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Sudoku solving algorithms. A typical Sudoku puzzle. A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box.
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 ...
Backtracking. Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. [1]
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.
Knuth's Algorithm X is an algorithm that finds all solutions to an exact cover problem. DLX is the name given to Algorithm X when it is implemented efficiently using Donald Knuth's Dancing Links technique on a computer. The exact cover problem can be generalized slightly to involve not only exactly-once constraints but also at-most-once ...
Eight queens puzzle. The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century.
O ( n ) {\displaystyle O (n)} (basic algorithm) In logic and computer science, the Davis–Putnam–Logemann–Loveland ( DPLL) algorithm is a complete, backtracking -based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
Breadth-first search ( BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Extra memory, usually a queue, is needed to keep track of the child nodes that were ...