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exactn
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There are 6 letters in EXACTN ( A1C3E1N1T1X8 )
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In mathematics, given a collection * * * * * * S * * * * * {\displaystyle {\mathcal {S}}} * of subsets of a set X, an exact cover is a subcollection * * * * * * * S * * * * ∗ * * * * * {\displaystyle {\mathcal {S}}^{*}} * of * * * * * * S * * * * * {\displaystyle {\mathcal {S}}} * such that each element in X is contained in exactly one subset in * * * * * * * S * * * * ∗ * * * * * {\displaystyle {\mathcal {S}}^{*}} * . * One says that each element in X is covered by exactly one subset in * * * * * * * S * * * * ∗ * * * * * {\displaystyle {\mathcal {S}}^{*}} * . * An exact cover is a kind of cover. * In computer science, the exact cover problem is a decision problem to determine if an exact cover exists. * The exact cover problem is NP-complete * and is one of Karp's 21 NP-complete problems. * The exact cover problem is a kind of constraint satisfaction problem. * An exact cover problem can be represented by an incidence matrix or a bipartite graph. * Knuth's Algorithm X is an algorithm that finds all solutions to an exact cover problem. DLX is the name given to Algorithm X when it is implemented efficiently using Donald Knuth's Dancing Links technique on a computer.The standard exact cover problem can be generalized slightly to involve not only "exactly one" constraints but also "at-most-one" constraints. * Finding Pentomino tilings and solving Sudoku are noteworthy examples of exact cover problems. * The N queens problem is a slightly generalized exact cover problem. |