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Introduction to Algorithms
A comprehensive update of the leading algorithms text, with new material on matchings in bipartite graphs, online algorithms, machine learning, and other topics.
Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. It covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers, with self-contained chapters and algorithms in pseudocode. Since the publication of the first edition, Introduction to Algorithms has become the leading algorithms text in universities worldwide as well as the standard reference for professionals. This fourth edition has been updated throughout.
New for the fourth edition
New chapters on matchings in bipartite graphs, online algorithms, and machine learningNew material on topics including solving recurrence equations, hash tables, potential functions, and suffix arrays140 new exercises and 22 new problemsReader feedback-informed improvements to old problemsClearer, more personal, and gender-neutral writing styleColor added to improve visual presentationNotes, bibliography, and index updated to reflect developments in the fieldWebsite with new supplementary material
Warning: Avoid counterfeit copies of Introduction to Algorithms by buying only from reputable retailers. Counterfeit and pirated copies are incomplete and contain errors.
Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. It covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers, with self-contained chapters and algorithms in pseudocode. Since the publication of the first edition, Introduction to Algorithms has become the leading algorithms text in universities worldwide as well as the standard reference for professionals. This fourth edition has been updated throughout.
New for the fourth edition
New chapters on matchings in bipartite graphs, online algorithms, and machine learningNew material on topics including solving recurrence equations, hash tables, potential functions, and suffix arrays140 new exercises and 22 new problemsReader feedback-informed improvements to old problemsClearer, more personal, and gender-neutral writing styleColor added to improve visual presentationNotes, bibliography, and index updated to reflect developments in the fieldWebsite with new supplementary material
Warning: Avoid counterfeit copies of Introduction to Algorithms by buying only from reputable retailers. Counterfeit and pirated copies are incomplete and contain errors.
1184 pages, Hardcover
First published January 1, 1989
About the author
Thomas H. Cormen
10 books123 followersThomas H. Cormen is the co-author of Introduction to Algorithms, along with Charles Leiserson, Ron Rivest, and Cliff Stein. He is a Full Professor of computer science at Dartmouth College and currently Chair of the Dartmouth College Writing Program.
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Displaying 1 - 30 of 289 reviews
April 7, 2013
What a terrible book. Though it's the cornerstone of many CS undergrad algorithm courses, this book fails in every way. In almost every way, Dasgupta and Papadimitriou's "Algorithms" is a much better choice: http://www.goodreads.com/book/show/13...
It tries to be a reference book presenting a good summary of algorithms but any of the interesting bits are left as "exercises to the student." Many of these exercises are do-able but far from trivial mental connections. A few require some mental Ah Ha moments.
It fails at being a reference book
It tries to be a text book (didactic) but it is too verbose and goes into too much depth on every topic along the way to be a useful guide. A possibly more useful organization would have been to have 2 virtual books, the first a much shorter textbook, the second an algorithm reference.
It fails at being a text book
It tries to be a workbook by presenting many exercises to the reader. The problem is that it provides inadequate scaffolding. It just goes ahead and gives you the answers to what could have been medium difficulty questions (since it's trying to be a mostly complete reference). This gives you no chance to flex your mental muscle on tractable problems. All of the harder problems are left as exercises without much help of how to approach them.
It tries to be a reference book presenting a good summary of algorithms but any of the interesting bits are left as "exercises to the student." Many of these exercises are do-able but far from trivial mental connections. A few require some mental Ah Ha moments.
It fails at being a reference book
It tries to be a text book (didactic) but it is too verbose and goes into too much depth on every topic along the way to be a useful guide. A possibly more useful organization would have been to have 2 virtual books, the first a much shorter textbook, the second an algorithm reference.
It fails at being a text book
It tries to be a workbook by presenting many exercises to the reader. The problem is that it provides inadequate scaffolding. It just goes ahead and gives you the answers to what could have been medium difficulty questions (since it's trying to be a mostly complete reference). This gives you no chance to flex your mental muscle on tractable problems. All of the harder problems are left as exercises without much help of how to approach them.
December 16, 2018
I think this book is incorrectly positioned as an "Introduction" to algorithms.
If you are interested in learning algorithms, this should probably not be the first book you read. I would instead recommend Robert Sedgewick's book or course on Coursera.
The problem with this comes down to the fact that is focuses too much on the mathematical details, while ignoring other interesting aspects. Many crucial aspects of classic algorithms are relegated to the exercises section instead of being covered front and center. Even when covering important algorithms, the book glosses over important details.
