Dancing Links is a way of implementing that algorithm efficiently. The key It is largely a direct implementation from Knuth’s pdf, but with a few object orientated. Algorithm X was invented by Donald Knuth to solve it. He even suggested an efficient implementation technique called Dancing Links, using doubly-linked. I found Knuth’s “Dancing Links” paper [1] very well written and a somewhat easy read (I had to reread certain parts a couple times). I had to write a sudoku solver.

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Dancing Links is a way of implementing that algorithm efficiently. This paper plays with a rather small set of concepts; I checked the wikipedia entries for the main keywords in the paper and Linke found them quite informative I have a CS degree. I’ve been working on a Sudoku Solver, my current solver uses the backtracking algorithm but it still takes too long. One requirement of using that algorithm is that backtracking must be done dancinf an exact reversal of eliminations.

Dancing Links

It is largely a direct implementation from Knuth’s pdf, but with a few object orientated optimizations actually since I did this a few months ago I don’t quite remember how much I strayed from lknks pdf. Stack Overflow works best with JavaScript enabled.

Is there no plugin to watch them dncing I am currently an amateur programmer in high school, teaching myself. In a game of Sudoku you can choose one of two strategies for propagating constraints. Well, what kind of questions do you have in particular? I also read Sudopedia’s version on it, and it seems that once it got to the Sudoku’s implementation, it got too abstract.

This removes x from the doubly-linked list. While removing all those columns, also remove all rows that have an X in the columns you’re removing because you’ve already satisfied the constraint, so knugh barred from choosing something that would satisfy it again. I’m hoping to get it down to less than a second for most cases. Constraint propagation eliminates bad choices based on existing knowledge so they never have to be tested.


[cs/] Dancing links

It’s a linked list. The inner knuyh iterator needs to go left not right, and the links need to be restored to the original, not repeat the cover operation. Anyone have an alternative? Sign up using Facebook. Each row and column in the matrix will consist of a circular doubly-linked list of nodes.

I haven’t profiled my code, but I did keep a bit of recursion in the solver our of convenience. Online resources would be preferred, but if there’s not much quality material online, books would be acceptable. Articles containing video clips.

Computer Science > Data Structures and Algorithms

likns It is also possible to solve one-cover problems in which a particular constraint is optional, but can be satisfied no more than once. Hope this supplements spliznork’s comment.

If the resulting matrix has no columns, then they have all been filled and the selected rows form the solution. Please follow proper reddiquette. At all times, each node in the matrix will point to the adjacent lknks to the left and right 1’s in the same rowabove and below 1’s in the same columnand the header for its column described below.

If you keep dajcing reference you can “undelete” the element and put it back in the list. Knuth even talks about dancing knnuth in his new Christmas Tree Lecture [6] specifically here at 4: An exact cover problem is a problem where you’re given a bunch of choices, and a set of constraints and your challenge is to select a bunch of the choices that will fill every constraint exactly once.

Millennial Perspectives in Computer Science. In addition to what others said, because for bookmarks, the abstract page works a lot better. So here’s my description of algorithm X: Search algorithms Linked lists Donald Knuth Sudoku. The full source code for this link is not available anymore.


The key point of dancing links is that in a linked list, when you remove a node which can be done efficently by modifying the pointers of its neighboursthe node that you’ve removed has all the information you need to add it back to the linked list in the case that it turns out you were wrong when you guessed it was part of the solution.

The only thing I remember is daancing it was green, old, big, linos lots of diagrams with arrows, and was owned by my high school library.

Dancing Links – Wikipedia

I will join you in your sadness, although PDF doesn’t handle typesetting. Also look at some danckng satisfiers. It’s an efficient representation for solving exact cover problems.

Then, searching for a solution is only a series of very cheap pointer twiddlings no recursion, no memory allocations necessary – hence the name “dancing links”. They have a number of tricks that they need to show the judges, and don’t want to perform any trick more than once. Specifically the uncover ColumnNode c method. By using this site, you agree to the Terms of Use dancong Privacy Policy. I began learning about linkss structures and algorithms from a dead-tree book.

This paper describes a clever way to do all of the above. The choices are the possible sequences they could incorporate into their routine.

Guess I ought to throw some of it up on Github. Until I read about it at that link, I had thought this must be a super advanced algorithm, but really once you can visualize it, its just a really ingenious but simple solution. What he’s going into here is a bit of a trick you can use when removing elements. Next read up on Constraint Satisfaction.

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