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, National Research University Higher School of Economics
Taught by: Alexander S. Kulikov, Visiting Professor
Department of Computer Science and EngineeringTaught by: Michael Levin, Lecturer
Computer ScienceTaught by: Daniel M Kane, Assistant Professor
Department of Computer Science and Engineering / Department of MathematicsTaught 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 |
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: 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: 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: 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: 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: 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
- 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
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National Research University 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.
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Ratings and Reviews
I love the teacher
The assignment should provide more problems related to BST and other trees.
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good course! I've got a lot from it.