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.

## Algorithms, Part II

Princeton University## About this Course

### Learner Career Outcomes

## 18%

## 22%

## 16%

## Skills you will gain

### Learner Career Outcomes

## 18%

## 22%

## 16%

### 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

**10 minutes to complete**

## Introduction

Welcome to Algorithms, Part II.

**10 minutes to complete**

**1 video**

**2 readings**

**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**

**2 readings**

**1 practice exercise**

**9 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.

**9 hours to complete**

**5 videos**

**1 reading**

**1 practice exercise**

**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**

**2 readings**

**1 practice exercise**

**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**

**1 reading**

**1 practice exercise**

**7 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.

**7 hours to complete**

**6 videos**

**2 readings**

**1 practice exercise**

**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**

**1 reading**

**1 practice exercise**

**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**

**2 readings**

**1 practice exercise**

**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**

**1 reading**

**1 practice exercise**

## Reviews

### TOP REVIEWS FROM ALGORITHMS, PART II

Pretty challenging course, but very good. Having a book is a must (at least it was for me), video lectures complement book nicely, and some topics are explained better in the Algorithms, 4th ed. book.

The algorithms are more difficult than part I, nevertheless Sedgewick's vids are still easy to understand. The only drawback maybe chapter 3, max flow min cut part, which is not very clarified.

Amazing course! Loved the theory and exercises! Just a note for others: Its part 1 had almost no dependency on book, but this part 2 has some dependency (e.g. chapter on Graph) on book as well.

An incredible course that covers a lot of vital algorithm on graphs and strings. I learned a lot of new material that I hadn't known before. Thank you very much for this amazing course!

## 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.

More questions? Visit the Learner Help Center.