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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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A very fast solution for problem 96 “sudoku” at project Euler look for grimbal in the forum does a propagate and search using these two methods explicitly. From Wikipedia, the free encyclopedia. Views Read Edit View history. This is useful when your algorithm is trying a “tree” of different possibilities to find some solution like a chess game for exapmlesince if you get stuck you can backtrack very easily. Email Required, but never shown. The Dancing Links Algorithm – An explanation that is less explanatory but more on implementation?

Each column will have a special node known as the “column header,” dancinh will be included in the column list, and will form a special row “control row” consisting of all the columns which still exist in the matrix. Anyone have an alternative? Want to add to the discussion?

Dancing Links – Wikipedia

Also my implementation in C should be fairly easy to read Ok, assuming you’ve got that, now you need to understand Algorithm X. According to Knuth, dancing links will equal or better such specifically written algorithms. The name dancing links stems from the way the algorithm works, knhth iterations of the algorithm cause the links to “dance” with partner links so as to resemble an “exquisitely choreographed dance. Just because it has a computer in it doesn’t make it programming.

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

This order ensures that any removed node is removed exactly once and in a predictable order, so it can be backtracked appropriately. I suggest looking on wikipedia, then if you still have some black area we can point you somewhere else.


If you’ve got a partial solution stored, then it’s actually a real solution, return it. There’s a lot of timing noise in just running one copy of Euler problem set through my solver. Next, for each row where the selected column contains a 1, traverse the row and remove it from other columns this makes those rows inaccessible and is how conflicts are prevented.

A nice way to represent problems of this sort is to draw out a table where the constraints are columns and the choices are rows, and you have a big X in cells where a particular choice fulfills that constraint. Search algorithms Linked lists Donald Knuth Sudoku. Well, what kind kunth questions do you have in particular?

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Dancing Links

This paper plays with a rather small set of concepts; I checked the wikipedia entries for the main keywords in the paper and I found them quite informative I have a CS degree. It’s an efficient representation for solving exact cover problems.

Assume that the row you found in 3 is in the solution, so remove all columns that it have an X in danclng row. Firstly you have to understand Exact Cover. Knuth said of it “Algorithm X is simply a statement of the obvious trial-and-error approach. Check out our faq. This paper describes a clever way to do all of the above.

Danccing did I miss that? To delete an element in a linked list, you just have to make the previous element point to a different element. I am currently an amateur programmer in high school, teaching myself. The columns are removed because they have been filled, and the rows are removed because they conflict with the selected row.

If a selected column doesn’t dqncing any rows, the current matrix is unsolvable and must be backtracked. As it turns out, given the right constraints and choices, sudoku can be described as an Exact Cover problem. I’m hoping to get it down to less than a second for most cases. Knuhh here’s my description of algorithm X: When an elimination occurs, all columns for which the selected row contains a 1 are removed, along with all rows including the selected row that contain a 1 in any of the removed columns.


I had to write a sudoku solver for one of my classes and I read that dancing links and algorithm x was one way to do it [2]. I’ve been curious if it’d be faster if I took that recursion out. Those that are interested in this ought to check out Knuth’s video lecture on the same subject, at the SCPD site: That plus the fact that if you make all your linked lists circular then suddenly you lose a lot of special cases is pretty much all dancing-links is.

Use of this site constitutes acceptance of our User Agreement and Privacy Policy. Knuth even talks about dancing links in his daancing 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.

Probably late, but it’s a double linked list in a toroidal ,inks Retrieved from ” https: Knuth’s paper gives a clear picture of these relationships and how the linsk removal and reinsertion works, and provides a slight relaxation of this limitation. Select a column representing a constraint.

Basically he uses dancing links to solve for certain n in the problem he sets up in that lecture. Articles containing video clips. Sign up using Facebook. Guess I ought to throw some of it up on Github. You could also see my comment on in the thread for problem 96 on page 3.