered.', 'duration': 253.14, 'highlights': ["The chapter emphasizes the limitation of a CPU to operate on a constant amount of information at once, with the comparison of data capacity to Google's storage (20 exabytes) and CPU operations (binary, integer arithmetic, logical operations) being key points.", "It focuses on the need for data structures to operate on and store a large amount of data, supporting various operations, and contrasts Python's data structures with the model being discussed, highlighting the relevance of this concept to the audience.", 'The structure of the class is outlined, emphasizing the two strategies for solving algorithm problems and the topics to be covered in the upcoming quizzes (data structures and sorting, shortest paths algorithms and graphs, dynamic programming).']}], 'duration': 538.02, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/ZA-tUyM_y7s/pics/ZA-tUyM_y7s2193630.jpg', 'highlights': ['Transition from 32-bit to 64-bit word size and its impact on memory limitation and hard drive capacity', 'Explanation of the word RAM model of computation and its theoretical brevity', 'Concept of memory addressing using bytes and the word size', 'The chapter emphasizes the limitation of a CPU to operate on a constant amount of information at once', 'It focuses on the need for data structures to operate on and store a large amount of data', 'The structure of the class is outlined, emphasizing the two strategies for solving algorithm problems']}], 'highlights': ['The course focuses on solving computational problems, proving correctness, arguing efficiency, and communicating ideas effectively, with an emphasis on writing over coding.', 'The class concentrates on proving the correctness and superiority of solutions, as well as on effectively communicating these ideas to others, requiring more writing than coding.', 'The formal definition of a problem is a binary relation between inputs and outputs, specifying which outputs are correct for each input, represented as a bipartite graph.', 'The likelihood of two individuals sharing the same birth time decreases with a larger space of inputs, such as including the year and hour of birth, making it less likely for a pair to have the same birth time.', 'Algorithms are needed to solve general problems with arbitrarily-sized inputs The chapter emphasizes the need for algorithms to solve problems with inputs of varying sizes.', 'The proposed algorithm involves interviewing students in a specific order, maintaining a record, and checking for matches to identify pairs, with an emphasis on efficiency and practical application.', 'The importance of being able to communicate algorithms effectively is emphasized, with the goal of being able to code it up to instruct a computer (quantifiable: ability to translate algorithm into code).', 'The use of induction is highlighted as a key concept that will be used throughout the class (quantifiable: frequency of use of induction throughout class).', 'The concept of efficiency in algorithms is introduced as a key focus (quantifiable: introduction of efficiency as a key concept).', "Introduces asymptotic analysis using big O notation to determine an algorithm's performance relative to input size.", 'Transition from 32-bit to 64-bit word size and its impact on memory limitation and hard drive capacity', 'Explanation of the word RAM model of computation and its theoretical brevity', 'The chapter emphasizes the limitation of a CPU to operate on a constant amount of information at once', 'It focuses on the need for data structures to operate on and store a large amount of data']}