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Contents Bulletin Scripting in shell and Perl Network troubleshooting History Humor

Algorithms and Data Structures

News

See Also Recommended Books Recommended Links Lecture Notes and E-books Donald Knuth TAOCP MMIX Project
Sorting Sorting Algorithms Coding Style Testing Sorting Algorithms Insertion sort

Selection Sort

Bubblesort Searching Fast string searching and pattern matching
Bit Tricks Compression Control Flow Decompilation  Regular expressions Combinatorial Algorithms Compiler Algorithms Graph Algorithms Libraries
Crypto algorithms Public Key Cryposystems Random Generators Operating System Algorithms Steganography Programming Languages History Humor Etc

"Languages come and go,
but algorithms stand the test of time"
"An algorithm must be seen to be believed."
Donald Knuth

Why should you want to know more about algorithms? There are a number of possible reasons:

For all these reasons it is useful to have a broad familiarity with a range of algorithms, and to understand what types of problems they can help to solve. This is especially important for open source developers. Algorithms are intrinsically connected with data structures because data structures are dreaming to become elegant algorithms the same way ordinary people are dreaming about Hollywood actors ;-)

I would like to note that the value of browsing the WEB in search of algorithms is somewhat questionable :-). One probably will be much better off buying Donald Knuth's TAOCP and ... disconnecting from the Internet for a couple of months. Internet contains way too much noise that suppress useful signal... This is especially true about algorithms.

Note: MIX assembler is not very essential :-). Actually it represent class of computers which became obsolete even before the first volume Knuth book was published (with the release of IBM 360 which took world by storm). You can use Intel assembler if you wish. I used to teach TAOCP on mainframes and IBM assembler was pretty much OK. Knuth probably would be better off using a derivative of S/360 architecture and assembler from the very beginning ;-).Later he updated MIX to MMIX with a new instruction set for use in future volumes, but still existing three volumes use an old one.  There are pages on Internet that have them rewritten in IBM 260 or other more modern instruction set.

An extremely important and often overlooked class of algorithms are compiler algorithms (lex analysis, parsing and code generation). They actually represent a very efficient paradigm for solving wide class of tasks similar to compilation of the program. For example complex conversions from one format to another. Also any complex program usually has its own command language and knowledge of compiler algorithms can prevent authors from making typical for amateurs blunders (which are common in open source software). In a way Greenspun's tenth rule - Wikipedia, the free encyclopedia

Any sufficiently complicated C or Fortran program contains an ad hoc, informally-specified, bug-ridden, slow implementation of half of Common Lisp.

can be reformulated to:

Any sufficiently complicated  contains an ad hoc, informally-specified, bug-ridden, slow implementation of half of a typical programming language interpreter.

Many authors writing about algorithms try to hide their lack of competence with abuse of mathematical symbolic. Excessive use of mathematics in presentation of algorithms is often counterproductive (verification fiasco can serve as a warning for all future generation; it buried such talented authors as E. Dijkstra, David Gries and many others). Please remember Famous Donald Knuth's citation about correctness proofs:

On March 22, 1977, as I was drafting Section 7.1 of The Art of Computer Programming, I read four papers by Peter van Emde Boas that turned out to be more appropriate for Chapter 8 than Chapter 7. I wrote a five-page memo entitled ``Notes on the van Emde Boas construction of priority deques: An instructive use of recursion,'' and sent it to Peter on March 29 (with copies also to Bob Tarjan and John Hopcroft). The final sentence was this: ``Beware of bugs in the above code; I have only proved it correct, not tried it.''

See also Softpanorama Computer Books Reviews / Algorithms

Dr. Nikolai Bezroukov

P.S: In order to save the bandwidth for humans (as opposed to robots ;-), previous years of  Old News  section were converted into separate pages.


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[Jan 07, 2013] BookCompiler construction

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[Sep 25, 2011] Algorithms in a Nutshell by George T. Heineman, Gary Pollice & Stanley Selkow

Sorting examples are in C and does not use object-oriented mumbo-jumbo. Which is a good sign.
Amazon.com/ O'Reilly

K. Jazayeri (San Jose, CA United States): Its pedestrian title gives a very wrong first-impression!, December 12, 2008

In recent years I have found most other non-textbooks on algorithms to be uninteresting mainly for two reasons. First, there are books that are re-released periodically in a new "programming language du jour" without adding real value (some moving from Pascal to C/C++ to Python, Java or C#). The second group are books that are rather unimaginative collections of elementary information, often augmenting their bulk with lengthy pages of source code (touted as "ready-to-use", but never actually usable).

I almost didn't pay any attention to this book because its title struck me as rather mundane and pedestrian .... what an uncommonly false first-impression that turned out to be!

The is a well-written book and a great practical and usable one for working software developers at any skill or experience level. It starts with a condensed set of introductory material. It then covers the gamut of common and some not-so-common algorithms grouped by problems/tasks that do come up in a variety of real-world applications.

I particularly appreciate the concise and thoughtful - and concise - descriptions -- chock-full of notes on applicability and usability -- with absolutely no fluff! If nothing else, this book can be a good quick index or a chit sheet before culling through more standard textbooks (many of which, in fact, mentioned as further references in each section).

I believe the authors have identified a valid "hole" in the technical bookshelves - and plugged it quite well! Regarding the book's title, ... now I feel it's just appropriately simple, honest, and down-to-earth.

[Jun 06, 2011]   CIS300 lecture notes

Licensed under a Creative Commons License. Can be reused by instructors.

