Algorithms, Part I

Princeton University via Coursera

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Provider

Coursera
Pricing

Free Online Course (Audit)
Languages

English
Duration & workload

54 hours
Sessions

On-Demand
Level

Intermediate
Subtitles

Arabic, French, Portuguese, Italian, German, Russian, English, Spanish, Korean, Thai, Indonesian, Kazakh, Hindi, Swedish, Greek, Chinese, Ukrainian, Japanese, Polish, Dutch, Turkish, Hungarian, Bengali, Pashto, Urdu, Azerbaijani, Farsi

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Overview

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. People who are interested in digging deeper into the content may wish to obtain the textbook Algorithms, Fourth Edition (upon which the course is based) or visit the website algs4.cs.princeton.edu for a wealth of additional material. This course does not offer a certificate upon completion.

Syllabus

Course Introduction

Welcome to Algorithms, Part I.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Symbol Table Applications

We consider various applications of symbol tables including sets, dictionary clients, indexing clients, and sparse vectors.

Taught by

Robert Sedgewick and Kevin Wayne

Reviews

4.5 rating, based on 62 Class Central reviews

4.9 rating at Coursera based on 11559 ratings

Start your review of Algorithms, Part I

Miguel Rey

Worst course I've ever taken. I was really engaged to this course and spent many hours studying, taking neat notes, researching, making diagrams and trying to understand what Sedgewick says. I have a background in programming and strong knowledge of…

Worst course I've ever taken. I was really engaged to this course and spent many hours studying, taking neat notes, researching, making diagrams and trying to understand what Sedgewick says. I have a background in programming and strong knowledge of relatively advanced mathematical topics such as logic, calculus and proofs. Almost every subject he explains is like an enigma that you'll have to find the answers to on your own. He does not care about explaining the concepts in an understandable manner. You have to read his book to have an clue of what he is explaining, since there is practically no material around about a lot of topics he covers; such as Quick-find and Union-Find algorithms and even so you end up even more confused because the lectures are inconsistent with what it is said in the book (the book alone does not help either). Also he's always changing the naming conventions and does not care to explain what exactly he means when he refers to variables or programming concepts to his liking. For example there is an operation in a couple of algorithms which is mathematically defined as "find" from the first lectures. In two different lectures he says "find" to refer to a certain operation and later he uses the term to refer to something else that is not even in the slides nor in the book. Also he explained vaguely a WHOLE mathematical proof on the performance of an algorithm just in words without writing down anything that may remotely help you. This proof was quite complex, it involved logarithms and series among other things. If you want to go through the lectures in a superficial manner getting the gist, fine but if you really care about understanding every concept and catch the essence of the course, it will be a nightmare. Although it is not likely that someone willing to do an course on algorithms is looking for superficial knowledge. If you really want to tear your hair out, take this course...
Ken Sellers @ken

Because I don't know Java (yet) and the homework can only be submitted in Java, I audited this course. Time well spent! Even without working the exercises, the lectures were easy to follow and highly interesting. I picked up several things that will likely help me write better code.
WickWack

This class (and part 2) are the best courses I've ever done online. The lectures are clear, concise, and interesting. The assignments are fascinating, touching on a whole range of topics (computational geometry, physics, etc.) while allowing us to…

This class (and part 2) are the best courses I've ever done online. The lectures are clear, concise, and interesting. The assignments are fascinating, touching on a whole range of topics (computational geometry, physics, etc.) while allowing us to use and adapt the algorithms discussed in lecture. That's probably my favorite point: rather than have us blindly implement an algorithm described in lecture, the assignments invite us to adapt and use the algorithm in a real application.

Another point: the course involves automated grading/feedback on the programming assignments. This feedback is incredibly detailed, giving information about error checking, performance testing, and even good coding style. As a new developer, I found this immensely helpful.
Wei En

Professor Sedgewick's explanation of algorithms and his use of visuals were excellent and instrumental in helping me to understand the content.

