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Sudoku can be solved using stochastic (random-based) algorithms. [9] [10] An example of this method is to: Randomly assign numbers to the blank cells in the grid. Calculate the number of errors. "Shuffle" the inserted numbers until the number of mistakes is reduced to zero. A solution to the puzzle is then found.
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 ...
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.
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 ...
Backtracking line search. In (unconstrained) mathematical optimization, a backtracking line search is a line search method to determine the amount to move along a given search direction. Its use requires that the objective function is differentiable and that its gradient is known. The method involves starting with a relatively large estimate of ...
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.