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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.
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]
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 ...
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.
SAT solver. In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem. On input a formula over Boolean variables, such as " ( x or y) and ( x or not y )", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make ...
This algorithm, also known as the "recursive backtracker" algorithm, is a randomized version of the depth-first search algorithm. Frequently implemented with a stack, this approach is one of the simplest ways to generate a maze using a computer. Consider the space for a maze being a large grid of cells (like a large chess board), each cell ...
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.
According to your reference backtracking is a subset of brute force, therefore this section IS in the scope of brute force. Can we say the algorithm is elevated to "backtracking"? When solving a sudoku the algorithm described will not test "3456" in positions 1-4 if "345" in positions 1-3 have already been proven invalid (it will advance to "346").