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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. [2] 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.
Backtracking is an important tool for solving constraint satisfaction problems, [2] such as crosswords, verbal arithmetic, Sudoku, and many other puzzles. It is often the most convenient technique for parsing , [ 3 ] for the knapsack problem and other combinatorial optimization problems.
Dancing Links. 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] Algorithm X is a recursive, nondeterministic, depth-first ...
One algorithm solves the eight rooks puzzle by generating the permutations of the numbers 1 through 8 (of which there are 8! = 40,320), and uses the elements of each permutation as indices to place a queen on each row. Then it rejects those boards with diagonal attacking positions. This animation illustrates backtracking to solve the problem. A ...
Solving sudokus by backtracking rename to: Solving sudokus by backtracking with color assignment current title: Solving sudokus by a brute-force algorithm rename to: Solving sudokus by simple backtracking In renaming these sections I would place this later section above the other since it is the nominal algorithm.
Solving Sudoku is an exact cover problem. More precisely, solving Sudoku is an exact hitting set problem, which is equivalent to an exact cover problem, when viewed as a problem to select possibilities such that each constraint set contains (i.e., is hit by) exactly one selected possibility.
1. Algorithm X with Knuth's suggested heuristic for selecting columns solves this problem as follows: Level 0. Step 1—The matrix is not empty, so the algorithm proceeds. Step 2—The lowest number of 1s in any column is two. Column 1 is the first column with two 1s and thus is selected (deterministically): 1. 2.
The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. [29] 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 ...