Week 1

Fundamentals of program design
Software development in Java: classes, objects, and packages

Week 2

Introduction to Computer Architecture
Introduction to Operating Systems
Week 3
Execution semantics
Software development in Java: interfaces and graphics
Week 4
What is a data structure?
A Case Study: Databases
Adding interfaces to the database
Sorting and Searching
Week 5
Time complexity measures
The stack data structure
Week 6
Activation-record stacks
Linked-list implementation of stacks
Queues
Week 7
Exam 1 (review)
Week 8
Doubly linked lists
Recursive processing of linked lists
Week 9
Execution traces of linked-list processing
Inductive (recursive) data structures
How to implement Conslists and other recursively defined data types in Java
Week 10
Introduction to binary trees
Week 12
Ordered trees
Spelling trees
Mutable trees, parent links, and node deletions
Week 13
Hash tables
Week 14
Exam 2 (review)
Week 15
Grammars and Trees
How to use lists and trees to build a compiler
AVL-Trees
Week 16
The Java Collections Framework
Review for Exam 3
Week 17
Priority queues and heap structures
Graphs

[Jun 06, 2011]   Algorithms and Data Structures by N. Wirth

January 1, 1985

Contents
Prefacee
1 Fundamental Data Structures
1.1 Introduction
1.2 The Concept of Data Type
1.3 Primitive Data Types
1.4 Standard Primitive Types
1.4.1 Integer types
1.4.2 The type REAL
1.4.3 The type BOOLEAN
1.4.4 The type CHAR
1.4.5 The type SET
1.5 The Array Structure
1.6 The Record Structure
1.7 Representation of Arrays, Records, and Sets
1.7.1 Representation of Arrays
1.7.2 Representation of Recors
1.7.3 Representation of Sets
1.8 The File (Sequence)
1.8.1 Elementary File Operators
1.8.2 Buffering Sequences
1.8.3 Buffering between Concurrent Processes
1.8.4 Textual Input and Output
1.9 Searching
1.9.1 Linear Search
1.9.2 Binary Search
1.9.3 Table Search
1.9.4 Straight String Search
1.9.5 The Knuth-Morris-Pratt String Search
1.9.6 The Boyer-Moore String Search
Exercises
2 Sorting
2.1 Introduction
2.2 Sorting Arrays
2.2.1 Sorting by Straight Insertion
2.2.2 Sorting by Straight Selection
2.2.3 Sorting by Straight Exchange
2.3 Advanced Sorting Methods
2.3.1 Insertion Sort by Diminishing Increment
2.3.2 Tree Sort
2.3.3 Partition Sort
2.3.4 Finding the Median
2.3.5 A Comparison of Array Sorting Methods
2.4 Sorting Sequences
2.4.1 Straight Merging
2.4.2 Natural Merging
2.4.3 Balanced Multiway Merging
2.4.4 Polyphase Sort
2.4.5 Distribution of Initial Runs
Exercises
6
3 Recursive Algorithms
3.1 Introduction
3.2 When Not to Use Recursion
3.3 Two Examples of Recursive Programs
3.4 Backtracking Algorithms
3.5 The Eight Queens Problem
3.6 The Stable Marriage Problem
3.7 The Optimal Selection Problem
Exercises
4 Dynamic Information Structures
4.1 Recursive Data Types
4.2 Pointers
4.3 Linear Lists
4.3.1 Basic Operations
4.3.2 Ordered Lists and Reorganizing Lists
4.3.3 An Application: Topological Sorting
4.4 Tree Structures
4.4.1 Basic Concepts and Definitions
4.4.2 Basic Operations on Binary Trees
4.4.3 Tree Search and Insertion
4.4.4 Tree Deletion
4.4.5 Analysis of Tree Search and Insertion
4.5 Balanced Trees
4.5.1 Balanced Tree Insertion
4.5.2 Balanced Tree Deletion
4.6 Optimal Search Trees
4.7 B-Trees
4.7.1 Multiway B-Trees
4.7.2 Binary B-Trees
4.8 Priority Search Trees
Exercises
5 Key Transformations (Hashing)
5.1 Introduction
5.2 Choice of a Hash Function
5.3 Collision handling
5.4 Analysis of Key Transformation
Exercises
Appendices
A The ASCII Character Set
B The Syntax of Oberon
Index

[Jun 05, 2011]   Data Structures and Algorithms  by Prof. Dr. Kurt Mehlhorn

Dec 31, 1984

Data Structures and Efficient Algorithms, Springer Verlag, EATCS Monographs, 1984.

The books are out of print and I have no idea, whether I will ever have time to revise them. The books are only partially available in electronic form; remember that the books were type-written. Many years ago, I started an effort to revise the books and, as a first step, some students converted the books to TeX. Being good students, they added comments. The outcome of their effort can be found below.

[Dec 30, 2010] BBVA Foundation Frontiers of Knowledge Awards

2010 award went to Donald Knuth !

The BBVA Foundation Frontiers of Knowledge Award in the Information and Communication Technologies category goes in this third edition to U.S. scientist Donald E. Knuth, for ďmaking computing a science by introducing formal mathematical techniques for the rigorous analysis of algorithmsĒ, in the words of the prize jury. The new awardee has also distinguished himself by ďadvocating for code that is simple, compact and intuitively understandable.Ē

Knuthís book The Art of Computer Programming is considered ďthe seminal work on computer science in the broadest sense, encompassing the algorithms and methods which lie at the heart of most computer systems, and doing so with uncommon depth and clarityĒ the citation continues. ďHis impact on the theory and practice of computer science is beyond parallel.Ē

Knuth laid the foundation for modern compilers, the programs which translate the high-level language of programmers into the binary language of computers. Programmers are thus able to write their code in a way that is closer to how a human being thinks, and their work is then converted into the language of machines.

The new laureate is also the ďfatherĒ of the analysis of algorithms, that is, the set of instructions conveyed to a computer so it carries out a given task. ďAlgorithmsĒ, the jury clarifies, ďare at the heart of todayís digital world, underlying everything we do with a computerĒ. Knuth systematized software design and ďerected the scaffolding on which we build modern computer programsĒ.

Knuth is also the author of todayís most widely used open-source typesetting languages for scientific texts, TeX and METAFONT. These two languages, in the juryís view, ďimport the aesthetics of typesetting into a program which has empowered authors to design beautiful documentsĒ.

[Jan 22, 2011] The Art of Computer Programming, Volume 4A

Combinatorial Algorithms, Part 1 (Upper Saddle River, New Jersey: Addison-Wesley, 2011), xvi+883pp.
ISBN 0-201-03804-8

(Preliminary drafts were previously published as paperback fascicles; see below.)

