René's URL Explorer Experiment


Title: Exact cover - Wikipedia

Open Graph Title: Exact cover - Wikipedia

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Jump to contenthttps://en.wikipedia.org/wiki/Exact_cover#bodyContent
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(Top) https://en.wikipedia.org/wiki/Exact_cover
1 Formal definition https://en.wikipedia.org/wiki/Exact_cover#Formal_definition
2 Basic examples https://en.wikipedia.org/wiki/Exact_cover#Basic_examples
2.1 Detailed example https://en.wikipedia.org/wiki/Exact_cover#Detailed_example
3 Representations https://en.wikipedia.org/wiki/Exact_cover#Representations
3.1 Exact hitting set https://en.wikipedia.org/wiki/Exact_cover#Exact_hitting_set
3.2 Incidence matrix https://en.wikipedia.org/wiki/Exact_cover#Incidence_matrix
3.3 Hypergraph https://en.wikipedia.org/wiki/Exact_cover#Hypergraph
3.4 Bipartite graph https://en.wikipedia.org/wiki/Exact_cover#Bipartite_graph
4 Finding solutions https://en.wikipedia.org/wiki/Exact_cover#Finding_solutions
5 Generalized exact cover https://en.wikipedia.org/wiki/Exact_cover#Generalized_exact_cover
6 Noteworthy examples https://en.wikipedia.org/wiki/Exact_cover#Noteworthy_examples
6.1 Pentomino tiling https://en.wikipedia.org/wiki/Exact_cover#Pentomino_tiling
6.2 Sudoku https://en.wikipedia.org/wiki/Exact_cover#Sudoku
6.3 N queens problem https://en.wikipedia.org/wiki/Exact_cover#N_queens_problem
7 See also https://en.wikipedia.org/wiki/Exact_cover#See_also
8 References https://en.wikipedia.org/wiki/Exact_cover#References
9 External links https://en.wikipedia.org/wiki/Exact_cover#External_links
中文https://zh.wikipedia.org/wiki/%E7%B2%BE%E7%A1%AE%E8%A6%86%E7%9B%96%E9%97%AE%E9%A2%98
Deutschhttps://de.wikipedia.org/wiki/Problem_der_exakten_%C3%9Cberdeckung
Françaishttps://fr.wikipedia.org/wiki/Probl%C3%A8me_de_la_couverture_exacte
Nederlandshttps://nl.wikipedia.org/wiki/Exacte_overdekking
Portuguêshttps://pt.wikipedia.org/wiki/Cobertura_exata
Edit linkshttps://www.wikidata.org/wiki/Special:EntityPage/Q388260#sitelinks-wikipedia
Articlehttps://en.wikipedia.org/wiki/Exact_cover
Talkhttps://en.wikipedia.org/wiki/Talk:Exact_cover
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Readhttps://en.wikipedia.org/wiki/Exact_cover
Edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit
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What links herehttps://en.wikipedia.org/wiki/Special:WhatLinksHere/Exact_cover
Related changeshttps://en.wikipedia.org/wiki/Special:RecentChangesLinked/Exact_cover
Upload filehttps://en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard
Permanent linkhttps://en.wikipedia.org/w/index.php?title=Exact_cover&oldid=1337874325
Page informationhttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=info
Cite this pagehttps://en.wikipedia.org/w/index.php?title=Special:CiteThisPage&page=Exact_cover&id=1337874325&wpFormIdentifier=titleform
Get shortened URLhttps://en.wikipedia.org/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FExact_cover
Download QR codehttps://en.wikipedia.org/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FExact_cover
Download as PDFhttps://en.wikipedia.org/w/index.php?title=Special:DownloadAsPdf&page=Exact_cover&action=show-download-screen
Printable versionhttps://en.wikipedia.org/w/index.php?title=Exact_cover&printable=yes
Wikidata itemhttps://www.wikidata.org/wiki/Special:EntityPage/Q388260
mathematicalhttps://en.wikipedia.org/wiki/Mathematical
combinatoricshttps://en.wikipedia.org/wiki/Combinatorics
subsetshttps://en.wikipedia.org/wiki/Subset
