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Algorithm X is an algorithm for solving the exact cover problem. It is a straightforward recursive , nondeterministic , depth-first , backtracking algorithm used by Donald Knuth to demonstrate an efficient implementation called DLX, which uses the dancing links technique.
Some of the better-known exact cover problems include tiling, the n queens problem, and Sudoku. The name dancing links , which was suggested by Donald Knuth , stems from the way the algorithm works, as iterations of the algorithm cause the links to "dance" with partner links so as to resemble an "exquisitely choreographed dance."
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.
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.
[15] [16] If the code employs a strong reasoning algorithm, incorporating backtracking is only needed for the most difficult Sudokus. An algorithm combining a constraint-model-based algorithm with backtracking would have the advantage of fast solving time – of the order of a few milliseconds [17] – and the ability to solve all sudokus. [5]
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 ...
Even when they terminate, parsers that use recursive descent with backtracking may require exponential time. Although predictive parsers are widely used, and are frequently chosen if writing a parser by hand, programmers often prefer to use a table-based parser produced by a parser generator , [ citation needed ] either for an LL( k ) language ...
An argument against the use of Backtracking line search, in particular in Large scale optimisation, is that satisfying Armijo's condition is expensive. There is a way (so-called Two-way Backtracking) to go around, with good theoretical guarantees and has been tested with good results on deep neural networks, see Truong & Nguyen (2020). (There ...