Russian translation (Moscow: Vil'iams), in preparation.
Chinese translation (Hong Kong: Pearson Education Asia), in preparation.

[Aug 14, 2009] Data Structures and Algorithms II by Alison Cawsey

[Apr 10, 2009] C++, Java, Algorithm and Data Structure Tutorials by Denis Kulagin.

Includes sections:

[Apr 25, 2008] Interview with Donald Knuth by Donald E. Knuth,Andrew Binstock


Andrew Binstock and Donald Knuth converse on the success of open source, the problem with multicore architecture, the disappointing lack of interest in literate programming, the menace of reusable code, and that urban legend about winning a programming contest with a single compilation.

Andrew Binstock: You are one of the fathers of the open-source revolution, even if you arenít widely heralded as such. You previously have stated that you released TeX as open source because of the problem of proprietary implementations at the time, and to invite corrections to the codeóboth of which are key drivers for open-source projects today. Have you been surprised by the success of open source since that time?

Donald Knuth: The success of open source code is perhaps the only thing in the computer field that hasnít surprised me during the past several decades. But it still hasnít reached its full potential; I believe that open-source programs will begin to be completely dominant as the economy moves more and more from products towards services, and as more and more volunteers arise to improve the code.

For example, open-source code can produce thousands of binaries, tuned perfectly to the configurations of individual users, whereas commercial software usually will exist in only a few versions. A generic binary executable file must include things like inefficient "sync" instructions that are totally inappropriate for many installations; such wastage goes away when the source code is highly configurable. This should be a huge win for open source.

Yet I think that a few programs, such as Adobe Photoshop, will always be superior to competitors like the Gimpófor some reason, I really donít know why! Iím quite willing to pay good money for really good software, if I believe that it has been produced by the best programmers.

Remember, though, that my opinion on economic questions is highly suspect, since Iím just an educator and scientist. I understand almost nothing about the marketplace.

Andrew: A story states that you once entered a programming contest at Stanford (I believe) and you submitted the winning entry, which worked correctly after a single compilation. Is this story true? In that vein, todayís developers frequently build programs writing small code increments followed by immediate compilation and the creation and running of unit tests. What are your thoughts on this approach to software development?

Donald: The story you heard is typical of legends that are based on only a small kernel of truth. Hereís what actually happened: John McCarthy decided in 1971 to have a Memorial Day Programming Race. All of the contestants except me worked at his AI Lab up in the hills above Stanford, using the WAITS time-sharing system; I was down on the main campus, where the only computer available to me was a mainframe for which I had to punch cards and submit them for processing in batch mode. I used Wirthís ALGOL W system (the predecessor of Pascal). My program didnít work the first time, but fortunately I could use Ed Satterthwaiteís excellent offline debugging system for ALGOL W, so I needed only two runs. Meanwhile, the folks using WAITS couldnít get enough machine cycles because their machine was so overloaded. (I think that the second-place finisher, using that "modern" approach, came in about an hour after I had submitted the winning entry with old-fangled methods.) It wasnít a fair contest.

As to your real question, the idea of immediate compilation and "unit tests" appeals to me only rarely, when Iím feeling my way in a totally unknown environment and need feedback about what works and what doesnít. Otherwise, lots of time is wasted on activities that I simply never need to perform or even think about. Nothing needs to be "mocked up."

Andrew: One of the emerging problems for developers, especially client-side developers, is changing their thinking to write programs in terms of threads. This concern, driven by the advent of inexpensive multicore PCs, surely will require that many algorithms be recast for multithreading, or at least to be thread-safe. So far, much of the work youíve published for Volume 4 of The Art of Computer Programming (TAOCP) doesnít seem to touch on this dimension. Do you expect to enter into problems of concurrency and parallel programming in upcoming work, especially since it would seem to be a natural fit with the combinatorial topics youíre currently working on?

Donald: The field of combinatorial algorithms is so vast that Iíll be lucky to pack its sequential aspects into three or four physical volumes, and I donít think the sequential methods are ever going to be unimportant. Conversely, the half-life of parallel techniques is very short, because hardware changes rapidly and each new machine needs a somewhat different approach. So I decided long ago to stick to what I know best. Other people understand parallel machines much better than I do; programmers should listen to them, not me, for guidance on how to deal with simultaneity.

Andrew: Vendors of multicore processors have expressed frustration at the difficulty of moving developers to this model. As a former professor, what thoughts do you have on this transition and how to make it happen? Is it a question of proper tools, such as better native support for concurrency in languages, or of execution frameworks? Or are there other solutions?

Donald: I donít want to duck your question entirely. I might as well flame a bit about my personal unhappiness with the current trend toward multicore architecture. To me, it looks more or less like the hardware designers have run out of ideas, and that theyíre trying to pass the blame for the future demise of Mooreís Law to the software writers by giving us machines that work faster only on a few key benchmarks! I wonít be surprised at all if the whole multithreading idea turns out to be a flop, worse than the "Titanium" approach that was supposed to be so terrificóuntil it turned out that the wished-for compilers were basically impossible to write.

Let me put it this way: During the past 50 years, Iíve written well over a thousand programs, many of which have substantial size. I canít think of even five of those programs that would have been enhanced noticeably by parallelism or multithreading. Surely, for example, multiple processors are no help to TeX.[1]

How many programmers do you know who are enthusiastic about these promised machines of the future? I hear almost nothing but grief from software people, although the hardware folks in our department assure me that Iím wrong.

I know that important applications for parallelism existórendering graphics, breaking codes, scanning images, simulating physical and biological processes, etc. But all these applications require dedicated code and special-purpose techniques, which will need to be changed substantially every few years.

Even if I knew enough about such methods to write about them in TAOCP, my time would be largely wasted, because soon there would be little reason for anybody to read those parts. (Similarly, when I prepare the third edition of Volume 3 I plan to rip out much of the material about how to sort on magnetic tapes. That stuff was once one of the hottest topics in the whole software field, but now it largely wastes paper when the book is printed.)

