Algorithms, Part II

Princeton University

About this Course

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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.  It does not offer a certificate upon completion.

Learner Career Outcomes

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started a new career after completing these courses

18%

got a tangible career benefit from this course

17%

got a pay increase or promotion

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Start instantly and learn at your own schedule.

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Intermediate Level

Approx. 63 hours to complete

English

Subtitles: Arabic, French, Portuguese (European), Chinese (Simplified), Italian, Vietnamese, Korean, German, Russian, Turkish, English, Spanish

Skills you will gain

GraphsData StructureAlgorithmsData Compression

Learner Career Outcomes

12%

started a new career after completing these courses

18%

got a tangible career benefit from this course

17%

got a pay increase or promotion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 63 hours to complete

English

Subtitles: Arabic, French, Portuguese (European), Chinese (Simplified), Italian, Vietnamese, Korean, German, Russian, Turkish, English, Spanish

Instructors

Instructor rating

4.8/5 (140 Ratings)

Robert Sedgewick

William O. Baker *39 Professor of Computer Science

Computer Science

922,925 Learners

6 Courses

Kevin Wayne

Phillip Y. Goldman '86 Senior Lecturer

Computer Science

900,396 Learners

4 Courses

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.

Syllabus - What you will learn from this course

Content Rating96%(4,872 ratings)

Week

Week 1

10 minutes to complete

Introduction

Welcome to Algorithms, Part II.

10 minutes to complete

1 video (Total 9 min), 2 readings

1 video

Course Introduction9m

2 readings

Welcome to Algorithms, Part II1m

Lecture Slides

2 hours to complete

Undirected Graphs

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.

2 hours to complete

6 videos (Total 98 min), 2 readings, 1 quiz

6 videos

Introduction to Graphs9m

Graph API14m

Depth-First Search26m

Breadth-First Search13m

Connected Components18m

Graph Challenges14m

2 readings

Overview1m

Lecture Slides

1 practice exercise

Interview Questions: Undirected Graphs (ungraded)30m

10 hours to complete

Directed Graphs

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.

10 hours to complete

5 videos (Total 68 min), 1 reading, 2 quizzes

5 videos

Introduction to Digraphs8m

Digraph API4m

Digraph Search20m

Topological Sort 12m

Strong Components20m

1 reading

Lecture Slides

1 practice exercise

Interview Questions: Directed Graphs (ungraded)30m

Week

Week 2

2 hours to complete

Minimum Spanning Trees

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.

2 hours to complete

6 videos (Total 85 min), 2 readings, 1 quiz

6 videos

Introduction to MSTs4m

Greedy Algorithm12m

Edge-Weighted Graph API11m

Kruskal's Algorithm12m

Prim's Algorithm33m

MST Context10m

2 readings

Overview1m

Lecture Slides

1 practice exercise

Interview Questions: Minimum Spanning Trees (ungraded)30m

10 hours to complete

Shortest Paths

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.

10 hours to complete

5 videos (Total 85 min), 1 reading, 2 quizzes

5 videos

Shortest Paths APIs10m

Shortest Path Properties14m

Dijkstra's Algorithm18m

Edge-Weighted DAGs19m

Negative Weights21m

1 reading

Lecture Slides

1 practice exercise

Interview Questions: Shortest Paths (ungraded)30m

Week

Week 3

8 hours to complete

Maximum Flow and Minimum Cut

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.

8 hours to complete

6 videos (Total 72 min), 2 readings, 2 quizzes

6 videos

Introduction to Maxflow10m

Ford–Fulkerson Algorithm6m

Maxflow–Mincut Theorem9m

Running Time Analysis8m

Java Implementation14m

Maxflow Applications22m

2 readings

Overview

Lecture Slides

1 practice exercise

Interview Questions: Maximum Flow (ungraded)30m

2 hours to complete

Radix Sorts

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.

2 hours to complete

6 videos (Total 85 min), 1 reading, 1 quiz

6 videos

Strings in Java17m

Key-Indexed Counting12m

LSD Radix Sort15m

MSD Radix Sort13m

3-way Radix Quicksort7m

Suffix Arrays19m

1 reading

Lecture Slides

1 practice exercise

Interview Questions: Radix Sorts (ungraded)30m

Week

Week 4

2 hours to complete

Tries

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.

2 hours to complete

3 videos (Total 75 min), 2 readings, 1 quiz

3 videos

R-way Tries32m

Ternary Search Tries22m

Character-Based Operations20m

2 readings

Overview10m

Lecture Slides

1 practice exercise

Interview Questions: Tries (ungraded)30m

10 hours to complete

Substring Search

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.

10 hours to complete

5 videos (Total 75 min), 1 reading, 2 quizzes

5 videos

Introduction to Substring Search6m

Brute-Force Substring Search10m

Knuth–Morris–Pratt33m

Boyer–Moore8m

Rabin–Karp16m

1 reading

Lecture Slides10m

1 practice exercise

Interview Questions: Substring Search (ungraded)30m

Week

Week 5

2 hours to complete

Regular Expressions

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.

2 hours to complete

5 videos (Total 83 min), 2 readings, 1 quiz

5 videos

Regular Expressions20m

REs and NFAs13m

NFA Simulation18m

NFA Construction11m

Regular Expression Applications20m

2 readings

Overview10m

Lecture Slides10m

1 practice exercise

Interview Questions: Regular Expressions (ungraded)30m

10 hours to complete

Data Compression

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.

10 hours to complete

4 videos (Total 80 min), 1 reading, 2 quizzes

4 videos

Introduction to Data Compression22m

Run-Length Coding5m

Huffman Compression24m

LZW Compression27m

1 reading

Lecture Slides10m

1 practice exercise

Interview Questions: Data Compression (ungraded)30m

Week

Week 6

1 hour to complete

Reductions

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.

1 hour to complete

4 videos (Total 40 min), 2 readings, 1 quiz

4 videos

Introduction to Reductions9m

Designing Algorithms8m

Establishing Lower Bounds9m

Classifying Problems12m

2 readings

Overview10m

Lecture Slides10m

1 practice exercise

Interview Questions: Reductions (ungraded)30m

2 hours to complete

Linear Programming (optional)

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.

2 hours to complete

4 videos (Total 61 min), 1 reading, 1 quiz

4 videos

Brewer's Problem21m

Simplex Algorithm11m

Simplex Implementations16m

Linear Programming Reductions11m

1 reading

Lecture Slides10m

1 practice exercise

Interview Questions: Linear Programming (ungraded)30m

2 hours to complete

Intractability

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.

2 hours to complete

6 videos (Total 85 min), 1 reading, 1 quiz

6 videos

Introduction to Intractability17m

Search Problems10m

P vs. NP16m

Classifying Problems13m

NP-Completeness12m

Coping with Intractability 14m

1 reading

Lecture Slides10m

1 practice exercise

Interview Questions: Intractability (ungraded)30m

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. 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.
When will I have access to the lectures and assignments?
Once you enroll, you’ll have access to all videos and programming assignments.
Do I need to pay for this course?
No. All features of this course are available for free.
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.
I have no familiarity with Java programming. Can I still take 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.
Which algorithms and data structures are covered in this course?
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.
What kinds of assessments are available in this course?
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.
I am/was not a Computer Science major. Is this course for me?
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.
How does this course differ from Design and Analysis of Algorithms?
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.
Will I earn university credit for completing the Course?
This Course doesn't carry university credit, but some universities may choose to accept Course Certificates for credit. Check with your institution to learn more. Online Degrees and Mastertrack™ Certificates on Coursera provide the opportunity to earn university credit.

More questions? Visit the Learner Help Center.

Algorithms, Part II