![]() Every row will have a 1 in every column (constraint) that it satisfies, and a 0 otherwise. Exact Cover And Dancing LinksĪn exact cover problem can be represented as a sparse matrix where the rows represent possibilities, and the columns represent constraints. I convert the Sudoku puzzle into an exact cover problem, solve that using the Dancing Links algorithm as described by Dr Donald Knuth, and then get the solution and map it onto the Grid. My class AlgorithmXSolver takes an unsolved Sudoku puzzle as an int (the Grid) and outputs the solved Sudoku puzzle. Algorithm X, Exact Cover Problem And Dancing Links Implementation I believe my Algorithm X implementation is one of the few ones in Java (at least, I couldn’t find much online).Īnyway, here goes. And thus an assigment that should have taken a week to do ended up swallowing the better part of a month as I struggled with understanding Knuth’s paper and then implementing a Solver in Java. I decided I would take a shot at using his technique to write a Sudoku Solver in Java. I read that no less than Dr Donald Knuth had thought and written about this, and he had described an algorithm to solve a Sudoku puzzle – Algorithm X+Dancing Links. Our prof told us that for the search engine he would give us a bunch of guidelines and classes to start us off, but wouldn’t give us anything for the Sudoku problem – it was billed as the more ‘open ended’ and ‘challenging’ of the two.īeing a nerd, I decided that I had to do the Sudoku Solver, and started reading online about Sudoku solving. Yes.For my Algorithms 1 course in Fall 2013, the final project was a choice between building a web search engine and an NxN Sudoku solver. The number must be found in one of the four tiles in the quadrant. ![]() Sorry, it's very vertical and horizontal. When she reached the third official rule, she realized that each quadrant must contain one of the numbers. The mutual exclusion for every column is the same rule as before, only in one row and one role. Every column for a number must have a row in which it's being occupied by that number. Each number must be contained in a second of the rules column. It's because you can actually derive this rule from this one over here and this one over here will not show the logical proof for it, but should make intuitive sense. An alternative rule is the reason I have a place down here. You can't put a number three here and repeat it here. It must be occupying one of the four columns for each number. ![]() We say for each row for each number there must be a column to model the first official rule that each were almost identical. You cannot leave empty tiles on the board for it to be a solution because it restricts and suspends. The second rule states that for each tile. There is a graphical showcase of what these rules are talking about. Each column had the same number, 1234, and each quadrant had the same number. Each row has to contain one of the numbers 1, 2, 34. The nine by nine rules are almost identical to the four x 4 rules. A Sudoku puzzle is used to satisfy a problem. We are asked to come up with a solution to the four x 4mm hmm.
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