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.
Analysis of Algorithms
提供方
Analysis of Algorithms
Princeton University
教學大綱 - 您將從這門課程中學到什麼
週
1Analysis 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（共 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
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2Recurrences
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（共 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
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3Generating 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（共 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
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4Asymptotics
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（共 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
講師
Robert Sedgewick
William O. Baker *39 Professor of Computer ScienceComputer Science
關於 Princeton University
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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