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Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. [3] Backtracking is a depth-first search (in contrast to a breadth-first search), because it will completely explore one branch to a possible solution before moving to another branch.
LDPC decoding is a common use-case for belief propagation, with slight modifications this approach can be used for solving Sudoku codes. [4] The constraint satisfaction using a tanner graph is shown in the figure on the right. denotes the entries of the sudoku in row-scan order.
The Dancing Links algorithm solving a polycube puzzle In computer science , dancing links ( DLX ) is a technique for adding and deleting a node from a circular doubly linked list . It is particularly useful for efficiently implementing backtracking algorithms, such as Knuth's Algorithm X for the exact cover problem . [ 1 ]
The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. [8] A puzzle can be expressed as a graph coloring problem. [9] The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The Sudoku graph has 81 vertices, one vertex for each cell.
The book is centered around Sudoku puzzles, using them as a jumping-off point "to discuss a broad spectrum of topics in mathematics". [1] In many cases these topics are presented through simplified examples which can be understood by hand calculation before extending them to Sudoku itself using computers. [3]
The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. [26] Many Sudoku solving algorithms , such as brute force -backtracking and dancing links can solve most 9×9 puzzles efficiently, but combinatorial explosion occurs as n increases, creating practical limits to the properties of Sudokus ...
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The Sudoku graph contains as a subgraph the rook's graph, which is defined in the same way using only the rows and columns (but not the blocks) of the Sudoku board. The 20-regular 81-vertex Sudoku graph should be distinguished from a different 20-regular graph on 81 vertices, the Brouwer–Haemers graph , which has smaller cliques (of size 3 ...