算法，第一部分

你将学到什么

课程概况

介绍基础数据类型、算法和数据结构，强调Java实现的应用和科学性能分析。特定主题包括：并查算法、基本可迭代数据类型（栈、队列和背包）、排序算法（快速排序、归并排序、堆排序）及应用、优先队列、二分查找树、红黑树、哈希表、符号表应用。

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.

课程大纲

周1
完成时间为 10 分钟
Course Introduction
Welcome to Algorithms, Part I.
1 个视频 （总计 9 分钟）, 2 个阅读材料
完成时间为 6 小时

Union−Find
We illustrate our basic approach to developing and analyzing algorithms by considering the dynamic connectivity problem. We introduce the union−find data type and consider several implementations (quick find, quick union, weighted quick union, and weighted quick union with path compression). Finally, we apply the union−find data type to the percolation problem from physical chemistry.
5 个视频 （总计 51 分钟）, 2 个阅读材料, 2 个测验
完成时间为 1 小时

Analysis of Algorithms
The basis of our approach for analyzing the performance of algorithms is the scientific method. We begin by performing computational experiments to measure the running times of our programs. We use these measurements to develop hypotheses about performance. Next, we create mathematical models to explain their behavior. Finally, we consider analyzing the memory usage of our Java programs.
6 个视频 （总计 66 分钟）, 1 个阅读材料, 1 个测验

周2
完成时间为 6 小时
Stacks and Queues
We consider two fundamental data types for storing collections of objects: the stack and the queue. We implement each using either a singly-linked list or a resizing array. We introduce two advanced Java features—generics and iterators—that simplify client code. Finally, we consider various applications of stacks and queues ranging from parsing arithmetic expressions to simulating queueing systems.
6 个视频 （总计 61 分钟）, 2 个阅读材料, 2 个测验
完成时间为 1 小时

Elementary Sorts
We introduce the sorting problem and Java's Comparable interface. We study two elementary sorting methods (selection sort and insertion sort) and a variation of one of them (shellsort). We also consider two algorithms for uniformly shuffling an array. We conclude with an application of sorting to computing the convex hull via the Graham scan algorithm.
6 个视频 （总计 63 分钟）, 1 个阅读材料, 1 个测验

周3
完成时间为 6 小时
Mergesort
We study the mergesort algorithm and show that it guarantees to sort any array of n items with at most n lg n compares. We also consider a nonrecursive, bottom-up version. We prove that any compare-based sorting algorithm must make at least n lg n compares in the worst case. We discuss using different orderings for the objects that we are sorting and the related concept of stability.
5 个视频 （总计 49 分钟）, 2 个阅读材料, 2 个测验
完成时间为 1 小时

Quicksort
We introduce and implement the randomized quicksort algorithm and analyze its performance. We also consider randomized quickselect, a quicksort variant which finds the kth smallest item in linear time. Finally, we consider 3-way quicksort, a variant of quicksort that works especially well in the presence of duplicate keys.
4 个视频 （总计 50 分钟）, 1 个阅读材料, 1 个测验

周4
完成时间为 6 小时
Priority Queues
We introduce the priority queue data type and an efficient implementation using the binary heap data structure. This implementation also leads to an efficient sorting algorithm known as heapsort. We conclude with an applications of priority queues where we simulate the motion of n particles subject to the laws of elastic collision.
4 个视频 （总计 74 分钟）, 2 个阅读材料, 2 个测验
完成时间为 1 小时

Elementary Symbol Tables
We define an API for symbol tables (also known as associative arrays, maps, or dictionaries) and describe two elementary implementations using a sorted array (binary search) and an unordered list (sequential search). When the keys are Comparable, we define an extended API that includes the additional methods min, max floor, ceiling, rank, and select. To develop an efficient implementation of this API, we study the binary search tree data structure and analyze its performance.
6 个视频 （总计 77 分钟）, 1 个阅读材料, 1 个测验

周5
完成时间为 1 小时
Balanced Search Trees
In this lecture, our goal is to develop a symbol table with guaranteed logarithmic performance for search and insert (and many other operations). We begin with 2−3 trees, which are easy to analyze but hard to implement. Next, we consider red−black binary search trees, which we view as a novel way to implement 2−3 trees as binary search trees. Finally, we introduce B-trees, a generalization of 2−3 trees that are widely used to implement file systems.
3 个视频 （总计 63 分钟）, 2 个阅读材料, 1 个测验
完成时间为 6 小时

