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
ofrecido por
Princeton University
Programa - Qué aprenderás en este curso
Semana
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 videos (Total 76 minutos), 2 readings, 1 quiz
2 lecturas
Getting Started10m
Exercises from Lecture 110m
1 ejercicio de práctica
Analysis of Algorithms4m
Semana
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 videos (Total 71 minutos), 1 reading, 3 quizzes
1 lectura
Exercises from Lecture 210m
3 ejercicios de práctica
Pop Quiz on Telescoping2m
Pop Quiz on the Master Theorem2m
Recurrences4m
Semana
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 videos (Total 84 minutos), 1 reading, 1 quiz
5 videos
Counting with Generating Functions27m
Catalan Numbers14m
Solving Recurrences18m
Exponential Generating Functions7m
1 lectura
Exercises from Lecture 310m
1 ejercicio de práctica
Generating Functions6m
Semana
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 videos (Total 83 minutos), 1 reading, 1 quiz
4 videos
Manipulating Expansions 19m
Asymptotics of Finite Sums 16m
Bivariate Asymptotics 28m
1 lectura
Exercises from Lecture 410m
1 ejercicio de práctica
Asymptotics4m
Instructor
Robert Sedgewick
William O. Baker *39 Professor of Computer ScienceComputer Science
Acerca de 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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