When it comes to implementing algorithms, I find the pseudo-code in this book much more complicated than it needs to be. Some examples that come to mind:
1. The quick sort discussion does not important / simpler approaches like 3 way quick sort.
2. The Red-Black trees implementation and explanation is much more complicated than the simpler approach described in Sedgewick's material.
Overall, this book does have its merits. Once you've learned basic algorithms from another source, you can come back to this book to understand the underlying mathematical proofs. But I would not recommend this to be your "introduction" to algorithms.
If you are interested in learning algorithms, this should probably not be the first book you read. I would instead recommend Robert Sedgewick's book or course on Coursera.
The problem with this comes down to the fact that is focuses too much on the mathematical details, while ignoring other interesting aspects. Many crucial aspects of classic algorithms are relegated to the exercises section instead of being covered front and center. Even when covering important algorithms, the book glosses over important details.
When it comes to implementing algorithms, I find the pseudo-code in this book much more complicated than it needs to be. Some examples that come to mind:
1. The quick sort discussion does not important / simpler approaches like 3 way quick sort.
2. The Red-Black trees implementation and explanation is much more complicated than the simpler approach described in Sedgewick's material.
Overall, this book does have its merits. Once you've learned basic algorithms from another source, you can come back to this book to understand the underlying mathematical proofs. But I would not recommend this to be your "introduction" to algorithms.
June 10, 2011
An essential book for every programmer, you can't read this kind of book on bus, you need to fully constraint while reading it. The exercises after each chapter are very important to fully understand the chapter you just read, and to activate your brain's neurons. The book in itself is an outstanding one, very organized, focused and small chapters makes it easier to understand the algorithms inside it.
It contains the essential and most popular algorithms, so you can't live wthout it if you are real programmer.
You can skip chapters/read about an algorithm you want to understand more, as if there is a previous idea/algorithm the authors directly mention that with chapter's number so you can go directly to it for more information. I've read the 2nd edition, and now reading this one, the 3rd edition.
It contains the essential and most popular algorithms, so you can't live wthout it if you are real programmer.
You can skip chapters/read about an algorithm you want to understand more, as if there is a previous idea/algorithm the authors directly mention that with chapter's number so you can go directly to it for more information. I've read the 2nd edition, and now reading this one, the 3rd edition.
March 22, 2011
Rather pointless to review this, as in most places this is the algorithms textbook. It's a good book that covers all the major algorithms in sufficient detail with every step clearly spelled out for the students' benefit.
Unfortunately, this neatness of presentation is also its most major drawback: (1) it spends more time describing algorithms than giving the reader an idea of how to design them, and (2) it can easily give the impression that algorithms is about spending a lot of time proving obvious correctness results, which is not how people think of algorithms in real life (whether in academia, or in "real world" applications). For this reason, I'd recommend not using this fat book, and instead using either Kleinberg and Tardos's Algorithm Design, or Dasgupta–Papadimitriou–Vazirani's Algorithms, or Skeina's The Algorithm Design Manual, which are all better at showing you how to think about algorithms the right way.
Unfortunately, this neatness of presentation is also its most major drawback: (1) it spends more time describing algorithms than giving the reader an idea of how to design them, and (2) it can easily give the impression that algorithms is about spending a lot of time proving obvious correctness results, which is not how people think of algorithms in real life (whether in academia, or in "real world" applications). For this reason, I'd recommend not using this fat book, and instead using either Kleinberg and Tardos's Algorithm Design, or Dasgupta–Papadimitriou–Vazirani's Algorithms, or Skeina's The Algorithm Design Manual, which are all better at showing you how to think about algorithms the right way.
September 28, 2015
Final exam: completed. This damn textbook: ignored from here on out.
Whenever I look at it now, all I can think of is Alex in Clockwork Orange: "Eggiwegs! I want to SMASH THEM!"
This book did not help me in my class, not one tiny bit. Like so many other math-oriented textbooks, there is literally not one damn thing in the book that is not teachable but the teaching moments are all lost in math gymnastics, over-explaining, under-explaining, etc. Please, just once, let someone with the teaching talent of Sal Khan (of Khan Academy) write a textbook about math. Just once. Why is that so hard? Just one textbook that is focused on teaching and not befuddling, obfuscating, or jerking students' chains; a book that is not 500 pages too long; a book that teaches fundamentals before moving on to fundamentals +1 and then fundamentals +2 (not jumping to fundamentals +1432)...I'm not holding my breath, no way. This will never happen because academic math people are writing the books.