The machine I use today has dual processors. I get to use them both only when Iím running two independent jobs at the same time; thatís nice, but it happens only a few minutes every week. If I had four processors, or eight, or more, I still wouldnít be any better off, considering the kind of work I doóeven though Iím using my computer almost every day during most of the day. So why should I be so happy about the future that hardware vendors promise? They think a magic bullet will come along to make multicores speed up my kind of work; I think itís a pipe dream. (Noóthatís the wrong metaphor! "Pipelines" actually work for me, but threads donít. Maybe the word I want is "bubble.")

From the opposite point of view, I do grant that web browsing probably will get better with multicores. Iíve been talking about my technical work, however, not recreation. I also admit that I havenít got many bright ideas about what I wish hardware designers would provide instead of multicores, now that theyíve begun to hit a wall with respect to sequential computation. (But my MMIX design contains several ideas that would substantially improve the current performance of the kinds of programs that concern me mostóat the cost of incompatibility with legacy x86 programs.)

Andrew: One of the few projects of yours that hasnít been embraced by a widespread community is literate programming. What are your thoughts about why literate programming didnít catch on? And is there anything youíd have done differently in retrospect regarding literate programming?

Donald: Literate programming is a very personal thing. I think itís terrific, but that might well be because Iím a very strange person. It has tens of thousands of fans, but not millions.

In my experience, software created with literate programming has turned out to be significantly better than software developed in more traditional ways. Yet ordinary software is usually okayóIíd give it a grade of C (or maybe C++), but not F; hence, the traditional methods stay with us. Since theyíre understood by a vast community of programmers, most people have no big incentive to change, just as Iím not motivated to learn Esperanto even though it might be preferable to English and German and French and Russian (if everybody switched).

Jon Bentley probably hit the nail on the head when he once was asked why literate programming hasnít taken the whole world by storm. He observed that a small percentage of the worldís population is good at programming, and a small percentage is good at writing; apparently I am asking everybody to be in both subsets.

Yet to me, literate programming is certainly the most important thing that came out of the TeX project. Not only has it enabled me to write and maintain programs faster and more reliably than ever before, and been one of my greatest sources of joy since the 1980sóit has actually been indispensable at times. Some of my major programs, such as the MMIX meta-simulator, could not have been written with any other methodology that Iíve ever heard of. The complexity was simply too daunting for my limited brain to handle; without literate programming, the whole enterprise would have flopped miserably.

If people do discover nice ways to use the newfangled multithreaded machines, I would expect the discovery to come from people who routinely use literate programming. Literate programming is what you need to rise above the ordinary level of achievement. But I donít believe in forcing ideas on anybody. If literate programming isnít your style, please forget it and do what you like. If nobody likes it but me, let it die.

On a positive note, Iíve been pleased to discover that the conventions of CWEB are already standard equipment within preinstalled software such as Makefiles, when I get off-the-shelf Linux these days.

Andrew: In Fascicle 1 of Volume 1, you reintroduced the MMIX computer, which is the 64-bit upgrade to the venerable MIX machine comp-sci students have come to know over many years. You previously described MMIX in great detail in MMIXware. Iíve read portions of both books, but canít tell whether the Fascicle updates or changes anything that appeared in MMIXware, or whether itís a pure synopsis. Could you clarify?

Donald: Volume 1 Fascicle 1 is a programmerís introduction, which includes instructive exercises and such things. The MMIXware book is a detailed reference manual, somewhat terse and dry, plus a bunch of literate programs that describe prototype software for people to build upon. Both books define the same computer (once the errata to MMIXware are incorporated from my website). For most readers of TAOCP, the first fascicle contains everything about MMIX that theyíll ever need or want to know.

I should point out, however, that MMIX isnít a single machine; itís an architecture with almost unlimited varieties of implementations, depending on different choices of functional units, different pipeline configurations, different approaches to multiple-instruction-issue, different ways to do branch prediction, different cache sizes, different strategies for cache replacement, different bus speeds, etc. Some instructions and/or registers can be emulated with software on "cheaper" versions of the hardware. And so on. Itís a test bed, all simulatable with my meta-simulator, even though advanced versions would be impossible to build effectively until another five years go by (and then we could ask for even further advances just by advancing the meta-simulator specs another notch).

Suppose you want to know if five separate multiplier units and/or three-way instruction issuing would speed up a given MMIX program. Or maybe the instruction and/or data cache could be made larger or smaller or more associative. Just fire up the meta-simulator and see what happens.

Andrew: As I suspect you donít use unit testing with MMIXAL, could you step me through how you go about making sure that your code works correctly under a wide variety of conditions and inputs? If you have a specific work routine around verification, could you describe it?

Donald: Most examples of machine language code in TAOCP appear in Volumes 1-3; by the time we get to Volume 4, such low-level detail is largely unnecessary and we can work safely at a higher level of abstraction. Thus, Iíve needed to write only a dozen or so MMIX programs while preparing the opening parts of Volume 4, and theyíre all pretty much toy programsónothing substantial. For little things like that, I just use informal verification methods, based on the theory that Iíve written up for the book, together with the MMIXAL assembler and MMIX simulator that are readily available on the Net (and described in full detail in the MMIXware book).

That simulator includes debugging features like the ones I found so useful in Ed Satterthwaiteís system for ALGOL W, mentioned earlier. I always feel quite confident after checking a program with those tools.

Andrew: Despite its formulation many years ago, TeX is still thriving, primarily as the foundation for LaTeX. While TeX has been effectively frozen at your request, are there features that you would want to change or add to it, if you had the time and bandwidth? If so, what are the major items you add/change?

Donald: I believe changes to TeX would cause much more harm than good. Other people who want other features are creating their own systems, and Iíve always encouraged further developmentóexcept that nobody should give their program the same name as mine. I want to take permanent responsibility for TeX and Metafont, and for all the nitty-gritty things that affect existing documents that rely on my work, such as the precise dimensions of characters in the Computer Modern fonts.

Andrew: One of the little-discussed aspects of software development is how to do design work on software in a completely new domain. You were faced with this issue when you undertook TeX: No prior art was available to you as source code, and it was a domain in which you werenít an expert. How did you approach the design, and how long did it take before you were comfortable entering into the coding portion?

