About this course: A good algorithm usually comes together with a set of good data structures that allow the algorithm to manipulate the data efficiently. In this course, we consider the common data structures that are used in various computational problems. You will learn how these data structures are implemented in different programming languages and will practice implementing them in our programming assignments. This will help you to understand what is going on inside a particular built-in implementation of a data structure and what to expect from it. You will also learn typical use cases for these data structures. A few examples of questions that we are going to cover in this class are the following: 1. What is a good strategy of resizing a dynamic array? 2. How priority queues are implemented in C++, Java, and Python? 3. How to implement a hash table so that the amortized running time of all operations is O(1) on average? 4. What are good strategies to keep a binary tree balanced? You will also learn how services like Dropbox manage to upload some large files instantly and to save a lot of storage space!

Who is this class for: Programmers with basic experience looking to understand the practical and conceptual underpinnings of algorithms, with the goal of becoming more effective software engineers. Computer science students and researchers as well as interdisciplinary students (studying electrical engineering, mathematics, bioinformatics, etc.) aiming to get more profound understanding of algorithms and hands-on experience implementing them and applying for real-world problems. Applicants who want to prepare for an interview in a high-tech company.

Created by: University of California, San Diego, Higher School of Economics

Taught by: Alexander S. Kulikov, Visiting Professor
Department of Computer Science and Engineering
Taught by: Michael Levin, Lecturer
Computer Science
Taught by: Daniel M Kane, Assistant Professor
Department of Computer Science and Engineering / Department of Mathematics
Taught by: Neil Rhodes, Adjunct Faculty
Computer Science and Engineering

Basic Info	Course 2 of 6 in the Data Structures and Algorithms Specialization
Level	Intermediate
Commitment	4 weeks of study, 5-10 hours/week
Language	English
How To Pass	Pass all graded assignments to complete the course.
User Ratings	4.6 stars Average User Rating 4.6See what learners said

Syllabus

WEEK 1

Basic Data Structures

In this module, you will learn about the basic data structures used throughout the rest of this course. We start this module by looking in detail at the fundamental building blocks: arrays and linked lists. From there, we build up two important data structures: stacks and queues. Next, we look at trees: examples of how they’re used in Computer Science, how they’re implemented, and the various ways they can be traversed. Once you’ve completed this module, you will be able to implement any of these data structures, as well as have a solid understanding of the costs of the operations, as well as the tradeoffs involved in using each data structure.

7 videos, 7 readings, 1 practice quiz

Reading: Welcome
Video: Arrays
Video: Singly-Linked Lists
Video: Doubly-Linked Lists
Reading: Slides and External References
Video: Stacks
Video: Queues
Reading: Slides and External References
Video: Trees
Video: Tree Traversal
Reading: Slides and External References
Practice Quiz: Basic Data Structures
Reading: Available Programming Languages
Reading: FAQ on Programming Assignments
Reading: Acknowledgements

Graded: Programming Assignment 1: Basic Data Structures

WEEK 2

Dynamic Arrays and Amortized Analysis

In this module, we discuss Dynamic Arrays: a way of using arrays when it is unknown ahead-of-time how many elements will be needed. Here, we also discuss amortized analysis: a method of determining the amortized cost of an operation over a sequence of operations. Amortized analysis is very often used to analyse performance of algorithms when the straightforward analysis produces unsatisfactory results, but amortized analysis helps to show that the algorithm is actually efficient. It is used both for Dynamic Arrays analysis and will also be used in the end of this course to analyze Splay trees.

5 videos, 1 reading

Video: Dynamic Arrays
Video: Amortized Analysis: Aggregate Method
Video: Amortized Analysis: Banker's Method
Video: Amortized Analysis: Physicist's Method
Video: Amortized Analysis: Summary
Reading: Slides and External References

Graded: Dynamic Arrays and Amortized Analysis

WEEK 3

Priority Queues and Disjoint Sets

We start this module by considering priority queues which are used to efficiently schedule jobs, either in the context of a computer operating system or in real life, to sort huge files, which is the most important building block for any Big Data processing algorithm, and to efficiently compute shortest paths in graphs, which is a topic we will cover in our next course. For this reason, priority queues have built-in implementations in many programming languages, including C++, Java, and Python. We will see that these implementations are based on a beautiful idea of storing a complete binary tree in an array that allows to implement all priority queue methods in just few lines of code. We will then switch to disjoint sets data structure that is used, for example, in dynamic graph connectivity and image processing. We will see again how simple and natural ideas lead to an implementation that is both easy to code and very efficient. By completing this module, you will be able to implement both these data structures efficiently from scratch.