Know who would be a perfect algorithms textbook author? Someone that has to struggle through learning the subject matter just like a student. I'd buy that author's book. This one, though...let's just say I'm glad I got an international edition and not a full-price US/Canada edition. If I burn it, I'm only out $20.
Whenever I look at it now, all I can think of is Alex in Clockwork Orange: "Eggiwegs! I want to SMASH THEM!"
This book did not help me in my class, not one tiny bit. Like so many other math-oriented textbooks, there is literally not one damn thing in the book that is not teachable but the teaching moments are all lost in math gymnastics, over-explaining, under-explaining, etc. Please, just once, let someone with the teaching talent of Sal Khan (of Khan Academy) write a textbook about math. Just once. Why is that so hard? Just one textbook that is focused on teaching and not befuddling, obfuscating, or jerking students' chains; a book that is not 500 pages too long; a book that teaches fundamentals before moving on to fundamentals +1 and then fundamentals +2 (not jumping to fundamentals +1432)...I'm not holding my breath, no way. This will never happen because academic math people are writing the books.
Know who would be a perfect algorithms textbook author? Someone that has to struggle through learning the subject matter just like a student. I'd buy that author's book. This one, though...let's just say I'm glad I got an international edition and not a full-price US/Canada edition. If I burn it, I'm only out $20.
November 30, 2007
While searching for a Bible of algorithms, I of course quickly gravitated towards Knuth's Art of Computer Programming series. It's thousands of pages long — a magnum opus still in progress; how could it not be the most desirable source?
My research quickly yielded mixed opinions from the community. Some loved Knuth's books, while others found their language impenetrable, their code irrelevant, or their assertions wrong or out of date.
All, on the other hand, universally praised Introduction to Algorithms. While my exposure to Knuth's work is still minimal, I can certainly echo the praise for Intro.
Intro's language is academic, but understandable. If one were to put Knuth's work on the "unreadable" extreme and O'Reilly's popular Head First series on the opposite extreme, Intro would fall somewhere in the middle, leaning towards Knuth.
Intro very smartly uses pseudocode that doesn't attempt to resemble any popular programming language (with its own idiosyncratic syntax and responsibilities). Oftentimes I skip straight to the pseudocode examples, as I find them immensely readable and translatable into practical, functioning code of any language.
This book is a must-have on the shelf of any computer scientist, and any practical programmer who wants to write more efficient code. Pick it up!
My research quickly yielded mixed opinions from the community. Some loved Knuth's books, while others found their language impenetrable, their code irrelevant, or their assertions wrong or out of date.
All, on the other hand, universally praised Introduction to Algorithms. While my exposure to Knuth's work is still minimal, I can certainly echo the praise for Intro.
Intro's language is academic, but understandable. If one were to put Knuth's work on the "unreadable" extreme and O'Reilly's popular Head First series on the opposite extreme, Intro would fall somewhere in the middle, leaning towards Knuth.
Intro very smartly uses pseudocode that doesn't attempt to resemble any popular programming language (with its own idiosyncratic syntax and responsibilities). Oftentimes I skip straight to the pseudocode examples, as I find them immensely readable and translatable into practical, functioning code of any language.
This book is a must-have on the shelf of any computer scientist, and any practical programmer who wants to write more efficient code. Pick it up!
December 13, 2007
An essential, well-written reference, and one it's quite possible to read through several times, picking up new info each time. That having been said....this book never, I felt, adequately communicated THE LOVE. The pseudocode employed throughout is absolutely wretched, at times (especially in later chapters) binding up and abstracting away subsidiary computational processes not with actual predefined functions but english descriptions of modifications thereof -- decide whether you're writing code samples for humans or humans-simulating-automata, please, and stick to one. This habit wouldn't be so obnoxious, save that several (although, admittedly, rare) "inline modifications of declaration" seem to require modifications of definition which would subsequently invalidate previous running-time or -space guarantees. As the STL if nothing else has taught us, usable spellbooks must include running-time analysis as part of their designs/contracts/documentations. I know the authors have released an updated edition; I do not yet own it, and could contrast with assurance only the two editions' coverage of string-matching algorithms.
That minor nit having been aired, CLR1 belongs in undergraduate curricula and on pros' bookshelves. Its illustrations, in particular, are highly effective and bring several fundamental algorithms to life better than I've seen elsewhere; its treatment of the Master Method is the best I've seen with an undergraduate audience. I'd like some algorithms from modern machine learning theory (SVM's, etc) and also multi-string / fuzzy-string matching, but those are admittedly advanced topics.
It's no Knuth, but it ain't bad.
