Algorithms, Part II

Princeton University via Coursera

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Coursera
Pricing

Free Online Course (Audit)
Languages

English
Duration & workload

63 hours
Sessions

On-Demand
Level

Intermediate
Subtitles

Arabic, French, Portuguese, Italian, German, Russian, English, Spanish, Korean, Thai, Indonesian, Japanese, Kazakh, Hindi, Swedish, Greek, Chinese, Ukrainian, Polish, Dutch, Turkish

Found in

Algorithms and Data Structures Courses

Overview

Class Central Tips

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.

Syllabus

Introduction

Welcome to Algorithms, Part II.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Taught by

Robert Sedgewick and Kevin Wayne

Reviews

4.8 rating, based on 21 Class Central reviews

4.9 rating at Coursera based on 1912 ratings

Start your review of Algorithms, Part II

Wei En

Professor Sedgewick's explanation of algorithms and his use of visuals were excellent and instrumental in helping me to understand the content. For this course, I only watched the videos, so I cannot give any feedback on the exercises programming a…

Professor Sedgewick's explanation of algorithms and his use of visuals were excellent and instrumental in helping me to understand the content.

For this course, I only watched the videos, so I cannot give any feedback on the exercises programming assignments. As far as I know from my experience in Algorithms I, which I nearly fully completed, the exercises tend to have a few challenging questions but a couple of questions which force you to simulate a computer and run the algorithms. Personally, I dislike these type of questions. On the other hand, the programming assignments are fun and force students to think out of the box. Also, the grading system is very detailed and gives a lot of useful feedback.

In general, this course is an great fit for anyone who wishes to learn more about algorithms; however, I would suggest taking Algorithms, Part I before taking this course.
WickWack

This class (and part 1) are the best courses I've ever done online. The lectures are clear, concise, and interesting. The assignments are fascinating, touching on a whole range of topics (data compression, scientific computing, etc) while allowing…

This class (and part 1) are the best courses I've ever done online. The lectures are clear, concise, and interesting. The assignments are fascinating, touching on a whole range of topics (data compression, scientific computing, etc) while allowing us to use and adapt the algorithms discussed in lecture. That's probably my favorite point: rather than have us blindly implement an algorithm described in lecture, the assignments invite us to adapt and use the algorithm in a real application.

Another point: the course involves automated grading/feedback on the programming assignments. This feedback is incredibly detailed, giving information about error checking, performance testing, and even good coding style. As a new developer, I found this immensely helpful.
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