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.
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Princeton University
Syllabus - What you will learn from this course
Week
110 minutes to complete
Course Introduction
Welcome to Algorithms, Part I.
1 video (Total 9 min), 2 readings
1 video
2 readings
Welcome to Algorithms, Part I1m
Lecture Slides
6 hours to complete
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 videos (Total 51 min), 2 readings, 2 quizzes
5 videos
Quick Find10m
Quick Union7m
Quick-Union Improvements13m
Union−Find Applications9m
2 readings
Overview1m
Lecture Slides
1 practice exercise
Interview Questions: Union–Find (ungraded)
1 hour to complete
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 videos (Total 66 min), 1 reading, 1 quiz
6 videos
Observations10m
Mathematical Models12m
Order-of-Growth Classifications14m
Theory of Algorithms11m
Memory8m
1 reading
Lecture Slides
1 practice exercise
Interview Questions: Analysis of Algorithms (ungraded)
Week
26 hours to complete
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 videos (Total 61 min), 2 readings, 2 quizzes
6 videos
Stacks16m
Resizing Arrays9m
Queues4m
Generics9m
Iterators7m
Stack and Queue Applications (optional)13m
2 readings
Overview1m
Lecture Slides
1 practice exercise
Interview Questions: Stacks and Queues (ungraded)
1 hour to complete
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 videos (Total 63 min), 1 reading, 1 quiz
6 videos
Selection Sort6m
Insertion Sort9m
Shellsort10m
Shuffling7m
Convex Hull13m
1 reading
Lecture Slides
1 practice exercise
Interview Questions: Elementary Sorts (ungraded)
Week
36 hours to complete
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 videos (Total 49 min), 2 readings, 2 quizzes
2 readings
Overview
Lecture Slides
1 practice exercise
Interview Questions: Mergesort (ungraded)
1 hour to complete
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 videos (Total 50 min), 1 reading, 1 quiz
1 reading
Lecture Slides
1 practice exercise
Interview Questions: Quicksort (ungraded)
Week
46 hours to complete
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 videos (Total 74 min), 2 readings, 2 quizzes
4 videos
Binary Heaps23m
Heapsort14m
Event-Driven Simulation (optional)22m
2 readings
Overview10m
Lecture Slides
1 practice exercise
Interview Questions: Priority Queues (ungraded)
1 hour to complete
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 videos (Total 77 min), 1 reading, 1 quiz
6 videos
Elementary Implementations9m
Ordered Operations6m
Binary Search Trees19m
Ordered Operations in BSTs10m
Deletion in BSTs9m
1 reading
Lecture Slides
1 practice exercise
Interview Questions: Elementary Symbol Tables (ungraded)8m
Week
51 hour to complete
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 videos (Total 63 min), 2 readings, 1 quiz
2 readings
Overview10m
Lecture Slides
1 practice exercise
Interview Questions: Balanced Search Trees (ungraded)6m
6 hours to complete
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 videos (Total 66 min), 1 reading, 1 quiz
5 videos
Line Segment Intersection5m
Kd-Trees29m
Interval Search Trees13m
Rectangle Intersection8m
1 reading
Lecture Slides
Week
61 hour to complete
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 videos (Total 50 min), 2 readings, 1 quiz
2 readings
Overview10m
Lecture Slides
1 practice exercise
Interview Questions: Hash Tables (ungraded)
26 minutes to complete
Symbol Table Applications
We consider various applications of symbol tables including sets, dictionary clients, indexing clients, and sparse vectors.
4 videos (Total 26 min), 1 reading
4 videos
Symbol Table Applications: Dictionary Clients (optional)5m
Symbol Table Applications: Indexing Clients (optional)7m
Symbol Table Applications: Sparse Vectors (optional)7m
1 reading
Lecture Slides
33%
started a new career after completing these courses
33%
got a tangible career benefit from this course
15%
got a pay increase or promotion
Top Reviews
This is a great class. I learned / re-learned a ton. The assignments were challenge and left a definite feel of accomplishment. The programming environment and automated grading system were excellent.
Good contents and the logic of the whole course structure is very clear for a novice like me. The weekly homework is also awesome. Would recommend to anyone who wants to learn about computer science.
Instructors
Kevin Wayne
Phillip Y. Goldman '86 Senior LecturerComputer Science
Robert Sedgewick
William O. Baker *39 Professor of Computer ScienceComputer Science
About Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. It is one of the eight universities of the Ivy League, and one of the nine Colonial Colleges founded before the American Revolution.
Frequently Asked Questions
When will I have access to the lectures and assignments?
Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.
Do I need to pay for this course?
No. All features of this course are available for free.
Can I earn a certificate in this course?
No. As per Princeton University policy, no certificates, credentials, or reports are awarded in connection with this course.
I have no familiarity with Java programming. Can I still take this course?
Our central thesis is that algorithms are best understood by implementing and testing them. Our use of Java is essentially expository, and we shy away from exotic language features, so we expect you would be able to adapt our code to your favorite language. However, we require that you submit the programming assignments in Java.
Which algorithms and data structures are covered in this course?
Part I focuses on elementary data structures, sorting, and searching. Topics include union-find, binary search, stacks, queues, bags, insertion sort, selection sort, shellsort, quicksort, 3-way quicksort, mergesort, heapsort, binary heaps, binary search trees, red−black trees, separate-chaining and linear-probing hash tables, Graham scan, and kd-trees.
Part II focuses on graph and string-processing algorithms. Topics include depth-first search, breadth-first search, topological sort, Kosaraju−Sharir, Kruskal, Prim, Dijkistra, Bellman−Ford, Ford−Fulkerson, LSD radix sort, MSD radix sort, 3-way radix quicksort, multiway tries, ternary search tries, Knuth−Morris−Pratt, Boyer−Moore, Rabin−Karp, regular expression matching, run-length coding, Huffman coding, LZW compression, and the Burrows−Wheeler transform.
What kinds of assessments are available in this course?
Weekly exercises, weekly programming assignments, weekly interview questions, and a final exam.
The exercises are primarily composed of short drill questions (such as tracing the execution of an algorithm or data structure), designed to help you master the material.
The programming assignments involve either implementing algorithms and data structures (deques, randomized queues, and kd-trees) or applying algorithms and data structures to an interesting domain (computational chemistry, computational geometry, and mathematical recreation). The assignments are evaluated using a sophisticated autograder that provides detailed feedback about style, correctness, and efficiency.
The interview questions are similar to those that you might find at a technical job interview. They are optional and not graded.
I am/was not a Computer Science major. Is this course for me?
This course is for anyone using a computer to address large problems (and therefore needing efficient algorithms). At Princeton, over 25% of all students take the course, including people majoring in engineering, biology, physics, chemistry, economics, and many other fields, not just computer science.
How does this course differ from Design and Analysis of Algorithms?
The two courses are complementary. This one is essentially a programming course that concentrates on developing code; that one is essentially a math course that concentrates on understanding proofs. This course is about learning algorithms in the context of implementing and testing them in practical applications; that one is about learning algorithms in the context of developing mathematical models that help explain why they are efficient. In typical computer science curriculums, a course like this one is taken by first- and second-year students and a course like that one is taken by juniors and seniors.
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