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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Anyone have an alternative? That’s the theory, but Donald Knuth is knkth a practitioner and you’d better know C or assembler to keep up with him.

I found Knuth’s “Dancing Links” paper [1] very well written and a somewhat easy | Hacker News

Knuth said of it “Algorithm X is simply a statement of the obvious trial-and-error approach. If you can’t, remove the row you tried from the potential solution structure, restore all the rows and columns you removed in steps 3 and 4 and try a different row.

Well then I will guess that this should help you: Guess I ought to throw some of it up on Github. Sign up using Facebook. Selecting a column with a low node count is a heuristic which improves performance in some cases, but is not essential to the algorithm.

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Hacker News new comments show ask jobs submit. Truly awesome, thanks again for the link. It is also possible to solve one-cover problems in which a particular constraint is optional, but can be satisfied no more than once.


If you run out of rows, then give up – there are no solutions. 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.

The inner loop’s iterator needs to go left not right, and the links need to be restored to the original, not repeat the cover operation. In that article that code is a copy of the cover method with some stuff in the for loop changed.

Also look at some constraint satisfiers. 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 linkks 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.

Then, searching for a solution is only a series of very cheap pointer twiddlings no recursion, no memory allocations necessary – hence the name “dancing kntuh. I don’t know who wrote it or what the title was. It’s a linked list.


Become a Redditor and subscribe to one of thousands of communities. In Algorithm X, rows and columns are regularly eliminated from and restored to the matrix. Especially true on arxiv. Submit a new link. Retrieved from ” https: Constraint propagation eliminates bad choices based on existing knowledge so they never have to be tested. They have a number of sequences which are groups of tricks that can be put together and they want to choose the ideal selection of sequences to cover all the tricks once.


I am currently an amateur programmer in high school, teaching myself.

At first I thought about “dancing links” in an html context and got outraged. I’ve been working on a Sudoku Solver, my current solver uses the backtracking algorithm but it still takes too long.

Computer Science > Data Structures and Algorithms

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Knuth explains dancing links. If you keep a reference you can “undelete” the element and put it back in the list. The name dancing links stems from the way the algorithm works, as iterations of the algorithm cause the links to “dance” with partner links so as to resemble an “exquisitely choreographed dance. Add it to some kind of structure where you’re storing potential solutions.