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.

Offered By

## Algorithms, Part II

## About this Course

### Learner Career Outcomes

## 18%

## 22%

## 16%

### Skills you will gain

### Learner Career Outcomes

## 18%

## 22%

## 16%

#### 100% online

#### Flexible deadlines

#### Intermediate Level

#### Approx. 36 hours to complete

#### English

### 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

#### 5.0

##### 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.

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.

Excellent course that provides a good introduction to more advanced algorithms that build on those presented in part 1 of the course. Thank you Professor Sedgewick and Kevin Wayne.

This class is amazing. If you follow this course schedule strictly, and finish the homework and interview questions, you are gonna to learn a lot of algorithm thinking methods.

This was a great overview of more advanced algorithms, and I also got to prep for interviews and use concepts in actual work. The theory at the end was very helpful as well

Rich content. Liked the teaching style as well. But wish that it had an as-strong supporting system as Part I's and mentors/fellow students could answer more questions.

Prof. Sedgewick does an amazing job in explaining the mechanics of the fundamental algorithms and data structures. I have thoroughly enjoyed this course (and Part I).

Awesome course. Helped me understand graph better. The API is simple and effective. I implemented the whole API and have been using it in my other graph solutions

I wrote my review on Linkedin. Thank you very much for the great course ! https://www.linkedin.com/pulse/algorithms-part-ii-mission-accomplished-luigi-selmi/

This is an excellent course as an introduction to algorithms. Together with part 1, the Princeton Algorithms series is the best MOOC course I've ever done.

Complex concepts in plain language. Challenging and interesting practice exercises. Without them it's impossible to fully understand theoretical part.

Excellent course and materials about algorithms and data structures. Very challenging exercises that make you think hard to achieve the passing score.

Dr. Sedgewick is simply amazing. I enjoy how he motivates the need for efficient algorithms and applications. I only wish he would offer more courses!

Every single programming assignment was both challenging and fun. I learned really good algorithms and overall I feel I'm a better Software Engineer

Excellent follow-on from Part I - covers additional algorithms in depth and the excellent examples really help to learn and understand the material.

Completed Algorithms I and II. Great course for students to learn data structures is a systematically way! Could be used in my research directly.

Provides excellent insights with reference to some of the advanced algorithms. Assignments for a great source of learning in the course.

Very well structured course on Algorithms and advanced data structures. Highly advised to anyone pursuing career in programming field.

Excellent! Sedgwick explains things in such a way that is both extremely intuitive but also makes the code practically write itself!

Very useful! Very interesting! Very good lectures, quite hard assignments, very smart auto-grader. Wide and friendly community!

## Frequently Asked Questions

When will I have access to the lectures and assignments?

Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

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.

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