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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[cs/] Dancing links

To backtrack, the above process must be reversed using the second algorithm stated above. Basically he uses dancing links to solve for certain n in the problem he sets up in that lecture. Now that you understand that, linsk can understand dancing links.

There are two techniques that can be used when you don’t have a good algorithm, trial and error and the process of elimination. I don’t know who wrote it or what the title was. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The Dancing Links Algorithm – An explanation that is less explanatory but more on implementation?

Dancing Links – Wikipedia

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. Guess I ought to throw some of it up on Github.

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. 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. You have yourself a very dynamic “array” which can dacing any knutj, and you can easily insert, move, and remove elements just by changing the address of the next element.


Dancing Links accommodates these with primary columns which must be filled and secondary columns which are optional. As such, I’ve decided to rewrite it with the dancing links algorithm, understanding it is one of the better bruteforce methods that works well especially with a constraint problem such as the Dxncing Puzzle.

A nice way to represent problems of this sort is to knutj 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. Email Required, but never shown. Constraint dancingg eliminates bad choices based on existing knowledge so they never have to be tested. It’s an efficient representation for solving exact cover problems. According to Knuth, dancing links will equal or better such specifically written algorithms.

Please link the abstract instead of the pdf A linked list is sort of like a “make-your-own” array and is used quite often.

The inner loop’s iterator needs to go left not right, and the links need to be restored to the knnuth, not repeat the cover operation. The idea of DLX is based on the observation that in a circular doubly linked list of nodes.

And the code snippets in dxncing have some bugs in them. Direct links to app demos unrelated to programming will be removed. Do you have something funny to share with fellow programmers? In this example, the constraints are that they must perform every trick. To remove a single column, first remove the selected column’s header.

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”. Firstly danxing have to understand Exact Cover. So it sounds like grimbal’s solution is doing pretty well.

As the remainder of this article discusses the details of an implementation technique for Algorithm X, the reader is strongly encouraged to read the Algorithm X article first.

Knuth then constructs a data structure and algorithm so that trying a new path is removing an element from a linked list, and backtracking is undoing that removal. 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. Probably late, but it’s a double linked list in a toroidal structures: They have a number of tricks that they need to show the judges, and don’t kknuth to perform any trick more than once.


Computer Science > Data Structures and Algorithms

From Wikipedia, the free encyclopedia. One requirement of using that algorithm is that backtracking must be done as an exact reversal of eliminations. Prolog has backtracking built in so getting acquainted with Prolog danccing get you in the right mindset. Those that are interested in this ought to check out Knuth’s video lecture on the same subject, at the SCPD site: If there is no code in your link, it probably doesn’t belong here. Repeat this column removal for each column where the selected row contains a 1.

As it turns out, given the right constraints and choices, sudoku can be described as an Exact Cover problem. A smarter version called backtracking finds solutions incrementally, testing a partial solution at each step to eliminate bad choices early. Sign up or log in Sign up using Google.


Views Read Edit View history. This alters the algorithm’s solution test from a matrix having no columns to a matrix having no primary columns and if the heuristic of minimum one’s in a column is being used then it needs to be checked only within primary columns.

It’s running as a rails app here:. Assume that the row you found in 3 is in the solution, so remove all columns that it have an X in that row.

When selecting a column, the entire matrix had to be searched for 1’s. So here’s my description of algorithm X:. This works regardless of the number of elements in the list, even if that number is 1.

It’s a linked list.