Overview
 Platform:
 Coursera
 Provider:
 Princeton University
 Length:
 6 weeks
 Effort:
 612 hours/week
 Language:
 English
 Course Link:
 Algorithms, Part II  Coursera
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 stringprocessing algorithms.
All the features of this course are available for free. It does not offer a certificate upon completion.
Syllabus
WEEK 1
Introduction
Welcome to Algorithms, Part II.
Undirected Graphs
We define an undirected graph API and consider the adjacencymatrix and adjacencylists representations. We introduce two classic algorithms for searching a graph—depthfirst search and breadthfirst 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 depthfirst search and breadthfirst search in digraphs and describe applications ranging from garbage collection to web crawling. Next, we introduce a depthfirst 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.
WEEK 2
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 shortestpaths 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 shortestpaths 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 edgeweighted digraphs with no negative cycles. We also consider applications ranging from contentaware fill to arbitrage.
WEEK 3
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 3way radix quicksort. We conclude with suffix sorting and related applications.
WEEK 4
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 characterbased 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 bruteforce 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.
WEEK 5
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 runlength 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.
WEEK 6
Reductions
Our lectures this week are centered on the idea of problemsolving 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 problemsolving 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 problemsolving 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 NPcomplete, 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
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