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For this class of problems, the instance data P would be the integers m and n, and the predicate F. In a typical backtracking solution to this problem, one could define a partial candidate as a list of integers c = (c[1], c[2], …, c[k]), for any k between 0 and n, that are to be assigned to the first k variables x[1], x[2], …, x[k]. The ...
When further backtracking or backjumping from the node, the variable of the node is removed from this set, and the set is sent to the node that is the destination of backtracking or backjumping. This algorithm works because the set maintained in a node collects all variables that are relevant to prove unsatisfiability in the leaves that are ...
Such problems are usually solved via search, in particular a form of backtracking or local search. Constraint propagation is another family of methods used on such problems; most of them are incomplete in general, that is, they may solve the problem or prove it unsatisfiable, but not always. Constraint propagation methods are also used in ...
In a general constraint satisfaction problem, every variable can take a value in a domain. A backtracking algorithm therefore iteratively chooses a variable and tests each of its possible values; for each value the algorithm is recursively run. Look ahead is used to check the effects of choosing a given variable to evaluate or to decide the ...
Backtracking search is a general algorithm for finding all (or some) 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.
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.
Recursive descent with backtracking is a technique that determines which production to use by trying each production in turn. Recursive descent with backtracking is not limited to LL( k ) grammars, but is not guaranteed to terminate unless the grammar is LL( k ).
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.