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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/algorithms-part2
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课程名称：算法（二） 课程概述：本课程涵盖了每位严肃程序员在算法和数据结构方面需要了解的基本信息，重点介绍了Java实现的应用和科学性能分析。第一部分涵盖了基本数据结构、排序和搜索算法，而第二部分则专注于图形和字符串处理算法。课程所有内容均可免费获取，但完成后不提供证书。 课程大纲： 1. **导言**：欢迎加入《算法（二）》课程。 2. **无向图**：定义无向图API，讨论邻接矩阵和邻接表的表示方式，介绍深度优先搜索和广度优先搜索这两种经典搜索算法，处理连通分量计算及相关应用。 3. **有向图**：研究有向图，包括在有向图中使用深度优先和广度优先搜索，讨论垃圾回收和网页爬虫等应用，介绍无环有向图的拓扑排序算法，并实现Kosaraju−Sharir算法计算强连通分量。 4. **最小生成树**：研究最小生成树问题，考虑通用贪心算法并实现经典的Kruskal和Prim算法，讨论应用和开放问题。 5. **最短路径**：分析最短路径问题和基本属性，介绍Dijkstra算法及用于加权有向图的Bellman−Ford−Moore算法，探讨内容感知填充和套利等应用。 6. **最大流与最小割**：介绍最大流和最小割问题，包含Ford−Fulkerson算法及其有效实现，讨论应用如二分匹配和棒球淘汰。 7. **基数排序**：探讨字符串及相关对象的专用排序算法，介绍LSD和MSD基数排序，以及三路基数快速排序，讨论后缀排序及相关应用。 8. **字典树**：研究字符串键的符号表算法，目标是实现一种比哈希表更灵活且速度快的数据结构，包括多路字典树和三叉搜索字典树。 9. **子字符串搜索**：比较字符串查找算法，从暴力算法到Knuth−Morris−Pratt算法，再到Boyer−Moore算法和Rabin−Karp指纹算法，分析运行时间。 10. **正则表达式**：探讨正则表达式的概念以及grep算法的实现，应用于文本中搜索子字符串。 11. **数据压缩**：实现经典数据压缩方案，包括游程编码、霍夫曼压缩和LZW压缩，使用基于优先队列和符号表的Java库进行高效实现。 12. **归约**：讨论将新问题归约为最大流和最短路径问题的思路，描述经典的未解决问题，并探索算法效率的问题。 13. **线性规划（可选）**：概述线性规划和单纯形法，讨论其在运筹学中的重要性及与已经考虑的算法的关系。 14. **难解性**：探讨是否存在通用问题求解模型，以及P、NP、NP-完全等复杂度类的介绍，讨论著名的P=NP问题及其对已处理算法的影响。 本课程提供了全面深入的算法学习内容，适合程序员和计算机科学爱好者。
Name:Introduction
Description:Welcome to Algorithms, Part II.
Name:Undirected Graphs
Description: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.
Name:Directed Graphs
Description: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.
Name:Minimum Spanning Trees
Description: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.
Name:Shortest Paths
Description: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.
Name:Maximum Flow and Minimum Cut
Description: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.
Name:Radix Sorts
Description: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.
Name:Tries
Description: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.
Name:Substring Search
Description: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.
Name:Regular Expressions
Description: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.
Name:Data Compression
Description: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.
Name:Reductions
Description: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.
Name:Linear Programming (optional)
Description: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.
Name:Intractability
Description: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.
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.
