Algorithms, Part II

Go to Course: https://www.coursera.org/learn/algorithms-part2

Introduction

### Course Review: Algorithms, Part II on Coursera #### Overview "Algorithms, Part II," offered on Coursera, is a continuation of an essential series for aspiring and practicing programmers who wish to deepen their understanding of algorithms and data structures. This course delves into more advanced topics such as graph-based and string-processing algorithms, building upon the foundational knowledge established in Part I. It provides invaluable insights into scientific performance analysis and practical applications through Java implementations. #### Course Features What stands out the most about this course is that it is completely free to access, allowing learners from all backgrounds to pursue knowledge without financial barriers. However, it's important to note that the course does not provide a certificate upon completion, which might be a downside for some learners looking to showcase their new skills formally. #### Syllabus Highlights The syllabus is comprehensive and covers a range of crucial topics, each designed to enhance your problem-solving skills and algorithmic knowledge: 1. **Undirected Graphs**: Understand the fundamentals of graph representations and traversal algorithms like depth-first search (DFS) and breadth-first search (BFS). 2. **Directed Graphs**: Investigate the complexities of directed graphs, including applications such as web crawling and garbage collection, and master the Kosaraju−Sharir algorithm. 3. **Minimum Spanning Trees**: Learn about the practical applications of Kruskal's and Prim's algorithms in solving the minimum spanning tree problem. 4. **Shortest Paths**: Analyze various shortest-path algorithms, including Dijkstra’s algorithm and the Bellman-Ford-Moore algorithm, and explore their applications. 5. **Maximum Flow and Minimum Cut**: Master the Ford−Fulkerson algorithm and its applications in real-world problems like bipartite matching. 6. **Radix Sorts and Tries**: Dive into specialized sorting algorithms tailored for strings, and explore efficient data structures that offer flexible operations for string processing. 7. **Substring Search**: Gain proficiency in algorithms for substring searches, including the Knuth-Morris-Pratt and Boyer-Moore algorithms. 8. **Regular Expressions and Data Compression**: Learn about string specification through regular expressions and discover various classic data compression techniques. 9. **Linear Programming and Intractability**: Wrap up with insights into linear programming and the complexities of systematically solving problems within different classes like P and NP. #### Learning Experience The course is designed with a balance of theory and practical coding assignments that reinforce learning. Students are encouraged to engage in problem-solving and implement algorithms using Java, which is particularly beneficial for those who wish to apply their knowledge directly to real-world programming challenges. The lectures are well-structured, each building on the last, making complex concepts more digestible. The focus on applications means that learners will not only understand how algorithms work but also where and how to apply them effectively. #### Recommendation I wholeheartedly recommend "Algorithms, Part II" to anyone eager to strengthen their algorithmic skills. Whether you are preparing for technical interviews, working on competitive programming, or aiming to become a more proficient programmer, this course is a treasure trove of knowledge. The free access and robust content make it an exceptional opportunity for both beginners and experienced engineers looking to refine their understanding of algorithms. In summary, "Algorithms, Part II" is not just about learning algorithms; it’s about developing a mindset for problem-solving and analytical thinking that can be applied across various domains in technology. Don't miss out on this chance to elevate your programming skills and expand your expertise in algorithms!

Syllabus

Introduction

Welcome to Algorithms, Part II.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.