That minor nit having been aired, CLR1 belongs in undergraduate curricula and on pros' bookshelves. Its illustrations, in particular, are highly effective and bring several fundamental algorithms to life better than I've seen elsewhere; its treatment of the Master Method is the best I've seen with an undergraduate audience. I'd like some algorithms from modern machine learning theory (SVM's, etc) and also multi-string / fuzzy-string matching, but those are admittedly advanced topics.
It's no Knuth, but it ain't bad.
February 3, 2012
I've been reading CLRS on and off for years. I read bits at a time and have been picking and choosing chapters to read and reread. I must say that without a doubt this is the best textbook I have ever read. I could not recommend it anymore for anyone that wishes to learn about data structures and algorithms well. The authors never skimp on the math and that's my favorite part of this book. Almost every idea that is presented is proven with a thorough proof. All of the pseudocode is completely golden and thoroughly tested. Read this, seriously.
February 25, 2015
Some people just really enjoy typing, I guess. Not so much communicating, though: I was already pretty familiar with almost all of the algorithms and data structures discussed (the bit on computational geometry was the only thing that was completely new), but I can honestly say that if Introduction to Algorithms had been my first textbook, I wouldn't be.
(Also, I wish editors would stop writers when they try to use 1-indexed arrays in their books. Or, for that matter, pseudocode in general. Machine-interpretable, human-readable high-level languages aren't a new concept.)
(Also, I wish editors would stop writers when they try to use 1-indexed arrays in their books. Or, for that matter, pseudocode in general. Machine-interpretable, human-readable high-level languages aren't a new concept.)
January 10, 2014
Well, technically I didn't finish reading all the chapters in the book, but at least I've read most of it. The topics in the book is well explained with concise example. But sometimes, I need to find out the explanation by myself, things that I found interesting but sometimes frustrating. If I run into this situation, sometimes I need to find another reference to help me understand the problem. But still, this is a good book.
Want to Read
March 11, 2021the hard way to learning algorithms
May 4, 2012
Ow you great book you, you served me well.
February 19, 2017
Introduction
Introduction to Algorithms, commonly known as CLRS after the initials of its four authors, is one of the most influential and comprehensive textbooks in computer science. Published by MIT Press, the third edition provides an extensive treatment of the principles, techniques and mathematical foundations underlying the design and analysis of algorithms. Although its title suggests an introductory textbook, its breadth, formal reasoning and technical depth make it particularly suitable for university students, postgraduate researchers and software engineers seeking a rigorous understanding of algorithms.
The book approaches algorithms as more than sequences of instructions that produce a desired result. It examines why algorithms work, how their correctness can be established, and how their computational efficiency can be measured. This combination of practical problem-solving and mathematical analysis distinguishes CLRS from programming guides that concentrate primarily on implementation.
Spanning more than 1,300 pages, the third edition serves both as a structured learning resource and as a long-term reference. Its scope is ambitious, covering foundational topics such as sorting and data structures alongside advanced material on graph algorithms, dynamic programming, computational complexity and optimisation. Its reputation rests on the authors' ability to present this extensive subject matter within a consistent analytical framework.
Content and Organisation
One of the book's greatest strengths is the breadth and systematic organisation of its material. The early chapters introduce the fundamentals of algorithmic analysis, including asymptotic notation, the analysis of algorithms and the mathematical techniques required to evaluate computational performance. These concepts establish the foundation for the more specialised chapters that follow.
The book then explores sorting algorithms, heaps, hash tables, search trees and other essential data structures. It progresses to more advanced techniques, including divide-and-conquer, dynamic programming, greedy algorithms and amortised analysis. Later sections address graph algorithms, network flows, linear programming, computational geometry, string matching, number-theoretic algorithms and computational complexity.
This organisation reflects a clear educational philosophy: understanding individual algorithms is important, but understanding the general techniques used to design them is even more valuable. Once readers recognise the principles behind divide-and-conquer or dynamic programming, for example, they can begin applying those ideas to problems they have not encountered before.
The third edition also expands the treatment of several important subjects. It includes dedicated chapters on van Emde Boas trees and multithreaded algorithms, while revising the presentation of divide-and-conquer, dynamic programming, greedy methods and flow networks. These additions strengthen the book's coverage of both foundational and more advanced algorithmic techniques.
Rather than limiting its attention to a narrow set of programming tasks, CLRS aims to provide a broad conceptual map of algorithm design. This makes it especially useful for students preparing for advanced courses or researchers who need a reliable reference across several areas of theoretical computer science.