Donald: Thatís another good question! Iíve discussed the answer in great detail in Chapter 10 of my book Literate Programming, together with Chapters 1 and 2 of my book Digital Typography. I think that anybody who is really interested in this topic will enjoy reading those chapters. (See also Digital Typography Chapters 24 and 25 for the complete first and second drafts of my initial design of TeX in 1977.)

Andrew: The books on TeX and the program itself show a clear concern for limiting memory usageóan important problem for systems of that era. Today, the concern for memory usage in programs has more to do with cache sizes. As someone who has designed a processor in software, the issues of cache-aware and cache-oblivious algorithms surely must have crossed your radar screen. Is the role of processor caches on algorithm design something that you expect to cover, even if indirectly, in your upcoming work?

Donald: I mentioned earlier that MMIX provides a test bed for many varieties of cache. And itís a software-implemented machine, so we can perform experiments that will be repeatable even a hundred years from now. Certainly the next editions of Volumes 1-3 will discuss the behavior of various basic algorithms with respect to different cache parameters.

In Volume 4 so far, I count about a dozen references to cache memory and cache-friendly approaches (not to mention a "memo cache," which is a different but related idea in software).

Andrew: What set of tools do you use today for writing TAOCP? Do you use TeX? LaTeX? CWEB? Word processor? And what do you use for the coding?

Donald: My general working style is to write everything first with pencil and paper, sitting beside a big wastebasket. Then I use Emacs to enter the text into my machine, using the conventions of TeX. I use tex, dvips, and gv to see the results, which appear on my screen almost instantaneously these days. I check my math with Mathematica.

I program every algorithm thatís discussed (so that I can thoroughly understand it) using CWEB, which works splendidly with the GDB debugger. I make the illustrations with MetaPost (or, in rare cases, on a Mac with Adobe Photoshop or Illustrator). I have some homemade tools, like my own spell-checker for TeX and CWEB within Emacs. I designed my own bitmap font for use with Emacs, because I hate the way the ASCII apostrophe and the left open quote have morphed into independent symbols that no longer match each other visually. I have special Emacs modes to help me classify all the tens of thousands of papers and notes in my files, and special Emacs keyboard shortcuts that make bookwriting a little bit like playing an organ. I prefer rxvt to xterm for terminal input. Since last December, Iíve been using a file backup system called backupfs, which meets my need beautifully to archive the daily state of every file.

According to the current directories on my machine, Iíve written 68 different CWEB programs so far this year. There were about 100 in 2007, 90 in 2006, 100 in 2005, 90 in 2004, etc. Furthermore, CWEB has an extremely convenient "change file" mechanism, with which I can rapidly create multiple versions and variations on a theme; so far in 2008 Iíve made 73 variations on those 68 themes. (Some of the variations are quite short, only a few bytes; others are 5KB or more. Some of the CWEB programs are quite substantial, like the 55-page BDD package that I completed in January.) Thus, you can see how important literate programming is in my life.

I currently use Ubuntu Linux, on a standalone laptopóit has no Internet connection. I occasionally carry flash memory drives between this machine and the Macs that I use for network surfing and graphics; but I trust my family jewels only to Linux. Incidentally, with Linux I much prefer the keyboard focus that I can get with classic FVWM to the GNOME and KDE environments that other people seem to like better. To each his own.

Andrew: You state in the preface of Fascicle 0 of Volume 4 of TAOCP that Volume 4 surely will comprise three volumes and possibly more. Itís clear from the text that youíre really enjoying writing on this topic. Given that, what is your confidence in the note posted on the TAOCP website that Volume 5 will see light of day by 2015?

Donald: If you check the Wayback Machine for previous incarnations of that web page, you will see that the number 2015 has not been constant.

Youíre certainly correct that Iím having a ball writing up this material, because I keep running into fascinating facts that simply canít be left outóeven though more than half of my notes donít make the final cut.

Precise time estimates are impossible, because I canít tell until getting deep into each section how much of the stuff in my files is going to be really fundamental and how much of it is going to be irrelevant to my book or too advanced. A lot of the recent literature is academic one-upmanship of limited interest to me; authors these days often introduce arcane methods that outperform the simpler techniques only when the problem size exceeds the number of protons in the universe. Such algorithms could never be important in a real computer application. I read hundreds of such papers to see if they might contain nuggets for programmers, but most of them wind up getting short shrift.

From a scheduling standpoint, all I know at present is that I must someday digest a huge amount of material that Iíve been collecting and filing for 45 years. I gain important time by working in batch mode: I donít read a paper in depth until I can deal with dozens of others on the same topic during the same week. When I finally am ready to read what has been collected about a topic, I might find out that I can zoom ahead because most of it is eminently forgettable for my purposes. On the other hand, I might discover that itís fundamental and deserves weeks of study; then Iíd have to edit my website and push that number 2015 closer to infinity.

Andrew: In late 2006, you were diagnosed with prostate cancer. How is your health today?

Donald: Naturally, the cancer will be a serious concern. I have superb doctors. At the moment I feel as healthy as ever, modulo being 70 years old. Words flow freely as I write TAOCP and as I write the literate programs that precede drafts of TAOCP. I wake up in the morning with ideas that please me, and some of those ideas actually please me also later in the day when Iíve entered them into my computer.

On the other hand, I willingly put myself in Godís hands with respect to how much more Iíll be able to do before cancer or heart disease or senility or whatever strikes. If I should unexpectedly die tomorrow, Iíll have no reason to complain, because my life has been incredibly blessed. Conversely, as long as Iím able to write about computer science, I intend to do my best to organize and expound upon the tens of thousands of technical papers that Iíve collected and made notes on since 1962.

Andrew: On your website, you mention that the Peoples Archive recently made a series of videos in which you reflect on your past life. In segment 93, "Advice to Young People," you advise that people shouldnít do something simply because itís trendy. As we know all too well, software development is as subject to fads as any other discipline. Can you give some examples that are currently in vogue, which developers shouldnít adopt simply because theyíre currently popular or because thatís the way theyíre currently done? Would you care to identify important examples of this outside of software development?

