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Princeton University
Algorithms, Part II
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  3. Algorithms
Princeton University

Algorithms, Part II

Robert Sedgewick
Kevin Wayne

Instructors: Robert Sedgewick

Instructors

Instructor ratings

We asked all learners to give feedback on our instructors based on the quality of their teaching style.

4.8 (294 ratings)
Robert Sedgewick
Robert Sedgewick
Princeton University
7 Courses•1,975,085 learners
Kevin Wayne
Kevin Wayne
Princeton University
5 Courses•1,927,005 learners

338,641 already enrolled

14 modules
Gain insight into a topic and learn the fundamentals.
4.9

(2,030 reviews)

Intermediate level
Some related experience required
Flexible schedule
6 weeks at 10 hours a week
Learn at your own pace
96%
Most learners liked this course

14 modules
Gain insight into a topic and learn the fundamentals.
4.9

(2,030 reviews)

Intermediate level
Some related experience required
Flexible schedule
6 weeks at 10 hours a week
Learn at your own pace
96%
Most learners liked this course
  • About
  • Modules
  • Recommendations
  • Testimonials
  • Reviews

Skills you'll gain

  • Java
  • Computer Programming
  • Algorithms
  • Network Routing
  • Graph Theory
  • Data Structures
  • Computational Thinking
  • Theoretical Computer Science
  • Operations Research

Details to know

Assessments

13 assignments

Taught in English

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There are 14 modules in this course

This course covers the essential information that every serious programmer needs to know about algorithms and data structures, with emphasis on applications and scientific performance analysis of Java implementations. Part I covers elementary data structures, sorting, and searching algorithms. Part II focuses on graph- and string-processing algorithms.

All the features of this course are available for free. People who are interested in digging deeper into the content may wish to obtain the textbook Algorithms, Fourth Edition (upon which the course is based) or visit the website algs4.cs.princeton.edu for a wealth of additional material. This course does not offer a certificate upon completion.

Welcome to Algorithms, Part II.

What's included

1 video2 readings

1 video•Total 9 minutes
  • Course Introduction•9 minutes
2 readings•Total 1 minute
  • Welcome to Algorithms, Part II•1 minute
  • Lecture Slides•0 minutes

We define an undirected graph API and consider the adjacency-matrix and adjacency-lists representations. We introduce two classic algorithms for searching a graph—depth-first search and breadth-first search. We also consider the problem of computing connected components and conclude with related problems and applications.

What's included

6 videos2 readings1 assignment

6 videos•Total 97 minutes
  • Introduction to Graphs•9 minutes
  • Graph API•14 minutes
  • Depth-First Search•26 minutes
  • Breadth-First Search•13 minutes
  • Connected Components•18 minutes
  • Graph Challenges•14 minutes
2 readings•Total 1 minute
  • Overview•1 minute
  • Lecture Slides•0 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Undirected Graphs (ungraded)•30 minutes

In this lecture we study directed graphs. We begin with depth-first search and breadth-first search in digraphs and describe applications ranging from garbage collection to web crawling. Next, we introduce a depth-first search based algorithm for computing the topological order of an acyclic digraph. Finally, we implement the Kosaraju−Sharir algorithm for computing the strong components of a digraph.

What's included

5 videos1 reading1 assignment1 programming assignment

5 videos•Total 67 minutes
  • Introduction to Digraphs•8 minutes
  • Digraph API•4 minutes
  • Digraph Search•20 minutes
  • Topological Sort •12 minutes
  • Strong Components•20 minutes
1 reading
  • Lecture Slides•0 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Directed Graphs (ungraded)•30 minutes
1 programming assignment•Total 480 minutes
  • WordNet•480 minutes

In this lecture we study the minimum spanning tree problem. We begin by considering a generic greedy algorithm for the problem. Next, we consider and implement two classic algorithm for the problem—Kruskal's algorithm and Prim's algorithm. We conclude with some applications and open problems.

What's included

6 videos2 readings1 assignment

6 videos•Total 84 minutes
  • Introduction to MSTs•4 minutes
  • Greedy Algorithm•12 minutes
  • Edge-Weighted Graph API•11 minutes
  • Kruskal's Algorithm•12 minutes
  • Prim's Algorithm•33 minutes
  • MST Context•10 minutes
2 readings•Total 1 minute
  • Overview•1 minute
  • Lecture Slides•0 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Minimum Spanning Trees (ungraded)•30 minutes

In this lecture we study shortest-paths problems. We begin by analyzing some basic properties of shortest paths and a generic algorithm for the problem. We introduce and analyze Dijkstra's algorithm for shortest-paths problems with nonnegative weights. Next, we consider an even faster algorithm for DAGs, which works even if the weights are negative. We conclude with the Bellman−Ford−Moore algorithm for edge-weighted digraphs with no negative cycles. We also consider applications ranging from content-aware fill to arbitrage.

