This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. In addition, this course covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings.
All the features of this course are available for free. It does not offer a certificate upon completion.
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プリンストン大学（Princeton University）
シラバス - 本コースの学習内容
週
12時間で修了
Analysis of Algorithms
We begin by considering historical context and motivation for the scientific study of algorithm performance. Then we consider a classic example that illustrates the key ingredients of the process: the analysis of Quicksort. The lecture concludes with a discussion of some resources that you might find useful during this course.
4件のビデオ （合計76分）, 2 readings, 1 quiz
2件の学習用教材
Getting Started10 分
Exercises from Lecture 110 分
1の練習問題
Analysis of Algorithms4 分
週
22時間で修了
Recurrences
We begin this lecture with an overview of recurrence relations, which provides us with a direct mathematical model for the analysis of algorithms. We finish by examining the fascinating oscillatory behavior of the divide-and-conquer recurrence corresponding to the mergesort algorithm and the general "master theorem" for related recurrences.
5件のビデオ （合計71分）, 1 reading, 3 quizzes
1件の学習用教材
Exercises from Lecture 210 分
3の練習問題
Pop Quiz on Telescoping2 分
Pop Quiz on the Master Theorem2 分
Recurrences4 分
週
32時間で修了
Generating Functions
Since the 17th century, scientists have been using generating functions to solve recurrences, so we continue with an overview of generating functions, emphasizing their utility in solving problems like counting the number of binary trees with N nodes.
5件のビデオ （合計84分）, 1 reading, 1 quiz
5件のビデオ
Counting with Generating Functions27 分
Catalan Numbers14 分
Solving Recurrences18 分
Exponential Generating Functions7 分
1件の学習用教材
Exercises from Lecture 310 分
1の練習問題
Generating Functions6 分
週
42時間で修了
Asymptotics
Exact answers are often cumbersome, so we next consider a scientific approach to developing approximate answers that, again, mathematicians and scientists have used for centuries.
4件のビデオ （合計83分）, 1 reading, 1 quiz
4件のビデオ
Standard Scale18 分
Manipulating Expansions 19 分
Asymptotics of Finite Sums 16 分
Bivariate Asymptotics 28 分
1件の学習用教材
Exercises from Lecture 410 分
1の練習問題
Asymptotics4 分
4.7
6件のレビュー人気のレビュー
This course is more about mathematic than algorithms, it teaches how to solve tricky combinatorial problems
This is great course if you already done some algorithms courses and want to go deeper.
講師
Robert Sedgewick
William O. Baker *39 Professor of Computer ScienceComputer Science
プリンストン大学（Princeton University）について
Princeton University is a private research university located in Princeton, New Jersey, United States. It is one of the eight universities of the Ivy League, and one of the nine Colonial Colleges founded before the American Revolution.
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Can I earn a certificate in this course?
No. As per Princeton University policy, no certificates, credentials, or reports are awarded in connection with this course.
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