Donald: Hmm. That question is almost contradictory, because Iím basically advising young people to listen to themselves rather than to others, and Iím one of the others. Almost every biography of every person whom you would like to emulate will say that he or she did many things against the "conventional wisdom" of the day.

Still, I hate to duck your questions even though I also hate to offend other peopleís sensibilitiesógiven that software methodology has always been akin to religion. With the caveat that thereís no reason anybody should care about the opinions of a computer scientist/mathematician like me regarding software development, let me just say that almost everything Iíve ever heard associated with the term "extreme programming" sounds like exactly the wrong way to go...with one exception. The exception is the idea of working in teams and reading each otherís code. That idea is crucial, and it might even mask out all the terrible aspects of extreme programming that alarm me.

I also must confess to a strong bias against the fashion for reusable code. To me, "re-editable code" is much, much better than an untouchable black box or toolkit. I could go on and on about this. If youíre totally convinced that reusable code is wonderful, I probably wonít be able to sway you anyway, but youíll never convince me that reusable code isnít mostly a menace.

Hereís a question that you may well have meant to ask: Why is the new book called Volume 4 Fascicle 0, instead of Volume 4 Fascicle 1? The answer is that computer programmers will understand that I wasnít ready to begin writing Volume 4 of TAOCP at its true beginning point, because we know that the initialization of a program canít be written until the program itself takes shape. So I started in 2005 with Volume 4 Fascicle 2, after which came Fascicles 3 and 4. (Think of Star Wars, which began with Episode 4.)

[Mar 5, 2008] JPerf 1.0.0  by Shevek

About: JPerf is a perfect hash function generator for Java. The principle of perfect hashing is to reduce the average constant overhead of a hash table by precomputing a hash function which is optimal for the key set. Other advantages include a reduction in memory usage. Finding such a hash function is hard, especially in the general case. These run-time savings come at a cost of increased map creation time. JPerf can create a perfect hash function for a given set of keys and values.

[Aug 25, 2007] Ben Pfaff GNU libavl

A well documented library
28 Sep 2006

Binary search trees provide O(lg n) performance on average for important operations such as item insertion, deletion, and search operations. Balanced trees provide O(lg n) even in the worst case.

GNU libavl is the most complete, well-documented collection of binary search tree and balanced tree library routines anywhere. It supports these kinds of trees:

Visit the online HTML version of libavl.

libavl's name is a historical accident: it originally implemented only AVL trees. Its name may change to something more appropriate in the future, such as ďlibsearchĒ. You should also expect this page to migrate to www.gnu.org sometime in the indefinite future.

Version 2.0

Version 2.0 of libavl was released on January 6, 2002. It is a complete rewrite of earlier versions implemented in a ďliterate programmingĒ fashion, such that in addition to being a useful library, it is also a book describing in full the algorithms behind the library.

Version 2.0.1 of libavl was released on August 24, 2002. It fixes some typos in the text and introduces an HTML output format. No bugs in the libavl code were fixed, because none were reported. Unlike 2.0, this version is compatible with recent releases of Texinfo. dvipdfm is now used for producing the PDF version.

Version 2.0.2 of libavl was released on December 28, 2004. It fixes a bug in tavl_delete() reported by Petr Silhavy a long time ago. This is the same fix posted here earlier. This version (again) works with recent versions of Texinfo, fixes a few typos in the text, and slightly enhances the HTML output format.

You can download the preformatted book or a source distribution that will allow you to use the library in your own programs. You can also use the source distribution to format the book yourself:

For an overview of the ideas behind libavl 2.0, see the poster presentation made on April 6, 2001, at Michigan

[Jul 10, 2007] Knuth Recent News

Paperback previews of new material for The Art of Computer Programming, called ``fascicles,'' have been published occasionally since 2005, and I spend most of my time these days grinding out new pages for the fascicles of the future. Early drafts of excerpts from some of this material are now ready for beta-testing.

I've put these drafts online primarily so that experts in the field can help me check the results; but brave souls who aren't afraid to look at relatively raw copy are welcome to look too. (Yes, the usual rewards apply if you find any mistakes.)

[Feb 12, 2005] News from Knuth Previews of Volume 4

I've been making some headway on actually writing Volume 4 of The Art of Computer Programming instead of merely preparing to write it, and some first drafts are now ready for beta-testing. I've put them online primarily so that experts in the field can help me check the results, but brave souls who aren't afraid to look at relatively raw copy are welcome to look too. (Yes, the usual rewards apply if you find any mistakes.)

[Jan 15, 2005] Bookpool Exclusive Excerpt from Volume 4 of The Art of Computer Programming

Volume 1, Fascicle 1: MMIX -- A RISC Computer for the New Millennium provides a programmer's introduction to the long-awaited MMIX, a RISC-based computer that replaces the original MIX, and describes the MMIX assembly language. It also presents new material on subroutines, coroutines and interpretive routines.

Volume 4, Fascicle 2: Generating All Tuples and Permutations begins his treatment of how to generate all possibilities. Specifically, it discusses the generation of all n-tuples, then extends those ideas to all permutations. Such algorithms provide a natural means by which many of the key ideas of combinatorial mathematics can be introduced and explored. Knuth illuminates important theories by discussing related games and puzzles. Even serious programming can be fun. Download the excerpt.

Volume 4, Fascicle 3: Generating All Combinations and Partitions. Estimated publication date July 2005.

[Jan 15, 2005] Graph Theory Lecture Notes 16

Minimum Spanning Trees
Def: A network (directed network) is a graph (digraph) where the edges (arcs) have been assigned non-negative real numbers. The numbers that have been assigned are called weights.

Def: A minimum spanning tree in a network is a spanning tree of the underlying graph which has the smallest sum of weights amongst all spanning trees.

Example: Suppose that the vertices of a graph represent towns and the edges of the graph are roads between these towns. Label each edge with the distance between the towns. If, in this network, it is desired to run telephone wires along the roads so that all the towns are connected. Where should the wires be put to minimize the amount of wire needed to do this? To answer the question, we need to find a minimum spanning tree in the network.

We give two greedy algorithms for finding minimum spanning trees.