What's included

5 videos1 reading1 assignment1 programming assignment

5 videos•Total 84 minutes
  • Shortest Paths APIs•10 minutes
  • Shortest Path Properties•14 minutes
  • Dijkstra's Algorithm•18 minutes
  • Edge-Weighted DAGs•19 minutes
  • Negative Weights•21 minutes
1 reading
  • Lecture Slides•0 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Shortest Paths (ungraded)•30 minutes
1 programming assignment•Total 480 minutes
  • Seam Carving•480 minutes

In this lecture we introduce the maximum flow and minimum cut problems. We begin with the Ford−Fulkerson algorithm. To analyze its correctness, we establish the maxflow−mincut theorem. Next, we consider an efficient implementation of the Ford−Fulkerson algorithm, using the shortest augmenting path rule. Finally, we consider applications, including bipartite matching and baseball elimination.

What's included

6 videos2 readings1 assignment1 programming assignment

6 videos•Total 72 minutes
  • Introduction to Maxflow•10 minutes
  • Ford–Fulkerson Algorithm•6 minutes
  • Maxflow–Mincut Theorem•9 minutes
  • Running Time Analysis•8 minutes
  • Java Implementation•14 minutes
  • Maxflow Applications•22 minutes
2 readings
  • Overview•0 minutes
  • Lecture Slides•0 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Maximum Flow (ungraded)•30 minutes
1 programming assignment•Total 360 minutes
  • Baseball Elimination•360 minutes

In this lecture we consider specialized sorting algorithms for strings and related objects. We begin with a subroutine to sort integers in a small range. We then consider two classic radix sorting algorithms—LSD and MSD radix sorts. Next, we consider an especially efficient variant, which is a hybrid of MSD radix sort and quicksort known as 3-way radix quicksort. We conclude with suffix sorting and related applications.

What's included

6 videos1 reading1 assignment

6 videos•Total 85 minutes
  • Strings in Java•17 minutes
  • Key-Indexed Counting•12 minutes
  • LSD Radix Sort•15 minutes
  • MSD Radix Sort•13 minutes
  • 3-way Radix Quicksort•7 minutes
  • Suffix Arrays•19 minutes
1 reading
  • Lecture Slides•0 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Radix Sorts (ungraded)•30 minutes

In this lecture we consider specialized algorithms for symbol tables with string keys. Our goal is a data structure that is as fast as hashing and even more flexible than binary search trees. We begin with multiway tries; next we consider ternary search tries. Finally, we consider character-based operations, including prefix match and longest prefix, and related applications.

What's included

3 videos2 readings1 assignment

3 videos•Total 75 minutes
  • R-way Tries•32 minutes
  • Ternary Search Tries•22 minutes
  • Character-Based Operations•20 minutes
2 readings•Total 10 minutes
  • Overview•10 minutes
  • Lecture Slides•0 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Tries (ungraded)•30 minutes

In this lecture we consider algorithms for searching for a substring in a piece of text. We begin with a brute-force algorithm, whose running time is quadratic in the worst case. Next, we consider the ingenious Knuth−Morris−Pratt algorithm whose running time is guaranteed to be linear in the worst case. Then, we introduce the Boyer−Moore algorithm, whose running time is sublinear on typical inputs. Finally, we consider the Rabin−Karp fingerprint algorithm, which uses hashing in a clever way to solve the substring search and related problems.

What's included

5 videos1 reading1 assignment1 programming assignment

5 videos•Total 74 minutes
  • Introduction to Substring Search•6 minutes
  • Brute-Force Substring Search•10 minutes
  • Knuth–Morris–Pratt•33 minutes
  • Boyer–Moore•8 minutes
  • Rabin–Karp•16 minutes
1 reading•Total 10 minutes
  • Lecture Slides•10 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Substring Search (ungraded)•30 minutes
1 programming assignment•Total 480 minutes
  • Boggle•480 minutes

A regular expression is a method for specifying a set of strings. Our topic for this lecture is the famous grep algorithm that determines whether a given text contains any substring from the set. We examine an efficient implementation that makes use of our digraph reachability implementation from Week 1.

What's included

5 videos2 readings1 assignment

5 videos•Total 83 minutes
  • Regular Expressions•20 minutes
  • REs and NFAs•13 minutes
  • NFA Simulation•18 minutes
  • NFA Construction•11 minutes
  • Regular Expression Applications•20 minutes
2 readings•Total 20 minutes
  • Overview•10 minutes
  • Lecture Slides•10 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Regular Expressions (ungraded)•30 minutes

We study and implement several classic data compression schemes, including run-length coding, Huffman compression, and LZW compression. We develop efficient implementations from first principles using a Java library for manipulating binary data that we developed for this purpose, based on priority queue and symbol table implementations from earlier lectures.

What's included

4 videos1 reading1 assignment1 programming assignment

4 videos•Total 80 minutes
  • Introduction to Data Compression•22 minutes
  • Run-Length Coding•5 minutes
  • Huffman Compression•24 minutes
  • LZW Compression•27 minutes
1 reading•Total 10 minutes
  • Lecture Slides•10 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Data Compression (ungraded)•30 minutes
1 programming assignment•Total 480 minutes
  • Burrows–Wheeler•480 minutes

Our lectures this week are centered on the idea of problem-solving models like maxflow and shortest path, where a new problem can be formulated as an instance of one of those problems, and then solved with a classic and efficient algorithm. To complete the course, we describe the classic unsolved problem from theoretical computer science that is centered on the concept of algorithm efficiency and guides us in the search for efficient solutions to difficult problems.

