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.

Author: Gulmaran Arami
Country: Rwanda
Language: English (Spanish)
Genre: Photos
Published (Last): 27 July 2017
Pages: 158
PDF File Size: 11.3 Mb
ePub File Size: 17.2 Mb
ISBN: 399-1-80973-210-6
Downloads: 51644
Price: Free* [*Free Regsitration Required]
Uploader: Darg

Submit a new link.

You browse my code here http: Millennial Perspectives in Computer Science. 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].

Well then I will guess that this should help you: I thought I had a good grip on most of the basics of programming, and a little bit of computer science theory such as big O notationbut then I checked out this. The columns are removed because they have been filled, and the rows are removed because they conflict with the selected row. It’s excellent that he explains the reduction to exact cover in the source.

After selecting a row, that row and a number of columns had to be searched for 1’s. You might be interested in my implementation in javascript.

If there is no code in your link, it probably doesn’t belong here. You should start by learning about backtracking search.

Hacker News new ,inks show ask jobs submit. Each element of a linked list contains 2 variables. 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.


Computer Science > Data Structures and Algorithms

Repeat this column removal for each column where the selected row contains a 1. One dnacing of using that algorithm is that backtracking must be done as an exact reversal of eliminations.

Select a column representing a constraint.

I understand almost none of it. Log in or sign up in seconds. I’d eventually like get a computer science degree, but meanwhile, I like to learn things on my own. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. I also read Sudopedia’s version on it, and it seems that once it got to the Sudoku’s implementation, it got too abstract.

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.

Especially true on arxiv. If the resulting matrix has no columns, then they have all been filled and the selected rows form the solution. Knuth’s paper gives a clear picture of these relationships and how the node removal and reinsertion works, and provides a slight relaxation of this limitation.

Dancing Links

Thymine 6, 1 23 Truly awesome, thanks again for the link. 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. From Wikipedia, the free encyclopedia. I have tried to read the Wiki and Knuth’s paper on it, however both of them are kinda hard to comprehend and extremely verbose. Eliminations are determined by selecting a column and a row in that column.


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.

[cs/] Dancing links

This page was last edited on 24 Decemberat If a selected column doesn’t have any rows, the current matrix is unsolvable and must be backtracked. I think he mentioned that it would be in his new book, but I had no idea there would be over pages of dancing links. Check out our faq. Knuth even talks about dancing links in his new Christmas Tree Lecture [6] specifically here at 4: As the remainder of this article discusses the details knith an implementation technique for Algorithm X, the reader is strongly encouraged to read the Algorithm X article first.

To delete an element in a linked list, you just have to make the previous element point to a different element. I used Knuth’s dancing links algorithm to generate many of the puzzles at my website. At all times, each node in the matrix will point to the adjacent nodes to the left and right 1’s in the same rowabove and below 1’s in the same columnand the header kknuth its column described below.

Direct links to app demos unrelated to programming will be removed. Online resources would be preferred, but if there’s not much quality material online, liks would be acceptable.