Mathematical Rigour and Algorithm Analysis
The defining characteristic of Introduction to Algorithms is its emphasis on mathematical rigour. Algorithms are presented not simply as procedures that appear to work, but as objects whose correctness and computational properties can be analysed systematically.
The authors explain how to establish correctness through mathematical reasoning, including loop invariants, induction and proofs of algorithmic properties. They also examine time and space complexity using asymptotic notation, enabling readers to compare algorithms independently of particular hardware or programming languages.
This analytical approach is essential because an algorithm's apparent simplicity does not necessarily imply efficiency. Two algorithms may produce identical results while exhibiting dramatically different running times as the input grows. CLRS provides the tools needed to understand these differences and to evaluate the trade-offs involved in selecting an appropriate solution.
Its treatment of asymptotic analysis is particularly valuable. Readers learn to reason about upper and lower bounds, distinguish worst-case performance from other measures, and understand why the growth rate of an algorithm often matters more than its performance on a small example.
The book also develops the mathematical foundations needed to analyse recursive algorithms, including recurrence relations and divide-and-conquer methods. These topics can initially appear abstract, but they provide a powerful framework for explaining the performance of algorithms used throughout computer science.
For students who want to understand not only which algorithm to use but also why it is correct and how efficiently it operates, this level of detail is one of the book's greatest assets.
The Value of Language-Independent Pseudocode
Another important feature is the use of high-level, language-independent pseudocode. Rather than presenting every algorithm in a particular programming language, the authors describe its essential operations in a notation designed to make the underlying logic clear.
This decision has significant educational advantages. Programming languages differ in syntax, libraries and implementation details, but the central principles of an algorithm generally remain the same. By separating algorithmic reasoning from language-specific conventions, CLRS allows readers to focus on the structure of a solution.
For example, a reader studying a graph traversal can concentrate on how vertices are discovered, how edges are examined and how the traversal progresses, without being distracted by the details of a particular software library.
The approach also makes the book relevant to readers working in different programming environments. The concepts can be translated into C++, Java, Python or other languages once the algorithm itself is understood.
However, this advantage comes with a practical limitation. The pseudocode is not generally intended to be copied directly into a software project. Readers must translate the algorithms into executable code, account for language-specific details and test their implementations. CLRS is therefore best understood as a textbook about algorithmic thinking rather than a collection of ready-made programming solutions.
Exercises and Independent Learning
The end-of-chapter exercises are an essential part of the book's educational value. They range from straightforward applications of the material to demanding problems that require substantial mathematical reasoning, creativity and persistence. Many are designed to test whether readers can transfer a technique to a new situation rather than merely repeat a worked example.
This emphasis on active problem-solving is particularly important in algorithm design. Recognising a familiar algorithm is not the same as knowing how to develop an efficient solution to an unfamiliar problem. CLRS encourages readers to analyse problems, identify relevant structures, choose suitable techniques and justify their decisions.
The exercises can also support preparation for technical interviews, particularly those involving data structures, graph algorithms, recursion and computational complexity. However, the book is much broader than an interview-preparation guide: many exercises explore theoretical questions that go well beyond the needs of routine software development.
Independent learners should be aware that some of the more challenging problems require considerable effort, and complete worked solutions are not available for every exercise. This can be frustrating when studying without an instructor or study group. Nevertheless, working through the problems is one of the most effective ways to develop the analytical skills that the book aims to teach.
Introduction to Algorithms, commonly known as CLRS after the initials of its four authors, is one of the most influential and comprehensive textbooks in computer science. Published by MIT Press, the third edition provides an extensive treatment of the principles, techniques and mathematical foundations underlying the design and analysis of algorithms. Although its title suggests an introductory textbook, its breadth, formal reasoning and technical depth make it particularly suitable for university students, postgraduate researchers and software engineers seeking a rigorous understanding of algorithms.
The book approaches algorithms as more than sequences of instructions that produce a desired result. It examines why algorithms work, how their correctness can be established, and how their computational efficiency can be measured. This combination of practical problem-solving and mathematical analysis distinguishes CLRS from programming guides that concentrate primarily on implementation.
Spanning more than 1,300 pages, the third edition serves both as a structured learning resource and as a long-term reference. Its scope is ambitious, covering foundational topics such as sorting and data structures alongside advanced material on graph algorithms, dynamic programming, computational complexity and optimisation. Its reputation rests on the authors' ability to present this extensive subject matter within a consistent analytical framework.
