Algorithms, Part I from Coursera

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.

What's inside

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.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Teaches algorithm analysis which is highly relevant to computer science

Develops algorithms and data structures, which are core skills for computer science

Taught by Robert Sedgewick and Kevin Wayne, who are recognized for their work in algorithms and data structures

Covers essential information every programmer needs to know

Uses Java implementations, which makes it immediately accessible to learners

Provides a wealth of additional material for those who want to dig deeper

Reviews summary

Algorithms i: essentials

learners say Algorithms, Part I is an engaging, challenging course covering fundamental topics in algorithms and data structures, ideal for students with some programming background and a desire to deepen their understanding. Through structured lectures, engaging assignments, and detailed explanations, the course imparts essential knowledge and skills. Highlights of the course include: - **Comprehensive Coverage**: The course comprehensively explores fundamental data structures like arrays, stacks, queues, trees, and graphs, along with essential algorithms for sorting, searching, and graph traversal. - **Engaging Lectures**: Led by renowned Professor Robert Sedgewick, the lectures clearly explain concepts with intuitive examples and animations, making complex topics accessible and enjoyable to grasp. - **Challenging Assignments**: Weekly programming assignments provide practical application of concepts learned in lectures, helping students solidify their understanding and develop problem-solving skills. - **Expert Feedback**: An automated grading system provides detailed feedback on assignments, highlighting errors and guiding students towards improvement. The active discussion forums offer support from TAs and peers, fostering a collaborative learning environment. - **Real-World Applications**: The course emphasizes the practical relevance of algorithms and data structures, showcasing their applications in various fields such as computational geometry, physics, and network analysis. Students appreciate the course's well-structured content, clear explanations, and challenging assignments that encourage critical thinking and problem-solving. While some assignments can be time-consuming, the sense of accomplishment upon completion is highly rewarding. The course effectively prepares students for further studies in algorithms and data structures and enhances their programming proficiency. Some students have noted that prior knowledge of programming concepts, particularly in Java, is beneficial for the course. Additionally, the course requires a significant time commitment, with assignments often taking longer than the estimated time. However, the comprehensive learning experience and the opportunity to master fundamental algorithms and data structures make this course highly recommended for motivated learners seeking to strengthen their programming skills.

The content is largely positive.

"learners say Algorithms, Part I is an engaging, challenging course covering fundamental topics in algorithms and data structures, ideal for students with some programming background and a desire to deepen their understanding."

"Highlights of the course include: - **Comprehensive Coverage**: The course comprehensively explores fundamental data structures like arrays, stacks, queues, trees, and graphs, along with essential algorithms for sorting, searching, and graph traversal."

"Led by renowned Professor Robert Sedgewick, the lectures clearly explain concepts with intuitive examples and animations, making complex topics accessible and enjoyable to grasp."

"Weekly programming assignments provide practical application of concepts learned in lectures, helping students solidify their understanding and develop problem-solving skills."

"An automated grading system provides detailed feedback on assignments, highlighting errors and guiding students towards improvement."

"The active discussion forums offer support from TAs and peers, fostering a collaborative learning environment."

"The course emphasizes the practical relevance of algorithms and data structures, showcasing their applications in various fields such as computational geometry, physics, and network analysis."

"Students appreciate the course's well-structured content, clear explanations, and challenging assignments that encourage critical thinking and problem-solving."

The content is largely negative.

"Some students have noted that prior knowledge of programming concepts, particularly in Java, is beneficial for the course."

"Additionally, the course requires a significant time commitment, with assignments often taking longer than the estimated time."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Algorithms, Part I with these activities:

Follow Tutorials on Merge Sort

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Explore online tutorials on merge sort to gain a deeper understanding of its implementation, performance analysis, and applications.

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Search for tutorials on merge sort
Follow along with the tutorial explanations
Implement merge sort in Java to practice the concepts

Write a Summary of Union-Find Algorithms

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Summarize the key concepts and implementation details of union-find algorithms to strengthen your understanding of disjoint-set operations.

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Review the course materials on union-find algorithms
Identify the main concepts and algorithms
Write a concise summary in your own words

Compile a Resource List of Java Libraries

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Gather and organize a list of useful Java libraries that can enhance your programming skills and project development.

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Research and identify relevant Java libraries
Categorize libraries based on their functionalities
Create a documentation or spreadsheet to store the information

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Solve LeetCode Problems

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Practice solving coding problems on LeetCode to reinforce your understanding of algorithm design and data structure implementation techniques.

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Create a LeetCode account
Choose a problem to solve
Implement the solution using Java
Submit your solution and review the results

Implement a Binary Search Tree

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Create a Java implementation of a binary search tree to reinforce your understanding of tree-based data structures and search algorithms.

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Design the interface for your binary search tree
Implement the insertion, search, and deletion methods
Test your implementation with various inputs

Review 'Algorithms, Fourth Edition'

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Read and review the assigned textbook to supplement your understanding of the course material and gain deeper insights into algorithms and data structures.

