Algorithms, Part I

Princeton University

About this Course

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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.

Learner Career Outcomes

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started a new career after completing these courses

34%

got a tangible career benefit from this course

17%

got a pay increase or promotion

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Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 53 hours to complete

English

Subtitles: English, Korean, Russian

Skills you will gain

Data StructureAlgorithmsJava Programming

Learner Career Outcomes

32%

started a new career after completing these courses

34%

got a tangible career benefit from this course

17%

got a pay increase or promotion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 53 hours to complete

English

Subtitles: English, Korean, Russian

Instructors

Instructor rating

4.81/5 (252 Ratings)

Kevin Wayne

Phillip Y. Goldman '86 Senior Lecturer

Computer Science

647,546 Learners

4 Courses

Robert Sedgewick

William O. Baker *39 Professor of Computer Science

Computer Science

664,789 Learners

6 Courses

Offered by

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.

Syllabus - What you will learn from this course

Content Rating98%(47,434 ratings)

Week

Week 1

10 minutes to complete

Course Introduction

Welcome to Algorithms, Part I.

10 minutes to complete

1 video (Total 9 min), 2 readings

1 video

Course Introduction9m

2 readings

Welcome to Algorithms, Part I1m

Lecture Slides

9 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.

9 hours to complete

5 videos (Total 51 min), 2 readings, 2 quizzes

5 videos

Dynamic Connectivity10m

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.

1 hour to complete

6 videos (Total 66 min), 1 reading, 1 quiz

6 videos

Analysis of Algorithms Introduction8m

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

Week 2

9 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.

9 hours to complete

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.

1 hour to complete

6 videos (Total 63 min), 1 reading, 1 quiz

6 videos

Sorting Introduction14m

Selection Sort6m

Insertion Sort9m

Shellsort10m

Shuffling7m

Convex Hull13m

1 reading

Lecture Slides

1 practice exercise

Interview Questions: Elementary Sorts (ungraded)

Week

Week 3

9 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.

9 hours to complete

5 videos (Total 49 min), 2 readings, 2 quizzes

5 videos

Mergesort23m

Bottom-up Mergesort3m

Sorting Complexity9m

Comparators6m

Stability5m

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.

1 hour to complete

4 videos (Total 50 min), 1 reading, 1 quiz

4 videos

Quicksort19m

Selection7m

Duplicate Keys11m

System Sorts11m

1 reading

Lecture Slides

1 practice exercise

Interview Questions: Quicksort (ungraded)

Week

Week 4

9 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.

9 hours to complete

4 videos (Total 74 min), 2 readings, 2 quizzes

4 videos

APIs and Elementary Implementations12m

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.

1 hour to complete

6 videos (Total 77 min), 1 reading, 1 quiz

6 videos

Symbol Table API21m

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

Week 5

1 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.

1 hour to complete

3 videos (Total 63 min), 2 readings, 1 quiz

3 videos

2−3 Search Trees16m

Red-Black BSTs35m

B-Trees (optional)10m

2 readings

Overview10m

Lecture Slides

1 practice exercise

Interview Questions: Balanced Search Trees (ungraded)6m

9 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.

9 hours to complete

5 videos (Total 66 min), 1 reading, 1 quiz

5 videos

1d Range Search8m

Line Segment Intersection5m

Kd-Trees29m

Interval Search Trees13m

Rectangle Intersection8m

1 reading

Lecture Slides

Week

Week 6

1 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.

1 hour to complete

4 videos (Total 50 min), 2 readings, 1 quiz

4 videos

Hash Tables18m

Separate Chaining7m

Linear Probing14m

Hash Table Context10m

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.

26 minutes to complete

4 videos (Total 26 min), 1 reading

4 videos

Symbol Table Applications: Sets (optional)5m

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

Frequently Asked Questions

When will I have access to the lectures and assignments?
Once you enroll, you’ll have access to all videos and programming 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.
Which 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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Algorithms, Part I