sethttps://en.wikipedia.org/wiki/Set_(mathematics)
[1]https://en.wikipedia.org/wiki/Exact_cover#cite_note-1
coverhttps://en.wikipedia.org/wiki/Cover_(topology)
partitionhttps://en.wikipedia.org/wiki/Partition_of_a_set
constraint satisfaction problemhttps://en.wikipedia.org/wiki/Constraint_satisfaction_problem
NP-hardhttps://en.wikipedia.org/wiki/NP-hard
cloud computinghttps://en.wikipedia.org/wiki/Cloud_computing
electronic circuit designhttps://en.wikipedia.org/wiki/Electronic_circuit_design
[2]https://en.wikipedia.org/wiki/Exact_cover#cite_note-2
heterogeneous relationhttps://en.wikipedia.org/wiki/Heterogeneous_relation
exact hitting sethttps://en.wikipedia.org/wiki/Exact_hitting_set
incidence matrixhttps://en.wikipedia.org/wiki/Incidence_matrix
bipartite graphhttps://en.wikipedia.org/wiki/Bipartite_graph
computer sciencehttps://en.wikipedia.org/wiki/Computer_science
decision problemhttps://en.wikipedia.org/wiki/Decision_problem
NP-completehttps://en.wikipedia.org/wiki/NP-complete
[3]https://en.wikipedia.org/wiki/Exact_cover#cite_note-:0-3
Karp's 21 NP-complete problemshttps://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems
[4]https://en.wikipedia.org/wiki/Exact_cover#cite_note-4
[3]https://en.wikipedia.org/wiki/Exact_cover#cite_note-:0-3
Knuth's Algorithm Xhttps://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X
algorithmhttps://en.wikipedia.org/wiki/Algorithm
Donald Knuthhttps://en.wikipedia.org/wiki/Donald_Knuth
Dancing Linkshttps://en.wikipedia.org/wiki/Dancing_Links
[5]https://en.wikipedia.org/wiki/Exact_cover#cite_note-knuth-5
Pentominohttps://en.wikipedia.org/wiki/Pentomino
Sudokuhttps://en.wikipedia.org/wiki/Sudoku
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unionhttps://en.wikipedia.org/wiki/Union_(set_theory)
coverhttps://en.wikipedia.org/wiki/Cover_(topology)
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empty sethttps://en.wikipedia.org/wiki/Empty_set
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https://en.wikipedia.org/wiki/File:Exact_cover_instance.svg
examplehttps://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X#Example
Knuth's Algorithm Xhttps://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=4
heterogeneous relationhttps://en.wikipedia.org/wiki/Heterogeneous_relation
conversehttps://en.wikipedia.org/wiki/Converse_relation
restrictedhttps://en.wikipedia.org/wiki/Restriction_(mathematics)
functionhttps://en.wikipedia.org/wiki/Function_(mathematics)
ontohttps://en.wikipedia.org/wiki/Onto
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mathematicshttps://en.wikipedia.org/wiki/Mathematics
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incidence matrixhttps://en.wikipedia.org/wiki/Incidence_matrix
detailed examplehttps://en.wikipedia.org/wiki/Exact_cover#Detailed_example
examplehttps://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X#Example
Knuth's Algorithm Xhttps://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X
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https://en.wikipedia.org/wiki/File:Exact-cover-bigraph-highlighted.svg
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=9
Algorithm Xhttps://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X
Donald Knuthhttps://en.wikipedia.org/wiki/Donald_Knuth
[5]https://en.wikipedia.org/wiki/Exact_cover#cite_note-knuth-5
recursivehttps://en.wikipedia.org/wiki/Recursion_(computer_science)
nondeterministichttps://en.wikipedia.org/wiki/Nondeterministic_algorithm
depth-firsthttps://en.wikipedia.org/wiki/Depth-first
backtrackinghttps://en.wikipedia.org/wiki/Backtracking