Content and Organisation
One of the book's greatest strengths is the breadth and systematic organisation of its material. The early chapters introduce the fundamentals of algorithmic analysis, including asymptotic notation, the analysis of algorithms and the mathematical techniques required to evaluate computational performance. These concepts establish the foundation for the more specialised chapters that follow.
The book then explores sorting algorithms, heaps, hash tables, search trees and other essential data structures. It progresses to more advanced techniques, including divide-and-conquer, dynamic programming, greedy algorithms and amortised analysis. Later sections address graph algorithms, network flows, linear programming, computational geometry, string matching, number-theoretic algorithms and computational complexity.
This organisation reflects a clear educational philosophy: understanding individual algorithms is important, but understanding the general techniques used to design them is even more valuable. Once readers recognise the principles behind divide-and-conquer or dynamic programming, for example, they can begin applying those ideas to problems they have not encountered before.
The third edition also expands the treatment of several important subjects. It includes dedicated chapters on van Emde Boas trees and multithreaded algorithms, while revising the presentation of divide-and-conquer, dynamic programming, greedy methods and flow networks. These additions strengthen the book's coverage of both foundational and more advanced algorithmic techniques.
Rather than limiting its attention to a narrow set of programming tasks, CLRS aims to provide a broad conceptual map of algorithm design. This makes it especially useful for students preparing for advanced courses or researchers who need a reliable reference across several areas of theoretical computer science.
Mathematical Rigour and Algorithm Analysis
The defining characteristic of Introduction to Algorithms is its emphasis on mathematical rigour. Algorithms are presented not simply as procedures that appear to work, but as objects whose correctness and computational properties can be analysed systematically.
The authors explain how to establish correctness through mathematical reasoning, including loop invariants, induction and proofs of algorithmic properties. They also examine time and space complexity using asymptotic notation, enabling readers to compare algorithms independently of particular hardware or programming languages.
This analytical approach is essential because an algorithm's apparent simplicity does not necessarily imply efficiency. Two algorithms may produce identical results while exhibiting dramatically different running times as the input grows. CLRS provides the tools needed to understand these differences and to evaluate the trade-offs involved in selecting an appropriate solution.
Its treatment of asymptotic analysis is particularly valuable. Readers learn to reason about upper and lower bounds, distinguish worst-case performance from other measures, and understand why the growth rate of an algorithm often matters more than its performance on a small example.
The book also develops the mathematical foundations needed to analyse recursive algorithms, including recurrence relations and divide-and-conquer methods. These topics can initially appear abstract, but they provide a powerful framework for explaining the performance of algorithms used throughout computer science.
For students who want to understand not only which algorithm to use but also why it is correct and how efficiently it operates, this level of detail is one of the book's greatest assets.
The Value of Language-Independent Pseudocode
Another important feature is the use of high-level, language-independent pseudocode. Rather than presenting every algorithm in a particular programming language, the authors describe its essential operations in a notation designed to make the underlying logic clear.
This decision has significant educational advantages. Programming languages differ in syntax, libraries and implementation details, but the central principles of an algorithm generally remain the same. By separating algorithmic reasoning from language-specific conventions, CLRS allows readers to focus on the structure of a solution.
For example, a reader studying a graph traversal can concentrate on how vertices are discovered, how edges are examined and how the traversal progresses, without being distracted by the details of a particular software library.
The approach also makes the book relevant to readers working in different programming environments. The concepts can be translated into C++, Java, Python or other languages once the algorithm itself is understood.
However, this advantage comes with a practical limitation. The pseudocode is not generally intended to be copied directly into a software project. Readers must translate the algorithms into executable code, account for language-specific details and test their implementations. CLRS is therefore best understood as a textbook about algorithmic thinking rather than a collection of ready-made programming solutions.
Exercises and Independent Learning
The end-of-chapter exercises are an essential part of the book's educational value. They range from straightforward applications of the material to demanding problems that require substantial mathematical reasoning, creativity and persistence. Many are designed to test whether readers can transfer a technique to a new situation rather than merely repeat a worked example.
This emphasis on active problem-solving is particularly important in algorithm design. Recognising a familiar algorithm is not the same as knowing how to develop an efficient solution to an unfamiliar problem. CLRS encourages readers to analyse problems, identify relevant structures, choose suitable techniques and justify their decisions.
The exercises can also support preparation for technical interviews, particularly those involving data structures, graph algorithms, recursion and computational complexity. However, the book is much broader than an interview-preparation guide: many exercises explore theoretical questions that go well beyond the needs of routine software development.
