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I just wanted to learn name of algorithms.. thanks
A general strategy in game algorithms is the minimax strategy, augmented with alpha-beta pruning. The minimax algorithm finds the best move, and alpha-beta pruning prevents it from going into branches of the game tree that cannot produce a better result than previous branches already have.
However, the chess game tree is too large to be completely examined. That is why computer chess engines only examine the tree up to a certain depth, and then use various methods to evaluate the positions. Many of these methods are based on heuristics. Also, a serious chess-playing program will have a library of openings so that it can play in the beginning by just consulting that library and not having to examine the game tree. Finally, many end games are completely solved, and these are also programmed in as a library.
Minimax
If you need an in-depth knowledge about AI algorithms, I think "artificial intelligence modern approach" book is the best source.
Wikipedia is a safe bet as a starting point. Did you look there?
Rybka seems to be a contender.
Have a look at the some of the free source chess codes, for instance Crafty or even better how about Fruit? It plays pretty much almost the same strength of Rybka. But there are many new algos out there. Day will come when human chess players will have to just say I am not playing vs this engine, and this article pretty much sums it up --> http://www.mychessblog.com/man-versus-machine-when-a-computer-will-become-world-chess-champion/
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Closed 10 years ago.
I have used a random mutation hill climbing algorithm as part of a project that I am working on, but was wondering whether it would be better to use simulated annealing to minimise the chance of getting stuck in any local optima.
The question I have is which one tends to be generally faster from your experience? Obviously there is a huge wealth of applications for both algorithms; this is more of a generalised pondering, if you like.
Thank you.
There's no way to tell in advance (unless your project is a 100% match to a well studied academic problem like a pure TSP - and even then ...). It depends on your project's constraints and your project's size (and if you implement the algorithms correctly).
So, to be sure, you have to implement both algorithms (and many others, like Tabu Search, ...) and use a Benchmarker like this one to compare them.
That being said, I 'd put my money on Simulated Annealing over Random Mutation Hill Climbing any day :)
Note: Simulated Annealing is a short but difficult algorithm: I only got it right in my 3th implementation and I 've seen see plenty of wrong implementations (that still output a pretty ok solution) in blogs, etc. It's easier just to reuse optimization algorithms.
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What areas of math are prerequisite for learning algorithms?
I guess it depends a lot about the kind of algorithm you want to use and how deeply you want to understand them.
The understand of the usual basic data structures needs almost no math background.
Most of the graphical algorithms requires knowledge of trigonometry and spatial geometry.
Algorithms about physics engine are easier to understand if you have some physics basis
If you want your program to help you to take decisions, you might need to study operational research which is a really huge sub-fields of math which includes graph theory, game theory, optimisation (which then includes analysis and linera albegra)
In any case, having a logic/mathematical mind obviously helps a lot for the understanding and to check/prove that your code can/cannot work.
If you're talking about simple programming you don't really need a lot of math. At this level, your problem solving and logic abilities are more important, but it's necessary that you get instructed in the basics of problem solving by using flow charts and process planing.
In the other side, math is known to improve your abilities and in some areas you would need to know math to achieve the expected results. For example, to create an animation engine knowing linear algebra is more than useful, so its physics.
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(edited)
For anyone interested in music and artificial intelligence:
Do you know of any music-composing algorithm that produces really interesting, fun or intelligent music? And not something sounding like a random noise.
(Previous, too broad question:)
What are some state of the art (very good, non-boring) music composition algorithms, software, researches that you have heard of?
Feel free to post any interesting link about this subject.
P.S. I don't mean programs that assist you at playing, but primarily anything that can compose melody by itself (or with little assistance).
OR: Analyses existing music pieces and tells how much it likes them :)
One of the leading researchers in algorithmic composition is David Cope of the University of California, Santa Cruz. His approach emphasizes machine learning, the results of which were impressively demonstrated in a 2006 performance.
http://www.wired.com/wired/archive/14.09/posts.html?pg=3
A good place to start would be with his aptly named book, The Algorithmic Composer, which covers much of his approach and provides most of the software he has written for his work.
http://books.google.com/books?id=rFGH07I2KTcC
Though not specifically algorithmic composition another invaluable resource is David Temperley's book, The Cognition of Basic Musical Structures, which provides quite a few models begging to be implemented.
http://books.google.com/books?id=IDoLEvTQuewC
Those two alone a pretty time consuming for anyone with an interest in that they are concrete enough that experimenting along the way is inevitable.
Hope that helps.
One possibility would be to use a hidden Markov model: feed it samples of music, and have it generate "similar" music.
One example: http://www.cogs.susx.ac.uk/users/christ/talks/music-making-with-HiMMs.pdf
I did something similar with Shakespeare's sonnets. The results were ... interesting. Amusing, at times.
There's a search engine that lets you whistle a tune and that searches for music alike. I'm not sure whether http://www.midomi.com/ is what I originally heard of. You can for example play the music and see if it finds what you intended.
A fellow student of me created a score composer for his Master's project. The input was humming or whistling and through FFT, music theory and combinatorial algorithms (I'm not sure whether it was simulated annealing). I'm not sure how it was related, but the project had something to do with the http://www.wikifonia.org/ project.
(edit)
I heard a talk from someone who worked at http://last.fm. They analyze music (machine learning) as one of the ways to overcome the cold start problem in their recommender system. They try to predict how much a new song resembles other songs.
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Closed 11 years ago.
Can someone give a brief list of Mathematics areas (like functions, calculus etc.,) to learn for understanding the Algorithm Analysis books (like Introduction to Algorithms)?
I would start with discrete mathematics. That would probably give you the best computational basis and intuition for what computer algorithms are about in terms of working with sets and discrete numbers in general. Also, something on data structures and algorithms would help as well. This would give you good background on things like sorting arrays, efficient searches etc. You could then move on to books on artificial intelligence (my best guess), but by this time you should definitely be ready to read some algorithms books. IMO, that is.
UPDATE
Also, calculus never hurts either if you're working with minimization/maximization/optimization problems. That might or might not bee needed depending on the specific algorithms you'd like to work with.
To start with:
number theory, especially induction.
basic set theory, sets and functions.
basic calculus, limits.
logarithms
discrete math (combinations, permutations, etc)
generating functions (adv. discrete math).
For Introduction to Algorithms the only things you really need to know are induction and some basic set theory. For the more advanced parts you also need to know some linear algebra and probability theory.
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Closed 12 years ago.
Christoph Koutschan has set up an interesting survey that tries to identify the most important algorithms "in the world". Since one of the criteria is that "the algorithm has to be widely used" I though that extending the survey to the huge group of users at Stack Overflow would be a natural thing to do.
So, what do you think? Which algorithms deserve a place in the Algorithm Hall of Fame?
I somewhat like this algorithm:
Write code.
Test code. If buggy, go to step 3. If not, go to step 4.
Rewrite code, then go back to step 2.
Get somebody else to test your code. If they discover any bugs, return to step 3, otherwise go to step 5.
Congratulations, your code has no obvious bugs! Now you wait for a user to stumble upon a hidden one, in which case you return to step 3 once again unless you're lucky and are no longer providing support for the code in question.
I'd say binary search since it's usually the first algorithm people learn. And the RSA encryption algorithms are pretty important.
Hashing, since it's the basis for so much in security, data structures, etc. Hashing algorithms have generated a lot of Ph.D. dissertations.