What's included

4 videos2 readings1 assignment

4 videos•Total 39 minutes
  • Introduction to Reductions•9 minutes
  • Designing Algorithms•8 minutes
  • Establishing Lower Bounds•9 minutes
  • Classifying Problems•12 minutes
2 readings•Total 20 minutes
  • Overview•10 minutes
  • Lecture Slides•10 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Reductions (ungraded)•30 minutes

The quintessential problem-solving model is known as linear programming, and the simplex method for solving it is one of the most widely used algorithms. In this lecture, we given an overview of this central topic in operations research and describe its relationship to algorithms that we have considered.

What's included

4 videos1 reading1 assignment

4 videos•Total 61 minutes
  • Brewer's Problem•21 minutes
  • Simplex Algorithm•11 minutes
  • Simplex Implementations•16 minutes
  • Linear Programming Reductions•11 minutes
1 reading•Total 10 minutes
  • Lecture Slides•10 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Linear Programming (ungraded)•30 minutes

Is there a universal problem-solving model to which all problems that we would like to solve reduce and for which we know an efficient algorithm? You may be surprised to learn that we do no know the answer to this question. In this lecture we introduce the complexity classes P, NP, and NP-complete, pose the famous P = NP question, and consider implications in the context of algorithms that we have treated in this course.

What's included

6 videos1 reading1 assignment

6 videos•Total 84 minutes
  • Introduction to Intractability•17 minutes
  • Search Problems•10 minutes
  • P vs. NP•16 minutes
  • Classifying Problems•13 minutes
  • NP-Completeness•12 minutes
  • Coping with Intractability •14 minutes
1 reading•Total 10 minutes
  • Lecture Slides•10 minutes
1 assignment•Total 30 minutes
  • Interview Questions: Intractability (ungraded)•30 minutes

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Instructors

Instructor ratings

Instructor ratings

We asked all learners to give feedback on our instructors based on the quality of their teaching style.

4.8 (294 ratings)
Robert Sedgewick
Robert Sedgewick
Princeton University
7 Courses•1,975,085 learners
Kevin Wayne
Kevin Wayne
Princeton University
5 Courses•1,927,005 learners

Offered by

Princeton University

Offered by

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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As always, I learned a lot from the courses from Professor Robert. Really great course, and I would like to recommend to anyone who is interested in programming neatly and elegantly.

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Reviewed on Jan 12, 2024

Great quality of academic content. Mr Sedgewick is a great lecturer and the programming tasks, though hard, help you dive deep into the Java implementations.

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Reviewed on Feb 27, 2021

Essential information that every serious programmer needs to know about algorithms and data structures, with emphasis on applications and scientific performance analysis of Java implementations.

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Frequently asked questions

Once you enroll, you’ll have access to all videos and programming assignments.

No. All features of this course are available for free.

No. As per Princeton University policy, no certificates, credentials, or reports are awarded in connection with this course.

Our central thesis is that algorithms are best understood by implementing and testing them. Our use of Java is essentially expository, and we shy away from exotic language features, so we expect you would be able to adapt our code to your favorite language. However, we require that you submit the programming assignments in Java.

Part II focuses on graph and string-processing algorithms. Topics include depth-first search, breadth-first search, topological sort, Kosaraju−Sharir, Kruskal, Prim, Dijkistra, Bellman−Ford, Ford−Fulkerson, LSD radix sort, MSD radix sort, 3-way radix quicksort, multiway tries, ternary search tries, Knuth−Morris−Pratt, Boyer−Moore, Rabin−Karp, regular expression matching, run-length coding, Huffman coding, LZW compression, and the Burrows−Wheeler transform.

Part I focuses on elementary data structures, sorting, and searching. Topics include union-find, binary search, stacks, queues, bags, insertion sort, selection sort, shellsort, quicksort, 3-way quicksort, mergesort, heapsort, binary heaps, binary search trees, red−black trees, separate-chaining and linear-probing hash tables, Graham scan, and kd-trees.

Weekly programming assignments and interview questions.

The programming assignments involve either implementing algorithms and data structures (graph algorithms, tries, and the Burrows–Wheeler transform) or applying algorithms and data structures to an interesting domain (computer graphics, computational linguistics, and data compression). The assignments are evaluated using a sophisticated autograder that provides detailed feedback about style, correctness, and efficiency.

The interview questions are similar to those that you might find at a technical job interview. They are optional and not graded.

This course is for anyone using a computer to address large problems (and therefore needing efficient algorithms). At Princeton, over 25% of all students take the course, including people majoring in engineering, biology, physics, chemistry, economics, and many other fields, not just computer science.

The two courses are complementary. This one is essentially a programming course that concentrates on developing code; that one is essentially a math course that concentrates on understanding proofs. This course is about learning algorithms in the context of implementing and testing them in practical applications; that one is about learning algorithms in the context of developing mathematical models that help explain why they are efficient. In typical computer science curriculums, a course like this one is taken by first- and second-year students and a course like that one is taken by juniors and seniors.

To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

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