algorithmhttps://en.wikipedia.org/wiki/Algorithm
Donald Knuthhttps://en.wikipedia.org/wiki/Donald_Knuth
Dancing Linkshttps://en.wikipedia.org/wiki/Dancing_Links
doubly linked listshttps://en.wikipedia.org/wiki/Doubly_linked_list
Dancing Linkshttps://en.wikipedia.org/wiki/Dancing_Links
permutationshttps://en.wikipedia.org/wiki/Permutation
[5]https://en.wikipedia.org/wiki/Exact_cover#cite_note-knuth-5
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=10
[6]https://en.wikipedia.org/wiki/Exact_cover#cite_note-6
N queens problemhttps://en.wikipedia.org/wiki/N_queens_problem
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=11
reducedhttps://en.wikipedia.org/wiki/Reduction_(complexity)
pentominoeshttps://en.wikipedia.org/wiki/Pentominoes
Sudokuhttps://en.wikipedia.org/wiki/Sudoku
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=12
Pentominohttps://en.wikipedia.org/wiki/Pentomino
pentominoeshttps://en.wikipedia.org/wiki/Pentominoes
Donald Knuthhttps://en.wikipedia.org/wiki/Donald_Knuth
[5]https://en.wikipedia.org/wiki/Exact_cover#cite_note-knuth-5
[7]https://en.wikipedia.org/wiki/Exact_cover#cite_note-7
https://en.wikipedia.org/wiki/File:Pentomino_Puzzle_Solution_8x8_Minus_Center.svg
Dancing Linkshttps://en.wikipedia.org/wiki/Dancing_Links
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=13
Sudokuhttps://en.wikipedia.org/wiki/Sudoku
Mathematics of Sudokuhttps://en.wikipedia.org/wiki/Mathematics_of_Sudoku
Sudoku solving algorithmshttps://en.wikipedia.org/wiki/Sudoku_solving_algorithms
Sudokuhttps://en.wikipedia.org/wiki/Sudoku
exact hitting sethttps://en.wikipedia.org/wiki/Exact_hitting_set
[8]https://en.wikipedia.org/wiki/Exact_cover#cite_note-8
intersectionhttps://en.wikipedia.org/wiki/Intersection_(set_theory)
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=14
N queens problemhttps://en.wikipedia.org/wiki/N_queens_problem
N queens problemhttps://en.wikipedia.org/wiki/N_queens_problem
chesshttps://en.wikipedia.org/wiki/Chess
queenshttps://en.wikipedia.org/wiki/Queen_(chess)
chessboardhttps://en.wikipedia.org/wiki/Chessboard
generalized exact cover problemhttps://en.wikipedia.org/wiki/Exact_cover#Generalized_exact_cover
[5]https://en.wikipedia.org/wiki/Exact_cover#cite_note-knuth-5
eight queens puzzlehttps://en.wikipedia.org/wiki/Eight_queens_puzzle
up tohttps://en.wikipedia.org/wiki/Up_to
rotationhttps://en.wikipedia.org/wiki/Rotation
reflectionhttps://en.wikipedia.org/wiki/Reflection_(mathematics)
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=15
Constraint satisfaction problemhttps://en.wikipedia.org/wiki/Constraint_satisfaction_problem
Dancing Linkshttps://en.wikipedia.org/wiki/Dancing_Links
Difference map algorithmhttps://en.wikipedia.org/wiki/Difference_map_algorithm
Karp's 21 NP-complete problemshttps://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems
Knuth's Algorithm Xhttps://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X
List of NP-complete problemshttps://en.wikipedia.org/wiki/List_of_NP-complete_problems
Partition of a sethttps://en.wikipedia.org/wiki/Partition_of_a_set
Perfect matchinghttps://en.wikipedia.org/wiki/Perfect_matching
3-dimensional matchinghttps://en.wikipedia.org/wiki/3-dimensional_matching
Set covering problemhttps://en.wikipedia.org/wiki/Set_covering_problem
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=16
^https://en.wikipedia.org/wiki/Exact_cover#cite_ref-1
^https://en.wikipedia.org/wiki/Exact_cover#cite_ref-2
"Design of network-based biocomputation circuits for the exact cover problem"https://doi.org/10.1088%2F1367-2630%2Fac175d