Kruskal's Algorithm

Let G be a network with n vertices. Sort the edges of G in increasing order by weight (ties can be in arbitrary order). Create a list T of edges by passing through the sorted list of edges and add to T any edge which does not create a circuit with the edges already in T. Stop when T contains n-1 edges. If you run out of edges before reaching n-1 in T, then the graph is disconnected and no spanning tree exists. If T contains n-1 edges, then these edges form a minimum spanning tree of G.

Pf: If the algorithm finishes, then T is a spanning tree (n-1 edges with no circuits in a graph with n vertices).

Suppose that S is a minimum spanning tree of G. If S is not T, let e = {x,y} be the first edge (by weight) in T which is not in S. Since S is a tree, there is a chain C, from x to y in S. C U e is a circuit in G, so not all of its edges can be in T. Let f be an edge in C which is not in T.
Suppose that wt f < wt e. Since the algorithm did not put f in T, f must have formed a circuit with earlier edges in T, but these edges are all in S as is f, so S would contain a circuit ... contradiction. Thus we have wt f >= wt e. Let S' = (S - {f}) U {e}. S' is connected and has n-1 edges, so it is a spanning tree of G. Since wt S' <= wt S, and S was a minimal spanning tree, we must have wt f = wt e. Thus, S' is also a minimum spanning tree having one more edge in common with T than S does.

This argument can now be repeated with S' in place of S, and so on, until we reach T, showing that T must have been a minimum spanning tree.

Prim's Algorithm

Let G be a network with n vertices. Pick a vertex and place it in a list L. Amongst all the edges with one endpoint in the list L and the other not in L, choose one with the smallest weight (arbitrarily select amongst ties) and add it to a list T and put the second vertex in L. Continue doing this until T has n-1 edges. If there are no more edges satisfying the condition and T does not have n-1 edges, then G is disconnected. If T has n-1 edges, then these form a minimum spanning tree of G.

[Jan 15, 2005]  NIST: minimum spanning tree

Definition: A minimum-weight tree in a weighted graph which contains all of the graph's vertices.

Also known as MST, shortest spanning tree, SST.

Generalization (I am a kind of ...)
spanning tree.

Aggregate parent (I am a part of or used in ...)
Christofides algorithm (1).

See also Kruskal's algorithm, Prim-Jarnik algorithm, Boruvka's algorithm, Steiner tree, arborescence, similar problems: all pairs shortest path, traveling salesman.

Note: A minimum spanning tree can be used to quickly find a near-optimal solution to the traveling salesman problem.

The term "shortest spanning tree" may be more common in the field of operations research.

A Steiner tree is allowed added connection points to reduce the total length even more.

Author: JLG

[Jan 15, 2005]  minimum spanning tree algorithms Kruskal and Prim algorithms covered.

[Jan 15, 2005] Data Structures and Algorithms Graph Algorithms 10.1 Minimum Spanning Trees

Suppose we have a group of islands that we wish to link with bridges so that it is possible to travel from one island to any other in the group. Further suppose that (as usual) our government wishes to spend the absolute minimum amount on this project (because other factors like the cost of using, maintaining, etc, these bridges will probably be the responsibility of some future government :-). The engineers are able to produce a cost for a bridge linking each possible pair of islands. The set of bridges which will enable one to travel from any island to any other at minimum capital cost to the government is the minimum spanning tree.

[Jan 15, 2005] [-PDF-] A blossoming algorithm for tree volumes of composite digraphs

[ View as HTML]
... combinatorial proof of the formula for forest volumes of composite digraphs obtained
by ... studied by Knuth [8] and Kelmans [6]. The number of spanning trees of G ...
Similar pages

[Jan 15, 2005]  Digraphs, theory, algorithms, applications

Web page for the book Digraphs: Theory, Algorithms and Applications, by JÝrgen Bang-Jensen and Gregory Gutin

JÝrgen Bang-Jensen and Gregory Gutin

Digraphs: Theory, Algorithms and Applications

Springer-Verlag, London
Springer Monographs in Mathematics
ISBN 1-85233-268-9
October 2000
754 pages; 186 figures; 705 exercises

Second printing has been released from Springer in April 2001.

Softcover version is available as of May 2002 at 29.50 British Pounds. The ISBN number is 1852336110.

[Jan 15, 2005] Links for Graph Partitioning

From InterTools: an archive of interactive tools for discrete optimization algorithms

[Jan 15, 2005] Algorithms and Software for Partitioning Graphs

Graph partitioning is an NP hard problem with numerous applications. It appears in various forms in parallel computing, sparse matrix reordering, circuit placement and other important disciplines. I've worked with Rob Leland for several years on heuristic methods for partitioning graphs, with a particular focus on parallel computing applications. Our contributions include:

More recently, I have worked with Tammy Kolda on alternatives to the standard graph partitioning model. A critique of the standard approach and a discussion of alternatives can be found below. I have also been working with Karen Devine and a number of other researchers on dynamic load balancing. Dynamic load balancing is fundamentally harder than static partitioning. Algorithms and implementations must run quickly in parallel without consuming much memory. Interfaces need to be subroutine calls instead of file transfers. And since the data is already distributed, the new partition should be similar to the current one to minimize the amount of data that needs to be redistributed. We are working to build a tool called Zoltan to address this plethora of challenges. Zoltan is designed to be extensible to different applications, algorithms and parallel architectures. For example, it is data-structure neutral - an object oriented interface separates the application data structures from those of Zoltan. The tool will also support a very general model of a parallel computer, facilitating the use of heterogeneous machines.

Closely related to Zoltan, I have been interested in the software challenges inherent in parallelizing unstructured computations. I feel that well-designed tools and libraries are the key to addressing this problem. I have worked with Ali Pinar and Steve Plimpton on algorithms for some of the kernel operations which arise in this setting, and relevant papers can be found here.

[Mar 28, 2000] An Introduction to Graph Algorithms

by Ute Loerch, Department of Computer Science, University of Auckland, Auckland, New Zealand, ute@cs.auckland.ac.nz

These lecture notes contain the reference material on graph algorithms for the course: Algorithms and Data Structures (415.220FT) and are based on Dr Michael Dinneen's lecture notes of the course 415.220SC given in 1999. Topics include computer representations (adjacency matrices and lists), graph searching (BFS and DFS), and basic graph algorithms such as computing the shortest distances between vertices and finding the (strongly) connected components.

