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Updated in [June 30th, 2023]
This course, Algorithms Part II, provides an overview of essential information related to algorithms and data structures. It focuses on applications and scientific performance analysis of Java implementations, with emphasis on graph- and string-processing algorithms. Part I of the course covers elementary data structures, sorting, and searching algorithms. All the features of this course are available for free and it does not offer a certificate upon completion.
[Applications]
Upon completion of this course, Algorithms Part II, students will have a better understanding of graph- and string-processing algorithms. They will be able to apply this knowledge to their own programming projects, as well as analyze the performance of Java implementations. Additionally, students will be able to use the course material to further their knowledge of algorithms and data structures.
[Career Path]
Recommended Career Path:Data Scientist:
Data Scientists are responsible for analyzing large amounts of data to identify patterns and trends, and then using this information to develop strategies and solutions. They use a variety of tools and techniques, such as machine learning, predictive analytics, and natural language processing, to uncover insights from data. Data Scientists must have strong problem-solving and analytical skills, as well as a deep understanding of mathematics, statistics, and computer science.
The demand for Data Scientists is growing rapidly, and the job outlook is very positive. Companies are increasingly relying on data to make decisions, and Data Scientists are in high demand to help them make sense of the data. As technology advances, the need for Data Scientists will continue to grow. Companies are also looking for Data Scientists with experience in specific industries, such as healthcare, finance, and retail.
[Education Path]
The recommended educational path for learners of this course is to pursue a degree in Computer Science. This degree will provide learners with a comprehensive understanding of the fundamentals of computer science, including algorithms, data structures, programming languages, software engineering, operating systems, databases, computer networks, artificial intelligence, and computer graphics. Learners will also gain an understanding of the development trends in computer science, such as cloud computing, big data, and machine learning.
The degree program typically consists of core courses in computer science, mathematics, and engineering, as well as electives in areas such as computer graphics, artificial intelligence, and software engineering. Learners will also have the opportunity to participate in research projects and internships.
The development trend in computer science is towards more complex algorithms and data structures, as well as the use of artificial intelligence and machine learning to solve complex problems. As such, learners should be prepared to stay up-to-date with the latest developments in the field. Additionally, learners should be prepared to develop their own algorithms and data structures, as well as to use existing algorithms and data structures to solve real-world problems.
Course 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.