Independent learners should be aware that some of the more challenging problems require considerable effort, and complete worked solutions are not available for every exercise. This can be frustrating when studying without an instructor or study group. Nevertheless, working through the problems is one of the most effective ways to develop the analytical skills that the book aims to teach.
December 16, 2019
Vilken nagelbitare!
July 26, 2010
Algorithms, which perform some sequence of mathematical operations, form the core of computer programming. Intended as a text for computer programming courses, especially undergraduate courses in data structures and graduate courses in algorithms, an “Introduction to Algorithms” provides a comprehensive overview, that will be appreciated technical professionals, as well.
The major topics presented are sorting, data structures, graph algorithms and a variety of selected topics. Computer programmers can draw desired algorithms directly from the text or use the clear explanations of the underlying mathematics to develop custom algorithms. The algorithms are presented in pseudocode that can be adapted to programming languages, such as C++ and Java. The focus is on design rather than implementation.
While a solid background in advanced mathematics and probability theory is needed to fully appreciate the material, non-programmers and IT professionals (such as this reviewer) will appreciate the numerous tips provided for improving the efficiency and thus reducing the cost of developing applications.
Any Computer Science student would find this text an essential resource, even if not specifically required for course work. However, the advanced mathematical principles needed to grasp the material are presented as exercises, intended to be worked through in class, so no solutions are provided, which may frustrate self-studiers and limit its utility as a reference. Although surprisingly well written, a book of this size and complexity is bound to have some errors. See http://mitpress.mit.edu/algorithms for the error list and supplemental information about the book (including solutions to some, but not all exercises, and an explanation of the corny professor jokes sprinkled throughout the text).
The major topics presented are sorting, data structures, graph algorithms and a variety of selected topics. Computer programmers can draw desired algorithms directly from the text or use the clear explanations of the underlying mathematics to develop custom algorithms. The algorithms are presented in pseudocode that can be adapted to programming languages, such as C++ and Java. The focus is on design rather than implementation.
While a solid background in advanced mathematics and probability theory is needed to fully appreciate the material, non-programmers and IT professionals (such as this reviewer) will appreciate the numerous tips provided for improving the efficiency and thus reducing the cost of developing applications.
Any Computer Science student would find this text an essential resource, even if not specifically required for course work. However, the advanced mathematical principles needed to grasp the material are presented as exercises, intended to be worked through in class, so no solutions are provided, which may frustrate self-studiers and limit its utility as a reference. Although surprisingly well written, a book of this size and complexity is bound to have some errors. See http://mitpress.mit.edu/algorithms for the error list and supplemental information about the book (including solutions to some, but not all exercises, and an explanation of the corny professor jokes sprinkled throughout the text).
April 19, 2015
This books is amazing.
It's a bit hard for beginners, but then again, it's one of those books which you always have to come back to. Each time you come back, you learn something new. The exercises themselves have tons of stuff hidden in them. You need to be patient and learn slowly. Don't try to gobble everything up.
If you let go of your fear, and actually make an effort to learn something from it, you can learn loads. I learned Network Flow algorithm by reading this book. It took me few days, but I did manage to learn the algorithm myself by reading just this book.
It's a bit hard for beginners, but then again, it's one of those books which you always have to come back to. Each time you come back, you learn something new. The exercises themselves have tons of stuff hidden in them. You need to be patient and learn slowly. Don't try to gobble everything up.
If you let go of your fear, and actually make an effort to learn something from it, you can learn loads. I learned Network Flow algorithm by reading this book. It took me few days, but I did manage to learn the algorithm myself by reading just this book.
January 8, 2025
Carino come lettura per staccare dai fantasy smut
Read
November 8, 2022Good, but not the best
April 29, 2018
It has ben 14 years since I touched a math-oriented theoretical work like this, and that hurt a lot while slogging through this textbook. After graduating a lot of the software engineering skills you pick up are geared towards practicality. I literally forgot some mathematical terms I had to look up again. Sadly, trying to understand it's lemma's with the help of the appendices is not doable as they are even heavier than the things they try to explain.
Besides that problematic point, it's an excellent guide (but not an introduction!) into algorithms & data structures including classic problems as sorting and searching with lists, trees, graphs and the like. Some extra background is provided along with alternatives that amused me after implementing the default solution. If you're not studying CS or you have but it was a long time ago, there might be better things to read. But it's still worth it.
Besides that problematic point, it's an excellent guide (but not an introduction!) into algorithms & data structures including classic problems as sorting and searching with lists, trees, graphs and the like. Some extra background is provided along with alternatives that amused me after implementing the default solution. If you're not studying CS or you have but it was a long time ago, there might be better things to read. But it's still worth it.