[Dec 31, 1998] Data Structures and Algorithms Table of Contents

Front Page
Course Outline

  1. Introduction
  2. Programming Strategies
  3. Data Structures
  4. Searching
  5. Complexity
  6. Queues
  7. Sorting
  8. Searching Revisited
  9. Dynamic Algorithms
  10. Graphs
  11. Huffman Encoding
  12. FFT
  13. Hard or Intractable Problems
  14. Games

    Appendices

    1. ANSI C
    2. Source code listings
    3. Getting these notes

    Slides

      Slides from 1998 lectures (PowerPoint).

    Course Management

    • Key Points from Lectures
    • Workshops
    • Past Exams
    • Tutorials

    Texts

    Texts available in UWA library
    Other on-line courses and texts
    Algorithm Animations
     

[Dec 31, 1994] Advanced Topics in Graph Algorithms

[Oct 8, 1993] Scalable Libraries for Graph Partitioning by Bhargava at all

School of Information Studies, Syracuse University

The key problem in efficiently executing irregular and unstructured data parallel applications is partitioning the data to minimize communication while balancing the load. Partitioning such applications can be posed as a graph-partitioning problem based on the computational graph. We are currently developing a library of partitioners (especially based on physical optimization) which aim to find good suboptimal solutions in parallel. The initial target use of these partitioning methods are for runtime support of data parallel compilers (HPF).

 

Algorithms Courses on the WWW

Dictionary of Algorithms and Data Structures

This web site is hosted in part by the Software Quality Group of the Software Diagnostics and Conformance Testing Division, Information Technology Laboratory.

This is a dictionary of algorithms, algorithmic techniques, data structures, archetypical problems, and related definitions. Algorithms include common functions, such as Ackermann's function. Problems include traveling salesman and Byzantine generals. Some entries have links to implementations and more information. Index pages list entries by area and by type. The two-level index has a total download 1/20 as big as this page.

C++ Algorithms and Data structures

PO - Algorithms, Data Structures nice collection of links

Recommended Links

Softpanorama Top Visited

Softpanorama Recommended

Please note that TAOCP was started as a compiler book. See also compiler algorithms. Algorithms programming also influenced by computer architecture. After fundamental paper of Donald Knuth, the design of a CPU instruction set can be viewed as an optimization problem.

See also:

Directories (usual mix :-)

Individual home pages

Lecture Notes, E-books and Tutorials

See also Algorithms Courses on the WWW and Data Structures in the Web

Lecture Notes

E-books


Magazines


Papers

[July 2, 1999] ACM Computing Research Repository -- great !


Libraries

LEDA - Main Page of LEDA Research -- C++ libraries, several restrictions apply (non-commercial use, no source code, etc.)

ubiqx -- The goal of the ubiqx project is to develop a set of clean, small, re-usable code modules which implement
fundamental constructs and mechanisms, and to make them available under the terms of the GNU Library
General Public License (LGPL).

Album of Algorithms and Techniques by Vladimir Zabrodsky -- This is the collection of the algorithms (at present about 50) from excellent textbooks (Cormen-Leiserson-Rivest, Knuth, Kruse, Marcello-Toth, Sedgewick, Wirth) translated into the Rexx language. You can study the Album online or offline. It is packed up by WinZip - find an icon of a little black butterfly on the cover page. Suggested by Tom Moran <tmoran8@yahoo.com>[Jan 23, 2000]

Brad Appleton's FTP Site At the moment, he has some C++ class libraries for implementing AVL trees 2-3 trees red-black trees (bottom up) command-line option & argument parsing (CmdLine and Options)


libavl manual - Table of Contents libavl -- A library for manipulation of AVL trees Ben Pfaff (GNU)

AVLTree 0.1.0
AVLTree is a small implementation of AVL trees for the C programming language. It is distributed under the Library Gnu Public License. This library does the basic stuff. It allows for inserts, searches, and deletes in O(log n) time. It also provides an interface to iterate through your entire AVL tree, in order by key, in O(n) time (the calls that allow the iterating take constant amortized time).

Combinatorial Algorithms


Sample Assignments

Sample Data Structures Programming Assignments

Programming Assignments

You can copy and modify these programming assignments, or use them as is for your own class. WARNING TO STUDENTS: These are only sample assignments; check with your instructor to find out what your actual programming assignments are.

Chapter 2:
A Simple Statistician Class
Chapter 3:
The List Class from Section 3.2 (with a fixed array)
A Preliminary Polynomial Class (with a fixed-size array)
Clean-up Notes for the Preliminary Polynomial
Chapter 4:
The List Class with a dynamic array.
The polynomial class with a dynamic array. The Bag with Receipts, using dynamic arrays.
Chapter 5:
Extending the Linked List Toolkit.
Extending the Linked List Toolkit (Version 2).
The List Class with a linked list.
The polynomial class with a linked list.
Using the polynomial in a CGI program.
Chapter 6:
The List Template Class with an External Iterator.
Chapter 7:
Evaluator for Postfix or Infix Expressions.
Chapter 8:
A Priority Queue Class.
A Simple Traffic Light Simulation.
Chapter 9:
Four Small Recursive Functions.
Four More Small Recursive Functions.
(Preliminary Version) A Recursive Permutation Generator.
Chapter 10:
A Binary Search Tree Implementation of the Bag (now using the new binary_tree_node from the second edition)
Chapter 11:
A Heap Implementation of the Priority Queue Class.
A B-Tree Implementation of the Set Class.
Chapter 12:
A Chained Hash Table.
Chapter 13:
A Quicksort Function.
The Standard Library Quicksort Function.
Chapter 14:
Ideas for Derived Game Classes from Section 14.3.
Preliminary Version of a Short Bonus Assignment on Inheritance.

Computer architecture

Instruction set usage patterns

Random Findings


Etc

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The Last but not Least


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