15 videos, 6 readings, 1 practice quiz

Video: Introduction
Video: Naive Implementations of Priority Queues
Reading: Slides
Video: Binary Trees
Reading: Tree Height Remark
Video: Basic Operations
Video: Complete Binary Trees
Video: Pseudocode
Reading: Slides and External References
Video: Heap Sort
Video: Building a Heap
Video: Final Remarks
Reading: Slides and External References
Video: Overview
Video: Naive Implementations
Reading: Slides and External References
Video: Trees for Disjoint Sets
Video: Union by Rank
Video: Path Compression
Video: Analysis (Optional)
Reading: Slides and External References
Practice Quiz: Priority Queues and Disjoint Sets

Graded: Priority Queues: Quiz

Graded: Quiz: Disjoint Sets

Graded: Programming Assignment 2: Priority Queues and Disjoint Sets

WEEK 4

Hash Tables

In this module you will learn about very powerful and widely used technique called hashing. Its applications include implementation of programming languages, file systems, pattern search, distributed key-value storage and many more. You will learn how to implement data structures to store and modify sets of objects and mappings from one type of objects to another one. You will see that naive implementations either consume huge amount of memory or are slow, and then you will learn to implement hash tables that use linear memory and work in O(1) on average! In the end, you will learn how hash functions are used in modern disrtibuted systems and how they are used to optimize storage of services like Dropbox, Google Drive and Yandex Disk!

22 videos, 4 readings, 1 practice quiz

Video: Applications of Hashing
Video: Analysing Service Access Logs
Video: Direct Addressing
Video: List-based Mapping
Video: Hash Functions
Video: Chaining Scheme
Video: Chaining Implementation and Analysis
Video: Hash Tables
Reading: Slides and External References
Video: Phone Book Problem
Video: Phone Book Problem - Continued
Video: Universal Family
Video: Hashing Integers
Video: Proof: Upper Bound for Chain Length (Optional)
Video: Proof: Universal Family for Integers (Optional)
Video: Hashing Strings
Video: Hashing Strings - Cardinality Fix
Reading: Slides and External References
Video: Search Pattern in Text
Video: Rabin-Karp's Algorithm
Video: Optimization: Precomputation
Video: Optimization: Implementation and Analysis
Reading: Slides and External References
Video: Instant Uploads and Storage Optimization in Dropbox
Video: Distributed Hash Tables
Reading: Slides and External References
Practice Quiz: Hashing

Graded: Hash Tables and Hash Functions

Graded: Programming Assignment 3: Hash Tables

WEEK 5

Binary Search Trees

In this module we study binary search trees, which are a data structure for doing searches on dynamically changing ordered sets. You will learn about many of the difficulties in accomplishing this task and the ways in which we can overcome them. In order to do this you will need to learn the basic structure of binary search trees, how to insert and delete without destroying this structure, and how to ensure that the tree remains balanced.

7 videos, 2 readings, 1 practice quiz

Video: Introduction
Video: Search Trees
Video: Basic Operations
Video: Balance
Reading: Slides and External References
Video: AVL Trees
Video: AVL Tree Implementation
Video: Split and Merge
Reading: Slides and External References
Practice Quiz: Binary Search Trees

WEEK 6

Binary Search Trees 2

In this module we continue studying binary search trees. We study a few non-trivial applications. We then study the new kind of balanced search trees - Splay Trees. They adapt to the queries dynamically and are optimal in many ways.

4 videos, 2 readings, 1 practice quiz

Video: Applications
Reading: Slides and External References
Video: Splay Trees: Introduction
Video: Splay Trees: Implementation
Video: (Optional) Splay Trees: Analysis
Reading: Slides and External References
Practice Quiz: Splay Trees

Graded: Programming Assignment 4: Binary Search Trees

FAQs

How It Works

Coursework

Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.

Help from Your Peers

Connect with thousands of other learners and debate ideas, discuss course material, and get help mastering concepts.

Certificates

Earn official recognition for your work, and share your success with friends, colleagues, and employers.

Creators

University of California, San Diego

UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory.

Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru

Pricing

	Audit	Purchase Course
Access to course materials	Available	Available
Access to graded materials	Not available	Available
Receive a final grade	Not available	Available
Earn a shareable Course Certificate	Not available	Available

Ratings and Reviews

Rated 4.6 out of 5 of 920 ratings

Great lectures and assignments - awesome course!

Great course! I figured disjoint sets was pretty interesting - the rest of the material I get by with no issues, but boy: the BST advanced assignments (splay trees) in week 6 is by far the hardest assignments I tried in both Algorithmic Toolbox and Data Structures. It's a pretty big jump in difficulty (I don't think they explained splay trees in the lectures very well; it was pretty fast), but I was so ecstatic when I solved it that I didn't mind.

Excellent excersises, well taught, good forums. This course is great and covers lots of data structures!

this is my second course that I have taken. I learned many things this course is more difficult than algorithmic toolbox but when you work hard you can finish all units

in the beginning i thought that i would not be able to continue because i dont have a lot of knowledge in c+, java or python, but i decided to learn c+ sonce the first course. these coursed were very difficult but i could finish then and this is all because of the professors whom were excellent and the challenging homework.

Thanks to everyone that has dedicated there time and resources to mke this wonderful course, I appreciate it a lot