Solving Sudoku with Dancing Links Rob Beezer
[email protected] Department of Mathematics and Computer Science University of Puget Sound Tacoma, Washington USA Stellenbosch University October 8, 2010 Available at http://buzzard.pugetsound.edu/talks.html Example: Combinatorial Enumeration Create all permutations of the set f0; 1; 2; 3g Simple example to demonstrate key ideas Creation, cardinality, existence? There are more efficient methods for this example Rob Beezer (U Puget Sound) Solving Sudoku with Dancing Links Stellenbosch U October 2010 2 / 37 Brute Force Backtracking BLACK = Forward BLUE = Solution RED = Backtrack root 0 1 2 0 1 3 3 0 2 1 0 2 3 3 0 3 1 0 3 1 0 2 0 0 1 2 2 0 1 3 0 2 1 3 0 2 3 0 3 1 3 0 3 3 1 0 2 1 0 0 0 1 2 0 1 0 2 1 0 2 0 3 1 0 3 1 0 2 0 0 1 2 3 0 0 2 0 0 3 0 1 0 2 2 0 1 0 1 2 0 2 0 2 2 0 3 0 3 2 root 1 0 2 0 1 0 0 1 0 2 0 0 2 0 3 0 0 3 2 0 1 1 0 2 3 0 1 0 1 3 0 2 0 2 3 0 3 0 3 2 1 0 1 0 2 . 0 1 1 0 1 3 0 0 2 1 0 2 3 0 0 3 1 0 3 2 1 1 0 0 .