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.
教學大綱 - 您將從這門課程中學到什麼
週
1完成時間為 2 小時
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 個視頻 （總計 76 分鐘）, 2 個閱讀材料, 1 個測驗
2 個閱讀材料
Getting Started10分鐘
Exercises from Lecture 110分鐘
1 個練習
Analysis of Algorithms4分鐘
週
2完成時間為 2 小時
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 個視頻 （總計 71 分鐘）, 1 個閱讀材料, 3 個測驗
1 個閱讀材料
Exercises from Lecture 210分鐘
3 個練習
Pop Quiz on Telescoping2分鐘
Pop Quiz on the Master Theorem2分鐘
Recurrences4分鐘
週
3完成時間為 2 小時
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 個視頻 （總計 84 分鐘）, 1 個閱讀材料, 1 個測驗
5 個視頻
Counting with Generating Functions27分鐘
Catalan Numbers14分鐘
Solving Recurrences18分鐘
Exponential Generating Functions7分鐘
1 個閱讀材料
Exercises from Lecture 310分鐘
1 個練習
Generating Functions6分鐘
週
4完成時間為 2 小時
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 個視頻 （總計 83 分鐘）, 1 個閱讀材料, 1 個測驗
4 個視頻
Standard Scale18分鐘
Manipulating Expansions 19分鐘
Asymptotics of Finite Sums 16分鐘
Bivariate Asymptotics 28分鐘
1 個閱讀材料
Exercises from Lecture 410分鐘
1 個練習
Asymptotics4分鐘
4.7
6 個審閱熱門審閱
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
關於 普林斯顿大学
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.
常見問題
我什么时候能够访问课程视频和作业？
注册以便获得证书后，您将有权访问所有视频、测验和编程作业（如果适用）。只有在您的班次开课之后，才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程，可能无法访问某些作业。
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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