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算法,第一部分經典課程

Algorithms, Part I

本課程主要涵蓋了所有認真程序員所需知道的算法和數據結構要點,重點強調Java實現的應用和科學性能分析。第一部分涵蓋了基本的可迭代數據類型、排序和搜索算法。

普林斯頓大學

Coursera

計算機

普通(中級)

31 小時

  • 英語, 韓語
  • 3476

課程概況

介紹基礎數據類型、算法和數據結構,強調Java實現的應用和科學性能分析。特定主題包括:并查算法、基本可迭代數據類型(棧、隊列和背包)、排序算法(快速排序、歸并排序、堆排序)及應用、優先隊列、二分查找樹、紅黑樹、哈希表、符號表應用。

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.

你將學到什么

Data Structure

Priority Queue

Algorithms

Java Programming

課程大綱

周1
完成時間為 10 分鐘
Course Introduction
Welcome to Algorithms, Part I.
1 個視頻 (總計 9 分鐘), 2 個閱讀材料
完成時間為 6 小時

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 個視頻 (總計 51 分鐘), 2 個閱讀材料, 2 個測驗
完成時間為 1 小時

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 個視頻 (總計 66 分鐘), 1 個閱讀材料, 1 個測驗

周2
完成時間為 6 小時
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 個視頻 (總計 61 分鐘), 2 個閱讀材料, 2 個測驗
完成時間為 1 小時

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 個視頻 (總計 63 分鐘), 1 個閱讀材料, 1 個測驗

周3
完成時間為 6 小時
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 個視頻 (總計 49 分鐘), 2 個閱讀材料, 2 個測驗
完成時間為 1 小時

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 個視頻 (總計 50 分鐘), 1 個閱讀材料, 1 個測驗

周4
完成時間為 6 小時
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 個視頻 (總計 74 分鐘), 2 個閱讀材料, 2 個測驗
完成時間為 1 小時

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 個視頻 (總計 77 分鐘), 1 個閱讀材料, 1 個測驗

周5
完成時間為 1 小時
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 個視頻 (總計 63 分鐘), 2 個閱讀材料, 1 個測驗
完成時間為 6 小時

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 個視頻 (總計 66 分鐘), 1 個閱讀材料, 1 個測驗

周6
完成時間為 1 小時
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 個視頻 (總計 50 分鐘), 2 個閱讀材料, 1 個測驗
完成時間為 26 分鐘

Symbol Table Applications
We consider various applications of symbol tables including sets, dictionary clients, indexing clients, and sparse vectors.
4 個視頻 (總計 26 分鐘), 1 個閱讀材料

預備知識

你只需要對Java編程有基本的熟悉程度。這門課主要針對的是,對工程或科學感興趣的大一大二學年本科生,以及對編程具有興趣和一定基礎的高中學生及專業人員。

參考資料

雖然這門課被設計為自給自足式的,但希望在六周課程以外擴展所學知識的同學,可以在我們編寫的教材中找到更深入廣泛的相關內容:《算法》第四版,艾迪生韋斯利出版社出版。

常見問題

本課程會講到哪些算法和數據結構?
第一部分將集中探討基礎數據結構、排序、查找。主題包括:并查算法、二分查找、棧、隊列、背包、插入排序、選擇排序、希爾排序、快速排序、三路快排、歸并排序、堆排序、二分堆、二分查找樹、紅黑樹、分離鏈接和線性探測哈希表、Graham掃描、kd樹。
第二部分將集中探討圖和字符串處理算法。主題包括:深度優先搜索、寬度優先搜索、拓撲排序、Kosaraju-Sharir算法、Kruskal算法、Prim算法、Dijkistra算法、Bellman-Ford算法、Ford-Fulkerson算法、LSD基數排序算法、MSD基數排序算法、三路基數快排算法、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、正則匹配、行程長度編碼、Huffman編碼、LZW壓縮、Burrows-Wheeler變換。

網上還有其它相關資源嗎?
有,我們的免費圖書網站包含教材概要、網絡練習、所有相關算法的Java實現(提供一鍵下載)、測試數據以及很多其它資源。

這門課同“算法設計與分析”課程有何不同?
兩門課是互補的,這門課更強調編程和代碼開發,而那門課更注重數學和證明。這門課側重于在實際應用的實現和測試中學習各種算法,而那門課側重于在解釋算法為何有效的數學建模中學習算法。在典型計算機科學課程設計中,這門課針對的是大一和大二學生,而那門課針對的是大三和大四學生。

我不是計算機專業學生,這門課適合我嗎?
沒問題,這門課適用于任何希望使用計算機解決大型問題的人(因為大型問題需要高效算法)。在普林斯頓的所有學生中,有超過25%的人選過這門課,包括工程、生物、物理、化學、經濟等諸多其它專業的學生。選修這門課的遠遠不只是計算機科學專業的學生。

不熟悉Java編程的話,能選這門課嗎?
我們的核心理念是,算法在實現和測試中是最容易理解的。Java在這里只是用于說明,我們在代碼中特意避開了稀奇古怪的內容。就算你使用其它語言,這門課的代碼你也應該能輕松適應。不過,我們要求這門課的編程作業用Java提交。如果你有其它語言的編程經驗,通過我們的教材《Java編程導論:跨學科研究方法》及相關免費圖書網站來學習我們的編程模型對你應該會有幫助。

沒有任何編程基礎的話,還能選這門課嗎?
也許不行。

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