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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Next, knuht 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. Retrieved from ” https: I then read some things around the internet to apply dancing links to sudoku solving [3] [4]. You have yourself a very dynamic “array” which can be any size, and you can easily insert, move, and remove elements just by changing the address of the next element.

It is also possible to solve one-cover problems in which a particular constraint is optional, but can be satisfied no more than once.

Sign up using Email and Password. Although this question is very old, I thought I’d add: 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 the pdf. In computer sciencedancing links is the technique suggested by Donald Knuth to efficiently implement his Algorithm X.

Next read up on Constraint Satisfaction. Dancing Links is a way of implementing that algorithm efficiently. Views Read Edit View history. One is the value you want to hold, and the other is a memory address pointer which points to the next variable.

By using this site, you agree to the Terms of Use and Privacy Policy. In that article that code is a copy of the cover method with some stuff in the for loop changed. And the code snippets in there have some bugs in them.


Thymine 6, 1 23 I understand almost none of it. Do you have something funny to share with fellow programmers?

A doubly linked list also stores the memory address of the previous variable so you danclng go backwards. The dumb version is called generate and test but there are often too many possible solutions to test them all.

I’m trying to get my head around how to visualise the list in memory.

A linked list is sort of like a “make-your-own” array and is used quite often. At all times, each node in the matrix will point to the adjacent nodes to the left and right 1’s in the same dancintabove and below 1’s in the same columnand the header for its column described below.

To backtrack, the above process must be reversed using the second algorithm stated above. Knuth even talks about dancing links in his new Christmas Tree Lecture [6] specifically here at 4: 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. At first I thought about “dancing links” in an html context and got outraged.

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

If a selected column doesn’t have any rows, the current matrix is unsolvable and must be backtracked. In a game of Sudoku you can choose one of two strategies for propagating constraints. Can someone try to explain the Dancing Links algorithm not in terms of its derivation but its implementation? Millennial Perspectives in Computer Science. Hacker News new comments show ask jobs submit.


Dancing Links accommodates these with primary columns which must be filled and secondary columns which are optional. If your table has no columns, stop dancinb you’ve solved it. Because the arxiv abstract page has nice links to more content, including other papers by the same author, and different versions of the same paper, and the source upload of the paper. When selecting a row, an entire column had to be searched for 1’s. In this example, the constraints are that they must perform every trick.


Dancing Links – Wikipedia

Since you’re just changing addresses, the value will still be in danicng, but now you have no way of referencing it. You could also see my comment on in the thread for problem 96 on page 3. Stack Overflow works best with JavaScript enabled. 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”. Truly awesome, thanks again for the link. After selecting a row, that row and a number of columns had to be searched for 1’s.

Submit a danciing link. Post as a guest Name. Welcome to Reddit, the front page of the internet. Select a column representing a constraint. Algorithm DLX will branch on the ways to fill a cell if some cell is difficult to fill, or on the ways to place a piece if some piece is difficult to place.

How did I miss that? If you can’t find a row, give up – there are no solutions. You should start by learning about backtracking search. That’s the theory, but Donald Knuth is also a practitioner and you’d better know C or assembler to keep up with him. I don’t know who wrote it or what the title was. There are two techniques that can be used when you don’t have a good algorithm, trial and error and the process of elimination.

Knuth said of it “Algorithm X is simply a statement of the obvious trial-and-error approach.