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- Knuths_Algorithm_X abstract ""Algorithm X" is the name Donald Knuth used in his paper "Dancing Links" to refer to "the most obvious trial-and-error approach" for finding all solutions to the exact cover problem. Technically, Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm. While Algorithm X is generally useful as a succinct explanation of how the exact cover problem may be solved, Knuth's intent in presenting it was merely to demonstrate the utility of the dancing links technique via an efficient implementation he called DLX.The exact cover problem is represented in Algorithm X using a matrix A consisting of 0s and 1s. The goal is to select a subset of the rows so that the digit 1 appears in each column exactly once.Algorithm X functions as follows:The nondeterministic choice of r means that the algorithm essentially clones itself into independent subalgorithms; each subalgorithm inherits the current matrix A, but reduces it with respect to a different row r.If column c is entirely zero, there are no subalgorithms and the process terminates unsuccessfully.The subalgorithms form a search tree in a natural way, with the original problem at the root and with level k containing each subalgorithm that corresponds to k chosen rows.Backtracking is the process of traversing the tree in preorder, depth first.Any systematic rule for choosing column c in this procedure will find all solutions, but some rules work much better than others.To reduce the number of iterations, Knuth suggests that the column choosing algorithm select a column with the lowest number of 1s in it.".
- Knuths_Algorithm_X wikiPageExternalLink polycube-solver.
- Knuths_Algorithm_X wikiPageExternalLink dancing-color.ps.gz.
- Knuths_Algorithm_X wikiPageExternalLink dlx.
- Knuths_Algorithm_X wikiPageID "3626542".
- Knuths_Algorithm_X wikiPageLength "15275".
- Knuths_Algorithm_X wikiPageOutDegree "25".
- Knuths_Algorithm_X wikiPageRevisionID "680339573".
- Knuths_Algorithm_X wikiPageWikiLink Algorithm.
- Knuths_Algorithm_X wikiPageWikiLink Algorithm_X.
- Knuths_Algorithm_X wikiPageWikiLink Backtracking.
- Knuths_Algorithm_X wikiPageWikiLink Category:Donald_Knuth.
- Knuths_Algorithm_X wikiPageWikiLink Category:Search_algorithms.
- Knuths_Algorithm_X wikiPageWikiLink Dancing_Links.
- Knuths_Algorithm_X wikiPageWikiLink Dancing_links.
- Knuths_Algorithm_X wikiPageWikiLink Depth-first.
- Knuths_Algorithm_X wikiPageWikiLink Depth-first_search.
- Knuths_Algorithm_X wikiPageWikiLink Deterministic_algorithm.
- Knuths_Algorithm_X wikiPageWikiLink Donald_Knuth.
- Knuths_Algorithm_X wikiPageWikiLink Doubly_linked_list.
- Knuths_Algorithm_X wikiPageWikiLink Exact_cover.
- Knuths_Algorithm_X wikiPageWikiLink Knuths_Algorithm_X.
- Knuths_Algorithm_X wikiPageWikiLink Nondeterministic_algorithm.
- Knuths_Algorithm_X wikiPageWikiLink Recursion_(computer_science).
- Knuths_Algorithm_X wikiPageWikiLink Search_tree.
- Knuths_Algorithm_X wikiPageWikiLinkText "Algorithm X".
- Knuths_Algorithm_X wikiPageWikiLinkText "Knuth's Algorithm X".
- Knuths_Algorithm_X wikiPageWikiLinkText "example".
- Knuths_Algorithm_X hasPhotoCollection Knuths_Algorithm_X.
- Knuths_Algorithm_X wikiPageUsesTemplate Template:Citation.
- Knuths_Algorithm_X wikiPageUsesTemplate Template:Donald_Knuth_navbox.
- Knuths_Algorithm_X wikiPageUsesTemplate Template:Reflist.
- Knuths_Algorithm_X subject Category:Donald_Knuth.
- Knuths_Algorithm_X subject Category:Search_algorithms.
- Knuths_Algorithm_X hypernym Knuth.
- Knuths_Algorithm_X comment ""Algorithm X" is the name Donald Knuth used in his paper "Dancing Links" to refer to "the most obvious trial-and-error approach" for finding all solutions to the exact cover problem. Technically, Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm.".
- Knuths_Algorithm_X label "Knuth's Algorithm X".
- Knuths_Algorithm_X sameAs Algorithme_X_de_Knuth.
- Knuths_Algorithm_X sameAs m.09qv19.
- Knuths_Algorithm_X sameAs Кнутов_алгоритам_Икс.
- Knuths_Algorithm_X sameAs Q6424025.
- Knuths_Algorithm_X sameAs Q6424025.
- Knuths_Algorithm_X wasDerivedFrom Knuths_Algorithm_Xoldid=680339573.
- Knuths_Algorithm_X isPrimaryTopicOf Knuths_Algorithm_X.