The exercises tend to have a few challenging questions but a couple of questions which force you to simulate a computer and run the algorithms. Personally, I dislike these type of questions. On the other hand, the programming assignments are fun and force students to think out of the box. Also, the grading system is very detailed and gives a lot of useful feedback.

In general, this course is an great fit for anyone who wishes to learn about algorithms and is new to the field.
Ilya Rudyak

This is kind of specific course on algorithms - authors have their own Java library, specific interests in applications and even their own terminology sometimes. This is course about Java realization of algorithms, not about math.

The best part of the course is of course problem sets with rigorous tests. There are a lot of additional exercises in their book if you're interested in programming of algorithms - many of them are from job interviews.
Anonymous

Difficult class, not for beginners. PowerPoint presentation slides are boring. It seems Professor Sedgewick has taught this class so many times that he've got tired of it.
Mark Wilbur

This course is an algorithms class intended to be the 2nd course taken by CS students at Princeton. From what I could tell the course was pretty true to the actual Princeton class, and the automated grader was great. This algorithms class was well designed and I’ll probably take the follow-up class.
Anonymous

I read some books and do some classes about algorithms,but I think this class is best way to learn algorithms.Prof Sedgewick explain algorithms and data structures very good.
Anonymous

this algorithm course is a practical one. this course uses java as the main algorithm description tool, and students will have much insight of java. it's useful to learn the different performance of different implementations of an algorithm. there'…

this algorithm course is a practical one. this course uses java as the main algorithm description tool, and students will have much insight of java.

it's useful to learn the different performance of different implementations of an algorithm. there's no much theoretical explanation in this course, and so it's a short for those who want real understanding of some tricky algorithms, such as quick-selection.

the assignments are also practical, not directly related to the algorithms taught, but about how to use them. from my point of view, it's not worth spending hours on finishing the assignments. however, if you are preparing for a tech interview, the interview questions provided by this course are pretty valuable.

in summary, if your are preparing for a top company's tech interview and have enough time, or you are an experienced programmer and want to refresh your algorithmic skills, this course is a good option. if you are a junior, going to your own college's algorithms courses is a better choice.
Anonymous

This is probably one of the best class I took in Algorithm. Yes, the assignments are challenging but you learn quite a bit by just doing so. Furthermore, I found the lectures well done. I find the instructor quite interesting and am motivated to do the next course given by this instructor.
Anonymous

I found this course quite challenging, but learned a lot. Discussion forums were very helpful, much higher standard than other courses I have taken. I enjoyed the lectures. Looking forward to part II. Lack of Java knowledge does make the course very difficult.
Anonymous

Great course. Lectures are very well done, best I have seen so far. Programming assignments were also quite good even though they are in Java, which I didn't know at the start of the course. Problem sets were good, but some work could be improve the interface. Everything was on time.
Anonymous

Hey everyone...
Im new student ...and im try to learn and do my best .
Almost i like it
And im go to shere thiss with my friends and others ...really
Because it's very helpful and interesting
Anonymous

I was first confuse at the first Union Find Video but as he illustrate through code and Demo Video I start to get a hand of it
Doumyo Nguiram Axel

Merci c'est un très bon cours, il nous permet d'être à jour et de s'exercer avec des exemples qu'ils donnent.
赵志勇

This is the most helpful algorithms course that I have taken. It's easy to understand each algorithm with the illustrations. The professor's tone is slow so I can catch it. Anyway, I will recommend it to my classmates and friends whenever talking about algorithm courses.
Tony_Chau

The great course lectures are doing well and the best I have seen. Programming homework is also good, even if they are Java, I do not know at the beginning of the course. The problem set is good, but some work can improve the interface. Everything is on time
Anonymous

I had some programming experience - mostly in Python - when started this course and it was very useful, interesting and inspiring. Prof. Sedgewick is a very good teacher.
Sergey Khaykin

This is the best course in Algorithms I've found on the internet. I've done it twice actually.
The lectures are clear and concise, the simulations explain clearly the algorithms in study.
The homeworks are challenging and interesting. Each assignment took me about 5 hours on average. It is a good refresh on Java as well. Looking forward for the next part of the course.

Sergey.
Zuzana Záborská