View Algorithms on Amazon

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Obtain a copy of the textbook
Read assigned chapters and sections
Take notes or summarize key points
Work through practice exercises and problems

Mentor a Beginner in Java Programming

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Share your knowledge and experience by mentoring a beginner in Java programming to reinforce your own understanding and develop your communication skills.

Browse courses on Java

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Identify a beginner who needs guidance
Establish a regular meeting schedule
Review basic Java concepts and answer questions
Provide hands-on coding exercises for practice

Career center

Learners who complete Algorithms, Part I will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists play a vital role in modern data-driven organizations. They work with large and complex datasets to uncover insights and help businesses make informed decisions. Proficiency in algorithms and data structures is a must for Data Scientists, as they need to be able to effectively process and analyze data. The course will provide you with a solid foundation in these essential concepts.

See salaries and explore the career path for Data Scientist

Computer Scientist

Computer Scientists research and develop new computing technologies. They need to have a strong understanding of algorithms and data structures to develop new and innovative solutions. This course will provide you with a solid foundation in these topics, which will prepare you for a successful career as a Computer Scientist.

See salaries and explore the career path for Computer Scientist

Artificial Intelligence Engineer

Artificial Intelligence Engineers design and develop artificial intelligence systems. They need to have a strong understanding of algorithms and data structures to develop efficient and intelligent systems. This course will provide you with the skills and knowledge you need to become a successful Artificial Intelligence Engineer.

See salaries and explore the career path for Artificial Intelligence Engineer

Machine Learning Engineer

Machine Learning Engineers develop and implement machine learning algorithms to solve real-world problems. They need to have a strong understanding of algorithms and data structures to develop efficient and accurate algorithms. This course will provide you with the skills and knowledge you need to become a successful Machine Learning Engineer.

See salaries and explore the career path for Machine Learning Engineer

Data Engineer

Data Engineers design and build systems to store and process data. They need to have a strong understanding of algorithms and data structures to develop efficient and scalable systems. This course will provide you with the skills and knowledge you need to become a successful Data Engineer.

See salaries and explore the career path for Data Engineer

Software Engineer

Software Engineers translate the lofty goals of computer scientists into practical solutions. They have the skills to write the code that turns those goals into reality. In this role, you will need to use algorithms and data structures to solve complex computational problems. This course offers a comprehensive introduction to algorithms and data structures that will help you to perform your job successfully and advance in your career.

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Data Analyst

Data Analysts use data to identify trends and patterns. They help businesses improve their operations and make better decisions by providing insights into the data. This course can help you become a more effective Data Analyst by providing you with strong knowledge in algorithms and data structures. These topics will enable you to efficiently organize and process large datasets, which is essential in this role.

See salaries and explore the career path for Data Analyst

Robotics Engineer

Robotics Engineers design and build robots. They need to have a strong understanding of algorithms and data structures to develop efficient and intelligent robots. This course will provide you with the skills and knowledge you need to become a successful Robotics Engineer.

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Research Scientist

Research Scientists conduct research to advance scientific knowledge. They need to have a strong understanding of algorithms and data structures to develop new and innovative solutions. This course will help you build a foundation in these topics, which will prepare you for a successful career as a Research Scientist.

See salaries and explore the career path for Research Scientist

Software Developer

Software Developers are responsible for designing, implementing, testing, and maintaining software. They need to have a strong understanding of algorithms and data structures to develop high-quality, efficient software solutions. By taking this course, you will build a solid foundation in algorithms and data structures that will make you an effective and valuable Software Developer.

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Web Developer

Web Developers design and develop websites. They need to have a strong understanding of algorithms and data structures to create efficient and user-friendly websites. This course will provide you with the skills and knowledge you need to become a successful Web Developer.

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Game Developer

Game Developers design and develop video games. They need to have a strong understanding of algorithms and data structures to develop efficient and engaging games. This course will provide you with the skills and knowledge you need to succeed as a Game Developer.

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Computer Programmer

Computer Programmers write, modify, and test code to create and maintain software. They need to have a strong understanding of algorithms and data structures to develop effective and efficient code. This course will provide you with a solid foundation in these topics, which will help you excel in your role as a Computer Programmer.

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Mobile Developer

Mobile Developers design and develop applications for mobile devices. They need to have a strong understanding of algorithms and data structures to create efficient and user-friendly apps. This course will provide you with the skills and knowledge you need to succeed as a Mobile Developer.

See salaries and explore the career path for Mobile Developer

Information Security Analyst

Information Security Analysts plan and implement security measures to protect an organization's computer networks and systems. They need to have a strong understanding of algorithms and data structures to develop effective security solutions. This course will help you build a foundation in these topics, which will help you become a more successful Information Security Analyst.

See salaries and explore the career path for Information Security Analyst