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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 ...
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.
A Sudoku solved by backtracking. Examples where backtracking can be used to solve puzzles or problems include: Puzzles such as eight queens puzzle, crosswords, verbal arithmetic, Sudoku [nb 1], and Peg Solitaire. Combinatorial optimization problems such as parsing and the knapsack problem.
(In such a case, the algorithm may be restarted with a different initial configuration.) On the other hand, it can solve problem sizes that are several orders of magnitude beyond the scope of a depth-first search. As an alternative to backtracking, solutions can be counted by recursively enumerating valid partial solutions, one row at a time.
Killer sudoku (also killer su doku, sumdoku, sum doku, sumoku, addoku, or samunamupure) 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, however, can take hours to solve.
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 ]
Wayne Gould (高樂德) (born 3 July 1945 in Hāwera, New Zealand) is a retired Hong Kong judge, most recently known for helping to popularise sudoku puzzles in the United Kingdom, and thereafter in the United States. He pioneered the global success and popularity of the Sudoku puzzle outside Japan where it had been popular for many years ...