Algorithmes, Partie I

Université de Princeton

À propos de ce cours

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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.

Résultats de carrière des étudiants

30%

ont commencé une nouvelle carrière après avoir terminé ce cours

30%

ont bénéficié d'un avantage concret dans leur carrières grâce à ce cours

16%

a obtenu une augmentation de salaire ou une promotion

100 % en ligne

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.

Niveau intermédiaire

Approx. 53 heures pour terminer

Anglais

Sous-titres : Français, Portugais (brésilien), Coréen, Russe, Anglais, Espagnol

Compétences que vous acquerrez

Data StructureAlgorithmsJava Programming

Résultats de carrière des étudiants

30%

ont commencé une nouvelle carrière après avoir terminé ce cours

30%

ont bénéficié d'un avantage concret dans leur carrières grâce à ce cours

16%

a obtenu une augmentation de salaire ou une promotion

100 % en ligne

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.

Niveau intermédiaire

Approx. 53 heures pour terminer

Anglais

Sous-titres : Français, Portugais (brésilien), Coréen, Russe, Anglais, Espagnol

Enseignants

Évaluation de l'enseignant

4.8/5 (758 notes)

Kevin Wayne

Phillip Y. Goldman '86 Senior Lecturer

Computer Science

869,727 étudiants

4 cours

Robert Sedgewick

William O. Baker *39 Professor of Computer Science

Computer Science

891,724 étudiants

6 cours

Offert par

Université de Princeton

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.

Programme du cours : ce que vous apprendrez dans ce cours

Évaluation du contenu98%(54,636 notes)

Semaine

Semaine 1

10 minutes pour terminer

Course Introduction

Welcome to Algorithms, Part I.

10 minutes pour terminer

1 vidéo (Total 9 min), 2 lectures

1 vidéo

Course Introduction9 min

2 lectures

Welcome to Algorithms, Part I1 min

Lecture Slides

9 heures pour terminer

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 heures pour terminer

5 vidéos (Total 51 min), 2 lectures, 2 quiz

5 vidéos

Dynamic Connectivity10 min

Quick Find10 min

Quick Union7 min

Quick-Union Improvements13 min

Union−Find Applications9 min

2 lectures

Overview1 min

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Union–Find (ungraded)

1 heure pour terminer

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 heure pour terminer

6 vidéos (Total 66 min), 1 lecture, 1 quiz

6 vidéos

Analysis of Algorithms Introduction8 min

Observations10 min

Mathematical Models12 min

Order-of-Growth Classifications14 min

Theory of Algorithms11 min

Memory8 min

1 lecture

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Analysis of Algorithms (ungraded)

Semaine

Semaine 2

9 heures pour terminer

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 heures pour terminer

6 vidéos (Total 61 min), 2 lectures, 2 quiz

6 vidéos

Stacks16 min

Resizing Arrays9 min

Queues4 min

Generics9 min

Iterators7 min

Stack and Queue Applications (optional)13 min

2 lectures

Overview1 min

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Stacks and Queues (ungraded)

1 heure pour terminer

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 heure pour terminer

6 vidéos (Total 63 min), 1 lecture, 1 quiz

6 vidéos

Sorting Introduction14 min

Selection Sort6 min

Insertion Sort9 min

Shellsort10 min

Shuffling7 min

Convex Hull13 min

1 lecture

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Elementary Sorts (ungraded)

Semaine

Semaine 3

9 heures pour terminer

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 heures pour terminer

5 vidéos (Total 49 min), 2 lectures, 2 quiz

5 vidéos

Mergesort23 min

Bottom-up Mergesort3 min

Sorting Complexity9 min

Comparators6 min

Stability5 min

2 lectures

Overview

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Mergesort (ungraded)

1 heure pour terminer

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 heure pour terminer

4 vidéos (Total 50 min), 1 lecture, 1 quiz

4 vidéos

Quicksort19 min

Selection7 min

Duplicate Keys11 min

System Sorts11 min

1 lecture

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Quicksort (ungraded)

Semaine

Semaine 4

9 heures pour terminer

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 heures pour terminer

4 vidéos (Total 74 min), 2 lectures, 2 quiz

4 vidéos

APIs and Elementary Implementations12 min

Binary Heaps23 min

Heapsort14 min

Event-Driven Simulation (optional)22 min

2 lectures

Overview10 min

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Priority Queues (ungraded)

2 heures pour terminer

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.

2 heures pour terminer

6 vidéos (Total 77 min), 1 lecture, 1 quiz

6 vidéos

Symbol Table API21 min

Elementary Implementations9 min

Ordered Operations6 min

Binary Search Trees19 min

Ordered Operations in BSTs10 min

Deletion in BSTs9 min

1 lecture

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Elementary Symbol Tables (ungraded)30 min

Semaine

Semaine 5

2 heures pour terminer

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.

2 heures pour terminer

3 vidéos (Total 63 min), 2 lectures, 1 quiz

3 vidéos

2−3 Search Trees16 min

Red-Black BSTs35 min

B-Trees (optional)10 min

2 lectures

Overview10 min

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Balanced Search Trees (ungraded)30 min

9 heures pour terminer

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 heures pour terminer

5 vidéos (Total 66 min), 1 lecture, 1 quiz

5 vidéos

1d Range Search8 min

Line Segment Intersection5 min

Kd-Trees29 min

Interval Search Trees13 min

Rectangle Intersection8 min

1 lecture

Lecture Slides

Semaine

Semaine 6

1 heure pour terminer

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 heure pour terminer

4 vidéos (Total 50 min), 2 lectures, 1 quiz

4 vidéos

Hash Tables18 min

Separate Chaining7 min

Linear Probing14 min

Hash Table Context10 min

2 lectures

Overview10 min

Lecture Slides

1 exercice pour s'entraîner

Interview Questions: Hash Tables (ungraded)

26 minutes pour terminer

Symbol Table Applications

We consider various applications of symbol tables including sets, dictionary clients, indexing clients, and sparse vectors.

26 minutes pour terminer

4 vidéos (Total 26 min), 1 lecture

4 vidéos

Symbol Table Applications: Sets (optional)5 min

Symbol Table Applications: Dictionary Clients (optional)5 min

Symbol Table Applications: Indexing Clients (optional)7 min

Symbol Table Applications: Sparse Vectors (optional)7 min

1 lecture

Lecture Slides

Foire Aux Questions

Quand aurai-je accès aux vidéos de cours et aux devoirs ?
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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Algorithmes, Partie I