Geometric Applications of BSTs
We start with 1d and 2d range searching, where the goal is to find all points in a given 1d or 2d interval. To accomplish this, we consider kd-trees, a natural generalization of BSTs when the keys are points in the plane (or higher dimensions). We also consider intersection problems, where the goal is to find all intersections among a set of line segments or rectangles.
5 个视频 （总计 66 分钟）, 1 个阅读材料, 1 个测验

周6
完成时间为 1 小时
Hash Tables
We begin by describing the desirable properties of hash function and how to implement them in Java, including a fundamental tenet known as the uniform hashing assumption that underlies the potential success of a hashing application. Then, we consider two strategies for implementing hash tables—separate chaining and linear probing. Both strategies yield constant-time performance for search and insert under the uniform hashing assumption.
4 个视频 （总计 50 分钟）, 2 个阅读材料, 1 个测验
完成时间为 26 分钟

Symbol Table Applications
We consider various applications of symbol tables including sets, dictionary clients, indexing clients, and sparse vectors.
4 个视频 （总计 26 分钟）, 1 个阅读材料

预备知识

你只需要对Java编程有基本的熟悉程度。这门课主要针对的是，对工程或科学感兴趣的大一大二学年本科生，以及对编程具有兴趣和一定基础的高中学生及专业人员。

参考资料

虽然这门课被设计为自给自足式的，但希望在六周课程以外扩展所学知识的同学，可以在我们编写的教材中找到更深入广泛的相关内容：《算法》第四版，艾迪生韦斯利出版社出版。

常见问题

本课程会讲到哪些算法和数据结构？
第一部分将集中探讨基础数据结构、排序、查找。主题包括：并查算法、二分查找、栈、队列、背包、插入排序、选择排序、希尔排序、快速排序、三路快排、归并排序、堆排序、二分堆、二分查找树、红黑树、分离链接和线性探测哈希表、Graham扫描、kd树。
第二部分将集中探讨图和字符串处理算法。主题包括：深度优先搜索、宽度优先搜索、拓扑排序、Kosaraju-Sharir算法、Kruskal算法、Prim算法、Dijkistra算法、Bellman-Ford算法、Ford-Fulkerson算法、LSD基数排序算法、MSD基数排序算法、三路基数快排算法、多路trie算法、三元查找trie算法、Knuth-Morris-Pratt算法、Boyer-Moore算法、Rabin-Karp算法、正则匹配、行程长度编码、Huffman编码、LZW压缩、Burrows-Wheeler变换。

网上还有其它相关资源吗？
有，我们的免费图书网站包含教材概要、网络练习、所有相关算法的Java实现（提供一键下载）、测试数据以及很多其它资源。

这门课同“算法设计与分析”课程有何不同？
两门课是互补的，这门课更强调编程和代码开发，而那门课更注重数学和证明。这门课侧重于在实际应用的实现和测试中学习各种算法，而那门课侧重于在解释算法为何有效的数学建模中学习算法。在典型计算机科学课程设计中，这门课针对的是大一和大二学生，而那门课针对的是大三和大四学生。

我不是计算机专业学生，这门课适合我吗？
没问题，这门课适用于任何希望使用计算机解决大型问题的人（因为大型问题需要高效算法）。在普林斯顿的所有学生中，有超过25%的人选过这门课，包括工程、生物、物理、化学、经济等诸多其它专业的学生。选修这门课的远远不只是计算机科学专业的学生。

不熟悉Java编程的话，能选这门课吗？
我们的核心理念是，算法在实现和测试中是最容易理解的。Java在这里只是用于说明，我们在代码中特意避开了稀奇古怪的内容。就算你使用其它语言，这门课的代码你也应该能轻松适应。不过，我们要求这门课的编程作业用Java提交。如果你有其它语言的编程经验，通过我们的教材《Java编程导论：跨学科研究方法》及相关免费图书网站来学习我们的编程模型对你应该会有帮助。

没有任何编程基础的话，还能选这门课吗？
也许不行。