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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. Although it has been established that approximately 5.96 x 10 26 final grids exist, a brute force algorithm can be a practical method to solve Sudoku puzzles.
The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. [30] 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 ...
Killer sudoku (also killer su doku, sumdoku, sum doku, sumoku, addoku, or samunanpure サムナンプレ sum-num(ber) pla(ce)) is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic ; the hardest ones ...
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.
He has also written puzzles for events including the World Sudoku Championship, U.S. Puzzle Championship, the MIT Mystery Hunt, Gen Con, and the Microsoft Puzzle Picnic. [4] In early 2012, Snyder founded his publishing company Grandmaster Puzzles. On April 9, 2012, he began selling his first title from the newly formed company, The Art of Sudoku.
This book is intended for a general audience interested in recreational mathematics, [7] including mathematically inclined high school students. [4] It is intended to counter the widespread misimpression that Sudoku is not mathematical, [5] [6] [8] and could help students appreciate the distinction between mathematical reasoning and rote calculation.
The constraints of Sudoku codes are non-linear: all symbols within a constraint (row, line, sub-grid) must be different from any other symbol within this constraint. Hence there is no all-zero codeword in Sudoku codes. Sudoku codes can be represented by probabilistic graphical model in which they take the form of a low-density parity-check code ...
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 ]
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