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For example, if manifolds of complementary dimension intersect transversally, the signed sum of the number of their intersection points does not change even if we isotope the manifolds to another transverse intersection. (The intersection points can be counted modulo 2, ignoring the signs, to obtain a coarser invariant.)
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7 Feedback arc set [2] [3]: GT8 Graph coloring [2] [3]: GT4
The crossed ladders problem may appear in various forms, with variations in name, using various lengths and heights, or requesting unusual solutions such as cases where all values are integers. Its charm has been attributed to a seeming simplicity which can quickly devolve into an "algebraic mess" (characterization attributed by Gardner to D. F ...
One solution using the even-odd rule is to transform (complex) polygons into simpler ones that are even-odd-equivalent before the intersection check. [10] This, however, is computationally expensive. It is less expensive to use the fast non-zero winding number algorithm, which gives the correct result even when the polygon overlaps itself.
Intersection types are useful for describing overloaded functions. [2] For example, if number => number is the type of function taking a number as an argument and returning a number, and string => string is the type of function taking a string as an argument and returning a string, then the intersection of these two types can be used to ...
In the modern era, it is often used as an example problem for various computer programming techniques. The eight queens puzzle is a special case of the more general n queens problem of placing n non-attacking queens on an n×n chessboard. Solutions exist for all natural numbers n with the exception of n = 2 and n = 3.
C# (/ ˌ s iː ˈ ʃ ɑːr p / see SHARP) [b] is a general-purpose high-level programming language supporting multiple paradigms.C# encompasses static typing, [16]: 4 strong typing, lexically scoped, imperative, declarative, functional, generic, [16]: 22 object-oriented (class-based), and component-oriented programming disciplines.
The intersection is the meet/infimum of and with respect to because: if L ∩ R ⊆ L {\displaystyle L\cap R\subseteq L} and L ∩ R ⊆ R , {\displaystyle L\cap R\subseteq R,} and if Z {\displaystyle Z} is a set such that Z ⊆ L {\displaystyle Z\subseteq L} and Z ⊆ R {\displaystyle Z\subseteq R} then Z ⊆ L ∩ R . {\displaystyle Z ...