November 19, 2010
The book gives a solid foundation of common non-trivial algorithms and data structures. It all comes with nice pseudocode, detailed walk-throughs and complexity analysis (along with worst case, average case and amortized complexity).
Personally I'd prefer to see the material in much more compact form, covering more of topics and more advanced or tricky algorithms and data structures. However, when something isn't clear, the detailed walk-throughs really help. Also, the exercises provided are invaluable.
I'd say is a must-read for every software engineer and computer scientist. If you aren't already familiar with the content from other sources, it's really worth investing a couple of years in it: read the book, try everything out with your favorite programming language and do exercises. Comparing to Knuth's "The Art of Computer Programming", it is a ten times easier read.
Personally I'd prefer to see the material in much more compact form, covering more of topics and more advanced or tricky algorithms and data structures. However, when something isn't clear, the detailed walk-throughs really help. Also, the exercises provided are invaluable.
I'd say is a must-read for every software engineer and computer scientist. If you aren't already familiar with the content from other sources, it's really worth investing a couple of years in it: read the book, try everything out with your favorite programming language and do exercises. Comparing to Knuth's "The Art of Computer Programming", it is a ten times easier read.
October 31, 2017
This is one of the worst college books I have ever used. The examples in the book are severely lacking the needed information to answer the questions in which you are forced to use outside resources aka other Data Structure books to find the info to solve their problems. It is amazing that this is an MIT book because it DOES NOT MEET THEIR STANDARD. The book is unorganized and bounces around like the authors have ADHD. The text is covering an extremely abstract computer algorithm theories and fails to provided the needed information to support understanding of the material.
January 18, 2019
Ok I may have rated this a little too harshly because of fresh graduate rage. It is by no means an entry book. However the main goal of the book seems to be to make a record of all well known / once frequently used algorithms.
But as a undergrad course book I agree with past self.
3.5/5
Past: Overrated piece of junk.
But as a undergrad course book I agree with past self.
3.5/5
Past: Overrated piece of junk.
August 6, 2021
This book is miscalled an “introduction” to algorithms. It is not an introduction at all, it's a Bible on the topic! It requires an above-average mathematical background as well. It is very well explained in-depth, with more than enough explanation. A must-read for any professional software developer. Highly recommended!
February 8, 2010
The textbook on algorithms. It does not do a very good job of teaching how to design algorithms, but it is an authoritative catalog of algorithms for a wide variety of situations.
December 14, 2021
Some days, it's the only sane source. Some days, it's too damn complex to make sense of.
April 5, 2024
I love Red-Black trees
February 17, 2025
A solid, exhaustive introduction to algorithms.
While this books is informative and rather useful—it covers all fundamental algorithms and data structures I could think of—I didn’t love it. I can’t pinpoint the reason exactly, but I suspect it’s because this book is rather dry. There is no cheekiness like in OSTEP or Introduction to Computing Systems, and there is no gentleness and care for the reader like in Discrete Mathematics with Applications. Still, the material is solid, the illustrations are excellent and the problems are an exciting challenge.
I read the fourth edition. I read most of chapters 1-4, 6-8, 10-16, 20-22.
While this books is informative and rather useful—it covers all fundamental algorithms and data structures I could think of—I didn’t love it. I can’t pinpoint the reason exactly, but I suspect it’s because this book is rather dry. There is no cheekiness like in OSTEP or Introduction to Computing Systems, and there is no gentleness and care for the reader like in Discrete Mathematics with Applications. Still, the material is solid, the illustrations are excellent and the problems are an exciting challenge.
I read the fourth edition. I read most of chapters 1-4, 6-8, 10-16, 20-22.
August 15, 2022
Very vast coverage of the whole syallabus.
Great depth to the algorithm and more on thier proof.
Things that I really don't like times I feel I am not feeling algorithms book rather a mathematics book only. It should contain more colorful diagram somewhat less mathematics and more more problems related to computer science implementation of algorithms.
Because of the most of mathematical rigor sometimes you loose your enthusiasm to read algorithms.
But overall a good read.
Great depth to the algorithm and more on thier proof.
Things that I really don't like times I feel I am not feeling algorithms book rather a mathematics book only. It should contain more colorful diagram somewhat less mathematics and more more problems related to computer science implementation of algorithms.
Because of the most of mathematical rigor sometimes you loose your enthusiasm to read algorithms.
But overall a good read.
May 23, 2017
Good book
February 6, 2024
Ruined my life for a semester but worth it
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