Algorithms: Design and Analysis, Part 1

In this course you will learn several fundamental principles of algorithm design. You'll learn the divide-and-conquer design paradigm, with applications to fast sorting, searching, and multiplication. You'll learn several blazingly fast primitives for computing on graphs, such as how to compute connectivity information and shortest paths. Finally, we'll study how allowing the computer to "flip coins" can lead to elegant and practical algorithms and data structures. Learn the answers to questions such as: How do data structures like heaps, hash tables, bloom filters, and balanced search trees actually work, anyway? How come QuickSort runs so fast? What can graph algorithms tell us about the structure of the Web and social networks? Did my 3rd-grade teacher explain only a suboptimal algorithm for multiplying two numbers?

Week 1: Introduction.  Asymptotic analysis including big-oh notation.  Divide-and-conquer algorithms for sorting, counting inversions, matrix multiplication, and closest pair.

Week 2: Running time analysis of divide-and-conquer algorithms.  The master method.  Introduction to randomized algorithms, with a probability review.  QuickSort.  

Week 3: More on randomized algorithms and probability.  Computing the median in linear time.  A randomized algorithm for the minimum graph cut problem.

Week 4: Graph primitives.  Depth- and breadth-first search.  Connected components in undirected graphs.  Topological sort in directed acyclic graphs.  Strongly connected components in directed graphs.

Week 5: Dijkstra's shortest-path algorithm.  Introduction to data structures.  Heaps and applications.

Week 6: Further data structures.  Hash tables and applications.  Balanced binary search trees.

No specific textbook is required for the course.  Much of the course material is covered by the well-known textbooks on algorithms, and the student is encouraged to consult their favorite for additional information.

• Will I get a statement of accomplishment after completing this class?

  Yes. Students who successfully complete the class will receive a statement of accomplishment signed by the instructor.

• What is the format of the class?

  The class consists of lecture videos, which are broken into small chunks, usually between eight and twelve minutes each. Some of these may contain integrated quiz questions. There will also be standalone quizzes that are not part of video lectures. There will be approximately two hours worth of video content per week.

• What should I know to take this class?

  How to program in at least one programming language (like C, Java, or Python); familiarity with proofs, including proofs by induction and by contradiction; and some discrete probability, like how to compute the probability that a poker hand is a full house. At Stanford, a version of this course is taken by sophomore, junior, and senior-level computer science majors.

• How does Algorithms: Design and Analysis differ from the Princeton University algorithms course?

  The two courses are complementary. That one emphasizes implementation and testing; this one focuses on algorithm design paradigms and relevant mathematical models for analysis. In a typical computer science curriculum, a course like this one is taken by juniors and seniors, and a course like that one is taken by first- and second-year students.