Bibcodehttps://en.wikipedia.org/wiki/Bibcode_(identifier)
2021NJPh...23h5004Khttps://ui.adsabs.harvard.edu/abs/2021NJPh...23h5004K
doihttps://en.wikipedia.org/wiki/Doi_(identifier)
10.1088/1367-2630/ac175dhttps://doi.org/10.1088%2F1367-2630%2Fac175d
ISSNhttps://en.wikipedia.org/wiki/ISSN_(identifier)
1367-2630https://search.worldcat.org/issn/1367-2630
ahttps://en.wikipedia.org/wiki/Exact_cover#cite_ref-:0_3-0
bhttps://en.wikipedia.org/wiki/Exact_cover#cite_ref-:0_3-1
M.R. Gareyhttps://en.wikipedia.org/wiki/Michael_Garey
D.S. Johnsonhttps://en.wikipedia.org/wiki/David_S._Johnson
Computers and Intractability: A Guide to the Theory of NP-Completenesshttps://en.wikipedia.org/wiki/Computers_and_Intractability:_A_Guide_to_the_Theory_of_NP-Completeness
ISBNhttps://en.wikipedia.org/wiki/ISBN_(identifier)
0-7167-1045-5https://en.wikipedia.org/wiki/Special:BookSources/0-7167-1045-5
^https://en.wikipedia.org/wiki/Exact_cover#cite_ref-4
Richard M. Karphttps://en.wikipedia.org/wiki/Richard_Karp
"Reducibility among combinatorial problems"https://web.archive.org/web/20110629023717/http://www.cs.berkeley.edu/~luca/cs172/karp.pdf
ISBNhttps://en.wikipedia.org/wiki/ISBN_(identifier)
0-3063-0707-3https://en.wikipedia.org/wiki/Special:BookSources/0-3063-0707-3
the originalhttp://www.cs.berkeley.edu/~luca/cs172/karp.pdf
ahttps://en.wikipedia.org/wiki/Exact_cover#cite_ref-knuth_5-0
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ehttps://en.wikipedia.org/wiki/Exact_cover#cite_ref-knuth_5-4
Knuth, Donaldhttps://en.wikipedia.org/wiki/Donald_Knuth
arXivhttps://en.wikipedia.org/wiki/ArXiv_(identifier)
cs/0011047https://arxiv.org/abs/cs/0011047
^https://en.wikipedia.org/wiki/Exact_cover#cite_ref-6
N queenshttps://en.wikipedia.org/wiki/N_queens_problem
^https://en.wikipedia.org/wiki/Exact_cover#cite_ref-7
Golomb, Solomon W.https://en.wikipedia.org/wiki/Solomon_W._Golomb
Polyominoes: Puzzles, Patterns, Problems, and Packingshttps://en.wikipedia.org/wiki/Polyominoes:_Puzzles,_Patterns,_Problems,_and_Packings
7https://archive.org/details/isbn_9780691085739/page/7
ISBNhttps://en.wikipedia.org/wiki/ISBN_(identifier)
0-691-02444-8https://en.wikipedia.org/wiki/Special:BookSources/0-691-02444-8
^https://en.wikipedia.org/wiki/Exact_cover#cite_ref-8
"Exact Cover Problem"https://www.stolaf.edu/people/hansonr/sudoku/exactcovermatrix.htm
edithttps://en.wikipedia.org/w/index.php?title=Exact_cover&action=edit§ion=17
Free Software implementation of an Exact Cover solver in Chttps://github.com/blynn/dlx
Exact Cover solver in Golanghttps://github.com/thomasjungblut/go-dancing-links
Exact coverhttps://www.mathreference.com/lan-cx-np,excov.html
The DLX formathttps://cs.stanford.edu/~knuth/programs/dlx2.w
Miniexacthttps://github.com/miniexact/miniexact/
PyPIhttps://pypi.org/project/miniexact/
https://en.wikipedia.org/w/index.php?title=Exact_cover&oldid=1337874325https://en.wikipedia.org/w/index.php?title=Exact_cover&oldid=1337874325
Categorieshttps://en.wikipedia.org/wiki/Help:Category
Theoretical computer sciencehttps://en.wikipedia.org/wiki/Category:Theoretical_computer_science
NP-complete problemshttps://en.wikipedia.org/wiki/Category:NP-complete_problems
Articles with short descriptionhttps://en.wikipedia.org/wiki/Category:Articles_with_short_description
Short description is different from Wikidatahttps://en.wikipedia.org/wiki/Category:Short_description_is_different_from_Wikidata
Creative Commons Attribution-ShareAlike 4.0 Licensehttps://en.wikipedia.org/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License
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