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This class is ultimately about learning two skills that are crucial for computer scientists: how to think about algorithms and how to talk about algorithms. Along the way, you'll pick up a bunch of algorithmic factsmergesort runs in O(n log n) time; the amortized time to search in a splay tree is O(log n); greedy algorithms usually don't produce optimal solutions; the traveling salesman problem is NPhardbut these aren't the point of the course. You can always look up mere facts in a textbook or on the web, provided you have enough intuition and experience to know what to look for. That's why we let you bring cheat sheets to the exams; we don't want you wasting your study time trying to memorize all the facts you've seen. You'll also practice a lot of algorithm design and analysis skillsfinding useful (counter)examples, developing induction proofs, solving recurrences, using bigOh notation, using probability, giving problems crisp mathematical descriptions, and so on. These skills are very useful, but they aren't really the point of the course either. At this point in your educational career, you should be able to pick up those skills on your own, once you know what you're trying to do.
The first main goal of this course is to help you develop algorithmic intuition. How do various algorithms really work? When you see a problem for the first time, how should you attack it? How do you tell which techniques will work at all, and which ones will work best? How do you judge whether one algorithm is better than another? How do you tell whether you have the best possible solution?
Our second main goal is to help you develop algorithmic language. It's not enough just to understand how to solve a problem; you also have to be able to explain your solution to somebody else. I don't mean just how to turn your algorithms into working codedespite what many students (and inexperienced programmers) think, 'somebody else' is not just a computer. Nobody programs alone. Code is read far more often than it is written, or even compiled. Perhaps more importantly in the short term, explaining something to somebody else is one of the best ways of clarifying your own understanding. As Richard Feynman apocryphally put it, "If you can't explain what you're doing to your grandmother, you don't understand it."
Unfortunately, there is no systematic procedureno algorithmto determine which algorithmic techniques are most effective at solving a given problem, or finding good ways to explain, analyze, optimize, or implement a given algorithm. Like many other human activities (music, writing, juggling, acting, martial arts, sports, cooking, programming, teaching, etc.), experts will disagree on the relative values of different techniques. Ultimately, the only way to master these skills is to make them your own, through practice, practice, and more practice. We can't teach you how to do well in this class. All we can do is lay out a few tools, show you how to use them, create opportunities for you to practice, and give you feedback based on our own experience and intuition. The rest is up to you.
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