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.

# Algorithms, Part I

Offered By

## Algorithms, Part I

## About this Course

### Learner Career Outcomes

## 32%

## 34%

## 17%

### Skills you will gain

### Learner Career Outcomes

## 32%

## 34%

## 17%

#### 100% online

#### Flexible deadlines

#### Intermediate Level

#### Approx. 33 hours to complete

#### English

## Syllabus - What you will learn from this course

**10 minutes to complete**

## Course Introduction

Welcome to Algorithms, Part I.

**10 minutes to complete**

**1 video**

**2 readings**

**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**

**2 readings**

**1 practice exercise**

**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**

**1 reading**

**1 practice exercise**

**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**

**2 readings**

**1 practice exercise**

**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**

**1 reading**

**1 practice exercise**

**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**

**2 readings**

**1 practice exercise**

**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**

**1 reading**

**1 practice exercise**

**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**

**2 readings**

**1 practice exercise**

**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**

**1 reading**

**1 practice exercise**

### Top reviews from Algorithms, Part I

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.

### About Princeton University

## 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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